/usr/include/CGAL/RS/algebraic_1.h is in libcgal-dev 4.7-4.
This file is owned by root:root, with mode 0o644.
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//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
// See the file LICENSE.LGPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
// Author: Luis Peñaranda <luis.penaranda@gmx.com>
#ifndef CGAL_RS_ALGEBRAIC_1_H
#define CGAL_RS_ALGEBRAIC_1_H
#include <boost/operators.hpp>
#include <CGAL/Real_embeddable_traits.h>
#include <CGAL/Gmpq.h>
#include <iostream>
namespace CGAL{
namespace RS_AK1{
// This class represents the simplest algebraic number one can think about.
// One algebraic number is represented by the polynomial of which it is
// root and the two endpoints of an interval that contains it, and no other
// root. Polynomial type and bound type are the first two template
// parameters.
//
// The third template parameter is a refiner, a function object that
// receives the polynomial and the bounds defining an algebraic number and
// an integer p, and modifies the two bounds until the difference between
// the two bounds is less than x*2^(-p), where x is the value of the
// represented algebraic number. The signature of a refiner must be:
// void
// Refiner_()(const Polynomial_&,Bound_&,Bound_&,int p);
//
// The fourth template argument is a comparator, a function object that
// receives the polynomials and bounds defining two algebraic numbres and
// just compares them, returning a CGAL::Comparison_result. The signature
// of a comparator must be:
// CGAL::Comparison_result
// Comparator_()(const Polynomial_&,Bound_&,Bound_&,
// const Polynomial_&,Bound_&,Bound_&);
// The comparator can modify the bounds, with the condition that the
// algebraic numbers remain consistent (one and only one root on each
// interval).
template <class Polynomial_,
class Bound_,
class Refiner_,
class Comparator_,
class Ptraits_>
class Algebraic_1:
boost::totally_ordered<Algebraic_1<Polynomial_,
Bound_,
Refiner_,
Comparator_,
Ptraits_>,
double>{
protected:
typedef Polynomial_ Polynomial;
typedef Bound_ Bound;
typedef Refiner_ Refiner;
typedef Comparator_ Comparator;
typedef Ptraits_ Ptraits;
typedef typename Ptraits::Coefficient_type Coefficient;
typedef typename Ptraits::Scale Scale;
typedef Algebraic_1<Polynomial,
Bound,
Refiner,
Comparator,
Ptraits>
Algebraic;
Polynomial pol;
mutable Bound left,right;
public:
Algebraic_1(){};
Algebraic_1(const Polynomial &p,
const Bound &l,
const Bound &r):pol(p),left(l),right(r){
CGAL_assertion(l<=r);
}
Algebraic_1(const Algebraic &a):
pol(a.pol),left(a.left),right(a.right){}
// XXX: This assumes that Gmpq is constructible from bound type and
// that polynomial coefficient type is constructible from mpz_t.
Algebraic_1(const Bound &b):left(b),right(b){
typedef typename Ptraits::Shift shift;
Gmpq q(b);
pol=Coefficient(mpq_denref(q.mpq()))*
shift()(Polynomial(1),1,0)-
Coefficient(mpq_numref(q.mpq()));
CGAL_assertion(left==right&&left==b);
}
// XXX: This implementation assumes that the bound type is Gmpfr
// and that T can be exactly converted to Gmpq. This constructor
// can handle types such as int, unsigned and long.
template <class T>
Algebraic_1(const T &t){
typedef typename Ptraits::Shift shift;
CGAL::Gmpq q(t);
pol=Coefficient(mpq_denref(q.mpq()))*
shift()(Polynomial(1),1,0)-
Coefficient(mpq_numref(q.mpq()));
left=Bound(t,std::round_toward_neg_infinity);
right=Bound(t,std::round_toward_infinity);
CGAL_assertion(left<=t&&right>=t);
}
// XXX: This constructor assumes the bound is a Gmpfr.
Algebraic_1(const CGAL::Gmpq &q){
typedef typename Ptraits::Shift shift;
pol=Coefficient(mpq_denref(q.mpq()))*
shift()(Polynomial(1),1,0)-
Coefficient(mpq_numref(q.mpq()));
left=Bound();
right=Bound();
mpfr_t b;
mpfr_init(b);
mpfr_set_q(b,q.mpq(),GMP_RNDD);
mpfr_swap(b,left.fr());
mpfr_set_q(b,q.mpq(),GMP_RNDU);
mpfr_swap(b,right.fr());
mpfr_clear(b);
CGAL_assertion(left<=q&&right>=q);
}
~Algebraic_1(){}
Algebraic_1& operator=(const Algebraic &a){
pol=a.get_pol();
left=a.get_left();
right=a.get_right();
return *this;
}
Polynomial get_pol()const{return pol;}
Bound& get_left()const{return left;}
Bound& get_right()const{return right;}
Algebraic operator-()const{
return Algebraic(Scale()(get_pol(),Coefficient(-1)),
-right,
-left);
}
#define CGAL_RS_COMPARE_ALGEBRAIC(_a) \
(Comparator()(get_pol(),get_left(),get_right(), \
(_a).get_pol(),(_a).get_left(),(_a).get_right()))
Comparison_result compare(Algebraic a)const{
return CGAL_RS_COMPARE_ALGEBRAIC(a);
};
#define CGAL_RS_COMPARE_ALGEBRAIC_TYPE(_t) \
bool operator<(_t t)const \
{Algebraic a(t);return CGAL_RS_COMPARE_ALGEBRAIC(a)==CGAL::SMALLER;} \
bool operator>(_t t)const \
{Algebraic a(t);return CGAL_RS_COMPARE_ALGEBRAIC(a)==CGAL::LARGER;} \
bool operator==(_t t)const \
{Algebraic a(t);return CGAL_RS_COMPARE_ALGEBRAIC(a)==CGAL::EQUAL;}
bool operator==(Algebraic a)const
{return CGAL_RS_COMPARE_ALGEBRAIC(a)==CGAL::EQUAL;}
bool operator!=(Algebraic a)const
{return CGAL_RS_COMPARE_ALGEBRAIC(a)!=CGAL::EQUAL;}
bool operator<(Algebraic a)const
{return CGAL_RS_COMPARE_ALGEBRAIC(a)==CGAL::SMALLER;}
bool operator<=(Algebraic a)const
{return CGAL_RS_COMPARE_ALGEBRAIC(a)!=CGAL::LARGER;}
bool operator>(Algebraic a)const
{return CGAL_RS_COMPARE_ALGEBRAIC(a)==CGAL::LARGER;}
bool operator>=(Algebraic a)const
{return CGAL_RS_COMPARE_ALGEBRAIC(a)!=CGAL::SMALLER;}
CGAL_RS_COMPARE_ALGEBRAIC_TYPE(double)
#undef CGAL_RS_COMPARE_ALGEBRAIC_TYPE
#undef CGAL_RS_COMPARE_ALGEBRAIC
#ifdef IEEE_DBL_MANT_DIG
#define CGAL_RS_DBL_PREC IEEE_DBL_MANT_DIG
#else
#define CGAL_RS_DBL_PREC 53
#endif
double to_double(){
typedef Real_embeddable_traits<Bound> RT;
typedef typename RT::To_double TD;
Refiner()(get_pol(),get_left(),get_right(),CGAL_RS_DBL_PREC);
CGAL_assertion(TD()(get_left())==TD()(get_right()));
return TD()(get_left());
}
std::pair<double,double> to_interval()const{
typedef Real_embeddable_traits<Bound> RT;
typedef typename RT::To_interval TI;
return std::make_pair(TI()(get_left()).first,
TI()(get_right()).second);
}
#undef CGAL_RS_DBL_PREC
void set_left(const Bound &l)const{
left=l;
}
void set_right(const Bound &r)const{
right=r;
}
void set_pol(const Polynomial &p){
pol=p;
}
}; // class Algebraic_1
} // namespace RS_AK1
// We define Algebraic_1 as real-embeddable
template <class Polynomial_,
class Bound_,
class Refiner_,
class Comparator_,
class Ptraits_>
class Real_embeddable_traits<RS_AK1::Algebraic_1<Polynomial_,
Bound_,
Refiner_,
Comparator_,
Ptraits_> >:
public INTERN_RET::Real_embeddable_traits_base<
RS_AK1::Algebraic_1<Polynomial_,
Bound_,
Refiner_,
Comparator_,
Ptraits_>,
CGAL::Tag_true>{
typedef Polynomial_ P;
typedef Bound_ B;
typedef Refiner_ R;
typedef Comparator_ C;
typedef Ptraits_ T;
public:
typedef RS_AK1::Algebraic_1<P,B,R,C,T> Type;
typedef CGAL::Tag_true Is_real_embeddable;
typedef bool Boolean;
typedef CGAL::Sign Sign;
typedef CGAL::Comparison_result Comparison_result;
typedef INTERN_RET::Real_embeddable_traits_base<Type,CGAL::Tag_true>
Base;
typedef typename Base::Compare Compare;
class Sgn:public std::unary_function<Type,CGAL::Sign>{
public:
CGAL::Sign operator()(const Type &a)const{
return Compare()(a,Type(0));
}
};
class To_double:public std::unary_function<Type,double>{
public:
double operator()(Type a)const{return a.to_double();}
};
class To_interval:
public std::unary_function<Type,std::pair<double,double> >{
public:
std::pair<double,double> operator()(const Type &a)const{
return a.to_interval();
}
};
class Is_zero:public std::unary_function<Type,Boolean>{
public:
bool operator()(const Type &a)const{
return Sgn()(a)==CGAL::ZERO;
}
};
class Is_finite:public std::unary_function<Type,Boolean>{
public:
bool operator()(const Type&)const{return true;}
};
class Abs:public std::unary_function<Type,Type>{
public:
Type operator()(const Type &a)const{
return Sgn()(a)==CGAL::NEGATIVE?-a:a;
}
};
};
template <class P,class B,class R,class C,class T>
inline
RS_AK1::Algebraic_1<P,B,R,C,T> min
BOOST_PREVENT_MACRO_SUBSTITUTION(RS_AK1::Algebraic_1<P,B,R,C,T> a,
RS_AK1::Algebraic_1<P,B,R,C,T> b){
return(a<b?a:b);
}
template <class P,class B,class R,class C,class T>
inline
RS_AK1::Algebraic_1<P,B,R,C,T> max
BOOST_PREVENT_MACRO_SUBSTITUTION(RS_AK1::Algebraic_1<P,B,R,C,T> a,
RS_AK1::Algebraic_1<P,B,R,C,T> b){
return(a>b?a:b);
}
template <class P,class B,class R,class C,class T>
inline
std::ostream& operator<<(std::ostream &o,
const RS_AK1::Algebraic_1<P,B,R,C,T> &a){
return(o<<'['<<a.get_pol()<<','<<
a.get_left()<<','<<
a.get_right()<<']');
}
// XXX: This function works, but it will be nice to rewrite it cleanly.
template <class P,class B,class R,class C,class T>
inline
std::istream& operator>>(std::istream &i,
RS_AK1::Algebraic_1<P,B,R,C,T> &a){
std::istream::int_type c;
P pol;
B lb,rb;
c=i.get();
if(c!='['){
CGAL_error_msg("error reading istream, \'[\' expected");
return i;
}
i>>pol;
c=i.get();
if(c!=','){
CGAL_error_msg("error reading istream, \',\' expected");
return i;
}
i>>lb;
c=i.get();
if(c!=','){
CGAL_error_msg("error reading istream, \',\' expected");
return i;
}
i>>rb;
c=i.get();
if(c!=']'){
CGAL_error_msg("error reading istream, \']\' expected");
return i;
}
a=RS_AK1::Algebraic_1<P,B,R,C,T>(pol,lb,rb);
return i;
}
} // namespace CGAL
#endif // CGAL_RS_ALGEBRAIC_1_H
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