A generic Division Floating Point Expression. More...

#include <ppl.hh>

Inheritance diagram for Parma_Polyhedra_Library::Division_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 >
typedef Linear_Form< FP_Interval_Type >	FP_Linear_Form
	Alias for a linear form with template argument `FP_Interval_Type`.

typedef Box< FP_Interval_Type >	FP_Interval_Abstract_Store
	Alias for a map that associates a variable index to an interval. More...

typedef std::map< dimension_type, FP_Linear_Form >	FP_Linear_Form_Abstract_Store
	Alias for a map that associates a variable index to a linear form. More...

typedef FP_Interval_Type::boundary_type	boundary_type
	The floating point format used by the analyzer.

typedef FP_Interval_Type::info_type	info_type
	The interval policy used by `FP_Interval_Type`.

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. More...

void	m_swap (Division_Floating_Point_Expression< FP_Interval_Type, FP_Format > &y)
	Swaps `*this` with `y`.

Constructors and Destructor
	Division_Floating_Point_Expression (Floating_Point_Expression< FP_Interval_Type, FP_Format > const num, Floating_Point_Expression< FP_Interval_Type, FP_Format > const den)
	Constructor with two parameters: builds the division floating point expression corresponding to `num` $\oslash$ `den`.

	~Division_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.

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

template<typename FP_Interval_Type , typename FP_Format >
void	swap (Division_Floating_Point_Expression< FP_Interval_Type, FP_Format > &x, Division_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. More...

static void	relative_error (const FP_Linear_Form &lf, FP_Linear_Form &result)
	Computes the relative error of a given linear form. More...

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`. More...

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. More...

Detailed Description

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

A generic Division 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.

Linearizationd of division 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 $\adivlf$ two sound abstract operator on linear forms such that:

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

$\left(i + \sum_{v \in \cV}i_{v}v\right) \adivlf i' = \left(i \adivifp i'\right) + \sum_{v \in \cV}\left(i_{v} \adivifp i'\right)v.$

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

$\linexprenv{e_{1} \oslash [a, b]}{\rho^{\#}}{\rho^{\#}_l} = \left(\linexprenv{e_{1}}{\rho^{\#}}{\rho^{\#}_l} \adivlf [a, b]\right) \aslf \left(\varepsilon_{\mathbf{f}}\left( \linexprenv{e_{1}}{\rho^{\#}}{\rho^{\#}_l} \right) \adivlf [a, b]\right) \aslf mf_{\mathbf{f}}[-1, 1],$

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

$\linexprenv{e_{1} \oslash e_{2}}{\rho^{\#}}{\rho^{\#}_l} = \linexprenv{e_{1} \oslash \iota\left( \linexprenv{e_{2}}{\rho^{\#}}{\rho^{\#}_l} \right)\rho^{\#}}{\rho^{\#}}{\rho^{\#}_l},$

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

Member Function Documentation

template<typename FP_Interval_Type , typename FP_Format >

bool Parma_Polyhedra_Library::Division_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 >.

Friends And Related Function Documentation

template<typename FP_Interval_Type , typename FP_Format >

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

template<typename FP_Interval_Type , typename FP_Format >

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

ppl.hh

Public Types

Public Member Functions

Related Functions

Additional Inherited Members

Detailed Description

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

Member Function Documentation

Friends And Related Function Documentation

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