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// Copyright (c) 2005,2006 INRIA Sophia-Antipolis (France)
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.6-branch/Number_types/include/CGAL/Root_of_traits.h $
// $Id: Root_of_traits.h 51456 2009-08-24 17:10:04Z spion $
//
//
// Author(s) : Sylvain Pion, Monique Teillaud, Athanasios Kakargias, Michael Hemmer
#ifndef CGAL_ROOT_OF_TRAITS_H
#define CGAL_ROOT_OF_TRAITS_H
#include <CGAL/number_type_basic.h>
#include <CGAL/Root_of_2.h>
#include <CGAL/Quotient.h>
CGAL_BEGIN_NAMESPACE
namespace internal {
template < typename NT, class Algebraic_category>
struct Root_of_traits_helper{
typedef Quotient<NT> Root_of_1;
typedef CGAL::Root_of_2<NT> Root_of_2;
struct Make_root_of_2{
typedef Root_of_2 result_type;
Root_of_2 operator()(const NT& a, const NT& b, const NT& c){
return Root_of_2(a,b,c);
}
Root_of_2 operator()(const NT& a, const NT& b, const NT& c, bool s){
return Root_of_2(a,b,c,s);
}
Root_of_2 operator()(const Root_of_1& a,
const Root_of_1& b,
const Root_of_1& c){
return Root_of_2(a,b,c);
}
Root_of_2 operator()(const Root_of_1& a,
const Root_of_1& b,
const Root_of_1& c,
bool s){
return Root_of_2(a,b,c,s);
}
};
};
template < typename FT>
struct Root_of_traits_helper < FT, Field_tag >
{
typedef FT Root_of_1;
private:
typedef Fraction_traits<FT> FrT;
// Field must be a Type (Decomposable)
BOOST_STATIC_ASSERT((FrT::Is_fraction::value));
typedef typename FrT::Numerator_type RT;
typedef typename FrT::Decompose Decompose;
public:
typedef CGAL::Root_of_2< RT > Root_of_2;
struct Make_root_of_2{
typedef Root_of_2 result_type;
Root_of_2
operator()(const FT& a, const FT& b, const FT& c){
return Root_of_2(a,b,c);
}
Root_of_2
operator()(const FT& a, const FT& b, const FT& c, bool smaller){
Decompose decompose;
RT a_num,b_num,c_num;
RT a_den,b_den,c_den; // Denomiantor same as RT
decompose(a,a_num,a_den);
decompose(b,b_num,b_den);
decompose(c,c_num,c_den);
RT a_ = a_num * b_den * c_den;
RT b_ = b_num * a_den * c_den;
RT c_ = c_num * a_den * b_den;
return make_root_of_2(a_,b_,c_,smaller);
}
};
};
template < typename NT >
struct Root_of_traits_helper < NT, Field_with_sqrt_tag >
{
typedef NT Root_of_1;
typedef NT Root_of_2;
struct Make_root_of_2{
typedef NT result_type;
// just a copy, not sure about the semantic of smaller
NT operator()(const NT& a, const NT& b, const NT& c, bool smaller){
// former make_root_of_2_sqrt()
CGAL_assertion( a != 0 );
NT discriminant = CGAL_NTS square(b) - a*c*4;
CGAL_assertion( discriminant >= 0 );
NT d = CGAL_NTS sqrt(discriminant);
if ((smaller && a>0) || (!smaller && a<0))
d = -d;
return (d-b)/(a*2);
}
// it's so easy
NT operator()(const NT& a, const NT& b, const NT& c){
return a + b * CGAL_NTS sqrt(c) ;
}
};
};
template < typename NT >
struct Root_of_traits_helper < NT, Field_with_kth_root_tag >
:public Root_of_traits_helper < NT, Field_with_sqrt_tag>{};
template < typename NT >
struct Root_of_traits_helper < NT, Field_with_root_of_tag >
:public Root_of_traits_helper < NT, Field_with_sqrt_tag>{};
} // namespace internal
// Default Traits class for NT types
template < typename NT >
struct Root_of_traits
: public internal::Root_of_traits_helper<NT,
typename Algebraic_structure_traits<NT>::Algebraic_category> {
typedef internal::Root_of_traits_helper<NT,
typename Algebraic_structure_traits<NT>::Algebraic_category> Base;
typedef typename Base::Root_of_1 RootOf_1;
typedef typename Base::Root_of_2 RootOf_2;
};
template <bool B>
struct Root_of_traits<Interval_nt<B> >{
typedef Interval_nt<B> Root_of_1;
typedef Interval_nt<B> Root_of_2;
typedef Root_of_1 RootOf_1;
typedef Root_of_2 RootOf_2;
struct Make_root_of_2{
typedef Interval_nt<B> result_type;
// just a copy, not sure about the semantic of smaller
Interval_nt<B> operator()(const Interval_nt<B>& a, const Interval_nt<B>& b, const Interval_nt<B>& c, bool smaller){
// former make_root_of_2_sqrt()
if (CGAL::possibly(a==0))
return Interval_nt<B>::largest();
Interval_nt<B> discriminant = CGAL_NTS square(b) - a*c*4;
CGAL_assertion(discriminant >= 0);
Interval_nt<B> d = CGAL_NTS sqrt(discriminant);
if ((smaller && a>0) || (!smaller && a<0))
d = -d;
return (d-b)/(a*2);
}
// it's so easy
Interval_nt<B> operator()(const Interval_nt<B>& a, const Interval_nt<B>& b, const Interval_nt<B>& c){
return a + b * CGAL_NTS sqrt(c) ;
}
};
};
template < class NT >
inline
typename Root_of_traits< NT >::Root_of_2
make_root_of_2(const NT &a, const NT &b, const NT &c)
{
typename Root_of_traits<NT>::Make_root_of_2 make_root_of_2;
return make_root_of_2(a,b,c);
}
template < class NT >
inline
typename Root_of_traits< NT >::Root_of_2
make_root_of_2(const NT &a, const NT &b, const NT &c,const bool smaller)
{
typename Root_of_traits<NT>::Make_root_of_2 make_root_of_2;
return make_root_of_2(a,b,c,smaller);
}
CGAL_END_NAMESPACE
#endif // CGAL_ROOT_OF_TRAITS_H
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