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// 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/v6.1/Number_types/include/CGAL/CORE_Expr.h $ // $Id: include/CGAL/CORE_Expr.h b26b07a1242 $ // 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 #include #include #include 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 { 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 coeffs; for(ForwardIterator it = begin; it != end; it++){ coeffs.push_back(*it); } CORE::Polynomial polynomial(coeffs); return Type(polynomial,k); } // TODO: Need to be fixed: polynomial.eval() cannot return // CORE::BigFloat, so this does not compile. /* template Type operator()( CORE::BigRat lower, CORE::BigRat upper, ForwardIterator begin, ForwardIterator end) const { std::vector coeffs; for(ForwardIterator it = begin; it != end; it++){ coeffs.push_back(*it); } CORE::Polynomial 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())){ //std::cout << "while"< { 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 operator()( const Type& x ) const { std::pair 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 #include #include #include namespace Eigen { template struct NumTraits; template<> struct NumTraits { 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 #endif // CGAL_CORE_EXPR_H