/usr/include/CGAL/leda_real.h is in libcgal-dev 4.2-5ubuntu1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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// 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); 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.
//
// 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(s) : Stefan Schirra, Michael Hemmer
#ifndef CGAL_LEDA_REAL_H
#define CGAL_LEDA_REAL_H
#include <CGAL/number_type_basic.h>
#ifdef CGAL_USE_LEDA
#include <CGAL/leda_coercion_traits.h>
#include <CGAL/utils.h>
#include <CGAL/Interval_nt.h>
#include <utility>
#include <CGAL/LEDA_basic.h>
#if CGAL_LEDA_VERSION < 500
#include <LEDA/real.h>
#include <LEDA/interval.h>
#else
#include <LEDA/numbers/real.h>
#endif
namespace CGAL {
template <> class Algebraic_structure_traits< leda_real >
#if CGAL_LEDA_VERSION >= 500
: public Algebraic_structure_traits_base< leda_real,
Field_with_root_of_tag > {
#else
: public Algebraic_structure_traits_base< leda_real,
Field_with_kth_root_tag > {
#endif
public:
typedef Tag_true Is_exact;
typedef Tag_true Is_numerical_sensitive;
class Sqrt
: public std::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return CGAL_LEDA_SCOPE::sqrt( x );
}
};
class Kth_root
: public std::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");
return CGAL_LEDA_SCOPE::root( x, k);
}
};
// Root_of is only available for LEDA versions >= 5.0
#if CGAL_LEDA_VERSION >= 500
class Root_of {
public:
typedef Type result_type;
// typedef leda_rational Boundary;
private:
template< class ForwardIterator >
inline
CGAL_LEDA_SCOPE::polynomial<Type>
make_polynomial(ForwardIterator begin,
ForwardIterator end) const {
CGAL_LEDA_SCOPE::growing_array<Type> coeffs;
for(ForwardIterator it = begin; it < end; it++)
coeffs.push_back(*it);
return CGAL_LEDA_SCOPE::polynomial<Type>(coeffs);
}
public:
template <class ForwardIterator>
Type operator()( int k,
ForwardIterator begin,
ForwardIterator end) const {
return CGAL_LEDA_SCOPE::diamond(k,make_polynomial(begin,end));
}
/* template <class ForwardIterator>
Type operator()( leda_rational lower,
leda_rational upper,
ForwardIterator begin,
ForwardIterator end) const {
return CGAL_LEDA_SCOPE::diamond(lower,upper,
make_polynomial(begin,end));
};*/
};
#endif
};
template <> class Real_embeddable_traits< leda_real >
: public INTERN_RET::Real_embeddable_traits_base< leda_real , CGAL::Tag_true > {
public:
class Abs
: public std::unary_function< Type, Type > {
public:
Type operator()( const Type& x ) const {
return CGAL_LEDA_SCOPE::abs( x );
}
};
class Sgn
: public std::unary_function< Type, ::CGAL::Sign > {
public:
::CGAL::Sign operator()( const Type& x ) const {
return (::CGAL::Sign) CGAL_LEDA_SCOPE::sign( x );
}
};
class Compare
: public std::binary_function< Type, Type,
Comparison_result > {
public:
Comparison_result operator()( const Type& x,
const Type& y ) const {
return (Comparison_result) CGAL_LEDA_SCOPE::compare( x, y );
}
CGAL_IMPLICIT_INTEROPERABLE_BINARY_OPERATOR_WITH_RT( Type,
Comparison_result )
};
class To_double
: public std::unary_function< Type, double > {
public:
double operator()( const Type& x ) const {
// this call is required to get reasonable values for the double
// approximation (as of LEDA-4.3.1)
x.improve_approximation_to(53);
return x.to_double();
}
};
class To_interval
: public std::unary_function< Type, std::pair< double, double > > {
public:
std::pair<double, double> operator()( const Type& x ) const {
#if CGAL_LEDA_VERSION >= 501
leda_bigfloat bnum = x.to_bigfloat();
leda_bigfloat berr = x.get_bigfloat_error();
double dummy;
double low = CGAL_LEDA_SCOPE::sub(bnum, berr, 53, CGAL_LEDA_SCOPE::TO_N_INF).to_double(dummy,
CGAL_LEDA_SCOPE::TO_N_INF);
double upp = CGAL_LEDA_SCOPE::add(bnum, berr, 53, CGAL_LEDA_SCOPE::TO_P_INF).to_double(dummy,
CGAL_LEDA_SCOPE::TO_P_INF);
std::pair<double, double> result(low, upp);
CGAL_postcondition(Type(result.first)<=x);
CGAL_postcondition(Type(result.second)>=x);
return result;
#else
CGAL_LEDA_SCOPE::interval temp(x); //bug in leda
std::pair<double, double> result(temp.lower_bound(),temp.upper_bound());
CGAL_postcondition_msg(Type(result.first)<=x,
"Known bug in LEDA <=5.0");
CGAL_postcondition_msg(Type(result.first)>=x,
"Known bug in LEDA <=5.0");
return result;
// If x is very small and we look closer at x
// (i.e. comparison or to_double() or to_bigfloat())
// then x gets 0, which is really bad.
// Therefore we do not touch x.
// The LEDA interval above returns (-inf, inf) for
// very small x, which is also bad and leads to
// problems lateron. The postcondition fails in this
// situation.
#endif
// Original CGAL to_interval:
// Protect_FPU_rounding<true> P (CGAL_FE_TONEAREST);
// double approx = z.to_double();
// double rel_error = z.get_double_error();
// FPU_set_cw(CGAL_FE_UPWARD);
// Interval_nt_advanced ina(-rel_error,rel_error);
// ina += 1;
// ina *= approx;
// return ina.pair();
}
};
};
template <>
class Output_rep< ::leda::real > {
const ::leda::real& t;
public:
//! initialize with a const reference to \a t.
Output_rep( const ::leda::real& tt) : t(tt) {}
//! perform the output, calls \c operator\<\< by default.
std::ostream& operator()( std::ostream& out) const {
out << CGAL_NTS to_double(t);
return out;
}
};
template <>
class Output_rep< ::leda::real, CGAL::Parens_as_product_tag > {
const ::leda::real& t;
public:
//! initialize with a const reference to \a t.
Output_rep( const ::leda::real& tt) : t(tt) {}
//! perform the output, calls \c operator\<\< by default.
std::ostream& operator()( std::ostream& out) const {
if (t<0) out << "(" << ::CGAL::oformat(t)<<")";
else out << ::CGAL::oformat(t);
return out;
}
};
} //namespace CGAL
// Unary + is missing for leda::real
namespace leda {
inline real operator+( const real& i) { return i; }
} // namespace leda
//since types are included by leda_coercion_traits.h:
#include <CGAL/leda_integer.h>
#include <CGAL/leda_rational.h>
#include <CGAL/leda_bigfloat.h>
#include <CGAL/leda_real.h>
#include <CGAL/LEDA_arithmetic_kernel.h>
#endif // CGAL_USE_LEDA
#endif // CGAL_LEDA_REAL_H
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