// Copyright (c) 2006-2008 Max-Planck-Institute Saarbruecken (Germany),
// INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.6.1/Number_types/include/CGAL/Gmpz.h $
// $Id: Gmpz.h 152a084 2021-09-21T13:34:58+02:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Michael Hemmer   <hemmer@mpi-inf.mpg.de>
//                 Sylvain Pion

#ifndef CGAL_GMPZ_H
#define CGAL_GMPZ_H

#include <CGAL/config.h>
#if defined(BOOST_MSVC)
#  pragma warning(push)
#  pragma warning(disable:4800) // complaint about performance in std::map where we can't do anything
#endif

#include <CGAL/number_type_basic.h>
#include <CGAL/Gmp_coercion_traits.h>
#include <CGAL/Quotient.h> // spec of AST for Quotient<Gmpz>

#include <string>
#include <locale>

#include <CGAL/Modular_traits.h>

namespace CGAL {

// Algebraic structure traits
template <> class Algebraic_structure_traits< Gmpz >
    : public Algebraic_structure_traits_base< Gmpz,
                                            Euclidean_ring_tag >  {
public:
    typedef Tag_true            Is_exact;
    typedef Tag_false           Is_numerical_sensitive;

    typedef INTERN_AST::Is_square_per_sqrt< Type >
    Is_square;
    class Integral_division
        : public CGAL::cpp98::binary_function< Type, Type,
                                Type > {
    public:
        Type operator()( const Type& x,
                const Type& y ) const {
            Gmpz result;
            mpz_divexact(result.mpz(), x.mpz(), y.mpz());
            CGAL_postcondition_msg(result * y == x, "exact_division failed\n");
            return result;
        }
    };

    class Gcd
        : public CGAL::cpp98::binary_function< Type, Type,
                                Type > {
    public:
        Type operator()( const Type& x,
                const Type& y ) const {
            Gmpz result;
            mpz_gcd(result.mpz(), x.mpz(), y.mpz());
            return result;

        }

        Type operator()( const Type& x,
                                        const int& y ) const {
          if (y > 0)
          {
              Gmpz Res;
              mpz_gcd_ui(Res.mpz(), x.mpz(), y);
              return Res;
          }
          return CGAL_NTS gcd(x, Gmpz(y));
        }

        Type operator()( const int& x,
                                        const Type& y ) const {
          return CGAL_NTS gcd(Gmpz(x), y );
        }
    };

    typedef INTERN_AST::Div_per_operator< Type > Div;
    typedef INTERN_AST::Mod_per_operator< Type > Mod;

    class Sqrt
        : public CGAL::cpp98::unary_function< Type, Type > {
    public:
        Type operator()( const Type& x ) const {
            Gmpz result;
            mpz_sqrt(result.mpz(), x.mpz());
            return result;
        }
    };
};

template <> class Real_embeddable_traits< Gmpz >
    : public INTERN_RET::Real_embeddable_traits_base< Gmpz , CGAL::Tag_true > {
public:
    class Sgn
        : public CGAL::cpp98::unary_function< Type, ::CGAL::Sign > {
    public:
        ::CGAL::Sign operator()( const Type& x ) const {
            return x.sign();
        }
    };

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

    class To_interval
        : public CGAL::cpp98::unary_function< Type, std::pair< double, double > > {
    public:
        std::pair<double, double> operator()( const Type& x ) const {
#if MPFR_VERSION_MAJOR >= 3
          MPFR_DECL_INIT (y, 53); /* Assume IEEE-754 */
          int r = mpfr_set_z (y, x.mpz(), MPFR_RNDA);
          double i = mpfr_get_d (y, MPFR_RNDA); /* EXACT but can overflow */
          if (r == 0 && is_finite (i))
            return std::pair<double, double>(i, i);
          else
          {
            double s = nextafter (i, 0);
            if (i < 0)
              return std::pair<double, double>(i, s);
            else
              return std::pair<double, double>(s, i);
          }
#else
          mpfr_t y;
          mpfr_init2 (y, 53); /* Assume IEEE-754 */
          mpfr_set_z (y, x.mpz(), GMP_RNDD);
          double i = mpfr_get_d (y, GMP_RNDD); /* EXACT but can overflow */
          mpfr_set_z (y, x.mpz(), GMP_RNDU);
          double s = mpfr_get_d (y, GMP_RNDU); /* EXACT but can overflow */
          mpfr_clear (y);
          return std::pair<double, double>(i, s);
#endif
        }
    };
};

template<> class Algebraic_structure_traits< Quotient<Gmpz> >
    : public INTERN_QUOTIENT::Algebraic_structure_traits_quotient_base<Quotient<Gmpz> >{
    // specialization of to double functor
public:
    typedef Quotient<Gmpz> Type;

    struct To_double: public CGAL::cpp98::unary_function<Quotient<Gmpz>, double>{
        double operator()(const Quotient<Gmpz>& quot){
            mpq_t  mpQ;
            mpq_init(mpQ);
            const Gmpz& n = quot.numerator();
            const Gmpz& d = quot.denominator();
            mpz_set(mpq_numref(mpQ), n.mpz());
            mpz_set(mpq_denref(mpQ), d.mpz());

            mpq_canonicalize(mpQ);

            double ret = mpq_get_d(mpQ);
            mpq_clear(mpQ);
            return ret;
        }
    };
};

//
// Needs_parens_as_product
//
template <>
struct Needs_parens_as_product<Gmpz> {
  bool operator()(const Gmpz& x) {
    return CGAL_NTS is_negative(x);
  }
};


/*! \ingroup NiX_Modular_traits_spec
 *  \brief a model of concept ModularTraits,
 *  specialization of NiX::Modular_traits.
 */
template<>
class Modular_traits< Gmpz > {
  typedef Residue RES;
 public:
    typedef Gmpz NT;
    typedef CGAL::Tag_true Is_modularizable;
    typedef Residue Residue_type;

    struct Modular_image{
        Residue_type operator()(const NT& a){
          NT tmp_1(a % NT(RES::get_current_prime()));
          return CGAL::Residue(int(mpz_get_si(tmp_1.mpz())));
        }
    };
    struct Modular_image_representative{
        NT operator()(const Residue_type& x){
          return NT(x.get_value());
        }
    };
};

} //namespace CGAL

#if defined(BOOST_MSVC)
#  pragma warning(pop)
#endif

namespace Eigen {
  template<class> struct NumTraits;
  template<> struct NumTraits<CGAL::Gmpz>
  {
    typedef CGAL::Gmpz Real;
    typedef CGAL::Gmpq NonInteger;
    typedef CGAL::Gmpz Nested;
    typedef CGAL::Gmpz Literal;

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

    enum {
      IsInteger = 1,
      IsSigned = 1,
      IsComplex = 0,
      RequireInitialization = 1,
      ReadCost = 6,
      AddCost = 30,
      MulCost = 50
    };
  };
}


//since types are included by Gmp_coercion_traits.h:
#include <CGAL/Gmpq.h>
#include <CGAL/Gmpzf.h>
#include <CGAL/GMP_arithmetic_kernel.h>

#endif // CGAL_GMPZ_H

