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// Copyright (c) 2002-2008 Max-Planck-Institute Saarbruecken (Germany) // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Polynomial/include/CGAL/Polynomial/modular_filter.h $ // $Id: include/CGAL/Polynomial/modular_filter.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Hemmer // // ============================================================================ // TODO: The comments are all original EXACUS comments and aren't adapted. So // they may be wrong now. #ifndef CGAL_POLYNOMIAL_MODULAR_FILTER_H #define CGAL_POLYNOMIAL_MODULAR_FILTER_H #include #include #include #include #include namespace CGAL { namespace internal { template inline bool may_have_common_factor_( const Polynomial& p1, const Polynomial& p2, ::CGAL::Tag_true){ // Enforce IEEE double precision and to nearest before using modular arithmetic CGAL::Protect_FPU_rounding pfr(CGAL_FE_TONEAREST); CGAL_precondition(p1.degree()!=-1); CGAL_precondition(p2.degree()!=-1); if(CGAL::total_degree(p1) == 0){ return p1.is_zero();} if(CGAL::total_degree(p2) == 0){ return p2.is_zero();} typedef Polynomial Polynomial_nt; typedef Modular_traits MT; typedef typename MT::Residue_type Polynomial_mt; typename MT::Modular_image modular_image; typename CGAL::Polynomial_traits_d::Degree_vector degree_vector_nt; typename CGAL::Polynomial_traits_d::Degree_vector degree_vector_mt; Polynomial_mt m1=modular_image(p1); Polynomial_mt m2=modular_image(p2); CGAL::Exponent_vector exp_vec_nt_1 = degree_vector_nt( p1 ); CGAL::Exponent_vector exp_vec_nt_2 = degree_vector_nt( p2 ); CGAL::Exponent_vector exp_vec_mt_1 = degree_vector_mt( m1 ); CGAL::Exponent_vector exp_vec_mt_2 = degree_vector_mt( m2 ); // return true if the exponent vector changes (degree loss) if( (exp_vec_nt_1 != exp_vec_mt_1) || (exp_vec_nt_2 != exp_vec_mt_2 ) ) return true; typename CGAL::Polynomial_traits_d::Total_degree tdegree_mt; if( tdegree_mt( CGAL::gcd( m1, m2 ) ) > 0 ) return true; else return false; } template inline bool may_have_common_factor_(const Polynomial& , const Polynomial& , ::CGAL::Tag_false) {return true;} /*! \ingroup CGAL_polynomial_utils * \brief tests whether \c P and \c Q may have a common factor. * * This function is based on a fast modular arithmetic and serves as a * filter to avoid expensive exact computations to determine whether \c P * and \c Q have a common factor.. * * If the function return false, then \c P and \c Q have no common factor for * sure. * \c P and \c Q have with a high probability a common factor, if it returns * true. */ template inline bool may_have_common_factor(const Polynomial& P, const Polynomial& Q){ // TODO: Should this compiler switch be renamed? #ifdef CGAL_MODULAR_FILTER_OFF return true; #endif CGAL_precondition( Residue::get_current_prime()!=0 ); typedef Polynomial POLY; typedef Modular_traits Mtr; typename Mtr::Is_modularizable is_modularizable; return internal::may_have_common_factor_(P,Q,is_modularizable); } /*! \ingroup CGAL_polynomial_utils * \brief tests whether the polynomial \c P may has a multiple root. * * This function is based on a fast modular arithmetic and serves as a * filter to avoid expensive exact computations to determine whether \c P * has a multiple root or not. * * If the function return false, then \c P has no multiple root for sure. * \c P has with a high probability a multiple root, if it returns true. */ template inline bool may_have_multiple_factor_(const Polynomial& P, CGAL::Tag_true ){ // Enforce IEEE double precision and to nearest before using modular arithmetic CGAL::Protect_FPU_rounding pfr(CGAL_FE_TONEAREST); // Create modular images of p typedef Polynomial Polynomial_nt; typedef Modular_traits MT; typedef typename MT::Residue_type Polynomial_mt; typename MT::Modular_image modular_image; typename CGAL::Polynomial_traits_d::Degree_vector degree_vector_nt; typename CGAL::Polynomial_traits_d::Degree_vector degree_vector_mt; Polynomial_mt m = modular_image( P ); CGAL::Exponent_vector exp_vec_nt = degree_vector_nt( P ); CGAL::Exponent_vector exp_vec_mt = degree_vector_mt( m ); if( exp_vec_nt != exp_vec_mt ) return true; // Check modular image to be square free typename CGAL::Polynomial_traits_d< Polynomial_mt >::Is_square_free is_square_free; return( !is_square_free( m ) ); } template< class NT > inline bool may_have_multiple_factor_( const Polynomial&, CGAL::Tag_false ) { return true; } template< class NT > inline bool may_have_multiple_factor( const Polynomial& P ) { if(CGAL::total_degree(P) <= 1) return false; // Modular filter CGAL_precondition( Residue::get_current_prime()!=0 ); typedef Polynomial POLY; typedef Modular_traits Mtr; typename Mtr::Is_modularizable is_modularizable; return internal::may_have_multiple_factor_(P, is_modularizable); } } //namespace internal } //namespace CGAL #endif //CGAL_MODULAR_FILTER_H