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// Copyright (c) 1999 // 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/Algebraic_foundations/include/CGAL/number_utils.h $ // $Id: include/CGAL/number_utils.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Stefan Schirra #ifndef CGAL_NUMBER_UTILS_H #define CGAL_NUMBER_UTILS_H #include #include #include #include #include namespace CGAL { CGAL_NTS_BEGIN_NAMESPACE // AST-Functor adapting functions UNARY template< class AS > inline void simplify( AS& x ) { typename Algebraic_structure_traits< AS >::Simplify simplify; simplify( x ); } template< class AS > inline typename Algebraic_structure_traits< AS >::Unit_part::result_type unit_part( const AS& x ) { typename Algebraic_structure_traits< AS >::Unit_part unit_part; return unit_part( x ); } template< class AS > inline typename Algebraic_structure_traits< AS >::Is_square::result_type is_square( const AS& x, typename Algebraic_structure_traits< AS >::Is_square::second_argument_type y ) { typename Algebraic_structure_traits< AS >::Is_square is_square; return is_square( x, y ); } template< class AS > inline typename Algebraic_structure_traits< AS >::Is_square::result_type is_square( const AS& x){ typename Algebraic_structure_traits< AS >::Is_square is_square; return is_square( x ); } template< class AS > inline typename Algebraic_structure_traits< AS >::Square::result_type square( const AS& x ) { typename Algebraic_structure_traits< AS >::Square square; return square( x ); } template< class AS > inline typename Algebraic_structure_traits< AS >::Inverse::result_type inverse( const AS& x ) { typename Algebraic_structure_traits< AS >::Inverse inverse; return inverse( x ); } template< class AS > inline typename Algebraic_structure_traits::Is_one::result_type is_one( const AS& x ) { typename Algebraic_structure_traits< AS >::Is_one is_one; return is_one( x ); } template< class AS > inline typename Algebraic_structure_traits< AS >::Sqrt::result_type sqrt( const AS& x ) { typename Algebraic_structure_traits< AS >::Sqrt sqrt; return sqrt( x ); } // AST-Functor adapting functions BINARY template< class A, class B > inline typename Algebraic_structure_traits< typename Coercion_traits::Type> ::Integral_division::result_type integral_division( const A& x, const B& y ) { typedef typename Coercion_traits::Type Type; typename Algebraic_structure_traits< Type >::Integral_division integral_division; return integral_division( x, y ); } template< class A, class B > inline typename Algebraic_structure_traits< typename Coercion_traits::Type> ::Divides::result_type divides( const A& x, const B& y ) { typedef typename Coercion_traits::Type Type; typename Algebraic_structure_traits< Type >::Divides divides; return divides( x, y ); } template< class Type > inline typename Algebraic_structure_traits::Divides::result_type divides( const Type& x, const Type& y, Type& q ) { typename Algebraic_structure_traits< Type >::Divides divides; return divides( x, y, q); } template< class A, class B > inline typename Algebraic_structure_traits< typename Coercion_traits::Type > ::Gcd::result_type gcd( const A& x, const B& y ) { typedef typename Coercion_traits::Type Type; typename Algebraic_structure_traits< Type >::Gcd gcd; return gcd( x, y ); } template< class A, class B > inline typename Algebraic_structure_traits< typename Coercion_traits::Type > ::Mod::result_type mod( const A& x, const B& y ) { typedef typename Coercion_traits::Type Type; typename Algebraic_structure_traits::Mod mod; return mod( x, y ); } template< class A, class B > inline typename Algebraic_structure_traits< typename Coercion_traits::Type>::Div::result_type div( const A& x, const B& y ) { typedef typename Coercion_traits::Type Type; typename Algebraic_structure_traits::Div div; return div( x, y ); } template< class A, class B > inline void div_mod( const A& x, const B& y, typename Coercion_traits::Type& q, typename Coercion_traits::Type& r ) { typedef typename Coercion_traits::Type Type; typename Algebraic_structure_traits< Type >::Div_mod div_mod; div_mod( x, y, q, r ); } // others template< class AS > inline typename Algebraic_structure_traits< AS >::Kth_root::result_type kth_root( int k, const AS& x ) { typename Algebraic_structure_traits< AS >::Kth_root kth_root; return kth_root( k, x ); } template< class Input_iterator > inline typename Algebraic_structure_traits< typename std::iterator_traits::value_type > ::Root_of::result_type root_of( int k, Input_iterator begin, Input_iterator end ) { typedef typename std::iterator_traits::value_type AS; return typename Algebraic_structure_traits::Root_of()( k, begin, end ); } // AST- and RET-functor adapting function template< class Number_type > inline // select a Is_zero functor typename std::conditional_t< std::is_same_v< typename Algebraic_structure_traits< Number_type >::Is_zero, Null_functor >, typename Real_embeddable_traits< Number_type >::Is_zero, typename Algebraic_structure_traits< Number_type >::Is_zero >::result_type is_zero( const Number_type& x ) { // We take the Algebraic_structure_traits<>::Is_zero functor by default. If it // is not available, we take the Real_embeddable_traits functor std::conditional_t< std::is_same_v< typename Algebraic_structure_traits< Number_type >::Is_zero, Null_functor > , typename Real_embeddable_traits< Number_type >::Is_zero, typename Algebraic_structure_traits< Number_type >::Is_zero > is_zero; return is_zero( x ); } template inline typename Real_embeddable_traits< typename Coercion_traits::Type > ::Compare::result_type compare(const A& a, const B& b) { typedef typename Coercion_traits::Type Type; typename Real_embeddable_traits::Compare compare; return compare (a,b); // return (a < b) ? SMALLER : (b < a) ? LARGER : EQUAL; } // RET-Functor adapting functions template< class Real_embeddable > inline //Real_embeddable typename Real_embeddable_traits< Real_embeddable >::Abs::result_type abs( const Real_embeddable& x ) { typename Real_embeddable_traits< Real_embeddable >::Abs abs; return abs( x ); } template< class Real_embeddable > inline //::Sign typename Real_embeddable_traits< Real_embeddable >::Sgn::result_type sign( const Real_embeddable& x ) { typename Real_embeddable_traits< Real_embeddable >::Sgn sgn; return sgn( x ); } template< class Real_embeddable > inline //bool typename Real_embeddable_traits< Real_embeddable >::Is_finite::result_type is_finite( const Real_embeddable& x ) { return typename Real_embeddable_traits< Real_embeddable >::Is_finite()( x ); } template< class Real_embeddable > inline typename Real_embeddable_traits< Real_embeddable >::Is_positive::result_type is_positive( const Real_embeddable& x ) { typename Real_embeddable_traits< Real_embeddable >::Is_positive is_positive; return is_positive( x ); } template< class Real_embeddable > inline typename Real_embeddable_traits< Real_embeddable >::Is_negative::result_type is_negative( const Real_embeddable& x ) { typename Real_embeddable_traits< Real_embeddable >::Is_negative is_negative; return is_negative( x ); } /* template< class Real_embeddable > inline typename Real_embeddable_traits< Real_embeddable >::Compare::result_type //Comparison_result compare( const Real_embeddable& x, const Real_embeddable& y ) { typename Real_embeddable_traits< Real_embeddable >::Compare compare; return compare( x, y ); } */ template< class Real_embeddable > inline typename Real_embeddable_traits< Real_embeddable >::To_double::result_type //double to_double( const Real_embeddable& x ) { typename Real_embeddable_traits< Real_embeddable >::To_double to_double; return to_double( x ); } template< class Real_embeddable > inline typename Real_embeddable_traits< Real_embeddable >::To_interval::result_type //std::pair< double, double > to_interval( const Real_embeddable& x) { typename Real_embeddable_traits< Real_embeddable >::To_interval to_interval; return to_interval( x ); } template typename Coercion_traits::Type approximate_sqrt(const NT& x, CGAL::Null_functor) { return sqrt(CGAL::to_double(x)); } template typename Sqrt::result_type approximate_sqrt(const NT& nt, Sqrt sqrt) { return sqrt(nt); } template decltype(auto) approximate_sqrt(const NT& nt) { // the initial version of this function was using Algebraic_category // for the dispatch but some ring type (like Gmpz) provides a Sqrt // functor even if not being Field_with_sqrt. typedef CGAL::Algebraic_structure_traits AST; typedef typename AST::Sqrt Sqrt; return approximate_sqrt(nt, Sqrt()); } template typename Same_uncertainty_nt::type compare_quotients(const NT& xnum, const NT& xden, const NT& ynum, const NT& yden) { // No assumptions on the sign of den are made // code assumes that SMALLER == - 1; CGAL_precondition( SMALLER == static_cast(-1) ); int xsign = sign(xnum) * sign(xden) ; int ysign = sign(ynum) * sign(yden) ; if (xsign == 0) return static_cast(-ysign); if (ysign == 0) return static_cast(xsign); // now (x != 0) && (y != 0) int diff = xsign - ysign; if (diff == 0) { int msign = sign(xden) * sign(yden); NT leftop = NT(xnum * yden * msign); NT rightop = NT(ynum * xden * msign); return CGAL::compare(leftop, rightop); } else { return (xsign < ysign) ? SMALLER : LARGER; } } CGAL_NTS_END_NAMESPACE } //namespace CGAL #endif // CGAL_NUMBER_UTILS_H