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// Copyright (c) 2002,2003 // 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/mpq_class.h $ // $Id: include/CGAL/mpq_class.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Sylvain Pion, Michael Hemmer #ifndef CGAL_MPQ_CLASS_H #define CGAL_MPQ_CLASS_H #include #include #include #include #include #include #include // This file gathers the necessary adaptors so that the following // C++ number types that come with GMP can be used by CGAL : // - mpq_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". #define CGAL_CHECK_GMP_EXPR_MPQ_CLASS \ static_assert( \ (::std::is_same< ::__gmp_expr< T , T >,Type>::value )); namespace CGAL { // AST for mpq_class template<> class Algebraic_structure_traits< mpq_class > : public Algebraic_structure_traits_base< mpq_class , Field_tag > { public: typedef mpq_class Type; typedef Field_tag Algebraic_category; typedef Tag_true Is_exact; typedef Tag_false Is_numerical_sensitive; struct Is_zero: public CGAL::cpp98::unary_function< mpq_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; return ::sgn(x) == 0; } }; struct Is_one: public CGAL::cpp98::unary_function< mpq_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; return x == 1; } }; struct Simplify: public CGAL::cpp98::unary_function< mpq_class , void > { void operator()( mpq_class& x) const { // do nothing because x is already canonical? x.canonicalize(); } }; struct Square: public CGAL::cpp98::unary_function< mpq_class , mpq_class > { mpq_class operator()( const mpq_class& x) const { return x*x; } }; struct Unit_part: public CGAL::cpp98::unary_function< mpq_class , mpq_class > { mpq_class operator()( const mpq_class& x) const { return( x == 0) ? mpq_class(1) : x; } }; struct Integral_division : public CGAL::cpp98::binary_function< mpq_class , mpq_class, mpq_class > { template mpq_class operator()( const ::__gmp_expr< T , U1 >& x, const ::__gmp_expr< T , U2 > & y) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; mpq_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 ) }; class Is_square : public CGAL::cpp98::binary_function< mpq_class, mpq_class&, bool > { public: bool operator()( const mpq_class& x, mpq_class& y ) const { y = mpq_class (::sqrt( x.get_num() ), ::sqrt( x.get_den() )) ; return y*y == x; // for efficiency, only handle den if num is a square } bool operator()( const mpq_class& x ) const { mpq_class y; return operator()(x,y); } }; }; // RET for mpq_class template < > class Real_embeddable_traits< mpq_class > : public INTERN_RET::Real_embeddable_traits_base< mpq_class , CGAL::Tag_true > { public: struct Is_zero: public CGAL::cpp98::unary_function< mpq_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; 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_MPQ_CLASS; return true; } }; struct Is_positive: public CGAL::cpp98::unary_function< mpq_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; return ::sgn(x) > 0; } }; struct Is_negative: public CGAL::cpp98::unary_function< mpq_class , bool > { template bool operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; return ::sgn(x) < 0; } }; struct Abs: public CGAL::cpp98::unary_function< mpq_class , mpq_class > { template mpq_class operator()( const ::__gmp_expr< T , U >& x) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; return ::abs(x); } }; struct Sgn : public CGAL::cpp98::unary_function< mpq_class, ::CGAL::Sign > { public: template ::CGAL::Sign operator()( const ::__gmp_expr< T , U >& x ) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; return (::CGAL::Sign) ::sgn( x ); } }; struct Compare : public CGAL::cpp98::binary_function< mpq_class, mpq_class, Comparison_result> { template Comparison_result operator()( const ::__gmp_expr< T , U1 >& x, const ::__gmp_expr< T , U2 >& y ) const { CGAL_CHECK_GMP_EXPR_MPQ_CLASS; // 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< mpq_class, double > { double operator()( const mpq_class& x ) const { return x.get_d(); } }; struct To_interval : public CGAL::cpp98::unary_function< mpq_class, std::pair< double, double > > { std::pair operator()( const mpq_class& x ) const { #if MPFR_VERSION_MAJOR >= 3 mpfr_exp_t emin = mpfr_get_emin(); mpfr_set_emin(-1073); MPFR_DECL_INIT (y, 53); /* Assume IEEE-754 */ int r = mpfr_set_q (y, x.get_mpq_t(), MPFR_RNDA); r = mpfr_subnormalize (y, r, MPFR_RNDA); /* Round subnormals */ double i = mpfr_get_d (y, MPFR_RNDA); /* EXACT but can overflow */ mpfr_set_emin(emin); /* Restore old value, users may care */ // With mpfr_set_emax(1024) we could drop the is_finite test 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_q (y, x.get_mpq_t(), GMP_RNDD); double i = mpfr_get_d (y, GMP_RNDD); /* EXACT but can overflow */ mpfr_set_q (y, x.get_mpq_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 // for GCD in Type traits #include namespace CGAL { /*! \ingroup NiX_Fraction_traits_spec * \brief Specialization of Fraction_traits for mpq_class */ template <> class Fraction_traits< mpq_class > { public: typedef mpq_class Type; typedef ::CGAL::Tag_true Is_fraction; typedef mpz_class Numerator_type; typedef mpz_class Denominator_type; typedef Algebraic_structure_traits< mpz_class >::Gcd Common_factor; class Decompose { public: typedef mpq_class first_argument_type; typedef mpz_class& second_argument_type; typedef mpz_class& third_argument_type; void operator () ( const mpq_class& rat, mpz_class& num, mpz_class& den) { num = rat.get_num(); den = rat.get_den(); } }; class Compose { public: typedef mpz_class first_argument_type; typedef mpz_class second_argument_type; typedef mpq_class result_type; mpq_class operator ()( const mpz_class& num , const mpz_class& den ) { mpq_class result(num, den); result.canonicalize(); return result; } }; }; template <> class Input_rep : public IO_rep_is_specialized { mpq_class& q; public: Input_rep( mpq_class& qq) : q(qq) {} std::istream& operator()( std::istream& in) const { internal::read_float_or_quotient(in, q); return in; } }; // Copied from leda_rational.h namespace internal { // See: Stream_support/include/CGAL/IO/io.h template void read_float_or_quotient(std::istream & is, ET& et); template <> inline void read_float_or_quotient(std::istream & is, mpq_class& et) { internal::read_float_or_quotient(is, et); } } // namespace internal } //namespace CGAL #undef CGAL_CHECK_GMP_EXPR_MPQ_CLASS #endif // CGAL_MPQ_CLASS_H