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// 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/v6.1/Number_types/include/CGAL/Root_of_traits.h $ // $Id: include/CGAL/Root_of_traits.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Sylvain Pion, Monique Teillaud, Athanasios Kakargias, Michael Hemmer #ifndef CGAL_ROOT_OF_TRAITS_H #define CGAL_ROOT_OF_TRAITS_H #include #include #include #include #include namespace CGAL { template < typename NT > struct Root_of_traits; template < class NT1, class NT2, class NT3 > inline auto make_root_of_2(const NT1 &a, const NT2 &b, const NT3 &c) { using NT = std::common_type_t; typename Root_of_traits::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::Make_root_of_2 make_root_of_2; return make_root_of_2(a,b,c,smaller); } template < class NT > inline typename Root_of_traits< NT >::Root_of_2 make_sqrt(const NT &a) { typename Root_of_traits::Make_sqrt make_sqrt; return make_sqrt(a); } template < class NT , class OutputIterator> inline OutputIterator compute_roots_of_2(const NT &a_, const NT &b_, const NT &c_, OutputIterator oit) { typedef typename Root_of_traits::Root_of_1 Root_of_1; typedef typename Root_of_traits::Root_of_2 Root_of_2; typename CGAL::Coercion_traits::Cast cast; Root_of_1 a(cast(a_)), b(cast(b_)), c(cast(c_)); if ( a != 0 ) { Root_of_1 a0_ (-b/(2*a)); Root_of_1 root_(CGAL_NTS square(a0_) - c/a); switch(CGAL::sign(root_)){ case CGAL::NEGATIVE: return oit; case CGAL::ZERO: *oit++ = Root_of_2(a0_); return oit; default: // two roots *oit++ = make_root_of_2(a0_,Root_of_1(-1),root_); *oit++ = make_root_of_2(a0_,Root_of_1( 1),root_); return oit; } } else { Root_of_1 cb = -c / b; *oit++ = Root_of_2(cb); return oit; } } namespace internal { BOOST_MPL_HAS_XXX_TRAIT_NAMED_DEF(Has_typedef_Arithmetic_kernel,Arithmetic_kernel,false) template >::value> struct Get_rational_type{ typedef Quotient type; }; template struct Get_rational_type{ typedef typename Get_arithmetic_kernel::Arithmetic_kernel::Rational type; }; //Default or not a field. //If no specialization of Get_arithmetic_kernel is available, a field type compatible with NT //is made using CGAL::Quotient template < typename NT, class Algebraic_category> struct Root_of_traits_helper{ // typedef Quotient Root_of_1; typedef typename Get_rational_type::type Root_of_1; typedef CGAL::Sqrt_extension Root_of_2; // typedef CGAL::Root_of_2 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) const { return Root_of_2(a,b,c); } Root_of_2 operator()(const NT& a, const NT& b, const NT& c, bool s) const { 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) const { 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) const { return Root_of_2(a,b,c,s); } }; private: typedef CGAL::Algebraic_structure_traits AST; public: typedef typename AST::Square Square; typedef typename AST::Inverse Inverse; struct Make_sqrt { typedef Root_of_2 result_type; Root_of_2 operator()(const NT& x) const { return Root_of_2(x,true); } }; }; template < typename FT> struct Root_of_traits_helper < FT, Field_tag > { typedef FT Root_of_1; private: typedef Fraction_traits FrT; // Field must be a Type (Decomposable) // We have the typedef as VC10 fails with // static_assert(FrT::Is_fraction::value) typedef typename FrT::Is_fraction ISF; static_assert(ISF::value); typedef typename FrT::Numerator_type RT; typedef typename FrT::Decompose Decompose; public: typedef CGAL::Sqrt_extension 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) const { return Root_of_2(a,b,c); } Root_of_2 operator()(const FT& a, const FT& b, const FT& c, bool smaller) const { 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); } }; private: typedef CGAL::Algebraic_structure_traits AST; public: typedef typename AST::Square Square; typedef typename AST::Inverse Inverse; struct Make_sqrt{ typedef Root_of_2 result_type; Root_of_2 operator()(const FT& x) const { return Root_of_2( FT(0),FT(1),x); } }; }; 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) const { // 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) const { return a + b * CGAL_NTS sqrt(c) ; } }; private: typedef CGAL::Algebraic_structure_traits AST; public: typedef typename AST::Square Square; typedef typename AST::Inverse Inverse; struct Make_sqrt{ typedef Root_of_2 result_type; Root_of_2 operator()(const NT& x) const { return CGAL::sqrt(x); } }; }; 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::Algebraic_category> { typedef internal::Root_of_traits_helper::Algebraic_category> Base; typedef typename Base::Root_of_1 RootOf_1; typedef typename Base::Root_of_2 RootOf_2; }; template struct Root_of_traits >{ typedef Interval_nt Root_of_1; typedef Interval_nt Root_of_2; typedef Root_of_1 RootOf_1; typedef Root_of_2 RootOf_2; struct Make_root_of_2{ typedef Interval_nt result_type; // just a copy, not sure about the semantic of smaller Interval_nt operator()(const Interval_nt& a, const Interval_nt& b, const Interval_nt& c, bool smaller) const { // former make_root_of_2_sqrt() if (CGAL::possibly(a==0)) return Interval_nt::largest(); Interval_nt discriminant = CGAL_NTS square(b) - a*c*4; CGAL_assertion(discriminant >= 0); Interval_nt 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 operator()(const Interval_nt& a, const Interval_nt& b, const Interval_nt& c) const { return a + b * CGAL_NTS sqrt(c) ; } }; private: typedef CGAL::Algebraic_structure_traits > AST; public: typedef typename AST::Square Square; typedef typename AST::Inverse Inverse; typedef typename AST::Sqrt Make_sqrt; }; } //namespace CGAL #include #endif // CGAL_ROOT_OF_TRAITS_H