A not necessarily closed, iso-oriented hyperrectangle. More...

#include <ppl.hh>

Public Types
typedef ITV	interval_type
	The type of intervals used to implement the box.

Public Member Functions
const ITV &	get_interval (Variable var) const
	Returns a reference the interval that bounds `var`. More...

void	set_interval (Variable var, const ITV &i)
	Sets to `i` the interval that bounds `var`. More...

bool	has_lower_bound (Variable var, Coefficient &n, Coefficient &d, bool &closed) const
	If the space dimension of `var` is unbounded below, return `false`. Otherwise return `true` and set `n`, `d` and `closed` accordingly. More...

bool	has_upper_bound (Variable var, Coefficient &n, Coefficient &d, bool &closed) const
	If the space dimension of `var` is unbounded above, return `false`. Otherwise return `true` and set `n`, `d` and `closed` accordingly. More...

Constraint_System	constraints () const
	Returns a system of constraints defining `*this`.

Constraint_System	minimized_constraints () const
	Returns a minimized system of constraints defining `*this`.

Congruence_System	congruences () const
	Returns a system of congruences approximating `*this`.

Congruence_System	minimized_congruences () const
	Returns a minimized system of congruences approximating `*this`.

memory_size_type	total_memory_in_bytes () const
	Returns the total size in bytes of the memory occupied by `*this`.

memory_size_type	external_memory_in_bytes () const
	Returns the size in bytes of the memory managed by `*this`.

int32_t	hash_code () const
	Returns a 32-bit hash code for `*this`. More...

void	ascii_dump () const
	Writes to `std::cerr` an ASCII representation of `*this`.

void	ascii_dump (std::ostream &s) const
	Writes to `s` an ASCII representation of `*this`.

void	print () const
	Prints `*this` to `std::cerr` using `operator<<`.

void	set_empty ()
	Causes the box to become empty, i.e., to represent the empty set.

Constructors, Assignment, Swap and Destructor
	Box (dimension_type num_dimensions=0, Degenerate_Element kind=UNIVERSE)
	Builds a universe or empty box of the specified space dimension. More...

	Box (const Box &y, Complexity_Class complexity=ANY_COMPLEXITY)
	Ordinary copy constructor. More...

template<typename Other_ITV >
	Box (const Box< Other_ITV > &y, Complexity_Class complexity=ANY_COMPLEXITY)
	Builds a conservative, upward approximation of `y`. More...

	Box (const Constraint_System &cs)
	Builds a box from the system of constraints `cs`. More...

	Box (const Constraint_System &cs, Recycle_Input dummy)
	Builds a box recycling a system of constraints `cs`. More...

	Box (const Generator_System &gs)
	Builds a box from the system of generators `gs`. More...

	Box (const Generator_System &gs, Recycle_Input dummy)
	Builds a box recycling the system of generators `gs`. More...

	Box (const Congruence_System &cgs)

	Box (const Congruence_System &cgs, Recycle_Input dummy)

template<typename T >
	Box (const BD_Shape< T > &bds, Complexity_Class complexity=POLYNOMIAL_COMPLEXITY)
	Builds a box containing the BDS `bds`. More...

template<typename T >
	Box (const Octagonal_Shape< T > &oct, Complexity_Class complexity=POLYNOMIAL_COMPLEXITY)
	Builds a box containing the octagonal shape `oct`. More...

	Box (const Polyhedron &ph, Complexity_Class complexity=ANY_COMPLEXITY)
	Builds a box containing the polyhedron `ph`. More...

	Box (const Grid &gr, Complexity_Class complexity=POLYNOMIAL_COMPLEXITY)
	Builds a box containing the grid `gr`. More...

template<typename D1 , typename D2 , typename R >
	Box (const Partially_Reduced_Product< D1, D2, R > &dp, Complexity_Class complexity=ANY_COMPLEXITY)
	Builds a box containing the partially reduced product `dp`. More...

Box &	operator= (const Box &y)
	The assignment operator (`*this` and `y` can be dimension-incompatible).

void	m_swap (Box &y)
	Swaps `this` with `y` (`this` and `y` can be dimension-incompatible).

Member Functions that Do Not Modify the Box
dimension_type	space_dimension () const
	Returns the dimension of the vector space enclosing `*this`.

dimension_type	affine_dimension () const
	Returns , if `this` is empty; otherwise, returns the affine dimension of `this`.

bool	is_empty () const
	Returns `true` if and only if `*this` is an empty box.

bool	is_universe () const
	Returns `true` if and only if `*this` is a universe box.

bool	is_topologically_closed () const
	Returns `true` if and only if `*this` is a topologically closed subset of the vector space.

bool	is_discrete () const
	Returns `true` if and only if `*this` is discrete.

bool	is_bounded () const
	Returns `true` if and only if `*this` is a bounded box.

bool	contains_integer_point () const
	Returns `true` if and only if `*this` contains at least one integer point.

bool	constrains (Variable var) const
	Returns `true` if and only if `var` is constrained in `*this`. More...

Poly_Con_Relation	relation_with (const Constraint &c) const
	Returns the relations holding between `*this` and the constraint `c`. More...

Poly_Con_Relation	relation_with (const Congruence &cg) const
	Returns the relations holding between `*this` and the congruence `cg`. More...

Poly_Gen_Relation	relation_with (const Generator &g) const
	Returns the relations holding between `*this` and the generator `g`. More...

bool	bounds_from_above (const Linear_Expression &expr) const
	Returns `true` if and only if `expr` is bounded from above in `*this`. More...

bool	bounds_from_below (const Linear_Expression &expr) const
	Returns `true` if and only if `expr` is bounded from below in `*this`. More...

bool	maximize (const Linear_Expression &expr, Coefficient &sup_n, Coefficient &sup_d, bool &maximum) const
	Returns `true` if and only if `this` is not empty and `expr` is bounded from above in `this`, in which case the supremum value is computed. More...

bool	maximize (const Linear_Expression &expr, Coefficient &sup_n, Coefficient &sup_d, bool &maximum, Generator &g) const
	Returns `true` if and only if `this` is not empty and `expr` is bounded from above in `this`, in which case the supremum value and a point where `expr` reaches it are computed. More...

bool	minimize (const Linear_Expression &expr, Coefficient &inf_n, Coefficient &inf_d, bool &minimum) const
	Returns `true` if and only if `this` is not empty and `expr` is bounded from below in `this`, in which case the infimum value is computed. More...

bool	minimize (const Linear_Expression &expr, Coefficient &inf_n, Coefficient &inf_d, bool &minimum, Generator &g) const
	Returns `true` if and only if `this` is not empty and `expr` is bounded from below in `this`, in which case the infimum value and a point where `expr` reaches it are computed. More...

bool	frequency (const Linear_Expression &expr, Coefficient &freq_n, Coefficient &freq_d, Coefficient &val_n, Coefficient &val_d) const
	Returns `true` if and only if there exist a unique value `val` such that `*this` saturates the equality `expr = val`. More...

bool	contains (const Box &y) const
	Returns `true` if and only if `*this` contains `y`. More...

bool	strictly_contains (const Box &y) const
	Returns `true` if and only if `*this` strictly contains `y`. More...

bool	is_disjoint_from (const Box &y) const
	Returns `true` if and only if `*this` and `y` are disjoint. More...

bool	OK () const
	Returns `true` if and only if `*this` satisfies all its invariants.

Space-Dimension Preserving Member Functions that May Modify the Box
void	add_constraint (const Constraint &c)
	Adds a copy of constraint `c` to the system of constraints defining `*this`. More...

void	add_constraints (const Constraint_System &cs)
	Adds the constraints in `cs` to the system of constraints defining `*this`. More...

void	add_recycled_constraints (Constraint_System &cs)
	Adds the constraints in `cs` to the system of constraints defining `*this`. More...

void	add_congruence (const Congruence &cg)
	Adds to `*this` a constraint equivalent to the congruence `cg`. More...

void	add_congruences (const Congruence_System &cgs)
	Adds to `*this` constraints equivalent to the congruences in `cgs`. More...

void	add_recycled_congruences (Congruence_System &cgs)
	Adds to `*this` constraints equivalent to the congruences in `cgs`. More...

void	refine_with_constraint (const Constraint &c)
	Use the constraint `c` to refine `*this`. More...

void	refine_with_constraints (const Constraint_System &cs)
	Use the constraints in `cs` to refine `*this`. More...

void	refine_with_congruence (const Congruence &cg)
	Use the congruence `cg` to refine `*this`. More...

void	refine_with_congruences (const Congruence_System &cgs)
	Use the congruences in `cgs` to refine `*this`. More...

void	propagate_constraint (const Constraint &c)
	Use the constraint `c` for constraint propagation on `*this`. More...

void	propagate_constraints (const Constraint_System &cs, dimension_type max_iterations=0)
	Use the constraints in `cs` for constraint propagation on `*this`. More...

void	unconstrain (Variable var)
	Computes the cylindrification of `this` with respect to space dimension `var`, assigning the result to `this`. More...

void	unconstrain (const Variables_Set &vars)
	Computes the cylindrification of `this` with respect to the set of space dimensions `vars`, assigning the result to `this`. More...

void	intersection_assign (const Box &y)
	Assigns to `this` the intersection of `this` and `y`. More...

void	upper_bound_assign (const Box &y)
	Assigns to `this` the smallest box containing the union of `this` and `y`. More...

bool	upper_bound_assign_if_exact (const Box &y)
	If the upper bound of `this` and `y` is exact, it is assigned to `this` and `true` is returned, otherwise `false` is returned. More...

void	difference_assign (const Box &y)
	Assigns to `this` the difference of `this` and `y`. More...

bool	simplify_using_context_assign (const Box &y)
	Assigns to `this` a meet-preserving simplification of `this` with respect to `y`. If `false` is returned, then the intersection is empty. More...

void	affine_image (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
	Assigns to `this` the affine image of `this` under the function mapping variable `var` to the affine expression specified by `expr` and `denominator`. More...

void	affine_form_image (Variable var, const Linear_Form< ITV > &lf)
	Assigns to `this` the affine form image of `this` under the function mapping variable `var` into the affine expression(s) specified by `lf`. More...

void	affine_preimage (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
	Assigns to `this` the affine preimage of `this` under the function mapping variable `var` to the affine expression specified by `expr` and `denominator`. More...

void	generalized_affine_image (Variable var, Relation_Symbol relsym, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
	Assigns to `this` the image of `this` with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$ , where $\mathord{\relsym}$ is the relation symbol encoded by `relsym`. More...

void	generalized_affine_preimage (Variable var, Relation_Symbol relsym, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
	Assigns to `this` the preimage of `this` with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$ , where $\mathord{\relsym}$ is the relation symbol encoded by `relsym`. More...

void	generalized_affine_image (const Linear_Expression &lhs, Relation_Symbol relsym, const Linear_Expression &rhs)
	Assigns to `this` the image of `this` with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$ , where $\mathord{\relsym}$ is the relation symbol encoded by `relsym`. More...

void	generalized_affine_preimage (const Linear_Expression &lhs, Relation_Symbol relsym, const Linear_Expression &rhs)
	Assigns to `this` the preimage of `this` with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$ , where $\mathord{\relsym}$ is the relation symbol encoded by `relsym`. More...

void	bounded_affine_image (Variable var, const Linear_Expression &lb_expr, const Linear_Expression &ub_expr, Coefficient_traits::const_reference denominator=Coefficient_one())
	Assigns to `this` the image of `this` with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$ . More...

void	bounded_affine_preimage (Variable var, const Linear_Expression &lb_expr, const Linear_Expression &ub_expr, Coefficient_traits::const_reference denominator=Coefficient_one())
	Assigns to `this` the preimage of `this` with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$ . More...

void	time_elapse_assign (const Box &y)
	Assigns to `this` the result of computing the time-elapse between `this` and `y`. More...

void	topological_closure_assign ()
	Assigns to `*this` its topological closure.

void	wrap_assign (const Variables_Set &vars, Bounded_Integer_Type_Width w, Bounded_Integer_Type_Representation r, Bounded_Integer_Type_Overflow o, const Constraint_System *cs_p=0, unsigned complexity_threshold=16, bool wrap_individually=true)
	Wraps the specified dimensions of the vector space. More...

void	drop_some_non_integer_points (Complexity_Class complexity=ANY_COMPLEXITY)
	Possibly tightens `*this` by dropping some points with non-integer coordinates. More...

void	drop_some_non_integer_points (const Variables_Set &vars, Complexity_Class complexity=ANY_COMPLEXITY)
	Possibly tightens `*this` by dropping some points with non-integer coordinates for the space dimensions corresponding to `vars`. More...

template<typename T >
Enable_If< Is_Same< T, Box >::value &&Is_Same_Or_Derived< Interval_Base, ITV >::value, void >::type	CC76_widening_assign (const T &y, unsigned *tp=0)
	Assigns to `this` the result of computing the CC76-widening between `this` and `y`. More...

template<typename T , typename Iterator >
Enable_If< Is_Same< T, Box >::value &&Is_Same_Or_Derived< Interval_Base, ITV >::value, void >::type	CC76_widening_assign (const T &y, Iterator first, Iterator last)
	Assigns to `this` the result of computing the CC76-widening between `this` and `y`. More...

void	widening_assign (const Box &y, unsigned *tp=0)
	Same as CC76_widening_assign(y, tp).

void	limited_CC76_extrapolation_assign (const Box &y, const Constraint_System &cs, unsigned *tp=0)
	Improves the result of the CC76-extrapolation computation by also enforcing those constraints in `cs` that are satisfied by all the points of `*this`. More...

template<typename T >
Enable_If< Is_Same< T, Box >::value &&Is_Same_Or_Derived< Interval_Base, ITV >::value, void >::type	CC76_narrowing_assign (const T &y)
	Assigns to `this` the result of restoring in `y` the constraints of `this` that were lost by CC76-extrapolation applications. More...

Member Functions that May Modify the Dimension of the Vector Space
void	add_space_dimensions_and_embed (dimension_type m)
	Adds `m` new dimensions and embeds the old box into the new space. More...

void	add_space_dimensions_and_project (dimension_type m)
	Adds `m` new dimensions to the box and does not embed it in the new vector space. More...

void	concatenate_assign (const Box &y)
	Seeing a box as a set of tuples (its points), assigns to `this` all the tuples that can be obtained by concatenating, in the order given, a tuple of `this` with a tuple of `y`. More...

void	remove_space_dimensions (const Variables_Set &vars)
	Removes all the specified dimensions. More...

void	remove_higher_space_dimensions (dimension_type new_dimension)
	Removes the higher dimensions so that the resulting space will have dimension `new_dimension`. More...

template<typename Partial_Function >
void	map_space_dimensions (const Partial_Function &pfunc)
	Remaps the dimensions of the vector space according to a partial function. More...

void	expand_space_dimension (Variable var, dimension_type m)
	Creates `m` copies of the space dimension corresponding to `var`. More...

void	fold_space_dimensions (const Variables_Set &vars, Variable dest)
	Folds the space dimensions in `vars` into `dest`. More...

Static Public Member Functions
static dimension_type	max_space_dimension ()
	Returns the maximum space dimension that a Box can handle.

static bool	can_recycle_constraint_systems ()
	Returns false indicating that this domain does not recycle constraints.

static bool	can_recycle_congruence_systems ()
	Returns false indicating that this domain does not recycle congruences.

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

template<typename ITV >
bool	operator== (const Box< ITV > &x, const Box< ITV > &y)
	Returns `true` if and only if `x` and `y` are the same box. More...

template<typename ITV >
bool	operator!= (const Box< ITV > &x, const Box< ITV > &y)
	Returns `true` if and only if `x` and `y` are not the same box. More...

template<typename ITV >
std::ostream &	operator<< (std::ostream &s, const Box< ITV > &box)
	Output operator. More...

template<typename To , typename ITV >
bool	rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir)
	Computes the rectilinear (or Manhattan) distance between `x` and `y`. More...

template<typename Temp , typename To , typename ITV >
bool	rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir)
	Computes the rectilinear (or Manhattan) distance between `x` and `y`. More...

template<typename Temp , typename To , typename ITV >
bool	rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)
	Computes the rectilinear (or Manhattan) distance between `x` and `y`. More...

template<typename To , typename ITV >
bool	euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir)
	Computes the euclidean distance between `x` and `y`. More...

template<typename Temp , typename To , typename ITV >
bool	euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir)
	Computes the euclidean distance between `x` and `y`. More...

template<typename Temp , typename To , typename ITV >
bool	euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)
	Computes the euclidean distance between `x` and `y`. More...

template<typename To , typename ITV >
bool	l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir)
	Computes the $L_\infty$ distance between `x` and `y`. More...

template<typename Temp , typename To , typename ITV >
bool	l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir)
	Computes the $L_\infty$ distance between `x` and `y`. More...

template<typename Temp , typename To , typename ITV >
bool	l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)
	Computes the $L_\infty$ distance between `x` and `y`. More...

template<typename Temp , typename To , typename ITV >
bool	rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)

template<typename Temp , typename To , typename ITV >
bool	rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir)

template<typename To , typename ITV >
bool	rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir)

template<typename Temp , typename To , typename ITV >
bool	euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)

template<typename Temp , typename To , typename ITV >
bool	euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir)

template<typename To , typename ITV >
bool	euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir)

template<typename Temp , typename To , typename ITV >
bool	l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)

template<typename Temp , typename To , typename ITV >
bool	l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir)

template<typename To , typename ITV >
bool	l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Box< ITV > &x, const Box< ITV > &y, const Rounding_Dir dir)

template<typename ITV >
void	swap (Box< ITV > &x, Box< ITV > &y)

template<typename ITV >
std::ostream &	operator<< (std::ostream &s, const Box< ITV > &box)

Detailed Description

template<typename ITV>
class Parma_Polyhedra_Library::Box< ITV >

A not necessarily closed, iso-oriented hyperrectangle.

A Box object represents the smash product of $n$ not necessarily closed and possibly unbounded intervals represented by objects of class ITV, where $n$ is the space dimension of the box.

An interval constraint (resp., interval congruence) is a syntactic constraint (resp., congruence) that only mentions a single space dimension.

The Box domain optimally supports:

tautological and inconsistent constraints and congruences;
the interval constraints that are optimally supported by the template argument class ITV;
the interval congruences that are optimally supported by the template argument class ITV.

Depending on the method, using a constraint or congruence that is not optimally supported by the domain will either raise an exception or result in a (possibly non-optimal) upward approximation.

The user interface for the Box domain is meant to be as similar as possible to the one developed for the polyhedron class C_Polyhedron.

Constructor & Destructor Documentation

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box	(	dimension_type	num_dimensions = `0`,
		Degenerate_Element	kind = `UNIVERSE`
	)

inlineexplicit

Builds a universe or empty box of the specified space dimension.

Parameters

num_dimensions	The number of dimensions of the vector space enclosing the box;
kind	Specifies whether the universe or the empty box has to be built.

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Box< ITV > &	y,
		Complexity_Class	complexity = `ANY_COMPLEXITY`
	)

inline

Ordinary copy constructor.

The complexity argument is ignored.

template<typename ITV >

template<typename Other_ITV >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Box< Other_ITV > &	y,
		Complexity_Class	complexity = `ANY_COMPLEXITY`
	)

inlineexplicit

Builds a conservative, upward approximation of y.

The complexity argument is ignored.

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box ( const Constraint_System & cs )

inlineexplicit

Builds a box from the system of constraints cs.

The box inherits the space dimension of cs.

Parameters

cs	A system of constraints: constraints that are not interval constraints are ignored (even though they may have contributed to the space dimension).

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Constraint_System &	cs,
		Recycle_Input	dummy
	)

inline

Builds a box recycling a system of constraints cs.

The box inherits the space dimension of cs.

Parameters

cs	A system of constraints: constraints that are not interval constraints are ignored (even though they may have contributed to the space dimension).
dummy	A dummy tag to syntactically differentiate this one from the other constructors.

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box ( const Generator_System & gs )

explicit

Builds a box from the system of generators gs.

Builds the smallest box containing the polyhedron defined by gs. The box inherits the space dimension of gs.

Exceptions

std::invalid_argument Thrown if the system of generators is not empty but has no points.

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Generator_System &	gs,
		Recycle_Input	dummy
	)

inline

Builds a box recycling the system of generators gs.

Builds the smallest box containing the polyhedron defined by gs. The box inherits the space dimension of gs.

Parameters

gs	The generator system describing the polyhedron to be approximated.
dummy	A dummy tag to syntactically differentiate this one from the other constructors.

Exceptions

std::invalid_argument Thrown if the system of generators is not empty but has no points.

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box ( const Congruence_System & cgs )

inlineexplicit

Builds the smallest box containing the grid defined by a system of congruences cgs. The box inherits the space dimension of cgs.

Parameters

cgs	A system of congruences: congruences that are not non-relational equality constraints are ignored (though they may have contributed to the space dimension).

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Congruence_System &	cgs,
		Recycle_Input	dummy
	)

inline

Builds the smallest box containing the grid defined by a system of congruences cgs, recycling cgs. The box inherits the space dimension of cgs.

Parameters

cgs	A system of congruences: congruences that are not non-relational equality constraints are ignored (though they will contribute to the space dimension).
dummy	A dummy tag to syntactically differentiate this one from the other constructors.

template<typename ITV >

template<typename T >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const BD_Shape< T > &	bds,
		Complexity_Class	complexity = `POLYNOMIAL_COMPLEXITY`
	)

explicit

Builds a box containing the BDS bds.

Builds the smallest box containing bds using a polynomial algorithm. The complexity argument is ignored.

template<typename ITV >

template<typename T >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Octagonal_Shape< T > &	oct,
		Complexity_Class	complexity = `POLYNOMIAL_COMPLEXITY`
	)

explicit

Builds a box containing the octagonal shape oct.

Builds the smallest box containing oct using a polynomial algorithm. The complexity argument is ignored.

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Polyhedron &	ph,
		Complexity_Class	complexity = `ANY_COMPLEXITY`
	)

explicit

Builds a box containing the polyhedron ph.

Builds a box containing ph using algorithms whose complexity does not exceed the one specified by complexity. If complexity is ANY_COMPLEXITY, then the built box is the smallest one containing ph.

template<typename ITV >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Grid &	gr,
		Complexity_Class	complexity = `POLYNOMIAL_COMPLEXITY`
	)

explicit

Builds a box containing the grid gr.

Builds the smallest box containing gr using a polynomial algorithm. The complexity argument is ignored.

template<typename ITV >

template<typename D1 , typename D2 , typename R >

Parma_Polyhedra_Library::Box< ITV >::Box	(	const Partially_Reduced_Product< D1, D2, R > &	dp,
		Complexity_Class	complexity = `ANY_COMPLEXITY`
	)

explicit

Builds a box containing the partially reduced product dp.

Builds a box containing ph using algorithms whose complexity does not exceed the one specified by complexity.

Member Function Documentation

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::constrains ( Variable var ) const

Returns true if and only if var is constrained in *this.

Exceptions

std::invalid_argument Thrown if var is not a space dimension of *this.

template<typename ITV >

Poly_Con_Relation Parma_Polyhedra_Library::Box< ITV >::relation_with ( const Constraint & c ) const

Returns the relations holding between *this and the constraint c.

Exceptions

std::invalid_argument Thrown if *this and constraint c are dimension-incompatible.

template<typename ITV >

Poly_Con_Relation Parma_Polyhedra_Library::Box< ITV >::relation_with ( const Congruence & cg ) const

Returns the relations holding between *this and the congruence cg.

Exceptions

std::invalid_argument Thrown if *this and constraint cg are dimension-incompatible.

template<typename ITV >

Poly_Gen_Relation Parma_Polyhedra_Library::Box< ITV >::relation_with ( const Generator & g ) const

Returns the relations holding between *this and the generator g.

Exceptions

std::invalid_argument Thrown if *this and generator g are dimension-incompatible.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::bounds_from_above ( const Linear_Expression & expr ) const

inline

Returns true if and only if expr is bounded from above in *this.

Exceptions

std::invalid_argument Thrown if expr and *this are dimension-incompatible.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::bounds_from_below ( const Linear_Expression & expr ) const

inline

Returns true if and only if expr is bounded from below in *this.

Exceptions

std::invalid_argument Thrown if expr and *this are dimension-incompatible.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::maximize	(	const Linear_Expression &	expr,
		Coefficient &	sup_n,
		Coefficient &	sup_d,
		bool &	maximum
	)		const

inline

Returns true if and only if *this is not empty and expr is bounded from above in *this, in which case the supremum value is computed.

Parameters

expr	The linear expression to be maximized subject to `*this`;
sup_n	The numerator of the supremum value;
sup_d	The denominator of the supremum value;
maximum	`true` if and only if the supremum is also the maximum value.

Exceptions

std::invalid_argument Thrown if expr and *this are dimension-incompatible.

If *this is empty or expr is not bounded from above, false is returned and sup_n, sup_d and maximum are left untouched.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::maximize	(	const Linear_Expression &	expr,
		Coefficient &	sup_n,
		Coefficient &	sup_d,
		bool &	maximum,
		Generator &	g
	)		const

inline

Returns true if and only if *this is not empty and expr is bounded from above in *this, in which case the supremum value and a point where expr reaches it are computed.

Parameters

expr	The linear expression to be maximized subject to `*this`;
sup_n	The numerator of the supremum value;
sup_d	The denominator of the supremum value;
maximum	`true` if and only if the supremum is also the maximum value;
g	When maximization succeeds, will be assigned the point or closure point where `expr` reaches its supremum value.

Exceptions

std::invalid_argument Thrown if expr and *this are dimension-incompatible.

If *this is empty or expr is not bounded from above, false is returned and sup_n, sup_d, maximum and g are left untouched.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::minimize	(	const Linear_Expression &	expr,
		Coefficient &	inf_n,
		Coefficient &	inf_d,
		bool &	minimum
	)		const

inline

Returns true if and only if *this is not empty and expr is bounded from below in *this, in which case the infimum value is computed.

Parameters

expr	The linear expression to be minimized subject to `*this`;
inf_n	The numerator of the infimum value;
inf_d	The denominator of the infimum value;
minimum	`true` if and only if the infimum is also the minimum value.

Exceptions

std::invalid_argument Thrown if expr and *this are dimension-incompatible.

If *this is empty or expr is not bounded from below, false is returned and inf_n, inf_d and minimum are left untouched.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::minimize	(	const Linear_Expression &	expr,
		Coefficient &	inf_n,
		Coefficient &	inf_d,
		bool &	minimum,
		Generator &	g
	)		const

inline

Returns true if and only if *this is not empty and expr is bounded from below in *this, in which case the infimum value and a point where expr reaches it are computed.

Parameters

expr	The linear expression to be minimized subject to `*this`;
inf_n	The numerator of the infimum value;
inf_d	The denominator of the infimum value;
minimum	`true` if and only if the infimum is also the minimum value;
g	When minimization succeeds, will be assigned a point or closure point where `expr` reaches its infimum value.

Exceptions

std::invalid_argument Thrown if expr and *this are dimension-incompatible.

If *this is empty or expr is not bounded from below, false is returned and inf_n, inf_d, minimum and g are left untouched.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::frequency	(	const Linear_Expression &	expr,
		Coefficient &	freq_n,
		Coefficient &	freq_d,
		Coefficient &	val_n,
		Coefficient &	val_d
	)		const

Returns true if and only if there exist a unique value val such that *this saturates the equality expr = val.

Parameters

expr	The linear expression for which the frequency is needed;
freq_n	If `true` is returned, the value is set to ; Present for interface compatibility with class Grid, where the frequency can have a non-zero value;
freq_d	If `true` is returned, the value is set to ;
val_n	The numerator of `val`;
val_d	The denominator of `val`;

Exceptions

std::invalid_argument Thrown if expr and *this are dimension-incompatible.

If false is returned, then freq_n, freq_d, val_n and val_d are left untouched.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::contains ( const Box< ITV > & y ) const

Returns true if and only if *this contains y.

Exceptions

std::invalid_argument Thrown if x and y are dimension-incompatible.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::strictly_contains ( const Box< ITV > & y ) const

inline

Returns true if and only if *this strictly contains y.

Exceptions

std::invalid_argument Thrown if x and y are dimension-incompatible.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::is_disjoint_from ( const Box< ITV > & y ) const

Returns true if and only if *this and y are disjoint.

Exceptions

std::invalid_argument Thrown if x and y are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::add_constraint ( const Constraint & c )

inline

Adds a copy of constraint c to the system of constraints defining *this.

Parameters

c	The constraint to be added.

Exceptions

std::invalid_argument Thrown if *this and constraint c are dimension-incompatible, or c is not optimally supported by the Box domain.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::add_constraints ( const Constraint_System & cs )

inline

Adds the constraints in cs to the system of constraints defining *this.

Parameters

cs	The constraints to be added.

Exceptions

std::invalid_argument Thrown if *this and cs are dimension-incompatible, or cs contains a constraint which is not optimally supported by the box domain.

template<typename T >

void Parma_Polyhedra_Library::Box< T >::add_recycled_constraints ( Constraint_System & cs )

inline

Adds the constraints in cs to the system of constraints defining *this.

Parameters

cs	The constraints to be added. They may be recycled.

Exceptions

std::invalid_argument Thrown if *this and cs are dimension-incompatible, or cs contains a constraint which is not optimally supported by the box domain.

Warning: The only assumption that can be made on cs upon successful or exceptional return is that it can be safely destroyed.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::add_congruence ( const Congruence & cg )

inline

Adds to *this a constraint equivalent to the congruence cg.

Parameters

cg	The congruence to be added.

Exceptions

std::invalid_argument Thrown if *this and congruence cg are dimension-incompatible, or cg is not optimally supported by the box domain.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::add_congruences ( const Congruence_System & cgs )

inline

Adds to *this constraints equivalent to the congruences in cgs.

Parameters

cgs	The congruences to be added.

Exceptions

std::invalid_argument Thrown if *this and cgs are dimension-incompatible, or cgs contains a congruence which is not optimally supported by the box domain.

template<typename T >

void Parma_Polyhedra_Library::Box< T >::add_recycled_congruences ( Congruence_System & cgs )

inline

Adds to *this constraints equivalent to the congruences in cgs.

Parameters

cgs	The congruence system to be added to `*this`. The congruences in `cgs` may be recycled.

Exceptions

std::invalid_argument Thrown if *this and cgs are dimension-incompatible, or cgs contains a congruence which is not optimally supported by the box domain.

Warning: The only assumption that can be made on cgs upon successful or exceptional return is that it can be safely destroyed.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::refine_with_constraint ( const Constraint & c )

inline

Use the constraint c to refine *this.

Parameters

c	The constraint to be used for refinement.

Exceptions

std::invalid_argument Thrown if *this and c are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::refine_with_constraints ( const Constraint_System & cs )

inline

Use the constraints in cs to refine *this.

Parameters

cs	The constraints to be used for refinement. To avoid termination problems, each constraint in `cs` will be used for a single refinement step.

Exceptions

std::invalid_argument Thrown if *this and cs are dimension-incompatible.

Note: The user is warned that the accuracy of this refinement operator depends on the order of evaluation of the constraints in cs, which is in general unpredictable. If a fine control on such an order is needed, the user should consider calling the method refine_with_constraint(const Constraint& c) inside an appropriate looping construct.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::refine_with_congruence ( const Congruence & cg )

inline

Use the congruence cg to refine *this.

Parameters

cg	The congruence to be used for refinement.

Exceptions

std::invalid_argument Thrown if *this and cg are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::refine_with_congruences ( const Congruence_System & cgs )

inline

Use the congruences in cgs to refine *this.

Parameters

cgs	The congruences to be used for refinement.

Exceptions

std::invalid_argument Thrown if *this and cgs are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::propagate_constraint ( const Constraint & c )

inline

Use the constraint c for constraint propagation on *this.

Parameters

c	The constraint to be used for constraint propagation.

Exceptions

std::invalid_argument Thrown if *this and c are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::propagate_constraints	(	const Constraint_System &	cs,
		dimension_type	max_iterations = `0`
	)

inline

Use the constraints in cs for constraint propagation on *this.

Parameters

cs	The constraints to be used for constraint propagation.
max_iterations	The maximum number of propagation steps for each constraint in `cs`. If zero (the default), the number of propagation steps will be unbounded, possibly resulting in an infinite loop.

Exceptions

std::invalid_argument Thrown if *this and cs are dimension-incompatible.

Warning: This method may lead to non-termination if max_iterations is 0.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::unconstrain ( Variable var )

inline

Computes the cylindrification of *this with respect to space dimension var, assigning the result to *this.

Parameters

var	The space dimension that will be unconstrained.

Exceptions

std::invalid_argument Thrown if var is not a space dimension of *this.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::unconstrain ( const Variables_Set & vars )

Computes the cylindrification of *this with respect to the set of space dimensions vars, assigning the result to *this.

Parameters

vars	The set of space dimension that will be unconstrained.

Exceptions

std::invalid_argument Thrown if *this is dimension-incompatible with one of the Variable objects contained in vars.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::intersection_assign ( const Box< ITV > & y )

Assigns to *this the intersection of *this and y.

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::upper_bound_assign ( const Box< ITV > & y )

Assigns to *this the smallest box containing the union of *this and y.

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::upper_bound_assign_if_exact ( const Box< ITV > & y )

inline

If the upper bound of *this and y is exact, it is assigned to *this and true is returned, otherwise false is returned.

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::difference_assign ( const Box< ITV > & y )

Assigns to *this the difference of *this and y.

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::simplify_using_context_assign ( const Box< ITV > & y )

Assigns to *this a meet-preserving simplification of *this with respect to y. If false is returned, then the intersection is empty.

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::affine_image	(	Variable	var,
		const Linear_Expression &	expr,
		Coefficient_traits::const_reference	denominator = `Coefficient_one()`
	)

Assigns to *this the affine image of *this under the function mapping variable var to the affine expression specified by expr and denominator.

Parameters

var	The variable to which the affine expression is assigned;
expr	The numerator of the affine expression;
denominator	The denominator of the affine expression (optional argument with default value 1).

Exceptions

std::invalid_argument Thrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a space dimension of *this.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::affine_form_image	(	Variable	var,
		const Linear_Form< ITV > &	lf
	)

Assigns to *this the affine form image of *this under the function mapping variable var into the affine expression(s) specified by lf.

Parameters

var	The variable to which the affine expression is assigned.
lf	The linear form on intervals with floating point boundaries that defines the affine expression(s). ALL of its coefficients MUST be bounded.

Exceptions

std::invalid_argument Thrown if lf and *this are dimension-incompatible or if var is not a dimension of *this.

This function is used in abstract interpretation to model an assignment of a value that is correctly overapproximated by lf to the floating point variable represented by var.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::affine_preimage	(	Variable	var,
		const Linear_Expression &	expr,
		Coefficient_traits::const_reference	denominator = `Coefficient_one()`
	)

Assigns to *this the affine preimage of *this under the function mapping variable var to the affine expression specified by expr and denominator.

Parameters

var	The variable to which the affine expression is substituted;
expr	The numerator of the affine expression;
denominator	The denominator of the affine expression (optional argument with default value 1).

Exceptions

std::invalid_argument Thrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a space dimension of *this.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::generalized_affine_image	(	Variable	var,
		Relation_Symbol	relsym,
		const Linear_Expression &	expr,
		Coefficient_traits::const_reference	denominator = `Coefficient_one()`
	)

Assigns to *this the image of *this with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$ , where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters

var	The left hand side variable of the generalized affine relation;
relsym	The relation symbol;
expr	The numerator of the right hand side affine expression;
denominator	The denominator of the right hand side affine expression (optional argument with default value 1).

Exceptions

std::invalid_argument Thrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a space dimension of *this.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::generalized_affine_preimage	(	Variable	var,
		Relation_Symbol	relsym,
		const Linear_Expression &	expr,
		Coefficient_traits::const_reference	denominator = `Coefficient_one()`
	)

Assigns to *this the preimage of *this with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$ , where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters

var	The left hand side variable of the generalized affine relation;
relsym	The relation symbol;
expr	The numerator of the right hand side affine expression;
denominator	The denominator of the right hand side affine expression (optional argument with default value 1).

Exceptions

std::invalid_argument Thrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a space dimension of *this.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::generalized_affine_image	(	const Linear_Expression &	lhs,
		Relation_Symbol	relsym,
		const Linear_Expression &	rhs
	)

Assigns to *this the image of *this with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$ , where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters

lhs	The left hand side affine expression;
relsym	The relation symbol;
rhs	The right hand side affine expression.

Exceptions

std::invalid_argument Thrown if *this is dimension-incompatible with lhs or rhs.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::generalized_affine_preimage	(	const Linear_Expression &	lhs,
		Relation_Symbol	relsym,
		const Linear_Expression &	rhs
	)

Assigns to *this the preimage of *this with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$ , where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters

lhs	The left hand side affine expression;
relsym	The relation symbol;
rhs	The right hand side affine expression.

Exceptions

std::invalid_argument Thrown if *this is dimension-incompatible with lhs or rhs.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::bounded_affine_image	(	Variable	var,
		const Linear_Expression &	lb_expr,
		const Linear_Expression &	ub_expr,
		Coefficient_traits::const_reference	denominator = `Coefficient_one()`
	)

Assigns to *this the image of *this with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$ .

Parameters

var	The variable updated by the affine relation;
lb_expr	The numerator of the lower bounding affine expression;
ub_expr	The numerator of the upper bounding affine expression;
denominator	The (common) denominator for the lower and upper bounding affine expressions (optional argument with default value 1).

Exceptions

std::invalid_argument Thrown if denominator is zero or if lb_expr (resp., ub_expr) and *this are dimension-incompatible or if var is not a space dimension of *this.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::bounded_affine_preimage	(	Variable	var,
		const Linear_Expression &	lb_expr,
		const Linear_Expression &	ub_expr,
		Coefficient_traits::const_reference	denominator = `Coefficient_one()`
	)

Assigns to *this the preimage of *this with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$ .

Parameters

var	The variable updated by the affine relation;
lb_expr	The numerator of the lower bounding affine expression;
ub_expr	The numerator of the upper bounding affine expression;
denominator	The (common) denominator for the lower and upper bounding affine expressions (optional argument with default value 1).

Exceptions

std::invalid_argument Thrown if denominator is zero or if lb_expr (resp., ub_expr) and *this are dimension-incompatible or if var is not a space dimension of *this.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::time_elapse_assign ( const Box< ITV > & y )

Assigns to *this the result of computing the time-elapse between *this and y.

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::wrap_assign	(	const Variables_Set &	vars,
		Bounded_Integer_Type_Width	w,
		Bounded_Integer_Type_Representation	r,
		Bounded_Integer_Type_Overflow	o,
		const Constraint_System *	cs_p = `0`,
		unsigned	complexity_threshold = `16`,
		bool	wrap_individually = `true`
	)

Wraps the specified dimensions of the vector space.

Parameters

vars	The set of Variable objects corresponding to the space dimensions to be wrapped.
w	The width of the bounded integer type corresponding to all the dimensions to be wrapped.
r	The representation of the bounded integer type corresponding to all the dimensions to be wrapped.
o	The overflow behavior of the bounded integer type corresponding to all the dimensions to be wrapped.
cs_p	Possibly null pointer to a constraint system. When non-null, the pointed-to constraint system is assumed to represent the conditional or looping construct guard with respect to which wrapping is performed. Since wrapping requires the computation of upper bounds and due to non-distributivity of constraint refinement over upper bounds, passing a constraint system in this way can be more precise than refining the result of the wrapping operation with the constraints in `*cs_p`.
complexity_threshold	A precision parameter which is ignored for the Box domain.
wrap_individually	A precision parameter which is ignored for the Box domain.

Exceptions

std::invalid_argument Thrown if *this is dimension-incompatible with one of the Variable objects contained in vars or with *cs_p.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::drop_some_non_integer_points ( Complexity_Class complexity = ANY_COMPLEXITY )

Possibly tightens *this by dropping some points with non-integer coordinates.

Parameters

complexity The maximal complexity of any algorithms used.

Note: Currently there is no optimality guarantee, not even if complexity is ANY_COMPLEXITY.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::drop_some_non_integer_points	(	const Variables_Set &	vars,
		Complexity_Class	complexity = `ANY_COMPLEXITY`
	)

Possibly tightens *this by dropping some points with non-integer coordinates for the space dimensions corresponding to vars.

Parameters

vars	Points with non-integer coordinates for these variables/space-dimensions can be discarded.
complexity	The maximal complexity of any algorithms used.

Note: Currently there is no optimality guarantee, not even if complexity is ANY_COMPLEXITY.

template<typename ITV >

template<typename T >

Enable_If<Is_Same<T, Box>::value && Is_Same_Or_Derived<Interval_Base, ITV>::value, void>::type Parma_Polyhedra_Library::Box< ITV >::CC76_widening_assign	(	const T &	y,
		unsigned *	tp = `0`
	)

Assigns to *this the result of computing the CC76-widening between *this and y.

Parameters

y	A box that must be contained in `*this`.
tp	An optional pointer to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

template<typename ITV >

template<typename T , typename Iterator >

Enable_If<Is_Same<T, Box>::value && Is_Same_Or_Derived<Interval_Base, ITV>::value, void>::type Parma_Polyhedra_Library::Box< ITV >::CC76_widening_assign	(	const T &	y,
		Iterator	first,
		Iterator	last
	)

Assigns to *this the result of computing the CC76-widening between *this and y.

Parameters

y	A box that must be contained in `*this`.
first	An iterator that points to the first stop-point.
last	An iterator that points one past the last stop-point.

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::limited_CC76_extrapolation_assign	(	const Box< ITV > &	y,
		const Constraint_System &	cs,
		unsigned *	tp = `0`
	)

Improves the result of the CC76-extrapolation computation by also enforcing those constraints in cs that are satisfied by all the points of *this.

Parameters

y	A box that must be contained in `*this`.
cs	The system of constraints used to improve the widened box.
tp	An optional pointer to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).

Exceptions

std::invalid_argument Thrown if *this, y and cs are dimension-incompatible or if cs contains a strict inequality.

template<typename ITV >

template<typename T >

Enable_If<Is_Same<T, Box>::value && Is_Same_Or_Derived<Interval_Base, ITV>::value, void>::type Parma_Polyhedra_Library::Box< ITV >::CC76_narrowing_assign ( const T & y )

Assigns to *this the result of restoring in y the constraints of *this that were lost by CC76-extrapolation applications.

Parameters

y	A Box that must contain `*this`.

Exceptions

std::invalid_argument Thrown if *this and y are dimension-incompatible.

Note: As was the case for widening operators, the argument y is meant to denote the value computed in the previous iteration step, whereas *this denotes the value computed in the current iteration step (in the decreasing iteration sequence). Hence, the call x.CC76_narrowing_assign(y) will assign to x the result of the computation $\mathtt{y} \Delta \mathtt{x}$ .

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::add_space_dimensions_and_embed ( dimension_type m )

inline

Adds m new dimensions and embeds the old box into the new space.

Parameters

m	The number of dimensions to add.

The new dimensions will be those having the highest indexes in the new box, which is defined by a system of interval constraints in which the variables running through the new dimensions are unconstrained. For instance, when starting from the box $\cB \sseq \Rset^2$ and adding a third dimension, the result will be the box

$\bigl\{\, (x, y, z)^\transpose \in \Rset^3 \bigm| (x, y)^\transpose \in \cB \,\bigr\}.$

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::add_space_dimensions_and_project ( dimension_type m )

inline

Adds m new dimensions to the box and does not embed it in the new vector space.

Parameters

m	The number of dimensions to add.

The new dimensions will be those having the highest indexes in the new box, which is defined by a system of bounded differences in which the variables running through the new dimensions are all constrained to be equal to 0. For instance, when starting from the box $\cB \sseq \Rset^2$ and adding a third dimension, the result will be the box

$\bigl\{\, (x, y, 0)^\transpose \in \Rset^3 \bigm| (x, y)^\transpose \in \cB \,\bigr\}.$

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::concatenate_assign ( const Box< ITV > & y )

Seeing a box as a set of tuples (its points), assigns to *this all the tuples that can be obtained by concatenating, in the order given, a tuple of *this with a tuple of y.

Let $B \sseq \Rset^n$ and $D \sseq \Rset^m$ be the boxes corresponding, on entry, to *this and y, respectively. Upon successful completion, *this will represent the box $R \sseq \Rset^{n+m}$ such that

$R \defeq \Bigl\{\, (x_1, \ldots, x_n, y_1, \ldots, y_m)^\transpose \Bigm| (x_1, \ldots, x_n)^\transpose \in B, (y_1, \ldots, y_m)^\transpose \in D \,\Bigl\}.$

Another way of seeing it is as follows: first increases the space dimension of *this by adding y.space_dimension() new dimensions; then adds to the system of constraints of *this a renamed-apart version of the constraints of y.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::remove_space_dimensions ( const Variables_Set & vars )

inline

Removes all the specified dimensions.

Parameters

vars	The set of Variable objects corresponding to the dimensions to be removed.

Exceptions

std::invalid_argument Thrown if *this is dimension-incompatible with one of the Variable objects contained in vars.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::remove_higher_space_dimensions ( dimension_type new_dimension )

Removes the higher dimensions so that the resulting space will have dimension new_dimension.

Exceptions

std::invalid_argument Thrown if new_dimension is greater than the space dimension of *this.

template<typename ITV >

template<typename Partial_Function >

void Parma_Polyhedra_Library::Box< ITV >::map_space_dimensions ( const Partial_Function & pfunc )

Remaps the dimensions of the vector space according to a partial function.

Parameters

pfunc The partial function specifying the destiny of each dimension.

The template type parameter Partial_Function must provide the following methods.

bool has_empty_codomain() const

returns true if and only if the represented partial function has an empty co-domain (i.e., it is always undefined). The has_empty_codomain() method will always be called before the methods below. However, if has_empty_codomain() returns true, none of the functions below will be called.

dimension_type max_in_codomain() const

returns the maximum value that belongs to the co-domain of the partial function.

bool maps(dimension_type i, dimension_type& j) const

Let $f$ be the represented function and $k$ be the value of i. If $f$ is defined in $k$ , then $f(k)$ is assigned to j and true is returned. If $f$ is undefined in $k$ , then false is returned.

The result is undefined if pfunc does not encode a partial function with the properties described in the specification of the mapping operator.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::expand_space_dimension	(	Variable	var,
		dimension_type	m
	)

inline

Creates m copies of the space dimension corresponding to var.

Parameters

var	The variable corresponding to the space dimension to be replicated;
m	The number of replicas to be created.

Exceptions

std::invalid_argument	Thrown if `var` does not correspond to a dimension of the vector space.
std::length_error	Thrown if adding `m` new space dimensions would cause the vector space to exceed dimension `max_space_dimension()`.

If *this has space dimension $n$ , with $n > 0$ , and var has space dimension $k \leq n$ , then the $k$ -th space dimension is expanded to m new space dimensions $n$ , $n+1$ , $\dots$ , $n+m-1$ .

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::fold_space_dimensions	(	const Variables_Set &	vars,
		Variable	dest
	)

Folds the space dimensions in vars into dest.

Parameters

vars	The set of Variable objects corresponding to the space dimensions to be folded;
dest	The variable corresponding to the space dimension that is the destination of the folding operation.

Exceptions

std::invalid_argument Thrown if *this is dimension-incompatible with dest or with one of the Variable objects contained in vars. Also thrown if dest is contained in vars.

If *this has space dimension $n$ , with $n > 0$ , dest has space dimension $k \leq n$ , vars is a set of variables whose maximum space dimension is also less than or equal to $n$ , and dest is not a member of vars, then the space dimensions corresponding to variables in vars are folded into the $k$ -th space dimension.

template<typename ITV >

const ITV & Parma_Polyhedra_Library::Box< ITV >::get_interval ( Variable var ) const

inline

Returns a reference the interval that bounds var.

Exceptions

std::invalid_argument Thrown if var is not a space dimension of *this.

template<typename ITV >

void Parma_Polyhedra_Library::Box< ITV >::set_interval	(	Variable	var,
		const ITV &	i
	)

inline

Sets to i the interval that bounds var.

Exceptions

std::invalid_argument Thrown if var is not a space dimension of *this.

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::has_lower_bound	(	Variable	var,
		Coefficient &	n,
		Coefficient &	d,
		bool &	closed
	)		const

inline

If the space dimension of var is unbounded below, return false. Otherwise return true and set n, d and closed accordingly.

Note: It is assumed that *this is a non-empty box having space dimension greater than or equal to that of var. An undefined behavior is obtained if this assumption is not met.

Let $I$ be the interval corresponding to variable var in the non-empty box *this. If $I$ is not bounded from below, simply return false (leaving all other parameters unchanged). Otherwise, set n, d and closed as follows:

n and d are assigned the integers and such that the fraction corresponds to the greatest lower bound of . The fraction is in canonical form, meaning that and have no common factors, is positive, and if is zero then is one;
closed is set to true if and only if the lower boundary of is closed (i.e., it is included in the interval).

template<typename ITV >

bool Parma_Polyhedra_Library::Box< ITV >::has_upper_bound	(	Variable	var,
		Coefficient &	n,
		Coefficient &	d,
		bool &	closed
	)		const

inline

If the space dimension of var is unbounded above, return false. Otherwise return true and set n, d and closed accordingly.

Note: It is assumed that *this is a non-empty box having space dimension greater than or equal to that of var. An undefined behavior is obtained if this assumption is not met.

Let $I$ be the interval corresponding to variable var in the non-empty box *this. If $I$ is not bounded from above, simply return false (leaving all other parameters unchanged). Otherwise, set n, d and closed as follows:

n and d are assigned the integers and such that the fraction corresponds to the least upper bound of . The fraction is in canonical form, meaning that and have no common factors, is positive, and if is zero then is one;
closed is set to true if and only if the upper boundary of is closed (i.e., it is included in the interval).

template<typename ITV >

int32_t Parma_Polyhedra_Library::Box< ITV >::hash_code ( ) const

inline

Returns a 32-bit hash code for *this.

If x and y are such that x == y, then x.hash_code() == y.hash_code().

Friends And Related Function Documentation

template<typename ITV >

void swap	(	Box< ITV > &	x,
		Box< ITV > &	y
	)

template<typename ITV >

bool operator==	(	const Box< ITV > &	x,
		const Box< ITV > &	y
	)

Note that x and y may be dimension-incompatible boxes: in this case, the value false is returned.

template<typename ITV >

bool operator!=	(	const Box< ITV > &	x,
		const Box< ITV > &	y
	)

Note that x and y may be dimension-incompatible boxes: in this case, the value true is returned.

template<typename ITV >

std::ostream & operator<<	(	std::ostream &	s,
		const Box< ITV > &	box
	)

template<typename To , typename ITV >

bool rectilinear_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir
	)

If the rectilinear distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using variables of type Checked_Number<To, Extended_Number_Policy>.

template<typename Temp , typename To , typename ITV >

bool rectilinear_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir
	)

If the rectilinear distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using variables of type Checked_Number<Temp, Extended_Number_Policy>.

template<typename Temp , typename To , typename ITV >

bool rectilinear_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir,
		Temp &	tmp0,
		Temp &	tmp1,
		Temp &	tmp2
	)

If the rectilinear distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using the temporary variables tmp0, tmp1 and tmp2.

template<typename To , typename ITV >

bool euclidean_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir
	)

If the euclidean distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using variables of type Checked_Number<To, Extended_Number_Policy>.

template<typename Temp , typename To , typename ITV >

bool euclidean_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir
	)

If the euclidean distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using variables of type Checked_Number<Temp, Extended_Number_Policy>.

template<typename Temp , typename To , typename ITV >

bool euclidean_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir,
		Temp &	tmp0,
		Temp &	tmp1,
		Temp &	tmp2
	)

If the euclidean distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using the temporary variables tmp0, tmp1 and tmp2.

template<typename To , typename ITV >

bool l_infinity_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir
	)

If the $L_\infty$ distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using variables of type Checked_Number<To, Extended_Number_Policy>.

template<typename Temp , typename To , typename ITV >

bool l_infinity_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir
	)

If the $L_\infty$ distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using variables of type Checked_Number<Temp, Extended_Number_Policy>.

template<typename Temp , typename To , typename ITV >

bool l_infinity_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		Rounding_Dir	dir,
		Temp &	tmp0,
		Temp &	tmp1,
		Temp &	tmp2
	)

If the $L_\infty$ distance between x and y is defined, stores an approximation of it into r and returns true; returns false otherwise.

The direction of the approximation is specified by dir.

All computations are performed using the temporary variables tmp0, tmp1 and tmp2.

template<typename Temp , typename To , typename ITV >

bool rectilinear_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir,
		Temp &	tmp0,
		Temp &	tmp1,
		Temp &	tmp2
	)

bool rectilinear_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir
	)

bool rectilinear_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir
	)

bool euclidean_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir,
		Temp &	tmp0,
		Temp &	tmp1,
		Temp &	tmp2
	)

bool euclidean_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir
	)

bool euclidean_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir
	)

bool l_infinity_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir,
		Temp &	tmp0,
		Temp &	tmp1,
		Temp &	tmp2
	)

bool l_infinity_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir
	)

bool l_infinity_distance_assign	(	Checked_Number< To, Extended_Number_Policy > &	r,
		const Box< ITV > &	x,
		const Box< ITV > &	y,
		const Rounding_Dir	dir
	)

void swap	(	Box< ITV > &	x,
		Box< ITV > &	y
	)

std::ostream & operator<<	(	std::ostream &	s,
		const Box< ITV > &	box
	)

ppl.hh

Public Types

Public Member Functions

Static Public Member Functions

Related Functions

Detailed Description

template<typename ITV> class Parma_Polyhedra_Library::Box< ITV >

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename ITV>
class Parma_Polyhedra_Library::Box< ITV >