A generic Difference Floating Point Expression. More...

#include <Difference_Floating_Point_Expression.defs.hh>

Inheritance diagram for Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >:

Collaboration diagram for Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >:

Public Types
typedef Floating_Point_Expression < FP_Interval_Type, FP_Format > ::FP_Linear_Form	FP_Linear_Form
	Alias for the Linear_Form<FP_Interval_Type> from Floating_Point_Expression.
typedef Floating_Point_Expression < FP_Interval_Type, FP_Format > ::FP_Interval_Abstract_Store	FP_Interval_Abstract_Store
	Alias for the Box<FP_Interval_Type> from Floating_Point_Expression.
typedef Floating_Point_Expression < FP_Interval_Type, FP_Format > ::FP_Linear_Form_Abstract_Store	FP_Linear_Form_Abstract_Store
	Alias for the std::map<dimension_type, FP_Linear_Form> from Floating_Point_Expression.
typedef Floating_Point_Expression < FP_Interval_Type, FP_Format > ::boundary_type	boundary_type
	Alias for the FP_Interval_Type::boundary_type from Floating_Point_Expression.
typedef Floating_Point_Expression < FP_Interval_Type, FP_Format > ::info_type	info_type
	Alias for the FP_Interval_Type::info_type from Floating_Point_Expression.
Public Types inherited from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >

Public Member Functions
bool	linearize (const FP_Interval_Abstract_Store &int_store, const FP_Linear_Form_Abstract_Store &lf_store, FP_Linear_Form &result) const
	Linearizes the expression in a given astract store.
void	m_swap (Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &y)
	Swaps `*this` with `y`.
Constructors and Destructor
	Difference_Floating_Point_Expression (Floating_Point_Expression< FP_Interval_Type, FP_Format > const x, Floating_Point_Expression< FP_Interval_Type, FP_Format > const y)
	Constructor with two parameters: builds the difference floating point expression corresponding to `x` $\ominus$ `y`.
	~Difference_Floating_Point_Expression ()
	Destructor.
Public Member Functions inherited from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >
virtual	~Floating_Point_Expression ()
	Destructor.

Private Member Functions
	Difference_Floating_Point_Expression (const Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &e)
	Inhibited copy constructor.
Difference_Floating_Point_Expression < FP_Interval_Type, FP_Format > &	operator= (const Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &e)
	Inhibited asssignment operator.

Private Attributes
Floating_Point_Expression < FP_Interval_Type, FP_Format > *	first_operand
	Pointer to the first operand.
Floating_Point_Expression < FP_Interval_Type, FP_Format > *	second_operand
	Pointer to the second operand.

Related Functions
(Note that these are not member functions.)
template<typename FP_Interval_Type , typename FP_Format >
void	swap (Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &x, Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &y)
	Swaps `x` with `y`.
template<typename FP_Interval_Type , typename FP_Format >
void	swap (Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &x, Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &y)

Additional Inherited Members
Static Public Member Functions inherited from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >
static bool	overflows (const FP_Linear_Form &lf)
	Verifies if a given linear form overflows.
static void	relative_error (const FP_Linear_Form &lf, FP_Linear_Form &result)
	Computes the relative error of a given linear form.
static void	intervalize (const FP_Linear_Form &lf, const FP_Interval_Abstract_Store &store, FP_Interval_Type &result)
	Makes `result` become an interval that overapproximates all the possible values of `lf` in the interval abstract store `store`.
Static Public Attributes inherited from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >
static FP_Interval_Type	absolute_error = compute_absolute_error()
	Absolute error.

Detailed Description

template<typename FP_Interval_Type, typename FP_Format>
class Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >

A generic Difference Floating Point Expression.

Template type parameters

The class template type parameter FP_Interval_Type represents the type of the intervals used in the abstract domain.
The class template type parameter FP_Format represents the floating point format used in the concrete domain.

Linearization of difference floating-point expressions

Let $i + \sum_{v \in \cV}i_{v}v$ and $i' + \sum_{v \in \cV}i'_{v}v$ be two linear forms, $\aslf$ and $\adlf$ two sound abstract operators on linear form such that:

$\left(i + \sum_{v \in \cV}i_{v}v\right) \aslf \left(i' + \sum_{v \in \cV}i'_{v}v\right) = \left(i \asifp i'\right) + \sum_{v \in \cV}\left(i_{v} \asifp i'_{v}\right)v,$

$\left(i + \sum_{v \in \cV}i_{v}v\right) \adlf \left(i' + \sum_{v \in \cV}i'_{v}v\right) = \left(i \adifp i'\right) + \sum_{v \in \cV}\left(i_{v} \adifp i'_{v}\right)v.$

Given an expression $e_{1} \ominus e_{2}$ and a composite abstract store $\left \llbracket \rho^{\#}, \rho^{\#}_l \right \rrbracket$ , we construct the interval linear form $\linexprenv{e_{1} \ominus e_{2}}{\rho^{\#}}{\rho^{\#}_l}$ on $\cV$ as follows:

$\linexprenv{e_{1} \ominus e_{2}}{\rho^{\#}}{\rho^{\#}_l} = \linexprenv{e_{1}}{\rho^{\#}}{\rho^{\#}_l} \adlf \linexprenv{e_{2}}{\rho^{\#}}{\rho^{\#}_l} \aslf \varepsilon_{\mathbf{f}}\left(\linexprenv{e_{1}}{\rho^{\#}}{\rho^{\#}_l} \right) \aslf \varepsilon_{\mathbf{f}}\left(\linexprenv{e_{2}}{\rho^{\#}}{\rho^{\#}_l} \right) \aslf mf_{\mathbf{f}}[-1, 1]$

where $\varepsilon_{\mathbf{f}}(l)$ is the linear form computed by calling method Floating_Point_Expression::relative_error on $l$ and $mf_{\mathbf{f}}$ is a rounding error defined in Floating_Point_Expression::absolute_error.

Definition at line 101 of file Difference_Floating_Point_Expression.defs.hh.

Member Typedef Documentation

template<typename FP_Interval_Type, typename FP_Format>

typedef Floating_Point_Expression<FP_Interval_Type, FP_Format>::boundary_type Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::boundary_type

Alias for the FP_Interval_Type::boundary_type from Floating_Point_Expression.

Reimplemented from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >.

Definition at line 136 of file Difference_Floating_Point_Expression.defs.hh.

template<typename FP_Interval_Type, typename FP_Format>

typedef Floating_Point_Expression<FP_Interval_Type, FP_Format>::FP_Interval_Abstract_Store Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::FP_Interval_Abstract_Store

Alias for the Box<FP_Interval_Type> from Floating_Point_Expression.

Reimplemented from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >.

Definition at line 120 of file Difference_Floating_Point_Expression.defs.hh.

template<typename FP_Interval_Type, typename FP_Format>

typedef Floating_Point_Expression<FP_Interval_Type, FP_Format>::FP_Linear_Form Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::FP_Linear_Form

Alias for the Linear_Form<FP_Interval_Type> from Floating_Point_Expression.

Reimplemented from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >.

Definition at line 112 of file Difference_Floating_Point_Expression.defs.hh.

template<typename FP_Interval_Type, typename FP_Format>

typedef Floating_Point_Expression<FP_Interval_Type, FP_Format>::FP_Linear_Form_Abstract_Store Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::FP_Linear_Form_Abstract_Store

Alias for the std::map<dimension_type, FP_Linear_Form> from Floating_Point_Expression.

Reimplemented from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >.

Definition at line 128 of file Difference_Floating_Point_Expression.defs.hh.

template<typename FP_Interval_Type, typename FP_Format>

typedef Floating_Point_Expression<FP_Interval_Type, FP_Format>::info_type Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::info_type

Alias for the FP_Interval_Type::info_type from Floating_Point_Expression.

Reimplemented from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >.

Definition at line 142 of file Difference_Floating_Point_Expression.defs.hh.

Constructor & Destructor Documentation

template<typename FP_Interval_Type , typename FP_Format >

Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::Difference_Floating_Point_Expression	(	Floating_Point_Expression< FP_Interval_Type, FP_Format > *const	x,
		Floating_Point_Expression< FP_Interval_Type, FP_Format > *const	y
	)

inline

Constructor with two parameters: builds the difference floating point expression corresponding to x $\ominus$ y.

Definition at line 35 of file Difference_Floating_Point_Expression.inlines.hh.

  : first_operand(x), second_operand(y){
  assert(x != 0);
  assert(y != 0);
}

template<typename FP_Interval_Type , typename FP_Format >

Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::~Difference_Floating_Point_Expression ( )

inline

Destructor.

Definition at line 46 of file Difference_Floating_Point_Expression.inlines.hh.

                                        {
  delete first_operand;
  delete second_operand;
}

template<typename FP_Interval_Type, typename FP_Format>

Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::Difference_Floating_Point_Expression ( const Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > & e )

private

Inhibited copy constructor.

Member Function Documentation

template<typename FP_Interval_Type , typename FP_Format >

bool Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::linearize	(	const FP_Interval_Abstract_Store &	int_store,
		const FP_Linear_Form_Abstract_Store &	lf_store,
		FP_Linear_Form &	result
	)		const

virtual

Linearizes the expression in a given astract store.

Makes result become the linearization of *this in the given composite abstract store.

Parameters:

int_store	The interval abstract store.
lf_store	The linear form abstract store.
result	The modified linear form.

Returns:: true if the linearization succeeded, false otherwise.

Note that all variables occuring in the expressions represented by first_operand and second_operand MUST have an associated value in 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 result is computed.

Implements Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >.

Definition at line 32 of file Difference_Floating_Point_Expression.templates.hh.

                                          {
  if (!first_operand->linearize(int_store, lf_store, result))
    return false;
  FP_Linear_Form rel_error;
  relative_error(result, rel_error);
  result += rel_error;
  FP_Linear_Form linearized_second_operand;
  if (!second_operand->linearize(int_store, lf_store,
                      linearized_second_operand))
    return false;
  result -= linearized_second_operand;
  relative_error(linearized_second_operand, rel_error);
  result += rel_error;
  result += this->absolute_error;
  return !this->overflows(result);
}

template<typename FP_Interval_Type , typename FP_Format >

void Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::m_swap ( Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > & y )

inline

Swaps *this with y.

Definition at line 54 of file Difference_Floating_Point_Expression.inlines.hh.

References Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::first_operand, Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::second_operand, and Parma_Polyhedra_Library::swap().

Referenced by Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::swap().

                                                                             {
  using std::swap;
  swap(first_operand, y.first_operand);
  swap(second_operand, y.second_operand);
}

template<typename FP_Interval_Type, typename FP_Format>

Difference_Floating_Point_Expression<FP_Interval_Type, FP_Format>& Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::operator= ( const Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > & e )

private

Inhibited asssignment operator.

Friends And Related Function Documentation

template<typename FP_Interval_Type , typename FP_Format >

void swap	(	Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &	x,
		Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &	y
	)

template<typename FP_Interval_Type , typename FP_Format >

void swap	(	Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &	x,
		Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format > &	y
	)

References Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::m_swap().

                                                                           {
  x.m_swap(y);
}

Member Data Documentation

template<typename FP_Interval_Type, typename FP_Format>

Floating_Point_Expression<FP_Interval_Type, FP_Format>* Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::first_operand

private

Pointer to the first operand.

Definition at line 191 of file Difference_Floating_Point_Expression.defs.hh.

Referenced by Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::m_swap().

template<typename FP_Interval_Type, typename FP_Format>

Floating_Point_Expression<FP_Interval_Type, FP_Format>* Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::second_operand

private

Pointer to the second operand.

Definition at line 193 of file Difference_Floating_Point_Expression.defs.hh.

Referenced by Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >::m_swap().

The documentation for this class was generated from the following files:

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Related Functions

Additional Inherited Members

Detailed Description

template<typename FP_Interval_Type, typename FP_Format> class Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

template<typename FP_Interval_Type, typename FP_Format>
class Parma_Polyhedra_Library::Difference_Floating_Point_Expression< FP_Interval_Type, FP_Format >