// Copyright (c) 2005,2006  INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.1/Filtered_kernel/include/CGAL/Lazy.h $
// $Id: Lazy.h 319383c 2020-05-20T09:47:58+02:00 Laurent Rineau
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Andreas Fabri, Sylvain Pion

#ifndef CGAL_LAZY_H
#define CGAL_LAZY_H

#include <CGAL/disable_warnings.h>

#include <CGAL/basic.h>
#include <CGAL/Handle.h>
#include <CGAL/Object.h>
#include <CGAL/Kernel/Type_mapper.h>
#include <CGAL/Profile_counter.h>
#include <CGAL/Kernel/Return_base_tag.h>
#include <CGAL/min_max_n.h>
#include <CGAL/Origin.h>
#include <CGAL/Bbox_2.h>
#include <CGAL/Bbox_3.h>
#include <vector>
#include <type_traits>
#include <CGAL/Default.h>
#include<CGAL/tss.h>
#include <CGAL/is_iterator.h>
#include <CGAL/transforming_iterator.h>

#include <boost/optional.hpp>
#include <boost/variant.hpp>
#ifdef CGAL_LAZY_KERNEL_DEBUG
#  include <boost/optional/optional_io.hpp>
#endif

#include <boost/mpl/has_xxx.hpp>

#include <boost/preprocessor/facilities/expand.hpp>
#include <boost/preprocessor/repetition/repeat_from_to.hpp>
#include <boost/preprocessor/repetition/repeat.hpp>
#include <boost/preprocessor/repetition/enum_params.hpp>
#include <boost/preprocessor/repetition/enum_binary_params.hpp>
#include <boost/preprocessor/repetition/enum.hpp>

namespace CGAL {

template <class E,
          class A,
          class E2A,
          class K>
class Lazy_kernel_base;

template <typename AT, typename ET, typename E2A> class Lazy;

template <typename ET_>
class Lazy_exact_nt;

template <typename AT, typename ET, typename E2A>
inline
const AT&
approx(const Lazy<AT,ET,E2A>& l)
{
  return l.approx();
}

// Where is this one (non-const) needed ?  Is it ?
template <typename AT, typename ET, typename E2A>
inline
AT&
approx(Lazy<AT,ET,E2A>& l)
{
  return l.approx();
}


template <typename AT, typename ET, typename E2A>
inline
const ET&
exact(const Lazy<AT,ET,E2A>& l)
{
  return l.exact();
}


template <typename AT, typename ET, typename E2A>
inline
unsigned
depth(const Lazy<AT,ET,E2A>& l)
{
  return l.depth();
}


#define CGAL_LAZY_FORWARD(T) \
  inline const T & approx(const T& d) { return d; } \
  inline const T & exact (const T& d) { return d; } \
  inline unsigned  depth (const T&  ) { return 0; }

CGAL_LAZY_FORWARD(Bbox_2)
CGAL_LAZY_FORWARD(Bbox_3)
#undef CGAL_LAZY_FORWARD

template<class T>inline std::enable_if_t<std::is_arithmetic<T>::value||std::is_enum<T>::value, T> approx(T d){return d;}
template<class T>inline std::enable_if_t<std::is_arithmetic<T>::value||std::is_enum<T>::value, T> exact (T d){return d;}
template<class T>inline std::enable_if_t<std::is_arithmetic<T>::value||std::is_enum<T>::value, unsigned> depth(T){return 0;}

// For tag classes: Return_base_tag, Homogeneous_tag, Null_vector, Origin
template<class T>inline std::enable_if_t<std::is_empty<T>::value, T> exact(T){return {};}
template<class T>inline std::enable_if_t<std::is_empty<T>::value, T> approx(T){return {};}
template<class T>inline std::enable_if_t<std::is_empty<T>::value, unsigned> depth(T){return 0;}

// For an iterator, exact/approx applies to the objects it points to
template <class T, class=std::enable_if_t<is_iterator_type<T,std::input_iterator_tag>::value>>
auto exact(T const& t) {return make_transforming_iterator(t,[](auto const&u)->decltype(auto){return CGAL::exact(u);});}
template <class T, class=std::enable_if_t<is_iterator_type<T,std::input_iterator_tag>::value>>
auto approx(T const& t) {return make_transforming_iterator(t,[](auto const&u)->decltype(auto){return CGAL::approx(u);});}
template <class T, class=std::enable_if_t<is_iterator_type<T,std::input_iterator_tag>::value>>
unsigned depth(T const&) {return 1;} // FIXME: depth(*t) would be better when t is valid, but not for end iterators, and the true answer would iterate on the range, but we can't do that with only one iterator... We need to replace iterators with ranges to solve that.

#ifdef CGAL_LAZY_KERNEL_DEBUG
template <class T>
void
print_at(std::ostream& os, const T& at)
{
  os << at;
}

template <class T>
void
print_at(std::ostream& os, const std::vector<T>& at)
{
  os << "std::vector";
}

template <>
void
print_at(std::ostream& os, const Object& o)
{
  os << "Object";
}

template <class T1, class T2>
void
print_at(std::ostream& os, const std::pair<T1,T2> & at)
{
  os << "[ " << at.first << " | " << at.second << " ]" << std::endl ;
}


template <typename AT, typename ET, typename E2A>
inline
void
print_dag(const Lazy<AT,ET,E2A>& l, std::ostream& os, int level = 0)
{
  l.print_dag(os, level);
}

inline
void
print_dag(double d, std::ostream& os, int level)
{
  for(int i = 0; i < level; i++)
    os << "    ";
  os << d << std::endl;
}

inline
void
msg(std::ostream& os, int level, const char* s)
{
    for(int i = 0; i < level; i++)
      os << "    ";
    os << s << std::endl;
}

inline
void
print_dag(const Null_vector&, std::ostream& os, int level)
{
  for(int i = 0; i < level; i++)
    os << "    ";
  os << "Null_vector" << std::endl;
}

inline
void
print_dag(const Origin&, std::ostream& os, int level)
{
  for(int i = 0; i < level; i++)
    os << "    ";
  os << "Origin" << std::endl;
}

inline
void
print_dag(const Return_base_tag&, std::ostream& os, int level)
{
  for(int i = 0; i < level; i++)
    os << "    ";
  os << "Return_base_tag" << std::endl;
}
#endif


struct Depth_base {
#ifdef CGAL_PROFILE
  unsigned depth_;
  Depth_base() { set_depth(0); }
  unsigned depth() const { return depth_; }
  void set_depth(unsigned i)
  {
    depth_ = i;
    CGAL_HISTOGRAM_PROFILER(std::string("[Lazy_kernel DAG depths]"), i);
                            //(unsigned) ::log2(double(i)));
  }
#else
  unsigned depth() const { return 0; }
  void set_depth(unsigned) {}
#endif
};


// Abstract base class for lazy numbers and lazy objects
template <typename AT_, typename ET, typename E2A>
class Lazy_rep : public Rep, public Depth_base
{
  Lazy_rep (const Lazy_rep&) = delete; // cannot be copied.

public:

  typedef AT_ AT;

  mutable AT at;
  mutable ET *et;

  Lazy_rep ()
    : at(), et(nullptr){}

  template<class A>
  Lazy_rep (A&& a)
      : at(std::forward<A>(a)), et(nullptr){}

  template<class A, class E>
  Lazy_rep (A&& a, E&& e)
      : at(std::forward<A>(a)), et(new ET(std::forward<E>(e))) {}

  const AT& approx() const
  {
      return at;
  }

  AT& approx()
  {
      return at;
  }

  const ET & exact() const
  {
    if (et==nullptr)
      update_exact();
    return *et;
  }

  ET & exact()
  {
    if (et==nullptr)
      update_exact();
    return *et;
  }

#ifdef CGAL_LAZY_KERNEL_DEBUG
  void print_at_et(std::ostream& os, int level) const
  {
    for(int i = 0; i < level; i++){
      os << "    ";
    }
    os << "Approximation: ";
    print_at(os, at);
    os << std::endl;
    if(! is_lazy()){
      for(int i = 0; i < level; i++){
        os << "    ";
      }
      os << "Exact: ";
      print_at(os, *et);
      os << std::endl;
#ifdef CGAL_LAZY_KERNEL_DEBUG_SHOW_TYPEID
      for(int i = 0; i < level; i++){
        os << "    ";
      }
      os << "  (type: " << typeid(*et).name() << ")" << std::endl;
#endif // CGAL_LAZY_KERNEL_DEBUG_SHOW_TYPEID
    }
  }

  virtual void print_dag(std::ostream& os, int level) const {}
#endif

  bool is_lazy() const { return et == nullptr; }
  virtual void update_exact() const = 0;
  virtual ~Lazy_rep() { delete et; }
};


template<typename AT, typename ET, typename AC, typename EC, typename E2A, typename...L>
class Lazy_rep_n :
  public Lazy_rep< AT, ET, E2A >, private EC
{
  // Lazy_rep_0 does not inherit from EC or take a parameter AC. It has different constructors.
  static_assert(sizeof...(L)>0, "Use Lazy_rep_0 instead");
  template <class Ei, class Ai, class E2Ai, class Ki> friend class Lazy_kernel_base;
  mutable std::tuple<L...> l; // L...l; is not yet allowed.
  const EC& ec() const { return *this; }
  template<std::size_t...I>
  void update_exact_helper(std::index_sequence<I...>) const {
    this->et = new ET(ec()( CGAL::exact( std::get<I>(l) ) ... ) );
    this->at = E2A()(*(this->et));
    l = std::tuple<L...>{};
  }
  public:
  void update_exact() const {
    update_exact_helper(std::make_index_sequence<sizeof...(L)>{});
  }
  template<class...LL>
  Lazy_rep_n(const AC& ac, const EC& ec, LL&&...ll) :
    Lazy_rep<AT, ET, E2A>(ac(CGAL::approx(ll)...)), EC(ec), l(std::forward<LL>(ll)...)
  {
    this->set_depth((std::max)({ -1, (int)CGAL::depth(ll)...}) + 1);
  }
#ifdef CGAL_LAZY_KERNEL_DEBUG
  private:
  template<std::size_t...I>
  void print_dag_helper(std::ostream& os, int level, std::index_sequence<I...>) const {
    this->print_at_et(os, level);
    if(this->is_lazy()){
# ifdef CGAL_LAZY_KERNEL_DEBUG_SHOW_TYPEID
      CGAL::msg(os, level, typeid(AC).name());
# endif
      CGAL::msg(os, level, "DAG with " "3" " child nodes:");
      using expander = int[];
      expander{0,(CGAL::print_dag(std::get<I>(l), os, level+1),0)...};
    }
  }
  public:
  void print_dag(std::ostream& os, int level) const {
    print_dag_helper(os, level, std::make_index_sequence<sizeof...L>{});
  }
#endif
};

//____________________________________________________________
// The rep for the leaf node

template <typename AT, typename ET, typename E2A>
class Lazy_rep_0 : public Lazy_rep<AT, ET, E2A>
{

  typedef Lazy_rep<AT, ET, E2A> Base;
public:

  void
  update_exact() const
  {
    this->et = new ET();
  }

  Lazy_rep_0()
    : Lazy_rep<AT,ET, E2A>() {}

  template<class A, class E>
  Lazy_rep_0(A&& a, E&& e)
    : Lazy_rep<AT,ET,E2A>(std::forward<A>(a), std::forward<E>(e)) {}

#if 0
  // unused. Find a less ambiguous placeholder if necessary
  Lazy_rep_0(const AT& a, void*)
    : Lazy_rep<AT,ET,E2A>(a) {}
#endif

  // E2A()(e) and std::forward<E>(e) could be evaluated in any order, but
  // that's ok, "forward" itself does not modify e, it may only mark it as
  // modifyable by the outer call, which is obviously sequenced after the inner
  // call E2A()(e).
  template<class E>
  Lazy_rep_0(E&& e)
    : Lazy_rep<AT,ET,E2A>(E2A()(e), std::forward<E>(e)) {}

  void
  print_dag(std::ostream& os, int level) const
  {
    this->print_at_et(os, level);
  }
};

// Macro helpers to build the kernel objects
#define CGAL_TYPEMAP_AC(z, n, t) typedef typename Type_mapper< t##n, LK, AK >::type A##n;
#define CGAL_TYPEMAP_EC(z, n, t) typedef typename Type_mapper< t##n, LK, EK >::type E##n;
#define CGAL_LEXACT(z,n,t) CGAL::exact( l##n )
#define CGAL_LARGS(z, n, t) L##n const& l##n

#undef CGAL_LAZY_PRINT_TYPEID

template < typename K1, typename K2 >
struct Approx_converter
{
  typedef K1         Source_kernel;
  typedef K2         Target_kernel;
  //typedef Converter  Number_type_converter;

  template < typename T >
  const typename T::AT&
  operator()(const T&t) const
  { return t.approx(); }

  const Null_vector&
  operator()(const Null_vector& n) const
  { return n; }

  const Bbox_2&
  operator()(const Bbox_2& b) const
  { return b; }

  const Bbox_3&
  operator()(const Bbox_3& b) const
  { return b; }
};

template < typename K1, typename K2 >
struct Exact_converter
{
  typedef K1         Source_kernel;
  typedef K2         Target_kernel;
  //typedef Converter  Number_type_converter;

  template < typename T >
  const typename T::ET&
  operator()(const T&t) const
  { return t.exact(); }

  const Null_vector&
  operator()(const Null_vector& n) const
  { return n; }

  const Bbox_2&
  operator()(const Bbox_2& b) const
  { return b; }

  const Bbox_3&
  operator()(const Bbox_3& b) const
  { return b; }
};

//____________________________________________________________



template <typename AC, typename EC, typename E2A, typename L1>
class Lazy_rep_with_vector_1
  : public Lazy_rep<std::vector<Object>, std::vector<Object>, E2A>
  , private EC
{
  typedef std::vector<Object> AT;
  typedef std::vector<Object> ET;
  typedef Lazy_rep<AT, ET, E2A> Base;

  mutable L1 l1_;

  const EC& ec() const { return *this; }

public:

  void
  update_exact() const
  {
// TODO : This looks really unfinished...
    std::vector<Object> vec;
    this->et = new ET();
    //this->et->reserve(this->at.size());
    ec()(CGAL::exact(l1_), std::back_inserter(*(this->et)));
    if(this->et==nullptr)
    E2A()(*(this->et));
    this->at = E2A()(*(this->et));
    // Prune lazy tree
    l1_ = L1();
  }

  Lazy_rep_with_vector_1(const AC& ac, const EC& /*ec*/, const L1& l1)
    : l1_(l1)
  {
    ac(CGAL::approx(l1), std::back_inserter(this->at));
  }

#ifdef CGAL_LAZY_KERNEL_DEBUG
  void
  print_dag(std::ostream& os, int level) const
  {
    this->print_at_et(os, level);
    os << "A Lazy_rep_with_vector_1 of size " <<  this->at.size() << std::endl;
    if(this->is_lazy()){
      CGAL::msg(os, level, "DAG with one child node:");
      CGAL::print_dag(l1_, os, level+1);

    }
  }
#endif
};


template <typename AC, typename EC, typename E2A, typename L1, typename L2>
class Lazy_rep_with_vector_2
  : public Lazy_rep<std::vector<Object>, std::vector<Object>, E2A>
  , private EC
{
  typedef std::vector<Object> AT;
  typedef std::vector<Object> ET;
  typedef Lazy_rep<AT, ET, E2A> Base;

  mutable L1 l1_;
  mutable L2 l2_;

  const EC& ec() const { return *this; }

public:

  void
  update_exact() const
  {
    this->et = new ET();
    this->et->reserve(this->at.size());
    ec()(CGAL::exact(l1_), CGAL::exact(l2_), std::back_inserter(*(this->et)));
    this->at = E2A()(*(this->et));
    // Prune lazy tree
    l1_ = L1();
    l2_ = L2();
  }

  Lazy_rep_with_vector_2(const AC& ac, const EC& /*ec*/, const L1& l1, const L2& l2)
    : l1_(l1), l2_(l2)
  {
    ac(CGAL::approx(l1), CGAL::approx(l2), std::back_inserter(this->at));
  }

#ifdef CGAL_LAZY_KERNEL_DEBUG
  void
  print_dag(std::ostream& os, int level) const
  {
    this->print_at_et(os, level);
    os << "A Lazy_rep_with_vector_2 of size " <<  this->at.size() << std::endl;
    if(this->is_lazy()){
      CGAL::msg(os, level, "DAG with two child nodes:");
      CGAL::print_dag(l1_, os, level+1);
      CGAL::print_dag(l2_, os, level+1);
    }
  }
#endif
};


template <typename AC, typename EC, typename E2A, typename L1, typename L2, typename R1>
class Lazy_rep_2_1
  : public Lazy_rep<typename R1::AT, typename R1::ET, E2A>
  , private EC
{
  typedef typename R1::AT AT;
  typedef typename R1::ET ET;
  typedef Lazy_rep<AT, ET, E2A> Base;

  mutable L1 l1_;
  mutable L2 l2_;

  const EC& ec() const { return *this; }

public:

  void
  update_exact() const
  {
    this->et = new ET();
    ec()(CGAL::exact(l1_), CGAL::exact(l2_), *(this->et));
    this->at = E2A()(*(this->et));
    // Prune lazy tree
    l1_ = L1();
    l2_ = L2();
  }

  Lazy_rep_2_1(const AC& ac, const EC& /*ec*/, const L1& l1, const L2& l2)
    : Lazy_rep<AT,ET,E2A>(), l1_(l1), l2_(l2)
  {
    ac(CGAL::approx(l1), CGAL::approx(l2), this->at);
  }

#ifdef CGAL_LAZY_KERNEL_DEBUG
  void
  print_dag(std::ostream& os, int level) const
  {
    this->print_at_et(os, level);
    os << "A Lazy_rep_2_1" << std::endl;
    if(this->is_lazy()){
      CGAL::msg(os, level, "DAG with two child nodes:");
      CGAL::print_dag(l1_, os, level+1);
      CGAL::print_dag(l2_, os, level+1);
    }
  }
#endif
};


//____________________________________________________________________________________
// The following rep class stores two non-const reference parameters of type R1 and R2

template <typename AC, typename EC, typename E2A, typename L1, typename L2, typename R1, typename R2>
class Lazy_rep_2_2
  : public Lazy_rep<std::pair<typename R1::AT,typename R2::AT>, std::pair<typename R1::ET, typename R2::ET>, E2A>
  , private EC
{
  typedef std::pair<typename R1::AT, typename R2::AT> AT;
  typedef std::pair<typename R1::ET, typename R2::ET> ET;
  typedef Lazy_rep<AT, ET, E2A> Base;

  mutable L1 l1_;
  mutable L2 l2_;

  const EC& ec() const { return *this; }

public:

  void
  update_exact() const
  {
    this->et = new ET();
    ec()(CGAL::exact(l1_), CGAL::exact(l2_), this->et->first, this->et->second );
    this->at = E2A()(*(this->et));
    // Prune lazy tree
    l1_ = L1();
    l2_ = L2();
  }

  Lazy_rep_2_2(const AC& ac, const EC& /*ec*/, const L1& l1, const L2& l2)
    : Lazy_rep<AT,ET,E2A>(), l1_(l1), l2_(l2)
  {
    ac(CGAL::approx(l1), CGAL::approx(l2), this->at.first, this->at.second);
  }

#ifdef CGAL_LAZY_KERNEL_DEBUG
  void
  print_dag(std::ostream& os, int level) const
  {
    this->print_at_et(os, level);
    os << "A Lazy_rep_2_2"  << std::endl;
    if(this->is_lazy()){
      CGAL::msg(os, level, "DAG with two child nodes:");
      CGAL::print_dag(l1_, os, level+1);
      CGAL::print_dag(l2_, os, level+1);
    }
  }
#endif
};


//____________________________________________________________
// The handle class
template <typename AT_, typename ET_, typename E2A>
class Lazy : public Handle
{
  template <class Exact_kernel_,
            class Approximate_kernel_,
            class E2A_>
  friend struct Lazy_kernel;

  template <class E_,
            class A_,
            class E2A_,
            class K_>
  friend class Lazy_kernel_base;

public :

  typedef Lazy<AT_, ET_, E2A>  Self;
  typedef Lazy_rep<AT_, ET_, E2A>   Self_rep;

  typedef AT_ AT; // undocumented
  typedef ET_ ET; // undocumented

  typedef AT  Approximate_type;
  typedef ET  Exact_type;

/*
  typedef Self Rep;

  const Rep& rep() const
  {
    return *this;
  }

  Rep& rep()
  {
    return *this;
  }
*/

  Lazy()
    : Handle(zero()) {}

  // Before Lazy::zero() used Boost.Thread, the definition of Lazy() was:
  //   Lazy()
  //   #ifndef CGAL_HAS_THREAD
  //     : Handle(zero()) {}
  //   #else
  //   {
  //     PTR = new Lazy_rep_0<AT, ET, E2A>();
  //   }
  //   #endif

  Lazy(Self_rep *r)
  {
    PTR = r;
  }

  Lazy(const ET& e)
  {
    PTR = new Lazy_rep_0<AT,ET,E2A>(e);
  }

  Lazy(ET&& e)
  {
    PTR = new Lazy_rep_0<AT,ET,E2A>(std::move(e));
  }

  friend void swap(Lazy& a, Lazy& b) noexcept
  { swap(static_cast<Handle&>(a), static_cast<Handle&>(b)); }

  const AT& approx() const
  { return ptr()->approx(); }

  const ET& exact() const
  { return ptr()->exact(); }

  AT& approx()
  { return ptr()->approx(); }

  ET& exact()
  { return ptr()->exact(); }

  unsigned depth() const
  {
    return ptr()->depth();
  }

  void print_dag(std::ostream& os, int level) const
  {
    ptr()->print_dag(os, level);
  }

  private:

  // We have a static variable for optimizing the default constructor,
  // which is in particular heavily used for pruning DAGs.
  static const Self & zero()
  {
    // Note that the new only happens inside an if() inside the macro
    // So it would be a mistake to put the new before the macro
    CGAL_STATIC_THREAD_LOCAL_VARIABLE(Self,z,(new Lazy_rep_0<AT, ET, E2A>()));
    return z;
  }

  Self_rep * ptr() const { return (Self_rep*) PTR; }
};

// The magic functor for Construct_bbox_[2,3], as there is no Lazy<Bbox>

template <typename LK, typename AC, typename EC>
struct Lazy_construction_bbox
{
  static const bool Protection = true;
  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename AC::result_type result_type;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

  template <typename L1>
  result_type operator()(const L1& l1) const
  {
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    // Protection is outside the try block as VC8 has the CGAL_CFG_FPU_ROUNDING_MODE_UNWINDING_VC_BUG
    Protect_FPU_rounding<Protection> P;
    try {
      return ac(CGAL::approx(l1));
    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);
      return ec(CGAL::exact(l1));
    }
  }
};


template <typename LK, typename AC, typename EC>
struct Lazy_construction_nt {
  Lazy_construction_nt(){}
  Lazy_construction_nt(LK const&){}

  static const bool Protection = true;

  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename LK::E2A E2A;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

  template<typename>
  struct result { };

#define CGAL_RESULT_NT(z, n, d)                                              \
  template< typename F, BOOST_PP_ENUM_PARAMS(n, class T) >              \
  struct result<F( BOOST_PP_ENUM_PARAMS(n, T) )> {                      \
    BOOST_PP_REPEAT(n, CGAL_TYPEMAP_EC, T)                                   \
    typedef Lazy_exact_nt<                                              \
      typename boost::remove_cv< typename boost::remove_reference <     \
      typename cpp11::result_of<EC( BOOST_PP_ENUM_PARAMS(n, E) )>::type >::type >::type > type; \
  };

  BOOST_PP_REPEAT_FROM_TO(1, 6, CGAL_RESULT_NT, _)

  template<class...L>
  auto operator()(L const&...l) const ->
  Lazy_exact_nt<std::remove_cv_t<std::remove_reference_t<decltype(ec(CGAL::exact(l)...))>>>
  {
    typedef std::remove_cv_t<std::remove_reference_t<decltype(ec(CGAL::exact(l)...))>> ET;
    typedef std::remove_cv_t<std::remove_reference_t<decltype(ac(CGAL::approx(l)...))>> AT;
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;
    try {
      return new Lazy_rep_n<AT, ET, AC, EC, To_interval<ET>, L... >(ac, ec, l...);
    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);
      return new Lazy_rep_0<AT,ET,To_interval<ET> >(ec( CGAL::exact(l)... ));
    }
  }

#undef CGAL_RESULT_NT
};


template <typename LK>
Object
make_lazy(const Object& eto)
{
  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename LK::E2A E2A;

  if (eto.is_empty())
    return Object();

#define CGAL_Kernel_obj(X) \
  if (const typename EK::X* ptr = object_cast<typename EK::X>(&eto)) \
    return make_object(typename LK::X(new Lazy_rep_0<typename AK::X, typename EK::X, E2A>(*ptr)));

#include <CGAL/Kernel/interface_macros.h>

//now handle vector
#define CGAL_Kernel_obj(X) \
      {  \
        const std::vector<typename EK::X>* v_ptr;\
        if ( (v_ptr = object_cast<std::vector<typename EK::X> >(&eto)) ) { \
          std::vector<typename LK::X> V;\
          V.resize(v_ptr->size());                           \
          for (unsigned int i = 0; i < v_ptr->size(); ++i)                \
            V[i] = typename LK::X( new Lazy_rep_0<typename AK::X,typename EK::X,E2A>((*v_ptr)[i])); \
          return make_object(V);                                      \
        }\
      }

CGAL_Kernel_obj(Point_2)
CGAL_Kernel_obj(Point_3)
#undef CGAL_Kernel_obj


  std::cerr << "object_cast inside Lazy_construction_rep::operator() failed. It needs more else if's (#2)" << std::endl;
  std::cerr << "dynamic type of the Object : " << eto.type().name() << std::endl;

  return Object();
}


// This functor selects the i'th element in a vector of Object's
// and casts it to what is in the Object

template <typename T2>
struct Ith {
  typedef T2 result_type;

  // We keep a Sign member object
  // for future utilisation, in case
  // we have pairs of 2 T2 objects e.g.
  // for a numeric_point vector returned
  // from a construction of a possible
  // lazy algebraic kernel

  int i;
  Sign sgn;

  Ith(int i_)
    : i(i_)
  {sgn=NEGATIVE;}

  Ith(int i_, bool b_)
    : i(i_)
  { sgn= (b_) ? POSITIVE : ZERO;}

  const T2&
  operator()(const std::vector<Object>& v) const
  {
    if(sgn==NEGATIVE)
    return *object_cast<T2>(&v[i]);

    typedef std::pair<T2,unsigned int >         Pair_type_1;
    typedef std::pair<T2,std::pair<bool,bool> > Pair_type_2;

    if(const Pair_type_1 *p1 = object_cast<Pair_type_1>(&v[i]))
            return p1->first;
    else if(const Pair_type_2 *p2 = object_cast<Pair_type_2>(&v[i]))
        return p2->first;

    CGAL_error_msg( " Unexpected encapsulated type ");
  }
};

// This functor selects the i'th element in a vector of T2's
template <typename T2>
struct Ith_for_intersection {
  typedef T2 result_type;
  int i;

  Ith_for_intersection(int i_)
    : i(i_)
  {}

  const T2&
  operator()(const Object& o) const
  {
    const std::vector<T2>* ptr = object_cast<std::vector<T2> >(&o);
    return (*ptr)[i];
  }
};

// This functor selects the i'th element in a vector of T2's
template <typename T2>
struct Ith_for_intersection_with_variant {
  typedef T2 result_type;
  int i;

  Ith_for_intersection_with_variant(int i_)
    : i(i_)
  {}

  template< BOOST_VARIANT_ENUM_PARAMS(typename U) >
  const T2&
  operator()(const boost::optional< boost::variant< BOOST_VARIANT_ENUM_PARAMS(U) > >& o) const
  {
    const std::vector<T2>* ptr = (boost::get<std::vector<T2> >(&(*o)));
    return (*ptr)[i];
  }

  template< BOOST_VARIANT_ENUM_PARAMS(typename U) >
  const T2&
  operator()(const boost::variant< BOOST_VARIANT_ENUM_PARAMS(U) >& o) const
  {
    const std::vector<T2>* ptr = (boost::get<std::vector<T2> >(&o));
    return (*ptr)[i];
  }
};

template <typename LK, typename AC, typename EC>
struct Lazy_cartesian_const_iterator_2
{
  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename LK::Cartesian_const_iterator_2 result_type;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

public:

  template < typename L1>
  result_type
  operator()(const L1& l1) const
  {
    return result_type(&l1);
  }

  template < typename L1>
  result_type
  operator()(const L1& l1, int) const
  {
    return result_type(&l1,2);
  }

};


template <typename LK, typename AC, typename EC>
struct Lazy_cartesian_const_iterator_3
{
  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename LK::Cartesian_const_iterator_3 result_type;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

public:

  template < typename L1>
  result_type
  operator()(const L1& l1) const
  {
    return result_type(&l1);
  }

  template < typename L1>
  result_type
  operator()(const L1& l1, int) const
  {
    return result_type(&l1,3);
  }

};


// This is the magic functor for functors that write their result in a  reference argument
// In a first version we assume that the references are of type Lazy<Something>,
// and that the result type is void

template <typename AC, typename EC, typename E2A>
struct Lazy_functor_2_1
{
  static const bool Protection = true;
  typedef void result_type;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

public:

  template <typename L1, typename L2, typename R1>
  void
  operator()(const L1& l1, const L2& l2, R1& r1) const
  {
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;
    try {
      // we suppose that R1 is a Lazy<Something>
      r1 = R1(new Lazy_rep_2_1<AC, EC, E2A, L1, L2, R1>(ac, ec, l1, l2));
    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);
      typename R1::ET et;
      ec(CGAL::exact(l1), CGAL::exact(l2), et);
      r1 = R1(new Lazy_rep_0<typename R1::AT,typename R1::ET,E2A>(et));
    }
  }
};


template <typename T>
struct First
{
   typedef typename T::first_type result_type;

   const typename T::first_type&
   operator()(const T& p) const
   {
     return p.first;
   }
 };

template <typename T>
struct Second
{
  typedef typename T::second_type result_type;

  const typename T::second_type&
  operator()(const T& p) const
  {
    return p.second;
  }
};

// This is the magic functor for functors that write their result in a reference argument
// In a first version we assume that the references are of type Lazy<Something>,
// and that the result type is void

//template <typename LK, typename AK, typename EK, typename AC, typename EC, typename EFT, typename E2A>
template <typename LK, typename AC, typename EC>
struct Lazy_functor_2_2
{
  static const bool Protection = true;

  typedef void result_type;
  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename LK::E2A E2A;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

public:

  template <typename L1, typename L2, typename R1, typename R2>
  void
  operator()(const L1& l1, const L2& l2, R1& r1, R2& r2) const
  {
    typedef Lazy<typename R1::AT, typename R1::ET, E2A> Handle_1;
    typedef Lazy<typename R2::AT, typename R2::ET, E2A> Handle_2;
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;
    try {
      typedef Lazy<std::pair<typename R1::AT, typename R2::AT>, std::pair<typename R1::ET, typename R2::ET>, E2A> Lazy_pair;
      Lazy_pair lv(new Lazy_rep_2_2<AC, EC, E2A, L1, L2, R1, R2>(ac, ec, l1, l2));
      // lv->approx() is a std::pair<R1::AT, R2::AT>;
      r1 = R1(Handle_1(new Lazy_rep_n<void, void, First<std::pair<typename R1::AT, typename R2::AT> >, First<std::pair<typename R1::ET, typename R2::ET> >, E2A, Lazy_pair>(First<std::pair<typename R1::AT, typename R2::AT> >(), First<std::pair<typename R1::ET, typename R2::ET> >(), lv)));
      r2 = R2(Handle_2(new Lazy_rep_n<void, void, Second<std::pair<typename R1::AT, typename R2::AT> >, Second<std::pair<typename R1::ET, typename R2::ET> >, E2A, Lazy_pair>(Second<std::pair<typename R1::AT, typename R2::AT> >(), Second<std::pair<typename R1::ET, typename R2::ET> >(), lv)));
    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);
      typename R1::ET et1, et2;
      ec(CGAL::exact(l1), CGAL::exact(l2), et1, et2);
      r1 = R1(Handle_1(new Lazy_rep_0<typename R1::AT,typename R1::ET,E2A>(et1)));
      r2 = R2(Handle_2(new Lazy_rep_0<typename R2::AT,typename R2::ET,E2A>(et2)));
    }
  }
};


// This is the magic functor for functors that write their result as Objects into an output iterator

template <typename LK, typename AC, typename EC>
struct Lazy_intersect_with_iterators
{
  static const bool Protection = true;
  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename LK::E2A E2A;
  typedef void result_type;
  typedef Lazy<Object, Object, E2A> Lazy_object;
  typedef Lazy<std::vector<Object>, std::vector<Object>, E2A> Lazy_vector;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

public:

  // In the example we intersect two Lazy<Segment>s
  // and write into a back_inserter(list<Object([Lazy<Point>,Lazy<Segment>]) >)
  template <typename L1, typename L2, typename OutputIterator>
  OutputIterator
  operator()(const L1& l1, const L2& l2, OutputIterator it) const
  {
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;
    try {
      Lazy_vector lv(new Lazy_rep_with_vector_2<AC, EC, E2A, L1, L2>(ac, ec, l1, l2));
      // lv.approx() is a std::vector<Object([AK::Point_2,AK::Segment_2])>
      // that is, when we get here we have constructed all approximate results
      for (unsigned int i = 0; i < lv.approx().size(); i++) {
// FIXME : I'm not sure how this work...
#define CGAL_Kernel_obj(X) if (object_cast<typename AK::X>(& (lv.approx()[i]))) { \
          *it++ = make_object(typename LK::X(new Lazy_rep_n<typename AK::X, typename EK::X, Ith<typename AK::X>, \
                                                                      Ith<typename EK::X>, E2A, Lazy_vector> \
                                                 (Ith<typename AK::X>(i), Ith<typename EK::X>(i), lv))); \
          continue; \
        }

#include <CGAL/Kernel/interface_macros.h>

        std::cerr << "we need  more casts" << std::endl;
      }

    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      // TODO: Instead of using a vector, write an iterator adapter
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);
      std::vector<Object> exact_objects;
      ec(CGAL::exact(l1), CGAL::exact(l2), std::back_inserter(exact_objects));
      for (std::vector<Object>::const_iterator oit = exact_objects.begin();
           oit != exact_objects.end();
           ++oit){
        *it++ = make_lazy<LK>(*oit);
      }
    }
    return it;
  }
};


template <typename T>
struct Object_cast
{
  typedef T result_type;

  const T&
  operator()(const Object& o) const
  {
    return *object_cast<T>(&o);
  }
};

// The following functor returns an Object with a Lazy<Something> inside
// As the nested kernels return Objects of AK::Something and EK::Something
// we have to unwrap them from the Object, and wrap them in a Lazy<Something>
//
// TODO: write operators for other than two arguments. For the current kernel we only need two for Intersect_2

template <typename LK, typename AC, typename EC>
struct Lazy_construction_object
{
  static const bool Protection = true;

  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename LK::E2A E2A;
  typedef typename AC::result_type AT;
  typedef typename EC::result_type ET;
  typedef Object result_type;

  typedef Lazy<Object, Object, E2A> Lazy_object;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

public:

  template <typename L1>
  result_type
  operator()(const L1& l1) const
  {
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;
    try {
      Lazy_object lo(new Lazy_rep_n<result_type, result_type, AC, EC, E2A, L1>(ac, ec, l1));

      if(lo.approx().is_empty())
        return Object();

#define CGAL_Kernel_obj(X) \
      if (object_cast<typename AK::X>(& (lo.approx()))) { \
        typedef Lazy_rep_n< typename AK::X, typename EK::X, Object_cast<typename AK::X>, Object_cast<typename EK::X>, E2A, Lazy_object> Lcr; \
        Lcr * lcr = new Lcr(Object_cast<typename AK::X>(), Object_cast<typename EK::X>(), lo); \
        return make_object(typename LK::X(lcr)); \
      }

#include <CGAL/Kernel/interface_macros.h>

      std::cerr << "object_cast inside Lazy_construction_rep::operator() failed. It needs more else if's (#1)" << std::endl;
      std::cerr << "dynamic type of the Object : " << lo.approx().type().name() << std::endl;

    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);
      ET eto = ec(CGAL::exact(l1));
      return make_lazy<LK>(eto);
    }
    return Object();
  }

  template <typename L1, typename L2>
  result_type
  operator()(const L1& l1, const L2& l2) const
  {
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;
    try {
      Lazy_object lo(new Lazy_rep_n<result_type, result_type, AC, EC, E2A, L1, L2>(ac, ec, l1, l2));

      if(lo.approx().is_empty())
        return Object();

#define CGAL_Kernel_obj(X) \
      if (object_cast<typename AK::X>(& (lo.approx()))) { \
        typedef Lazy_rep_n<typename AK::X, typename EK::X, Object_cast<typename AK::X>, Object_cast<typename EK::X>, E2A, Lazy_object> Lcr; \
        Lcr * lcr = new Lcr(Object_cast<typename AK::X>(), Object_cast<typename EK::X>(), lo); \
        return make_object(typename LK::X(lcr)); \
      }

#include <CGAL/Kernel/interface_macros.h>

    // We now check vector<X>

#define CGAL_Kernel_obj(X) \
      {  \
        const std::vector<typename AK::X>* v_ptr;\
        if ( (v_ptr = object_cast<std::vector<typename AK::X> >(& (lo.approx()))) ) { \
          std::vector<typename LK::X> V;\
          V.resize(v_ptr->size());                           \
          for (unsigned int i = 0; i < v_ptr->size(); i++) {               \
            V[i] = typename LK::X(new Lazy_rep_n<typename AK::X, typename EK::X, Ith_for_intersection<typename AK::X>, \
                                                 Ith_for_intersection<typename EK::X>, E2A, Lazy_object> \
                                  (Ith_for_intersection<typename AK::X>(i), Ith_for_intersection<typename EK::X>(i), lo)); \
          }                                                           \
          return make_object(V);                                      \
        }\
      }

CGAL_Kernel_obj(Point_2)
CGAL_Kernel_obj(Point_3)
#undef CGAL_Kernel_obj

      std::cerr << "object_cast inside Lazy_construction_rep::operator() failed. It needs more else if's (#1)" << std::endl;
      std::cerr << "dynamic type of the Object : " << lo.approx().type().name() << std::endl;

    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);
      ET eto = ec(CGAL::exact(l1), CGAL::exact(l2));
      return make_lazy<LK>(eto);
    }
    return Object();
  }

  template <typename L1, typename L2, typename L3>
  result_type
  operator()(const L1& l1, const L2& l2, const L3& l3) const
  {
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;
    try {
      Lazy_object lo(new Lazy_rep_n<result_type, result_type, AC, EC, E2A, L1, L2, L3>(ac, ec, l1, l2, l3));

      if(lo.approx().is_empty())
        return Object();

#define CGAL_Kernel_obj(X) \
      if (object_cast<typename AK::X>(& (lo.approx()))) { \
        typedef Lazy_rep_n<typename AK::X, typename EK::X, Object_cast<typename AK::X>, Object_cast<typename EK::X>, E2A, Lazy_object> Lcr; \
        Lcr * lcr = new Lcr(Object_cast<typename AK::X>(), Object_cast<typename EK::X>(), lo); \
        return make_object(typename LK::X(lcr)); \
      }

#include <CGAL/Kernel/interface_macros.h>

      std::cerr << "object_cast inside Lazy_construction_rep::operator() failed. It needs more else if's (#1)" << std::endl;
      std::cerr << "dynamic type of the Object : " << lo.approx().type().name() << std::endl;

    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);
      ET eto = ec(CGAL::exact(l1), CGAL::exact(l2), CGAL::exact(l3));
      return make_lazy<LK>(eto);
    }
    return Object();
  }

};



//____________________________________________________________
// The magic functor that has Lazy<Something> as result type.
// Two versions are distinguished: one that needs to fiddle
// with result_of and another that can forward the result types.

namespace internal {
BOOST_MPL_HAS_XXX_TRAIT_DEF(result_type)

// lift boost::get into a functor with a result_type member name and
// extend it to operate on optionals

// TODO there is a mismatch between the result_type typedef and the
// actual return type of operator()
template<typename T>
struct Variant_cast {
  typedef T result_type;

  template<BOOST_VARIANT_ENUM_PARAMS(typename U)>
  const T&
  operator()(const boost::optional< boost::variant< BOOST_VARIANT_ENUM_PARAMS(U) > >& o) const {
    // can throw but should never because we always build it inside
    // a static visitor with the right type
    return boost::get<T>(*o);
  }

  template<BOOST_VARIANT_ENUM_PARAMS(typename U)>
  T&
  operator()(boost::optional< boost::variant< BOOST_VARIANT_ENUM_PARAMS(U) > >& o) const {
    // can throw but should never because we always build it inside
    // a static visitor with the right type, if it throws bad_get
    return boost::get<T>(*o);
  }
};


template<typename Result, typename AK, typename LK, typename EK, typename Origin>
struct Fill_lazy_variant_visitor_2 : boost::static_visitor<> {
  Fill_lazy_variant_visitor_2(Result& r, Origin& o) : r(&r), o(&o) {}
  Result* r;
  Origin* o;

  template<typename T>
  void operator()(const T&) {
    // the equivalent type we are currently matching in the lazy kernel
    typedef T AKT;
    typedef typename Type_mapper<AKT, AK, EK>::type EKT;
    typedef typename Type_mapper<AKT, AK, LK>::type LKT;

    typedef Lazy_rep_n<AKT, EKT, Variant_cast<AKT>, Variant_cast<EKT>, typename LK::E2A, Origin> Lcr;
    Lcr * lcr = new Lcr(Variant_cast<AKT>(), Variant_cast<EKT>(), *o);

    *r = LKT(lcr);
  }

  template<typename T>
  void operator()(const std::vector<T>& t) {
    typedef T AKT;
    typedef typename Type_mapper<AKT, AK, EK>::type EKT;
    typedef typename Type_mapper<AKT, AK, LK>::type LKT;

    std::vector<LKT> V;
    V.resize(t.size());
    for (unsigned int i = 0; i < t.size(); i++) {
      V[i] = LKT(new Lazy_rep_n<AKT, EKT, Ith_for_intersection<AKT>,
                 Ith_for_intersection<EKT>, typename LK::E2A, Origin>
                 (Ith_for_intersection<AKT>(i), Ith_for_intersection<EKT>(i), *o));
    }

    *r = V;
  }
};

template<typename Result, typename AK, typename LK, typename EK>
struct Fill_lazy_variant_visitor_0 : boost::static_visitor<> {
  Fill_lazy_variant_visitor_0(Result& r) : r(&r) {}
  Result* r;

  template<typename T>
  void operator()(const T& t) {
    // the equivalent type we are currently matching in the lazy kernel
    typedef T EKT;
    typedef typename Type_mapper<EKT, EK, AK>::type AKT;
    typedef typename Type_mapper<EKT, EK, LK>::type LKT;

    *r = LKT(new Lazy_rep_0<AKT, EKT, typename LK::E2A>(t));
  }

  template<typename T>
  void operator()(const std::vector<T>& t) {
    typedef T EKT;
    typedef typename Type_mapper<EKT, EK, AK>::type AKT;
    typedef typename Type_mapper<EKT, EK, LK>::type LKT;

    std::vector<LKT> V;
    V.resize(t.size());
    for (unsigned int i = 0; i < t.size(); i++) {
      V[i] = LKT(new Lazy_rep_0<AKT, EKT, typename LK::E2A>(t[i]));
    }

    *r = V;
  }
};

} // internal

template <typename LK, typename AC, typename EC>
struct Lazy_construction_variant {
  static const bool Protection = true;

  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename LK::E2A E2A;


  template<typename>
  struct result {
    // this does not default, if you want to make a lazy lazy-kernel,
    // you are on your own
  };

  #define CGAL_RESULT(z, n, d) \
    template< typename F, BOOST_PP_ENUM_PARAMS(n, class T) >            \
    struct result<F( BOOST_PP_ENUM_PARAMS(n, T) )> {                    \
      BOOST_PP_REPEAT(n, CGAL_TYPEMAP_AC, T)                            \
      typedef typename Type_mapper<                                     \
        typename cpp11::result_of<AC( BOOST_PP_ENUM_PARAMS(n, A) )>::type, AK, LK>::type type; \
    };

  BOOST_PP_REPEAT_FROM_TO(1, 9, CGAL_RESULT, _)

  template <typename L1, typename L2>
  typename result<Lazy_construction_variant(L1, L2)>::type
  operator()(const L1& l1, const L2& l2) const {
    typedef typename cpp11::result_of<Lazy_construction_variant(L1, L2)>::type result_type;

    typedef typename cpp11::result_of<AC(typename Type_mapper<L1, LK, AK>::type,
                                         typename Type_mapper<L2, LK, AK>::type)>::type AT;
    typedef typename cpp11::result_of<EC(typename Type_mapper<L1, LK, EK>::type,
                                         typename Type_mapper<L2, LK, EK>::type)>::type ET;

    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;

    try {
      Lazy<AT, ET, E2A> lazy(new Lazy_rep_n<AT, ET, AC, EC, E2A, L1, L2>(AC(), EC(), l1, l2));

      // the approximate result requires the trait with types from the AK
      AT approx_v = lazy.approx();
      // the result we build
      result_type res;

      if(!approx_v) {
        // empty
        return res;
      }

      // the static visitor fills the result_type with the correct unwrapped type
      internal::Fill_lazy_variant_visitor_2< result_type, AK, LK, EK, Lazy<AT, ET, E2A> > visitor(res, lazy);
      boost::apply_visitor(visitor, *approx_v);

      return res;
    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);

      ET exact_v = EC()(CGAL::exact(l1), CGAL::exact(l2));
      result_type res;

      if(!exact_v) {
        return res;
      }

      internal::Fill_lazy_variant_visitor_0<result_type, AK, LK, EK> visitor(res);
      boost::apply_visitor(visitor, *exact_v);
      return res;
    }
  }

  template <typename L1, typename L2, typename L3>
  typename result<Lazy_construction_variant(L1, L2, L3)>::type
  operator()(const L1& l1, const L2& l2, const L3& l3) const {
    typedef typename result<Lazy_construction_variant(L1, L2, L3)>::type result_type;

    typedef typename cpp11::result_of<AC(typename Type_mapper<L1, LK, AK>::type,
                                         typename Type_mapper<L2, LK, AK>::type,
                                         typename Type_mapper<L3, LK, AK>::type)>::type AT;
    typedef typename cpp11::result_of<EC(typename Type_mapper<L1, LK, EK>::type,
                                         typename Type_mapper<L2, LK, EK>::type,
                                         typename Type_mapper<L3, LK, EK>::type)>::type ET;

    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp);
    Protect_FPU_rounding<Protection> P;
    try {
      Lazy<AT, ET, E2A> lazy(new Lazy_rep_n<AT, ET, AC, EC, E2A, L1, L2, L3>(AC(), EC(), l1, l2, l3));

      // the approximate result requires the trait with types from the AK
      AT approx_v = lazy.approx();
      // the result we build
      result_type res;

      if(!approx_v) {
        // empty
        return res;
      }

      // the static visitor fills the result_type with the correct unwrapped type
      internal::Fill_lazy_variant_visitor_2< result_type, AK, LK, EK, Lazy<AT, ET, E2A> > visitor(res, lazy);
      boost::apply_visitor(visitor, *approx_v);

      return res;
    } catch (Uncertain_conversion_exception&) {
      CGAL_BRANCH_PROFILER_BRANCH(tmp);
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);

      ET exact_v = EC()(CGAL::exact(l1), CGAL::exact(l2), CGAL::exact(l3));
      result_type res;

      if(!exact_v) {
        return res;
      }

      internal::Fill_lazy_variant_visitor_0< result_type, AK, LK, EK> visitor(res);
      boost::apply_visitor(visitor, *exact_v);
      return res;
    }
  }
};

template<typename LK, typename AC, typename EC, typename E2A = Default,
         bool has_result_type = internal::has_result_type<AC>::value && internal::has_result_type<EC>::value >
struct Lazy_construction;


// we have a result type, low effort
template<typename LK, typename AC, typename EC, typename E2A_>
struct Lazy_construction<LK, AC, EC, E2A_, true> {
  static const bool Protection = true;

  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename boost::remove_cv<
    typename boost::remove_reference < typename AC::result_type >::type >::type AT;
  typedef typename boost::remove_cv<
    typename boost::remove_reference < typename EC::result_type >::type >::type  ET;

  typedef typename Default::Get<E2A_, typename LK::E2A>::type E2A;

  typedef typename Type_mapper<AT, AK, LK>::type result_type;

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

#define CGAL_CONSTRUCTION_OPERATOR(z, n, d  )                           \
  template<BOOST_PP_ENUM_PARAMS(n, class L)>                            \
  result_type                                                           \
  operator()( BOOST_PP_ENUM(n, CGAL_LARGS, _) ) const {                 \
    typedef Lazy< AT, ET, E2A> Handle;                                  \
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp); \
    Protect_FPU_rounding<Protection> P;                                 \
    try {                                                               \
      return result_type( Handle(new Lazy_rep_n<AT, ET, AC, EC, E2A, BOOST_PP_ENUM_PARAMS(n, L)>(ac, ec, BOOST_PP_ENUM_PARAMS(n, l)))); \
    } catch (Uncertain_conversion_exception&) {                          \
      CGAL_BRANCH_PROFILER_BRANCH(tmp);                                 \
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);          \
      return result_type( Handle(new Lazy_rep_0<AT,ET,E2A>(ec( BOOST_PP_ENUM(n, CGAL_LEXACT, _) ))) ); \
    }                                                                   \
  }

  // arity 1-8
  BOOST_PP_REPEAT_FROM_TO(1, 9, CGAL_CONSTRUCTION_OPERATOR, _)

  // nullary
  result_type
  operator()() const
  {
    typedef Lazy<AT, ET, E2A> Handle;
    return result_type( Handle(new Lazy_rep_0<AT,ET,E2A>()) );
  }

#undef CGAL_CONSTRUCTION_OPERATOR

};


template <typename LK, typename AC, typename EC, typename E2A_>
struct Lazy_construction<LK, AC, EC, E2A_, false>
{
  static const bool Protection = true;

  typedef typename LK::Approximate_kernel AK;
  typedef typename LK::Exact_kernel EK;
  typedef typename Default::Get<E2A_, typename LK::E2A>::type E2A;

  template<typename>
  struct result {
    // this does not default, if you want to make a lazy lazy-kernel,
    // you are on your own
  };

  CGAL_NO_UNIQUE_ADDRESS AC ac;
  CGAL_NO_UNIQUE_ADDRESS EC ec;

  // acquire the result_type of the approximate kernel, map it back to the lazy kernel object
#define CGAL_RESULT(z, n, d) \
template< typename F, BOOST_PP_ENUM_PARAMS(n, class T) > \
struct result<F( BOOST_PP_ENUM_PARAMS(n, T) )> { \
  BOOST_PP_REPEAT(n, CGAL_TYPEMAP_AC, T)                                     \
  typedef typename Type_mapper< typename cpp11::result_of<AC( BOOST_PP_ENUM_PARAMS(n, A) )>::type, AK, LK>::type type; \
};

  BOOST_PP_REPEAT_FROM_TO(1, 9, CGAL_RESULT, _)

#define CGAL_CONSTRUCTION_OPERATOR(z, n, d)                                      \
  template<BOOST_PP_ENUM_PARAMS(n, class L)>                            \
  typename cpp11::result_of<Lazy_construction(BOOST_PP_ENUM_PARAMS(n, L))>::type \
  operator()( BOOST_PP_ENUM(n, CGAL_LARGS, _) ) const {                            \
    BOOST_PP_REPEAT(n, CGAL_TYPEMAP_EC, L)                                     \
    BOOST_PP_REPEAT(n, CGAL_TYPEMAP_AC, L)                                     \
    typedef typename boost::remove_cv< typename boost::remove_reference < \
                                        typename cpp11::result_of< EC(BOOST_PP_ENUM_PARAMS(n, E)) >::type >::type >::type ET; \
    typedef typename boost::remove_cv< typename boost::remove_reference < \
                                        typename cpp11::result_of< AC(BOOST_PP_ENUM_PARAMS(n, A)) >::type >::type >::type AT; \
    typedef Lazy< AT, ET, E2A> Handle; \
    typedef typename cpp11::result_of<Lazy_construction(BOOST_PP_ENUM_PARAMS(n, L))>::type result_type; \
    CGAL_BRANCH_PROFILER(std::string(" failures/calls to   : ") + std::string(CGAL_PRETTY_FUNCTION), tmp); \
    Protect_FPU_rounding<Protection> P;                                   \
    try {                                                                 \
      return result_type( Handle(new Lazy_rep_n<AT, ET, AC, EC, E2A, BOOST_PP_ENUM_PARAMS(n, L)>(ac, ec, BOOST_PP_ENUM_PARAMS(n, l)))); \
    } catch (Uncertain_conversion_exception&) {                          \
      CGAL_BRANCH_PROFILER_BRANCH(tmp);                                 \
      Protect_FPU_rounding<!Protection> P2(CGAL_FE_TONEAREST);          \
      return result_type( Handle(new Lazy_rep_0<AT,ET,E2A>(ec( BOOST_PP_ENUM(n, CGAL_LEXACT, _) ))) ); \
    }                                                                   \
  }

  // arity 1-8
  BOOST_PP_REPEAT_FROM_TO(1, 9, CGAL_CONSTRUCTION_OPERATOR, _)

  // nullary
  typename Type_mapper< typename cpp11::result_of<AC()>::type ,AK, LK>::type
  operator()() const
  {
    typedef typename cpp11::result_of<AC()>::type AT;
    typedef typename cpp11::result_of<EC()>::type ET;
    typedef Lazy<AT, ET, E2A> Handle;
    typedef typename Type_mapper< typename cpp11::result_of<AC()>::type ,AK, LK>::type result_type;

    return result_type( Handle(new Lazy_rep_0<AT,ET,E2A>()) );
  }
};

} //namespace CGAL

#undef CGAL_TYPEMAP_AC
#undef CGAL_TYPEMAP_EC
#undef CGAL_LEXACT
#undef CGAL_LARGS

#include <CGAL/enable_warnings.h>

#endif // CGAL_LAZY_H