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/* Declarations for the Sum_Floating_Point_Expression class and
its constituents.
Copyright (C) 2001-2010 Roberto Bagnara <bagnara@cs.unipr.it>
Copyright (C) 2010-2016 BUGSENG srl (http://bugseng.com)
This file is part of the Parma Polyhedra Library (PPL).
The PPL is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The PPL is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.
For the most up-to-date information see the Parma Polyhedra Library
site: http://bugseng.com/products/ppl/ . */
#ifndef PPL_Sum_Floating_Point_Expression_defs_hh
#define PPL_Sum_Floating_Point_Expression_defs_hh 1
#include "Floating_Point_Expression_defs.hh"
#include "globals_defs.hh"
#include "Sum_Floating_Point_Expression_types.hh"
#include <map>
namespace Parma_Polyhedra_Library {
//! Swaps \p x with \p y.
/*! \relates Sum_Floating_Point_Expression */
template <typename FP_Interval_Type, typename FP_Format>
void swap(Sum_Floating_Point_Expression<FP_Interval_Type, FP_Format>& x,
Sum_Floating_Point_Expression<FP_Interval_Type, FP_Format>& y);
/*! \brief
A generic Sum Floating Point Expression.
\ingroup PPL_CXX_interface
\par Template type parameters
- The class template type parameter \p FP_Interval_Type represents the type
of the intervals used in the abstract domain.
- The class template type parameter \p FP_Format represents the floating
point format used in the concrete domain.
\par Linearization of sum floating-point expressions
Let \f$i + \sum_{v \in \cV}i_{v}v \f$ and
\f$i' + \sum_{v \in \cV}i'_{v}v \f$
be two linear forms and \f$\aslf\f$ a sound abstract operator on linear
forms such that:
\f[
\left(i + \sum_{v \in \cV}i_{v}v \right)
\aslf
\left(i' + \sum_{v \in \cV}i'_{v}v \right)
=
\left(i \asifp i'\right)
+ \sum_{v \in \cV}\left(i_{v} \asifp i'_{v} \right)v.
\f]
Given an expression \f$e_{1} \oplus e_{2}\f$ and a composite
abstract store \f$\left \llbracket \rho^{\#}, \rho^{\#}_l \right
\rrbracket\f$, we construct the interval linear form
\f$\linexprenv{e_{1} \oplus e_{2}}{\rho^{\#}}{\rho^{\#}_l}\f$
as follows:
\f[
\linexprenv{e_{1} \oplus e_{2}}{\rho^{\#}}{\rho^{\#}_l}
=
\linexprenv{e_{1}}{\rho^{\#}}{\rho^{\#}_l}
\aslf
\linexprenv{e_{2}}{\rho^{\#}}{\rho^{\#}_l}
\aslf
\varepsilon_{\mathbf{f}}\left(\linexprenv{e_{1}}{\rho^{\#}}{\rho^{\#}_l}
\right)
\aslf
\varepsilon_{\mathbf{f}}\left(\linexprenv{e_{2}}{\rho^{\#}}{\rho^{\#}_l}
\right)
\aslf
mf_{\mathbf{f}}[-1, 1]
\f]
where \f$\varepsilon_{\mathbf{f}}(l)\f$ is the linear form computed by
calling method <CODE>Floating_Point_Expression::relative_error</CODE>
on \f$l\f$ and \f$mf_{\mathbf{f}}\f$ is a rounding error defined in
<CODE>Floating_Point_Expression::absolute_error</CODE>.
*/
template <typename FP_Interval_Type, typename FP_Format>
class Sum_Floating_Point_Expression
: public Floating_Point_Expression<FP_Interval_Type, FP_Format> {
public:
/*! \brief
Alias for the Linear_Form<FP_Interval_Type> from
Floating_Point_Expression.
*/
typedef typename
Floating_Point_Expression<FP_Interval_Type, FP_Format>
::FP_Linear_Form FP_Linear_Form;
/*! \brief
Alias for the Box<FP_Interval_Type> from
Floating_Point_Expression.
*/
typedef typename
Floating_Point_Expression<FP_Interval_Type, FP_Format>
::FP_Interval_Abstract_Store FP_Interval_Abstract_Store;
/*! \brief
Alias for the std::map<dimension_type, FP_Linear_Form> from
Floating_Point_Expression.
*/
typedef typename
Floating_Point_Expression<FP_Interval_Type, FP_Format>::
FP_Linear_Form_Abstract_Store FP_Linear_Form_Abstract_Store;
/*! \brief
Alias for the FP_Interval_Type::boundary_type from
Floating_Point_Expression.
*/
typedef typename
Floating_Point_Expression<FP_Interval_Type, FP_Format>::boundary_type
boundary_type;
/*! \brief
Alias for the FP_Interval_Type::info_type from Floating_Point_Expression.
*/
typedef typename
Floating_Point_Expression<FP_Interval_Type, FP_Format>::info_type info_type;
//! \name Constructors and Destructor
//@{
/*! \brief
Constructor with two parameters: builds the sum floating point expression
corresponding to \p x \f$\oplus\f$ \p y.
*/
Sum_Floating_Point_Expression(
Floating_Point_Expression<FP_Interval_Type, FP_Format>* const x,
Floating_Point_Expression<FP_Interval_Type, FP_Format>* const y);
//! Destructor.
~Sum_Floating_Point_Expression();
//@} // Constructors and Destructor
/*! \brief
Linearizes the expression in a given astract store.
Makes \p result become the linearization of \p *this in the given
composite abstract store.
\param int_store The interval abstract store.
\param lf_store The linear form abstract store.
\param result The modified linear form.
\return <CODE>true</CODE> if the linearization succeeded,
<CODE>false</CODE> otherwise.
Note that all variables occuring in the expressions represented
by \p first_operand and \p second_operand MUST have an associated value in
\p int_store. If this precondition is not met, calling the method
causes an undefined behavior.
See the class description for a detailed explanation of how \p result
is computed.
*/
bool linearize(const FP_Interval_Abstract_Store& int_store,
const FP_Linear_Form_Abstract_Store& lf_store,
FP_Linear_Form& result) const;
//! Swaps \p *this with \p y.
void m_swap(Sum_Floating_Point_Expression<FP_Interval_Type, FP_Format>& y);
private:
//! Pointer to the first operand.
Floating_Point_Expression<FP_Interval_Type, FP_Format>* first_operand;
//! Pointer to the second operand.
Floating_Point_Expression<FP_Interval_Type, FP_Format>* second_operand;
#ifdef PPL_DOXYGEN_INCLUDE_IMPLEMENTATION_DETAILS
/*! \brief
Inhibited copy constructor.
*/
#endif // PPL_DOXYGEN_INCLUDE_IMPLEMENTATION_DETAILS
Sum_Floating_Point_Expression(
const Sum_Floating_Point_Expression<FP_Interval_Type, FP_Format>& e);
#ifdef PPL_DOXYGEN_INCLUDE_IMPLEMENTATION_DETAILS
/*! \brief
Inhibited assignment operator.
*/
#endif // PPL_DOXYGEN_INCLUDE_IMPLEMENTATION_DETAILS
Sum_Floating_Point_Expression<FP_Interval_Type, FP_Format>&
operator=(const Sum_Floating_Point_Expression<FP_Interval_Type,
FP_Format>& e);
}; // class Sum_Floating_Point_Expression
} // namespace Parma_Polyhedra_Library
#include "Sum_Floating_Point_Expression_inlines.hh"
#include "Sum_Floating_Point_Expression_templates.hh"
#endif // !defined(PPL_Sum_Floating_Point_Expression_defs_hh)
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