#include <Rcpp.h>
// Copyright (c) 2002-2004,2007
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.1/Number_types/include/CGAL/CORE_Expr.h $
// $Id: include/CGAL/CORE_Expr.h 50cfbde3b84 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Sylvain Pion, Michael Hemmer

#ifndef CGAL_CORE_EXPR_H
#define CGAL_CORE_EXPR_H

#include <CGAL/disable_warnings.h>

#include <CGAL/number_type_basic.h>
#include <CGAL/CORE_coercion_traits.h>
#include <utility>


namespace CGAL {

template <> class Algebraic_structure_traits< CORE::Expr >
  : public Algebraic_structure_traits_base< CORE::Expr,
                                            Field_with_root_of_tag >  {
  public:
    typedef Tag_true            Is_exact;
    typedef Tag_true            Is_numerical_sensitive;

    class Sqrt
      : public CGAL::cpp98::unary_function< Type, Type > {
      public:
        Type operator()( const Type& x ) const {
          return CORE::sqrt( x );
        }
    };

    class Kth_root
      : public CGAL::cpp98::binary_function<int, Type, Type> {
      public:
        Type operator()( int k,
                                        const Type& x) const {
          CGAL_precondition_msg( k > 0, "'k' must be positive for k-th roots");
          // CORE::radical isn't implemented for negative values of x, so we
          //  have to handle this case separately
          if( x < 0 && k%2 != 0)
            return -CORE::radical( -x, k );

          return CORE::radical( x, k );
        }
    };

    class Root_of {
      public:
//        typedef CORE::BigRat Boundary;
        typedef Type   result_type;


      public:
        // constructs the kth roots of the polynomial
        // given by the iterator range, starting from 0.
        template< class ForwardIterator >
        Type operator()( int k,
                                        ForwardIterator begin,
                                        ForwardIterator end) const {
            std::vector<Type> coeffs;
            for(ForwardIterator it = begin; it != end; it++){
                coeffs.push_back(*it);
            }
            CORE::Polynomial<Type> polynomial(coeffs);
            return Type(polynomial,k);
        }

// TODO: Need to be fixed: polynomial<CORE::Expr>.eval() cannot return
//       CORE::BigFloat, so this does not compile.

/*        template <class ForwardIterator>
        Type operator()( CORE::BigRat lower,
                                        CORE::BigRat upper,
                                        ForwardIterator begin,
                                        ForwardIterator end) const {
            std::vector<Type> coeffs;
            for(ForwardIterator it = begin; it != end; it++){
                 coeffs.push_back(*it);
            }
            CORE::Polynomial<Type> polynomial(coeffs);
            CORE::BigFloat lower_bf, upper_bf;
            CORE::BigFloat eval_at_lower(0), eval_at_upper(0);

            CORE::extLong r(16),a(16);
            while((eval_at_lower.isZeroIn() ||
                   eval_at_upper.isZeroIn())){
                //Rcpp::Rcout << "while"<<std::endl;
                r*=2;
                a*=2;
                lower_bf.approx(lower,r,a);
                upper_bf.approx(upper,r,a);
                // The most expensive precond I've ever seen :)),
                // since the coefficients of the polynomial are CORE::Expr
                // TODO: be sure that lower_bf, upper_bf contain exactly one root
                //NiX_expensive_precond(
                //     CORE::Sturm(polynomial).numberOfRoots(lower_bf,upper_bf)==1);
                eval_at_lower = polynomial.eval(lower_bf);
                eval_at_upper = polynomial.eval(upper_bf);
            }
            CORE::BFInterval interval(lower_bf,upper_bf);

            return Type(polynomial,interval);
        };  */
    };

    class Is_zero
      : public CGAL::cpp98::unary_function< Type, bool > {
      public:
        bool operator()( const Type& x ) const {
          return x.isZero();
        }
    };

};

template <> class Real_embeddable_traits< CORE::Expr >
  : public INTERN_RET::Real_embeddable_traits_base< CORE::Expr , CGAL::Tag_true > {
  public:
    class Abs
      : public CGAL::cpp98::unary_function< Type, Type > {
      public:
        Type operator()( const Type& x ) const {
            return CORE::abs( x );
        }
    };

    class Sgn
      : public CGAL::cpp98::unary_function< Type, ::CGAL::Sign > {
      public:
        ::CGAL::Sign operator()( const Type& x ) const {
          return (::CGAL::Sign) CORE::sign( x );
        }
    };

    class Compare
      : public CGAL::cpp98::binary_function< Type, Type,
                                Comparison_result > {
      public:
        Comparison_result operator()( const Type& x,
                                            const Type& y ) const {
          return (Comparison_result) CORE::cmp( x, y );
        }

        CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR_WITH_RT( Type,
                                                      Comparison_result )

    };

    class To_double
      : public CGAL::cpp98::unary_function< Type, double > {
      public:
        double operator()( const Type& x ) const {
          x.approx(53,1075);
          return x.doubleValue();
        }
    };

    class To_interval
      : public CGAL::cpp98::unary_function< Type, std::pair< double, double > > {
      public:
        std::pair<double, double> operator()( const Type& x ) const {
            std::pair<double,double> result;
            x.approx(53,1075);
            x.doubleInterval(result.first, result.second);
            CGAL_expensive_assertion(result.first  <= x);
            CGAL_expensive_assertion(result.second >= x);
            return result;
        }
    };
};

inline const CORE::Expr& approx(const CORE::Expr& d) { return d; }
inline const CORE::Expr& exact(const CORE::Expr& d) { return d; }
inline int depth(const CORE::Expr&){ return -1; }

} // namespace CGAL

//since types are included by CORE_coercion_traits.h:
#include <CGAL/CORE_BigInt.h>
#include <CGAL/CORE_BigRat.h>
#include <CGAL/CORE_BigFloat.h>
#include <CGAL/CORE_arithmetic_kernel.h>

namespace Eigen {
  template<class> struct NumTraits;
  template<> struct NumTraits<CORE::Expr>
  {
    typedef CORE::Expr Real;
    typedef CORE::Expr NonInteger;
    typedef CORE::Expr Nested;
    typedef CORE::Expr Literal;

    static inline Real epsilon() { return 0; }
    static inline Real dummy_precision() { return 0; }

    enum {
      IsInteger = 0,
      IsSigned = 1,
      IsComplex = 0,
      RequireInitialization = 1,
      ReadCost = 6,
      AddCost = 200,
      MulCost = 200
    };
  };
}

#include <CGAL/enable_warnings.h>

#endif // CGAL_CORE_EXPR_H

