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// Copyright (c) 2002-2004,2007
// 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/v6.1.1/Number_types/include/CGAL/CORE_Expr.h $
// $Id: include/CGAL/CORE_Expr.h 08b27d3db14 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Sylvain Pion, Michael Hemmer
#ifndef CGAL_CORE_EXPR_H
#define CGAL_CORE_EXPR_H
#include <CGAL/disable_warnings.h>
#include <CGAL/number_type_basic.h>
#include <CGAL/CORE_coercion_traits.h>
#include <utility>
namespace CGAL {
template <> class Algebraic_structure_traits< CORE::Expr >
: public Algebraic_structure_traits_base< CORE::Expr,
Field_with_root_of_tag > {
public:
typedef Tag_true Is_exact;
typedef Tag_true Is_numerical_sensitive;
class Sqrt
: public CGAL::cpp98::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return CORE::sqrt( x );
}
};
class Kth_root
: public CGAL::cpp98::binary_function<int, Type, Type> {
public:
Type operator()( int k,
const Type& x) const {
CGAL_precondition_msg( k > 0, "'k' must be positive for k-th roots");
// CORE::radical isn't implemented for negative values of x, so we
// have to handle this case separately
if( x < 0 && k%2 != 0)
return -CORE::radical( -x, k );
return CORE::radical( x, k );
}
};
class Root_of {
public:
// typedef CORE::BigRat Boundary;
typedef Type result_type;
public:
// constructs the kth roots of the polynomial
// given by the iterator range, starting from 0.
template< class ForwardIterator >
Type operator()( int k,
ForwardIterator begin,
ForwardIterator end) const {
std::vector<Type> coeffs;
for(ForwardIterator it = begin; it != end; it++){
coeffs.push_back(*it);
}
CORE::Polynomial<Type> polynomial(coeffs);
return Type(polynomial,k);
}
// TODO: Need to be fixed: polynomial<CORE::Expr>.eval() cannot return
// CORE::BigFloat, so this does not compile.
/* template <class ForwardIterator>
Type operator()( CORE::BigRat lower,
CORE::BigRat upper,
ForwardIterator begin,
ForwardIterator end) const {
std::vector<Type> coeffs;
for(ForwardIterator it = begin; it != end; it++){
coeffs.push_back(*it);
}
CORE::Polynomial<Type> polynomial(coeffs);
CORE::BigFloat lower_bf, upper_bf;
CORE::BigFloat eval_at_lower(0), eval_at_upper(0);
CORE::extLong r(16),a(16);
while((eval_at_lower.isZeroIn() ||
eval_at_upper.isZeroIn())){
//std::cout << "while"<<std::endl;
r*=2;
a*=2;
lower_bf.approx(lower,r,a);
upper_bf.approx(upper,r,a);
// The most expensive precond I've ever seen :)),
// since the coefficients of the polynomial are CORE::Expr
// TODO: be sure that lower_bf, upper_bf contain exactly one root
//NiX_expensive_precond(
// CORE::Sturm(polynomial).numberOfRoots(lower_bf,upper_bf)==1);
eval_at_lower = polynomial.eval(lower_bf);
eval_at_upper = polynomial.eval(upper_bf);
}
CORE::BFInterval interval(lower_bf,upper_bf);
return Type(polynomial,interval);
}; */
};
class Is_zero
: public CGAL::cpp98::unary_function< Type, bool > {
public:
bool operator()( const Type& x ) const {
return x.isZero();
}
};
};
template <> class Real_embeddable_traits< CORE::Expr >
: public INTERN_RET::Real_embeddable_traits_base< CORE::Expr , CGAL::Tag_true > {
public:
class Abs
: public CGAL::cpp98::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return CORE::abs( x );
}
};
class Sgn
: public CGAL::cpp98::unary_function< Type, ::CGAL::Sign > {
public:
::CGAL::Sign operator()( const Type& x ) const {
return (::CGAL::Sign) CORE::sign( x );
}
};
class Compare
: public CGAL::cpp98::binary_function< Type, Type,
Comparison_result > {
public:
Comparison_result operator()( const Type& x,
const Type& y ) const {
return (Comparison_result) CORE::cmp( x, y );
}
CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR_WITH_RT( Type,
Comparison_result )
};
class To_double
: public CGAL::cpp98::unary_function< Type, double > {
public:
double operator()( const Type& x ) const {
x.approx(53,1075);
return x.doubleValue();
}
};
class To_interval
: public CGAL::cpp98::unary_function< Type, std::pair< double, double > > {
public:
std::pair<double, double> operator()( const Type& x ) const {
std::pair<double,double> result;
x.approx(53,1075);
x.doubleInterval(result.first, result.second);
CGAL_expensive_assertion(result.first <= x);
CGAL_expensive_assertion(result.second >= x);
return result;
}
};
};
inline const CORE::Expr& approx(const CORE::Expr& d) { return d; }
inline const CORE::Expr& exact(const CORE::Expr& d) { return d; }
inline int depth(const CORE::Expr&){ return -1; }
} // namespace CGAL
//since types are included by CORE_coercion_traits.h:
#include <CGAL/CORE_BigInt.h>
#include <CGAL/CORE_BigRat.h>
#include <CGAL/CORE_BigFloat.h>
#include <CGAL/CORE_arithmetic_kernel.h>
namespace Eigen {
template<class> struct NumTraits;
template<> struct NumTraits<CORE::Expr>
{
typedef CORE::Expr Real;
typedef CORE::Expr NonInteger;
typedef CORE::Expr Nested;
typedef CORE::Expr Literal;
static inline Real epsilon() { return 0; }
static inline Real dummy_precision() { return 0; }
enum {
IsInteger = 0,
IsSigned = 1,
IsComplex = 0,
RequireInitialization = 1,
ReadCost = 6,
AddCost = 200,
MulCost = 200
};
};
}
#include <CGAL/enable_warnings.h>
#endif // CGAL_CORE_EXPR_H
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