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// Copyright (c) 2006-2008 Max-Planck-Institute Saarbruecken (Germany), // 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/Gmpz.h $ // $Id: include/CGAL/Gmpz.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Hemmer // Sylvain Pion #ifndef CGAL_GMPZ_H #define CGAL_GMPZ_H #include #if defined(BOOST_MSVC) # pragma warning(push) # pragma warning(disable:4800) // complaint about performance in std::map where we can't do anything #endif #include #include #include // spec of AST for Quotient #include #include #include namespace CGAL { // Algebraic structure traits template <> class Algebraic_structure_traits< Gmpz > : public Algebraic_structure_traits_base< Gmpz, Euclidean_ring_tag > { public: typedef Tag_true Is_exact; typedef Tag_false Is_numerical_sensitive; typedef INTERN_AST::Is_square_per_sqrt< Type > Is_square; class Integral_division : public CGAL::cpp98::binary_function< Type, Type, Type > { public: Type operator()( const Type& x, const Type& y ) const { Gmpz result; mpz_divexact(result.mpz(), x.mpz(), y.mpz()); CGAL_postcondition_msg(result * y == x, "exact_division failed\n"); return result; } }; class Gcd : public CGAL::cpp98::binary_function< Type, Type, Type > { public: Type operator()( const Type& x, const Type& y ) const { Gmpz result; mpz_gcd(result.mpz(), x.mpz(), y.mpz()); return result; } Type operator()( const Type& x, const int& y ) const { if (y > 0) { Gmpz Res; mpz_gcd_ui(Res.mpz(), x.mpz(), y); return Res; } return CGAL_NTS gcd(x, Gmpz(y)); } Type operator()( const int& x, const Type& y ) const { return CGAL_NTS gcd(Gmpz(x), y ); } }; typedef INTERN_AST::Div_per_operator< Type > Div; typedef INTERN_AST::Mod_per_operator< Type > Mod; class Sqrt : public CGAL::cpp98::unary_function< Type, Type > { public: Type operator()( const Type& x ) const { Gmpz result; mpz_sqrt(result.mpz(), x.mpz()); return result; } }; }; template <> class Real_embeddable_traits< Gmpz > : public INTERN_RET::Real_embeddable_traits_base< Gmpz , CGAL::Tag_true > { public: class Sgn : public CGAL::cpp98::unary_function< Type, ::CGAL::Sign > { public: ::CGAL::Sign operator()( const Type& x ) const { return x.sign(); } }; class To_double : public CGAL::cpp98::unary_function< Type, double > { public: double operator()( const Type& x ) const { 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 { #if MPFR_VERSION_MAJOR >= 3 MPFR_DECL_INIT (y, 53); /* Assume IEEE-754 */ int r = mpfr_set_z (y, x.mpz(), MPFR_RNDA); double i = mpfr_get_d (y, MPFR_RNDA); /* EXACT but can overflow */ if (r == 0 && is_finite (i)) return std::pair(i, i); else { double s = nextafter (i, 0); if (i < 0) return std::pair(i, s); else return std::pair(s, i); } #else mpfr_t y; mpfr_init2 (y, 53); /* Assume IEEE-754 */ mpfr_set_z (y, x.mpz(), GMP_RNDD); double i = mpfr_get_d (y, GMP_RNDD); /* EXACT but can overflow */ mpfr_set_z (y, x.mpz(), GMP_RNDU); double s = mpfr_get_d (y, GMP_RNDU); /* EXACT but can overflow */ mpfr_clear (y); return std::pair(i, s); #endif } }; }; template<> class Algebraic_structure_traits< Quotient > : public INTERN_QUOTIENT::Algebraic_structure_traits_quotient_base >{ // specialization of to double functor public: typedef Quotient Type; struct To_double: public CGAL::cpp98::unary_function, double>{ double operator()(const Quotient& quot){ mpq_t mpQ; mpq_init(mpQ); const Gmpz& n = quot.numerator(); const Gmpz& d = quot.denominator(); mpz_set(mpq_numref(mpQ), n.mpz()); mpz_set(mpq_denref(mpQ), d.mpz()); mpq_canonicalize(mpQ); double ret = mpq_get_d(mpQ); mpq_clear(mpQ); return ret; } }; }; // // Needs_parens_as_product // template <> struct Needs_parens_as_product { bool operator()(const Gmpz& x) { return CGAL_NTS is_negative(x); } }; /*! \ingroup NiX_Modular_traits_spec * \brief a model of concept ModularTraits, * specialization of NiX::Modular_traits. */ template<> class Modular_traits< Gmpz > { typedef Residue RES; public: typedef Gmpz NT; typedef CGAL::Tag_true Is_modularizable; typedef Residue Residue_type; struct Modular_image{ Residue_type operator()(const NT& a){ NT tmp_1(a % NT(RES::get_current_prime())); return CGAL::Residue(int(mpz_get_si(tmp_1.mpz()))); } }; struct Modular_image_representative{ NT operator()(const Residue_type& x){ return NT(x.get_value()); } }; }; } //namespace CGAL #if defined(BOOST_MSVC) # pragma warning(pop) #endif namespace Eigen { template struct NumTraits; template<> struct NumTraits { typedef CGAL::Gmpz Real; typedef CGAL::Gmpq NonInteger; typedef CGAL::Gmpz Nested; typedef CGAL::Gmpz Literal; static inline Real epsilon() { return 0; } static inline Real dummy_precision() { return 0; } enum { IsInteger = 1, IsSigned = 1, IsComplex = 0, RequireInitialization = 1, ReadCost = 6, AddCost = 30, MulCost = 50 }; }; } //since types are included by Gmp_coercion_traits.h: #include #include #include #endif // CGAL_GMPZ_H