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dust3d/thirdparty/cgal/CGAL-5.1/include/CGAL/Algebraic_kernel_d_1.h

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// Copyright (c) 2006-2009 Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v5.1/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d_1.h $
// $Id: Algebraic_kernel_d_1.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Michael Hemmer <hemmer@mpi-inf.mpg.de>
// Sebastian Limbach <slimbach@mpi-inf.mpg.de>
// Michael Kerber <mkerber@mpi-inf.mpg.de>
//
// ============================================================================
#ifndef CGAL_ALGEBRAIC_KERNEL_D_1_H
#define CGAL_ALGEBRAIC_KERNEL_D_1_H
#include <CGAL/disable_warnings.h>
#ifndef CGAL_AK_ENABLE_DEPRECATED_INTERFACE
#define CGAL_AK_ENABLE_DEPRECATED_INTERFACE 0
#endif
#include <CGAL/basic.h>
#include <CGAL/Algebraic_kernel_d/flags.h>
#include <CGAL/Polynomial.h>
#include <CGAL/Arithmetic_kernel.h>
#include <CGAL/Algebraic_kernel_d/Algebraic_real_d_1.h>
#include <CGAL/Algebraic_kernel_d/Descartes.h>
#include <CGAL/Algebraic_kernel_d/Real_roots.h>
#include <CGAL/Algebraic_kernel_d/refine_zero_against.h>
#include <CGAL/Algebraic_kernel_d/Interval_evaluate_1.h>
#include <CGAL/Algebraic_kernel_d/bound_between_1.h>
#include <CGAL/ipower.h>
namespace CGAL {
namespace internal {
template< class AlgebraicReal1, class Isolator_ >
class Algebraic_kernel_d_1_base {
public:
typedef AlgebraicReal1 Algebraic_real_1;
typedef Isolator_ Isolator;
typedef typename Algebraic_real_1::Coefficient Coefficient;
typedef typename Algebraic_real_1::Bound Bound;
typedef typename Algebraic_real_1::Polynomial_1 Polynomial_1;
// TODO: Other choice?
typedef int size_type;
typedef int Multiplicity_type;
private:
typedef CGAL::Polynomial_traits_d< Polynomial_1 > PT_1;
protected:
// Some functors used for STL calls
template<typename A,typename B>
struct Pair_first : public CGAL::cpp98::unary_function<std::pair<A,B>,A> {
A operator() (std::pair<A,B> pair) const { return pair.first; }
};
template<typename A,typename B>
struct Pair_second : public CGAL::cpp98::unary_function<std::pair<A,B>,B> {
B operator() (std::pair<A,B> pair) const { return pair.second; }
};
public:
class Algebraic_real_traits {
public:
typedef Algebraic_real_1 Type;
struct Bound_between
: public CGAL::cpp98::binary_function< Type, Type, Bound > {
Bound operator()( const Type& t1,
const Type& t2 ) const {
#if CGAL_AK_DONT_USE_SIMPLE_BOUND_BETWEEN
#warning uses deprecated bound_between_1 functor
return t1.rational_between( t2 );
#else
return internal::simple_bound_between(t1,t2);
#endif
}
};
struct Lower_bound
: public CGAL::cpp98::unary_function< Type, Bound > {
Bound operator()( const Type& t ) const {
return t.low();
}
};
struct Upper_bound
: public CGAL::cpp98::unary_function< Type, Bound > {
Bound operator()( const Type& t ) const {
return t.high();
}
};
struct Refine
: public CGAL::cpp98::unary_function< Type, void > {
void operator()( const Type& t ) const {
t.refine();
}
void operator()( Type& t, int rel_prec ) const {
// If t is zero, we can refine the interval to
// infinite precission
if( CGAL::is_zero( t ) ) {
t = Type(0);
} else {
// Refine until both boundaries have the same sign
while( CGAL::sign( t.high() ) !=
CGAL::sign( t.low() ) )
t.refine();
CGAL_assertion( CGAL::sign( t.high() ) != CGAL::ZERO &&
CGAL::sign( t.low() ) != CGAL::ZERO );
// Calculate the needed precision
Bound prec = Bound(1) /
CGAL::ipower( Bound(2), rel_prec );
// Refine until precision is reached
while( CGAL::abs( t.high() - t.low() ) /
(CGAL::max)( CGAL::abs( t.high() ),
CGAL::abs( t.low() ) ) > prec ) {
t.refine();
CGAL_assertion( CGAL::sign( t.high() ) != CGAL::ZERO &&
CGAL::sign( t.low() ) != CGAL::ZERO );
}
}
}
};
struct Approximate_absolute_1:
public CGAL::cpp98::binary_function<Algebraic_real_1,int,std::pair<Bound,Bound> >{
std::pair<Bound,Bound>
operator()(const Algebraic_real_1& x, int prec) const {
Lower_bound lower;
Upper_bound upper;
Refine refine;
Bound l = lower(x);
Bound u = upper(x);
Bound error = CGAL::ipower(Bound(2),CGAL::abs(prec));
while((prec>0)?((u-l)*error>Bound(1)):((u-l)>error)){
refine(x);
u = upper(x);
l = lower(x);
}
return std::make_pair(l,u);
}
};
struct Approximate_relative_1:
public CGAL::cpp98::binary_function<Algebraic_real_1,int,std::pair<Bound,Bound> >{
std::pair<Bound,Bound>
operator()(const Algebraic_real_1& x, int prec) const {
if(CGAL::is_zero(x)) return std::make_pair(Bound(0),Bound(0));
Lower_bound lower;
Upper_bound upper;
Refine refine;
Bound l = lower(x);
Bound u = upper(x);
Bound error = CGAL::ipower(Bound(2),CGAL::abs(prec));
Bound min_b = (CGAL::min)(CGAL::abs(u),CGAL::abs(l));
while((prec>0)?((u-l)*error>min_b):((u-l)>error*min_b)){
refine(x);
u = upper(x);
l = lower(x);
min_b = (CGAL::min)(CGAL::abs(u),CGAL::abs(l));
}
return std::make_pair(l,u);
}
};
#if CGAL_AK_ENABLE_DEPRECATED_INTERFACE
typedef Lower_bound Lower_boundary;
typedef Upper_bound Upper_boundary;
typedef Bound_between Boundary_between;
#endif
}; // class Algebraic_real_traits
struct Construct_algebraic_real_1;
// Functors of Algebraic_kernel_d_1
struct Solve_1 {
public:
template <class OutputIterator>
OutputIterator
operator()(const Polynomial_1& p, OutputIterator oi) const {
#if CGAL_AK_ENABLE_DEPRECATED_INTERFACE
#else
CGAL_precondition(!CGAL::is_zero(p));
#endif
internal::Real_roots< Algebraic_real_1, Isolator > real_roots;
std::list< int > mults;
std::list< Algebraic_real_1 > roots;
real_roots( p, std::back_inserter(roots), std::back_inserter( mults ) );
CGAL_assertion(roots.size()==mults.size());
std::list<int>::iterator mit =mults.begin();
typename std::list< Algebraic_real_1 >::iterator rit = roots.begin();
while(rit != roots.end()) {
//*oi++ = std::make_pair(*rit, (unsigned int)(*mit));
*oi++ = std::make_pair(*rit, *mit);
rit++;
mit++;
}
return oi;
}
#if 1 || CGAL_AK_ENABLE_DEPRECATED_INTERFACE
template< class OutputIterator >
OutputIterator operator()(
const Polynomial_1& p,
OutputIterator oi ,
bool known_to_be_square_free) const {
return this->operator()(p,known_to_be_square_free,oi);
}
#endif
template< class OutputIterator >
OutputIterator operator()(
const Polynomial_1& p,
bool known_to_be_square_free,
OutputIterator oi) const {
internal::Real_roots< Algebraic_real_1, Isolator > real_roots;
#if CGAL_AK_ENABLE_DEPRECATED_INTERFACE
#else
CGAL_precondition(!CGAL::is_zero(p));
#endif
std::list<Algebraic_real_1> roots;
if( known_to_be_square_free ){
real_roots(p,std::back_inserter(roots));
}else{
std::list<int> dummy;
real_roots(p,std::back_inserter(roots),std::back_inserter(dummy));
}
return std::copy(roots.begin(),roots.end(),oi);
}
#if CGAL_AK_ENABLE_DEPRECATED_INTERFACE
template< class OutputIteratorRoots , class OutputIteratorMults >
std::pair<OutputIteratorRoots,OutputIteratorMults>
operator()(
const Polynomial_1& p,
OutputIteratorRoots roi,
OutputIteratorMults moi) const {
internal::Real_roots< Algebraic_real_1, Isolator > real_roots;
real_roots(p,roi,moi);
return std::make_pair(roi,moi);
}
#endif
protected:
/*
// TODO: Can we avoid to use this?
struct Greater_compare :
public CGAL::cpp98::binary_function<Algebraic_real_1,Algebraic_real_1,bool> {
bool operator() (const Algebraic_real_1& a, const Algebraic_real_1& b)
const {
return a>b;
}
};
*/
public:
template< class OutputIterator >
OutputIterator operator()(const Polynomial_1& p, Bound l, Bound u,
OutputIterator res) const {
std::vector<std::pair<Algebraic_real_1,Multiplicity_type> > roots;
this->operator() (p,std::back_inserter(roots));
Algebraic_real_1 alg_l=Construct_algebraic_real_1()(l);
Algebraic_real_1 alg_u=Construct_algebraic_real_1()(u);
typedef typename
std::vector<std::pair<Algebraic_real_1,Multiplicity_type> >::iterator
Iterator;
Pair_first<Algebraic_real_1,Multiplicity_type> pair_first;
Iterator it_start=std::lower_bound
(::boost::make_transform_iterator(roots.begin(),pair_first),
::boost::make_transform_iterator(roots.end(),pair_first),
alg_l).base();
Iterator it_end=std::upper_bound
(::boost::make_transform_iterator(it_start,pair_first),
::boost::make_transform_iterator(roots.end(),pair_first),
alg_u).base();
std::copy(it_start,it_end,res);
return res;
}
template< class OutputIterator >
OutputIterator operator()(const Polynomial_1& p,
bool known_to_be_square_free,
Bound l, Bound u,
OutputIterator res) const {
std::vector<Algebraic_real_1 > roots;
this->operator() (p,known_to_be_square_free,std::back_inserter(roots));
Algebraic_real_1 alg_l=Construct_algebraic_real_1()(l);
Algebraic_real_1 alg_u=Construct_algebraic_real_1()(u);
typedef typename
std::vector<Algebraic_real_1>::iterator
Iterator;
Iterator it_start=std::lower_bound(roots.begin(),roots.end(),alg_l);
Iterator it_end=std::upper_bound(it_start,roots.end(),alg_u);
std::copy(it_start,it_end,res);
return res;
}
};
class Number_of_solutions_1
: public CGAL::cpp98::unary_function<Polynomial_1,size_type> {
public:
size_type operator()
(const Polynomial_1& p) const {
std::vector<std::pair<Algebraic_real_1,Multiplicity_type> > roots;
Solve_1()(p,std::back_inserter(roots));
return static_cast<size_type>(roots.size());
}
};
struct Sign_at_1
: public CGAL::cpp98::binary_function< Polynomial_1, Algebraic_real_1, CGAL::Sign > {
CGAL::Sign operator()( const Polynomial_1& p, const Algebraic_real_1& ar ) const {
if(CGAL::is_zero(p)) return ZERO;
if(CGAL::degree(p)==0) return p.sign_at(0);
if( ar.low() == ar.high() ) return p.sign_at( ar.low() );
if (p == ar.polynomial()) {
return ZERO;
}
Polynomial_1 g = gcd_utcf(p,ar.polynomial());
if (g.sign_at(ar.low()) != g.sign_at(ar.high())) return ZERO;
while(internal::descartes(p,ar.low(),ar.high()) > 0) ar.refine();
while( p.sign_at(ar.low()) == ZERO ) ar.refine();
while( p.sign_at(ar.high()) == ZERO ) ar.refine();
CGAL::Sign result = p.sign_at(ar.low());
CGAL_assertion(result == p.sign_at(ar.high()));
return result;
}
};
struct Is_zero_at_1
: public CGAL::cpp98::binary_function< Polynomial_1, Algebraic_real_1, bool > {
bool operator()( const Polynomial_1& p, const Algebraic_real_1& ar ) const {
if(CGAL::is_zero(p)) return true;
if( ar.low() == ar.high() ) return p.sign_at( ar.low() ) == ZERO;
Polynomial_1 g = gcd_utcf(p,ar.polynomial());
return g.sign_at(ar.low()) != g.sign_at(ar.high());
}
};
struct Is_square_free_1
: public CGAL::cpp98::unary_function< Polynomial_1, bool > {
bool operator()( const Polynomial_1& p ) const {
typename CGAL::Polynomial_traits_d< Polynomial_1 >::Is_square_free isf;
return isf(p);
}
};
struct Is_coprime_1
: public CGAL::cpp98::binary_function< Polynomial_1, Polynomial_1, bool > {
bool operator()( const Polynomial_1& p1, const Polynomial_1& p2 ) const {
typename CGAL::Polynomial_traits_d< Polynomial_1 >::Total_degree total_degree;
// TODO: Is GCD already filtered?
return( total_degree( gcd_utcf( p1, p2 ) ) == 0 );
}
};
struct Make_square_free_1
: public CGAL::cpp98::unary_function< Polynomial_1, Polynomial_1 > {
Polynomial_1 operator()( const Polynomial_1& p ) const {
return typename CGAL::Polynomial_traits_d< Polynomial_1 >::Make_square_free()( p );
}
};
struct Make_coprime_1 {
typedef bool result_type;
typedef Polynomial_1 first_argument_type;
typedef Polynomial_1 second_argument_type;
typedef Polynomial_1 third_argument_type;
typedef Polynomial_1 fourth_argument_type;
typedef Polynomial_1 fifth_argument_type;
bool operator()( const Polynomial_1& p1,
const Polynomial_1& p2,
Polynomial_1& g, // ggT utcf
Polynomial_1& q1, // Rest utcf
Polynomial_1& q2 ) const {
g = typename CGAL::Polynomial_traits_d< Polynomial_1 >::Gcd_up_to_constant_factor()( p1, p2 );
q1 = p1 / g;
q2 = p2 / g;
return CGAL::is_one(g);
}
};
struct Square_free_factorize_1 {
template< class OutputIterator>
OutputIterator operator()( const Polynomial_1& p, OutputIterator it) const {
typename PT_1::Square_free_factorize_up_to_constant_factor sqff;
return sqff(p,it);
}
};
struct Compute_polynomial_1 : public CGAL::cpp98::unary_function<Algebraic_real_1,
Polynomial_1> {
Polynomial_1 operator()(const Algebraic_real_1& x) const {
return x.polynomial();
}
};
struct Construct_algebraic_real_1 {
public:
typedef Algebraic_real_1 result_type;
result_type operator() (int a) const {
return Algebraic_real_1(a);
}
result_type operator() (Bound a) const {
return Algebraic_real_1(a);
}
result_type operator()
(typename CGAL::First_if_different<Coefficient,Bound>::Type a) const {
Coefficient coeffs[2] = {a,Coefficient(-1)};
Polynomial_1 p = typename PT_1::Construct_polynomial()
(coeffs,coeffs+2);
std::vector<Algebraic_real_1 > roots;
Solve_1()(p,true,std::back_inserter(roots));
CGAL_assertion(roots.size() == size_type(1));
return roots[0];
}
result_type operator() (Polynomial_1 p,size_type i)
const {
std::vector<Algebraic_real_1 > roots;
Solve_1()(p,true,std::back_inserter(roots));
CGAL_assertion( size_type(roots.size()) > i);
return roots[i];
}
result_type operator() (Polynomial_1 p,
Bound l, Bound u) const {
CGAL_precondition(l<u);
return Algebraic_real_1(p,l,u);
}
};
struct Compare_1
: public CGAL::cpp98::binary_function<Algebraic_real_1,
Algebraic_real_1,
CGAL::Comparison_result>{
typedef CGAL::Comparison_result result_type;
result_type operator() (Algebraic_real_1 a,Algebraic_real_1 b) const {
return typename Real_embeddable_traits<Algebraic_real_1>
::Compare() (a,b);
}
result_type operator() (Algebraic_real_1 a,int b) const {
return this->operator()(a,Construct_algebraic_real_1()(b));
}
result_type operator() (Algebraic_real_1 a,Bound b) const {
return this->operator()(a,Construct_algebraic_real_1()(b));
}
result_type operator()
(Algebraic_real_1 a,
typename CGAL::First_if_different<Coefficient,Bound>::Type b) const {
return this->operator()(a,Construct_algebraic_real_1()(b));
}
result_type operator() (int a, Algebraic_real_1 b) const {
return this->operator()(Construct_algebraic_real_1()(a),b);
}
result_type operator() (Bound a,Algebraic_real_1 b) const {
return this->operator()(Construct_algebraic_real_1()(a),b);
}
result_type operator()
(typename CGAL::First_if_different<Coefficient,Bound>::Type a,
Algebraic_real_1 b) const {
return this->operator()(Construct_algebraic_real_1()(a),b);
}
};
public:
struct Isolate_1 : public CGAL::cpp98::binary_function
< Algebraic_real_1,Polynomial_1,std::pair<Bound,Bound> > {
public:
std::pair<Bound,Bound> operator() (const Algebraic_real_1 a,
const Polynomial_1 p) const {
if(p == a.polynomial()) return std::make_pair(a.low(),a.high());
std::vector<Algebraic_real_1> roots;
// First isolate p...
Solve_1()(p,false,std::back_inserter(roots));
typedef typename std::vector<Algebraic_real_1>::iterator Iterator;
// Binary search on the root to find a place where a could be inserted
std::pair<Iterator,Iterator> it_pair
= equal_range(roots.begin(),roots.end(),a);
CGAL_assertion(std::distance(it_pair.first,it_pair.second)==0 ||
std::distance(it_pair.first,it_pair.second)==1);
// If we can insert a in two places, it must have been in roots already
bool a_in_roots = std::distance(it_pair.first,it_pair.second)==1;
if(a_in_roots) {
// TODO: can we rely on the property that the isolating intervals
// of the roots in p are isolating from each other. What
// if p was factorized during isolation? Is that still
// guaranteed? To be sure, we do it this way:
if(it_pair.first!=roots.begin()) {
it_pair.first->strong_refine(*(it_pair.first-1));
}
if(it_pair.second!=roots.end()) {
it_pair.first->strong_refine(*(it_pair.second));
}
return std::make_pair(it_pair.first->low(),it_pair.first->high());
} else {
// Refine a until disjoint from neighbors
// This is probably not even necessary since the isolating
// interval of a isolates against all roots of p thanks to the
// comparisons. But to be sure...
if(it_pair.first!=roots.begin()) {
a.strong_refine(*(it_pair.first-1));
}
if(it_pair.first!=roots.end()) {
a.strong_refine(*(it_pair.first));
}
return std::make_pair(a.low(),a.high());
}
}
};
typedef typename Algebraic_real_traits::Bound_between Bound_between_1;
typedef typename Algebraic_real_traits::Approximate_absolute_1 Approximate_absolute_1;
typedef typename Algebraic_real_traits::Approximate_relative_1 Approximate_relative_1;
#define CGAL_ALGEBRAIC_KERNEL_1_PRED(Y,Z) Y Z() const { return Y(); }
#define CGAL_ALGEBRAIC_KERNEL_1_PRED_WITH_KERNEL \
Y Z() const { return Y((const Algebraic_kernel_d_1*)this); }
CGAL_ALGEBRAIC_KERNEL_1_PRED(Is_square_free_1,
is_square_free_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Make_square_free_1,
make_square_free_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Square_free_factorize_1,
square_free_factorize_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Is_coprime_1,
is_coprime_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Make_coprime_1,
make_coprime_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Solve_1,
solve_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Number_of_solutions_1,
number_of_solutions_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Construct_algebraic_real_1,
construct_algebraic_real_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Sign_at_1,
sign_at_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Is_zero_at_1,
is_zero_at_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Compare_1,compare_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Bound_between_1,
bound_between_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Approximate_absolute_1,
approximate_absolute_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Approximate_relative_1,
approximate_relative_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Compute_polynomial_1,
compute_polynomial_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Isolate_1,
isolate_1_object);
// Deprecated
#if CGAL_AK_ENABLE_DEPRECATED_INTERFACE
typedef Bound Boundary;
typedef typename Algebraic_real_traits::Refine Refine_1;
typedef typename Algebraic_real_traits::Lower_bound Lower_bound_1;
typedef typename Algebraic_real_traits::Upper_bound Upper_bound_1;
typedef typename Algebraic_real_traits::Lower_bound Lower_boundary_1;
typedef typename Algebraic_real_traits::Upper_bound Upper_boundary_1;
typedef Bound_between_1 Boundary_between_1;
CGAL_ALGEBRAIC_KERNEL_1_PRED(Refine_1, refine_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Lower_bound_1, lower_bound_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Upper_bound_1, upper_bound_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Lower_boundary_1, lower_boundary_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Upper_boundary_1, upper_boundary_1_object);
CGAL_ALGEBRAIC_KERNEL_1_PRED(Boundary_between_1, boundary_between_1_object);
#endif
#undef CGAL_ALGEBRAIC_KERNEL_1_PRED
};
} // namespace internal
template< class Coefficient,
class Bound = typename CGAL::Get_arithmetic_kernel< Coefficient >::Arithmetic_kernel::Rational,
class RepClass = internal::Algebraic_real_rep< Coefficient, Bound >,
class Isolator = internal::Descartes< typename CGAL::Polynomial_type_generator<Coefficient,1>::Type, Bound > >
class Algebraic_kernel_d_1
: public internal::Algebraic_kernel_d_1_base<
// Template argument #1 (AlgebraicReal1)
internal::Algebraic_real_d_1<
Coefficient,
Bound,
::CGAL::Handle_policy_no_union,
RepClass >,
// Template argument #2 (Isolator_)
Isolator >
{};
} //namespace CGAL
#include <CGAL/enable_warnings.h>
#endif // CGAL_ALGEBRAIC_KERNEL_D_1_H
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