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// Copyright (c) 2002,2003,2007 // 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/mpz_class.h $ // $Id: include/CGAL/mpz_class.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Sylvain Pion, Michael Hemmer #ifndef CGAL_MPZ_CLASS_H #define CGAL_MPZ_CLASS_H // This file gathers the necessary adaptors so that the following // C++ number types that come with GMP can be used by CGAL : // - mpz_class // Note that GMP++ use the expression template mechanism, which makes things // a little bit complicated in order to make square(x+y) work for example. // Reading gmpxx.h shows that ::__gmp_expr is the mp[zqf]_class proper, // while ::__gmp_expr is the others "expressions". #include #include #include #include #include #include #include #include #include #define CGAL_CHECK_GMP_EXPR \ static_assert( \ (::std::is_same< ::__gmp_expr< T , T >,Type>::value )); namespace CGAL { // AST for mpz_class template<> class Algebraic_structure_traits< mpz_class > :public Algebraic_structure_traits_base< mpz_class , Euclidean_ring_tag > { public: typedef mpz_class Type; typedef Euclidean_ring_tag Algebraic_category; typedef Tag_true Is_exact; typedef Tag_false Is_numerical_sensitive; struct Is_zero: public CGAL::cpp98::unary_function< mpz_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR; return ::sgn(x) == 0; } }; struct Is_one: public CGAL::cpp98::unary_function< mpz_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR; return x == 1; } }; struct Simplify: public CGAL::cpp98::unary_function< mpz_class , void > { template void operator()( const ::__gmp_expr< T ,U >&) const { CGAL_CHECK_GMP_EXPR; } }; struct Square: public CGAL::cpp98::unary_function< mpz_class , mpz_class > { mpz_class operator()( const mpz_class& x) const { return x*x; } }; struct Unit_part: public CGAL::cpp98::unary_function< mpz_class , mpz_class > { mpz_class operator()( const mpz_class& x) const { return (x < 0) ? -1 : 1; } }; struct Integral_division: public CGAL::cpp98::binary_function< mpz_class , mpz_class, mpz_class > { template mpz_class operator()( const ::__gmp_expr< T , U1 >& x, const ::__gmp_expr< T , U2 >& y) const { CGAL_CHECK_GMP_EXPR; mpz_class result = x / y; CGAL_precondition_msg( result * y == x, "'x' must be divisible by 'y' in " "Algebraic_structure_traits::Integral_div()(x,y)" ); return result; } CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR( Type ) }; struct Gcd : public CGAL::cpp98::binary_function< mpz_class, mpz_class, mpz_class > { mpz_class operator()( const mpz_class& x, const mpz_class& y) const { mpz_class c; mpz_gcd(c.get_mpz_t(),x.get_mpz_t(), y.get_mpz_t() ); return c; } CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR( Type ) }; struct Div : public CGAL::cpp98::binary_function< mpz_class, mpz_class, mpz_class > { template mpz_class operator()( const ::__gmp_expr< T , U1 >& x, const ::__gmp_expr< T , U2 >& y) const { CGAL_CHECK_GMP_EXPR; return x / y; } CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR( Type ) }; struct Mod : public CGAL::cpp98::binary_function< mpz_class, mpz_class, mpz_class > { template mpz_class operator()( const ::__gmp_expr< T , U1 >& x, const ::__gmp_expr< T , U2 >& y) const { CGAL_CHECK_GMP_EXPR; return x % y; } CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR( Type ) }; struct Div_mod { typedef mpz_class first_argument_type; typedef mpz_class second_argument_type; typedef mpz_class& third_argument_type; typedef mpz_class& fourth_argument_type; typedef void result_type; void operator()( const mpz_class& x, const mpz_class& y, mpz_class& q, mpz_class& r ) const { typedef Algebraic_structure_traits Traits; Traits::Div actual_div; Traits::Mod actual_mod; q = actual_div( x, y ); r = actual_mod( x, y ); // use mpz_tdiv_qr to do both at once return; } }; struct Sqrt: public CGAL::cpp98::unary_function< mpz_class , mpz_class > { template mpz_class operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR; return ::sqrt(x); } }; /*struct Is_square: public CGAL::cpp98::binary_function< mpz_class , mpz_class& , bool > { template bool operator()( const ::__gmp_expr< T , U >& x, mpz_class& r){ r = ::sqrt(x); return (r*r==x) ? true : false; } template bool operator()(const ::__gmp_expr< T , U >& x){ mpz_class r = ::sqrt(x); return (r*r==x) ? true : false; } };*/ }; } //namespace CGAL #include // for `sign( ::cmp(x, y) )`, below namespace CGAL { // RET for mpz_class template<> class Real_embeddable_traits< mpz_class > : public INTERN_RET::Real_embeddable_traits_base< mpz_class , CGAL::Tag_true > { public: struct Is_zero: public CGAL::cpp98::unary_function< mpz_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR; return ::sgn(x) == 0; } }; struct Is_finite: public CGAL::cpp98::unary_function { template bool operator()( const ::__gmp_expr< T , U >& ) const { CGAL_CHECK_GMP_EXPR; return true; } }; struct Is_positive: public CGAL::cpp98::unary_function< mpz_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR; return ::sgn(x) > 0; } }; struct Is_negative: public CGAL::cpp98::unary_function< mpz_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR; return ::sgn(x) < 0; } }; struct Abs: public CGAL::cpp98::unary_function< mpz_class , mpz_class > { template mpz_class operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR; return ::abs(x); } }; struct Sgn : public CGAL::cpp98::unary_function< mpz_class, ::CGAL::Sign > { public: template ::CGAL::Sign operator()( const ::__gmp_expr< T , U >& x ) const { CGAL_CHECK_GMP_EXPR; return (::CGAL::Sign) ::sgn( x ); } }; struct Compare : public CGAL::cpp98::binary_function< mpz_class, mpz_class, Comparison_result > { template Comparison_result operator()( const ::__gmp_expr< T , U1 >& x, const ::__gmp_expr< T , U2 >& y ) const { CGAL_CHECK_GMP_EXPR; // cmp returns any int value, not just -1/0/1... return (Comparison_result) CGAL_NTS sign( ::cmp(x, y) ); } CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR_WITH_RT ( Type, Comparison_result) }; struct To_double : public CGAL::cpp98::unary_function< mpz_class, double > { double operator()( const mpz_class& x ) const { return x.get_d(); } }; struct To_interval : public CGAL::cpp98::unary_function< mpz_class, std::pair< double, double > > { std::pair operator()( const mpz_class& x ) const { #if MPFR_VERSION_MAJOR >= 3 MPFR_DECL_INIT (y, 53); /* Assume IEEE-754 */ int r = mpfr_set_z (y, x.get_mpz_t(), 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.get_mpz_t(), GMP_RNDD); double i = mpfr_get_d (y, GMP_RNDD); /* EXACT but can overflow */ mpfr_set_z (y, x.get_mpz_t(), GMP_RNDU); double s = mpfr_get_d (y, GMP_RNDU); /* EXACT but can overflow */ mpfr_clear (y); return std::pair(i, s); #endif } }; }; } //namespace CGAL #include #include #include #include namespace CGAL { /*! \ingroup NiX_Modular_traits_spec * \brief a model of concept ModularTraits, * specialization of NiX::Modular_traits. */ template<> class Modular_traits< mpz_class > { public: typedef mpz_class NT; typedef CGAL::Tag_true Is_modularizable; typedef Residue Residue_type; struct Modular_image{ Residue_type operator()(const mpz_class& a){ NT tmp(CGAL::mod(a,NT(Residue::get_current_prime()))); return CGAL::Residue(int(mpz_get_si(tmp.get_mpz_t()))); } }; struct Modular_image_representative{ NT operator()(const Residue_type& x){ return NT(x.get_value()); } }; }; } //namespace CGAL #include namespace CGAL { template <> struct Split_double { void operator()(double d, mpz_class &num, mpz_class &den) const { std::pair p = split_numerator_denominator(d); num = mpz_class(p.first); den = mpz_class(p.second); } }; } //namespace CGAL #undef CGAL_CHECK_GMP_EXPR #endif // CGAL_MPZ_CLASS_H