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// Copyright (c) 2007 INRIA Sophia-Antipolis (France), Max-Planck-Institute // Saarbruecken (Germany). // All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Modular_arithmetic/include/CGAL/Modular_arithmetic/Residue_type.h $ // $Id: include/CGAL/Modular_arithmetic/Residue_type.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Sylvain Pion, Michael Hemmer, Alexander Kobel #ifndef CGAL_RESIDUE_TYPE_H #define CGAL_RESIDUE_TYPE_H #include #include #include #include #include #include #include #include namespace CGAL { class Residue; Residue operator + (const Residue&); Residue operator - (const Residue&); std::ostream& operator << (std::ostream& os, const Residue& p); std::istream& operator >> (std::istream& is, Residue& p); /*! \ingroup CGAL_Modular_traits * \brief This class represents the Field Z mod p. * * This class uses the type double for representation. * Therefore the value of p is restricted to primes less than 2^26. * By default p is set to 67108859. * * It provides the standard operators +,-,*,/ as well as in&output. * * \see Modular_traits */ class Residue: boost::ordered_field_operators1< Residue, boost::ordered_field_operators2< Residue, int > >{ public: typedef Residue Self; typedef Residue NT; private: static const double& get_static_CST_CUT() { static const double CST_CUT = std::ldexp( 3., 51 ); return CST_CUT; } static int& prime_int_internal() { CGAL_STATIC_THREAD_LOCAL_VARIABLE(int, prime_int, 67111067); return prime_int; } static inline int get_prime_int(){ return prime_int_internal(); } static double& prime_internal() { CGAL_STATIC_THREAD_LOCAL_VARIABLE(double, prime, 67111067.0); return prime; } static inline double get_prime(){ return prime_internal(); } static double& prime_inv_internal() { CGAL_STATIC_THREAD_LOCAL_VARIABLE(double, prime_inv, 0.000000014900672045640400859667452463541); return prime_inv; } static inline double get_prime_inv(){ return prime_inv_internal(); } /* Quick integer rounding, valid if a<2^51. for double */ static inline double RES_round (double a){ // call CGAL::Protect_FPU_rounding pfr(CGAL_FE_TONEAREST) // before using modular arithmetic CGAL_assertion(FPU_get_cw() == CGAL_FE_TONEAREST); return ( (a + get_static_CST_CUT()) - get_static_CST_CUT()); } /* Big modular reduction (e.g. after multiplication) */ static inline double RES_reduce (double a){ double result = a - get_prime() * RES_round(a * get_prime_inv()); CGAL_postcondition(2*result < get_prime()); CGAL_postcondition(2*result > -get_prime()); return result; } /* Little modular reduction (e.g. after a simple addition). */ static inline double RES_soft_reduce (double a){ double p = get_prime(); double b = 2*a; return (b>p) ? a-p : ((b<-p) ? a+p : a); } /* -a */ static inline double RES_negate(double a){ return RES_soft_reduce(-a); } /* a*b */ static inline double RES_mul (double a, double b){ double c = a*b; return RES_reduce(c); } /* a+b */ static inline double RES_add (double a, double b){ double c = a+b; return RES_soft_reduce(c); } /* a^-1, using Bezout (extended Euclidean algorithm). */ static inline double RES_inv (double ri1){ CGAL_precondition (ri1 != 0.0); double bi = 0.0; double bi1 = 1.0; double ri = get_prime(); double p, tmp, tmp2; Real_embeddable_traits::Abs double_abs; while (double_abs(ri1) != 1.0) { p = RES_round(ri/ri1); tmp = bi - p * bi1; tmp2 = ri - p * ri1; bi = bi1; ri = ri1; bi1 = tmp; ri1 = tmp2; }; return ri1 * RES_soft_reduce(bi1); /* Quicker !!!! */ } /* a/b */ static inline double RES_div (double a, double b){ return RES_mul(a, RES_inv(b)); } public: /*! \brief sets the current prime. * * Note that you are going to change a static member! * \pre p is prime, but we abstained from such a test. * \pre 0 < p < 2^26 * */ static int set_current_prime(int p){ int old_prime = get_prime_int(); prime_int_internal() = p; prime_internal() = double(p); prime_inv_internal() = 1.0 / double(p); return old_prime; } /*! \brief returns the current prime. */ static int get_current_prime(){ return get_prime_int(); } int get_value() const{ CGAL_precondition(2*x_ < get_prime()); CGAL_precondition(2*x_ > -get_prime()); return int(x_); } private: double x_; public: //! constructor of Residue, from int Residue(int n = 0){ x_= RES_reduce(n); } //! constructor of Residue, from long Residue (long n) { x_= RES_soft_reduce (static_cast< double > (n % get_prime_int())); } //! constructor of Residue, from long long Residue (long long n) { x_= RES_soft_reduce (static_cast< double > (n % get_prime_int())); } //! Access operator for x, \c const const double& x() const { return x_; } //! Access operator for x double& x() { return x_; } Self& operator += (const Self& p2) { x() = RES_add(x(),p2.x()); return (*this); } Self& operator -= (const Self& p2){ x() = RES_add(x(),RES_negate(p2.x())); return (*this); } Self& operator *= (const Self& p2){ x() = RES_mul(x(),p2.x()); return (*this); } Self& operator /= (const Self& p2) { x() = RES_div(x(),p2.x()); return (*this); } // Self& operator += (int p2) { x() = RES_add(x(),Residue(p2).x()); return (*this); } Self& operator -= (int p2){ x() = RES_add(x(),Residue(-p2).x()); return (*this); } Self& operator *= (int p2){ x() = RES_mul(x(),Residue(p2).x()); return (*this); } Self& operator /= (int p2) { x() = RES_div(x(),Residue(p2).x()); return (*this); } friend Self operator + (const Self&); friend Self operator - (const Self&); }; inline Residue operator + (const Residue& p1) { return p1; } inline Residue operator - (const Residue& p1){ typedef Residue RES; Residue r; r.x() = RES::RES_negate(p1.x()); return r; } inline bool operator == (const Residue& p1, const Residue& p2) { return ( p1.x()==p2.x() ); } inline bool operator == (const Residue& p1, int p2) { return ( p1 == Residue(p2) ); } inline bool operator < (const Residue& p1, const Residue& p2) { return ( p1.x() < p2.x() ); } inline bool operator < (const Residue& p1, int p2) { return ( p1.x() < Residue(p2).x() ); } // I/O inline std::ostream& operator << (std::ostream& os, const Residue& p) { typedef Residue RES; os <<"("<< int(p.x())<<"%"<> (std::istream& is, Residue& p) { char ch; int prime; is >> p.x(); is >> ch; // read the % is >> prime; // read the prime CGAL_precondition(prime==Residue::get_current_prime()); return is; } } //namespace CGAL #endif // CGAL_RESIDUE_TYPE_H