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// Copyright (c) 1999,2007 // 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/leda_real.h $ // $Id: include/CGAL/leda_real.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Stefan Schirra, Michael Hemmer #ifndef CGAL_LEDA_REAL_H #define CGAL_LEDA_REAL_H #include #include #include #include #include #include #include namespace CGAL { template <> class Algebraic_structure_traits< leda_real > : public Algebraic_structure_traits_base< leda_real, 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 CGAL_LEDA_SCOPE::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"); return CGAL_LEDA_SCOPE::root( x, k); } }; // Root_of is only available for LEDA versions >= 5.0 class Root_of { public: typedef Type result_type; // typedef leda_rational Boundary; private: template< class ForwardIterator > inline CGAL_LEDA_SCOPE::polynomial make_polynomial(ForwardIterator begin, ForwardIterator end) const { CGAL_LEDA_SCOPE::growing_array coeffs; for(ForwardIterator it = begin; it < end; it++) coeffs.push_back(*it); return CGAL_LEDA_SCOPE::polynomial(coeffs); } public: template Type operator()( int k, ForwardIterator begin, ForwardIterator end) const { return CGAL_LEDA_SCOPE::diamond(k,make_polynomial(begin,end)); } /* template Type operator()( leda_rational lower, leda_rational upper, ForwardIterator begin, ForwardIterator end) const { return CGAL_LEDA_SCOPE::diamond(lower,upper, make_polynomial(begin,end)); };*/ }; }; template <> class Real_embeddable_traits< leda_real > : public INTERN_RET::Real_embeddable_traits_base< leda_real , CGAL::Tag_true > { public: class Abs : public CGAL::cpp98::unary_function< Type, Type > { public: Type operator()( const Type& x ) const { return CGAL_LEDA_SCOPE::abs( x ); } }; class Sgn : public CGAL::cpp98::unary_function< Type, ::CGAL::Sign > { public: ::CGAL::Sign operator()( const Type& x ) const { return (::CGAL::Sign) CGAL_LEDA_SCOPE::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) CGAL_LEDA_SCOPE::compare( 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 { // this call is required to get reasonable values for the double // approximation (as of LEDA-4.3.1) x.improve_approximation_to(53); return x.to_double(); } }; class To_interval : public CGAL::cpp98::unary_function< Type, std::pair< double, double > > { public: std::pair operator()( const Type& x ) const { leda_bigfloat bnum = x.to_bigfloat(); leda_bigfloat berr = x.get_bigfloat_error(); double dummy; double low = CGAL_LEDA_SCOPE::sub(bnum, berr, 53, CGAL_LEDA_SCOPE::TO_N_INF).to_double(dummy, CGAL_LEDA_SCOPE::TO_N_INF); double upp = CGAL_LEDA_SCOPE::add(bnum, berr, 53, CGAL_LEDA_SCOPE::TO_P_INF).to_double(dummy, CGAL_LEDA_SCOPE::TO_P_INF); std::pair result(low, upp); CGAL_postcondition(Type(result.first)<=x); CGAL_postcondition(Type(result.second)>=x); return result; // Original CGAL to_interval: // Protect_FPU_rounding P (CGAL_FE_TONEAREST); // double approx = z.to_double(); // double rel_error = z.get_double_error(); // FPU_set_cw(CGAL_FE_UPWARD); // Interval_nt_advanced ina(-rel_error,rel_error); // ina += 1; // ina *= approx; // return ina.pair(); } }; }; template <> class Output_rep< ::leda::real > : public IO_rep_is_specialized { const ::leda::real& t; public: //! initialize with a const reference to \a t. Output_rep( const ::leda::real& tt) : t(tt) {} //! perform the output, calls \c operator\<\< by default. std::ostream& operator()( std::ostream& out) const { out << CGAL_NTS to_double(t); return out; } }; template <> class Output_rep< ::leda::real, CGAL::Parens_as_product_tag > : public IO_rep_is_specialized { const ::leda::real& t; public: //! initialize with a const reference to \a t. Output_rep( const ::leda::real& tt) : t(tt) {} //! perform the output, calls \c operator\<\< by default. std::ostream& operator()( std::ostream& out) const { if (t<0) out << "(" << ::CGAL::IO::oformat(t)<<")"; else out << ::CGAL::IO::oformat(t); return out; } }; inline const leda_real& approx(const leda_real& d) { return d; } inline const leda_real& exact(const leda_real& d) { return d; } inline int depth(const leda_real&){ return -1; } } //namespace CGAL // Unary + is missing for leda::real namespace leda { inline real operator+( const real& i) { return i; } } // namespace leda //since types are included by LEDA_coercion_traits.h: #include #include #include #include #endif // CGAL_LEDA_REAL_H