/****************************************************************************
 * Core Library Version 1.7, August 2004
 * Copyright (c) 1995-2004 Exact Computation Project
 * All rights reserved.
 *
 * This file is part of CGAL (www.cgal.org).
 *
 * File: Expr.h
 * Synopsis: a class of Expression in Level 3
 *
 * Written by
 *       Koji Ouchi <ouchi@simulation.nyu.edu>
 *       Chee Yap <yap@cs.nyu.edu>
 *       Igor Pechtchanski <pechtcha@cs.nyu.edu>
 *       Vijay Karamcheti <vijayk@cs.nyu.edu>
 *       Chen Li <chenli@cs.nyu.edu>
 *       Zilin Du <zilin@cs.nyu.edu>
 *       Sylvain Pion <pion@cs.nyu.edu>
 *       Vikram Sharma<sharma@cs.nyu.edu>
 *
 * WWW URL: http://cs.nyu.edu/exact/
 * Email: exact@cs.nyu.edu
 *
 * $URL: https://github.com/CGAL/cgal/blob/v5.5.2/CGAL_Core/include/CGAL/CORE/Promote.h $
 * $Id: Promote.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
 * SPDX-License-Identifier: LGPL-3.0-or-later
 ***************************************************************************/

#ifndef __PROMOTE_H__
#define __PROMOTE_H__

#include <CGAL/CORE/Impl.h>

namespace CORE {

/// hasExactDivision()
///   CHECKING if NT has exact division
///   NOTE: it is important that the compiler does not try to
///   prove theorems about arithmetic identities like "x*(y/x) == y"
///   USAGE:  If you want to check if a number type NT has exact division, do for example,
///            if (hasExactDivision< NT >::check()) ...
///                   We use this in Polynomial<NT> class.
template < class NT >
struct hasExactDivision {
  static bool check() {                // This default function is supposed to work for NT other than BigRat or Expr
     return false;
  }
};

template<> struct hasExactDivision<Expr> {
  static bool check() {
     return true;
  }
};
template<> struct hasExactDivision<BigRat> {
  static bool check() {
     return true;
  }
};

template<typename T1, typename T2>
class Promotion;

template<typename T>
class Promotion<T, T> {
  public:
    typedef T ResultT;
};

#define MAX_TYPE(T1, T2)                \
  typename Promotion<T1, T2>::ResultT

#define DEFINE_MAX_TYPE(T1, T2, Tr)        \
  template<> class Promotion<T1, T2> {        \
    public:                                \
      typedef Tr ResultT;                \
  };                                        \
  template<> class Promotion<T2, T1> {        \
    public:                                \
      typedef Tr ResultT;                \
  };

/*
 * For example:
 *
 * DEFINE_MAX_TYPE(BigInt, BigRat, BigRat)           // define the promotion
 *
 * template<typename T1, typename T2>                 // define function f with type templates
 *   MAX_TYPE(T1, T2) f(T1& , T2& );
 *
 * or
 *
 * template<typename T1, typename T2>                 // define function f with type templates
 *   const MAX_TYPE(T1, T2)& f(T1& , T2& );
 *
 * BigInt  a  =  1;
 * BigRat  b  = "1/3";
 * BigRat  c  =  f(a, b);                        // or, typename Promotion<BigInt, BigRat>::ResultT c = f(a,b);
 *
 * REMARK: this mechanism is used by the eval function for polynomial evaluation (see Poly.tcc)
 * where the two types are NT (type of coefficients) and N (type of evaluation point).
 */

/*
 * primary types: (11)
 *
 *         bool,
 *        char, unsigned char,
 *        short, unsigned short,
 *         int, unsigned int,
 *        long, unsigned long,
 *        float, double
 *
 * CORE types: (5)
 *
 *         BigInt < BigFloat < BigRat < Real < Expr
 *
 *      (NOTE: BigFloat here must be error-free)
 *
 */

class BigInt;
class BigFloat;
class BigRat;
class Expr;

DEFINE_MAX_TYPE(long, BigInt, BigInt)
DEFINE_MAX_TYPE(long, BigFloat, BigFloat)
DEFINE_MAX_TYPE(long, BigRat, BigRat)
DEFINE_MAX_TYPE(long, Expr, Expr)

DEFINE_MAX_TYPE(int, BigInt, BigInt)
DEFINE_MAX_TYPE(int, BigFloat, BigFloat)
DEFINE_MAX_TYPE(int, BigRat, BigRat)
DEFINE_MAX_TYPE(int, Expr, Expr)

DEFINE_MAX_TYPE(BigInt, BigFloat, BigFloat)
DEFINE_MAX_TYPE(BigInt, BigRat, BigRat)
DEFINE_MAX_TYPE(BigInt, Expr, Expr)

DEFINE_MAX_TYPE(BigFloat, BigRat, BigRat)
DEFINE_MAX_TYPE(BigFloat, Expr, Expr)

DEFINE_MAX_TYPE(BigRat, Expr, Expr)

} //namespace CORE

#endif //__PROMOTE_H__
