Public Types | Public Member Functions | Static Public Member Functions | Friends | Related Functions

Parma_Polyhedra_Library::Octagonal_Shape< T > Class Template Reference
[C++ Language Interface]

An octagonal shape. More...

#include <ppl.hh>

List of all members.

Public Types

typedef T coefficient_type_base
 The numeric base type upon which OSs are built.
typedef N coefficient_type
 The (extended) numeric type of the inhomogeneous term of the inequalities defining an OS.

Public Member Functions

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<<.
bool ascii_load (std::istream &s)
 Loads from s an ASCII representation (as produced by ascii_dump(std::ostream&) const) and sets *this accordingly. Returns true if successful, false otherwise.
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.
Constructors, Assignment, Swap and Destructor
 Octagonal_Shape (dimension_type num_dimensions=0, Degenerate_Element kind=UNIVERSE)
 Builds an universe or empty OS of the specified space dimension.
 Octagonal_Shape (const Octagonal_Shape &x, Complexity_Class complexity=ANY_COMPLEXITY)
 Ordinary copy constructor.
template<typename U >
 Octagonal_Shape (const Octagonal_Shape< U > &y, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds a conservative, upward approximation of y.
 Octagonal_Shape (const Constraint_System &cs)
 Builds an OS from the system of constraints cs.
 Octagonal_Shape (const Congruence_System &cgs)
 Builds an OS from a system of congruences.
 Octagonal_Shape (const Generator_System &gs)
 Builds an OS from the system of generators gs.
 Octagonal_Shape (const Polyhedron &ph, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds an OS from the polyhedron ph.
template<typename Interval >
 Octagonal_Shape (const Box< Interval > &box, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds an OS out of a box.
 Octagonal_Shape (const Grid &grid, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds an OS that approximates a grid.
template<typename U >
 Octagonal_Shape (const BD_Shape< U > &bd, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds an OS from a BD shape.
Octagonal_Shapeoperator= (const Octagonal_Shape &y)
 The assignment operator. (*this and y can be dimension-incompatible.).
void swap (Octagonal_Shape &y)
 Swaps *this with octagon y. (*this and y can be dimension-incompatible.).
 ~Octagonal_Shape ()
 Destructor.
Member Functions that Do Not Modify the Octagonal_Shape
dimension_type space_dimension () const
 Returns the dimension of the vector space enclosing *this.
dimension_type affine_dimension () const
 Returns $0$, if *this is empty; otherwise, returns the affine dimension of *this.
Constraint_System constraints () const
 Returns the 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 (equality) congruences satisfied by *this.
Congruence_System minimized_congruences () const
 Returns a minimal system of (equality) congruences satisfied by *this with the same affine dimension as *this.
bool contains (const Octagonal_Shape &y) const
 Returns true if and only if *this contains y.
bool strictly_contains (const Octagonal_Shape &y) const
 Returns true if and only if *this strictly contains y.
bool is_disjoint_from (const Octagonal_Shape &y) const
 Returns true if and only if *this and y are disjoint.
Poly_Con_Relation relation_with (const Constraint &c) const
 Returns the relations holding between *this and the constraint c.
Poly_Con_Relation relation_with (const Congruence &cg) const
 Returns the relations holding between *this and the congruence cg.
Poly_Gen_Relation relation_with (const Generator &g) const
 Returns the relations holding between *this and the generator g.
bool is_empty () const
 Returns true if and only if *this is an empty OS.
bool is_universe () const
 Returns true if and only if *this is a universe OS.
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 OS.
bool is_topologically_closed () const
 Returns true if and only if *this is a topologically closed subset of the vector space.
bool contains_integer_point () const
 Returns true if and only if *this contains (at least) an integer point.
bool constrains (Variable var) const
 Returns true if and only if var is constrained in *this.
bool bounds_from_above (const Linear_Expression &expr) const
 Returns true if and only if expr is bounded from above in *this.
bool bounds_from_below (const Linear_Expression &expr) const
 Returns true if and only if expr is bounded from below in *this.
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.
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.
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.
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.
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.
bool OK () const
 Checks if all the invariants are satisfied.
Space-Dimension Preserving Member Functions that May Modify the Octagonal_Shape
void add_constraint (const Constraint &c)
 Adds a copy of constraint c to the system of constraints defining *this.
void add_constraints (const Constraint_System &cs)
 Adds the constraints in cs to the system of constraints defining *this.
void add_recycled_constraints (Constraint_System &cs)
 Adds the constraints in cs to the system of constraints of *this.
void add_congruence (const Congruence &cg)
 Adds to *this a constraint equivalent to the congruence cg.
void add_congruences (const Congruence_System &cgs)
 Adds to *this constraints equivalent to the congruences in cgs.
void add_recycled_congruences (Congruence_System &cgs)
 Adds to *this constraints equivalent to the congruences in cgs.
void refine_with_constraint (const Constraint &c)
 Uses a copy of constraint c to refine the system of octagonal constraints defining *this.
void refine_with_congruence (const Congruence &cg)
 Uses a copy of congruence cg to refine the system of octagonal constraints of *this.
void refine_with_constraints (const Constraint_System &cs)
 Uses a copy of the constraints in cs to refine the system of octagonal constraints defining *this.
void refine_with_congruences (const Congruence_System &cgs)
 Uses a copy of the congruences in cgs to refine the system of octagonal constraints defining *this.
void unconstrain (Variable var)
 Computes the cylindrification of *this with respect to space dimension var, assigning the result to *this.
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.
void intersection_assign (const Octagonal_Shape &y)
 Assigns to *this the intersection of *this and y.
void upper_bound_assign (const Octagonal_Shape &y)
 Assigns to *this the smallest OS that contains the convex union of *this and y.
bool upper_bound_assign_if_exact (const Octagonal_Shape &y)
 If the upper bound of *this and y is exact, it is assigned to *this and true is returned, otherwise false is returned.
bool integer_upper_bound_assign_if_exact (const Octagonal_Shape &y)
 If the integer upper bound of *this and y is exact, it is assigned to *this and true is returned; otherwise false is returned.
void difference_assign (const Octagonal_Shape &y)
 Assigns to *this the smallest octagon containing the set difference of *this and y.
bool simplify_using_context_assign (const Octagonal_Shape &y)
 Assigns to *this a meet-preserving simplification of *this with respect to y. If false is returned, then the intersection is empty.
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 into the affine expression specified by expr and denominator.
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 into the affine expression specified by expr and denominator.
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 transfer function $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym.
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 transfer function $\mathrm{lhs}' \relsym \mathrm{rhs}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym.
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 $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$.
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 affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym.
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.
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 $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$.
void time_elapse_assign (const Octagonal_Shape &y)
 Assigns to *this the result of computing the time-elapse between *this and y.
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 *pcs=0, unsigned complexity_threshold=16, bool wrap_individually=true)
 Wraps the specified dimensions of the vector space.
void drop_some_non_integer_points (Complexity_Class complexity=ANY_COMPLEXITY)
 Possibly tightens *this by dropping some points with non-integer coordinates.
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.
void topological_closure_assign ()
 Assigns to *this its topological closure.
void CC76_extrapolation_assign (const Octagonal_Shape &y, unsigned *tp=0)
 Assigns to *this the result of computing the CC76-extrapolation between *this and y.
template<typename Iterator >
void CC76_extrapolation_assign (const Octagonal_Shape &y, Iterator first, Iterator last, unsigned *tp=0)
 Assigns to *this the result of computing the CC76-extrapolation between *this and y.
void BHMZ05_widening_assign (const Octagonal_Shape &y, unsigned *tp=0)
 Assigns to *this the result of computing the BHMZ05-widening between *this and y.
void widening_assign (const Octagonal_Shape &y, unsigned *tp=0)
 Same as BHMZ05_widening_assign(y, tp).
void limited_BHMZ05_extrapolation_assign (const Octagonal_Shape &y, const Constraint_System &cs, unsigned *tp=0)
 Improves the result of the BHMZ05-widening computation by also enforcing those constraints in cs that are satisfied by all the points of *this.
void CC76_narrowing_assign (const Octagonal_Shape &y)
 Restores from y the constraints of *this, lost by CC76-extrapolation applications.
void limited_CC76_extrapolation_assign (const Octagonal_Shape &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.
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 OS into the new space.
void add_space_dimensions_and_project (dimension_type m)
 Adds m new dimensions to the OS and does not embed it in the new space.
void concatenate_assign (const Octagonal_Shape &y)
 Assigns to *this the concatenation of *this and y, taken in this order.
void remove_space_dimensions (const Variables_Set &vars)
 Removes all the specified dimensions.
void remove_higher_space_dimensions (dimension_type new_dimension)
 Removes the higher dimensions so that the resulting space will have dimension new_dimension.
template<typename Partial_Function >
void map_space_dimensions (const Partial_Function &pfunc)
 Remaps the dimensions of the vector space according to a partial function.
void expand_space_dimension (Variable var, dimension_type m)
 Creates m copies of the space dimension corresponding to var.
void fold_space_dimensions (const Variables_Set &vars, Variable dest)
 Folds the space dimensions in vars into dest.
template<typename Interval_Info >
void refine_fp_interval_abstract_store (Box< Interval< T, Interval_Info > > &store) const
 Refines store with the constraints defining *this.

Static Public Member Functions

static dimension_type max_space_dimension ()
 Returns the maximum space dimension that an OS can handle.
static bool can_recycle_constraint_systems ()
 Returns false indicating that this domain cannot recycle constraints.
static bool can_recycle_congruence_systems ()
 Returns false indicating that this domain cannot recycle congruences.

Friends

bool operator== (const Octagonal_Shape< T > &x, const Octagonal_Shape< T > &y)
 Returns true if and only if x and y are the same octagon.

Related Functions

(Note that these are not member functions.)


template<typename T >
std::ostream & operator<< (std::ostream &s, const Octagonal_Shape< T > &oct)
 Output operator.
template<typename T >
bool operator!= (const Octagonal_Shape< T > &x, const Octagonal_Shape< T > &y)
 Returns true if and only if x and y are different shapes.
template<typename To , typename T >
bool rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Octagonal_Shape< T > &x, const Octagonal_Shape< T > &y, Rounding_Dir dir)
 Computes the rectilinear (or Manhattan) distance between x and y.
template<typename Temp , typename To , typename T >
bool rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Octagonal_Shape< T > &x, const Octagonal_Shape< T > &y, Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)
 Computes the rectilinear (or Manhattan) distance between x and y.
template<typename To , typename T >
bool euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Octagonal_Shape< T > &x, const Octagonal_Shape< T > &y, Rounding_Dir dir)
 Computes the euclidean distance between x and y.
template<typename Temp , typename To , typename T >
bool euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Octagonal_Shape< T > &x, const Octagonal_Shape< T > &y, Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)
 Computes the euclidean distance between x and y.
template<typename To , typename T >
bool l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Octagonal_Shape< T > &x, const Octagonal_Shape< T > &y, Rounding_Dir dir)
 Computes the $L_\infty$ distance between x and y.
template<typename Temp , typename To , typename T >
bool l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const Octagonal_Shape< T > &x, const Octagonal_Shape< T > &y, Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2)
 Computes the $L_\infty$ distance between x and y.
template<typename T >
void swap (Parma_Polyhedra_Library::Octagonal_Shape< T > &x, Parma_Polyhedra_Library::Octagonal_Shape< T > &y)
 Specializes std::swap.

Detailed Description

template<typename T>
class Parma_Polyhedra_Library::Octagonal_Shape< T >

An octagonal shape.

The class template Octagonal_Shape<T> allows for the efficient representation of a restricted kind of topologically closed convex polyhedra called octagonal shapes (OSs, for short). The name comes from the fact that, in a vector space of dimension 2, bounded OSs are polygons with at most eight sides. The closed affine half-spaces that characterize the OS can be expressed by constraints of the form

\[ ax_i + bx_j \leq k \]

where $a, b \in \{-1, 0, 1\}$ and $k$ is a rational number, which are called octagonal constraints.

Based on the class template type parameter T, a family of extended numbers is built and used to approximate the inhomogeneous term of octagonal constraints. These extended numbers provide a representation for the value $+\infty$, as well as rounding-aware implementations for several arithmetic functions. The value of the type parameter T may be one of the following:

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

The OS domain optimally supports:

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.

A constraint is octagonal if it has the form

\[ \pm a_i x_i \pm a_j x_j \relsym b \]

where $\mathord{\relsym} \in \{ \leq, =, \geq \}$ and $a_i$, $a_j$, $b$ are integer coefficients such that $a_i = 0$, or $a_j = 0$, or $a_i = a_j$. The user is warned that the above octagonal Constraint object will be mapped into a correct and optimal approximation that, depending on the expressive power of the chosen template argument T, may loose some precision. Also note that strict constraints are not octagonal.

For instance, a Constraint object encoding $3x + 3y \leq 1$ will be approximated by:

On the other hand, depending from the context, a Constraint object encoding $3x - y \leq 1$ will be either upward approximated (e.g., by safely ignoring it) or it will cause an exception.

In the following examples it is assumed that the type argument T is one of the possible instances listed above and that variables x, y and z are defined (where they are used) as follows:

    Variable x(0);
    Variable y(1);
    Variable z(2);
Example 1
The following code builds an OS corresponding to a cube in $\Rset^3$, given as a system of constraints:
    Constraint_System cs;
    cs.insert(x >= 0);
    cs.insert(x <= 3);
    cs.insert(y >= 0);
    cs.insert(y <= 3);
    cs.insert(z >= 0);
    cs.insert(z <= 3);
    Octagonal_Shape<T> oct(cs);
In contrast, the following code will raise an exception, since constraints 7, 8, and 9 are not octagonal:
    Constraint_System cs;
    cs.insert(x >= 0);
    cs.insert(x <= 3);
    cs.insert(y >= 0);
    cs.insert(y <= 3);
    cs.insert(z >= 0);
    cs.insert(z <= 3);
    cs.insert(x - 3*y <= 5);    // (7)
    cs.insert(x - y + z <= 5);  // (8)
    cs.insert(x + y + z <= 5);  // (9)
    Octagonal_Shape<T> oct(cs);

Constructor & Destructor Documentation

template<typename T >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( dimension_type  num_dimensions = 0,
Degenerate_Element  kind = UNIVERSE 
) [inline, explicit]

Builds an universe or empty OS of the specified space dimension.

Parameters:
num_dimensions The number of dimensions of the vector space enclosing the OS;
kind Specifies whether the universe or the empty OS has to be built.
template<typename T >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const Octagonal_Shape< T > &  x,
Complexity_Class  complexity = ANY_COMPLEXITY 
) [inline]

Ordinary copy constructor.

The complexity argument is ignored.

template<typename T >
template<typename U >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const Octagonal_Shape< U > &  y,
Complexity_Class  complexity = ANY_COMPLEXITY 
) [inline, explicit]

Builds a conservative, upward approximation of y.

The complexity argument is ignored.

template<typename T >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const Constraint_System cs  )  [inline, explicit]

Builds an OS from the system of constraints cs.

The OS inherits the space dimension of cs.

Parameters:
cs A system of octagonal constraints.
Exceptions:
std::invalid_argument Thrown if cs contains a constraint which is not optimally supported by the Octagonal shape domain.
template<typename T >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const Congruence_System cgs  )  [inline, explicit]

Builds an OS from a system of congruences.

The OS inherits the space dimension of cgs

Parameters:
cgs A system of congruences.
Exceptions:
std::invalid_argument Thrown if cgs contains a congruence which is not optimally supported by the Octagonal shape domain.
template<typename T >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const Generator_System gs  )  [explicit]

Builds an OS from the system of generators gs.

Builds the smallest OS containing the polyhedron defined by gs. The OS 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 T >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const Polyhedron ph,
Complexity_Class  complexity = ANY_COMPLEXITY 
) [explicit]

Builds an OS from the polyhedron ph.

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

template<typename T >
template<typename Interval >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const Box< Interval > &  box,
Complexity_Class  complexity = ANY_COMPLEXITY 
) [inline, explicit]

Builds an OS out of a box.

The OS inherits the space dimension of the box. The built OS is the most precise OS that includes the box.

Parameters:
box The box representing the OS to be built.
complexity This argument is ignored as the algorithm used has polynomial complexity.
Exceptions:
std::length_error Thrown if the space dimension of box exceeds the maximum allowed space dimension.
template<typename T >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const Grid grid,
Complexity_Class  complexity = ANY_COMPLEXITY 
) [inline, explicit]

Builds an OS that approximates a grid.

The OS inherits the space dimension of the grid. The built OS is the most precise OS that includes the grid.

Parameters:
grid The grid used to build the OS.
complexity This argument is ignored as the algorithm used has polynomial complexity.
Exceptions:
std::length_error Thrown if the space dimension of grid exceeds the maximum allowed space dimension.
template<typename T >
template<typename U >
Parma_Polyhedra_Library::Octagonal_Shape< T >::Octagonal_Shape ( const BD_Shape< U > &  bd,
Complexity_Class  complexity = ANY_COMPLEXITY 
) [inline, explicit]

Builds an OS from a BD shape.

The OS inherits the space dimension of the BD shape. The built OS is the most precise OS that includes the BD shape.

Parameters:
bd The BD shape used to build the OS.
complexity This argument is ignored as the algorithm used has polynomial complexity.
Exceptions:
std::length_error Thrown if the space dimension of bd exceeds the maximum allowed space dimension.

Member Function Documentation

template<typename T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::contains ( const Octagonal_Shape< T > &  y  )  const

Returns true if and only if *this contains y.

Exceptions:
std::invalid_argument Thrown if *this and y are dimension-incompatible.
template<typename T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::strictly_contains ( const Octagonal_Shape< T > &  y  )  const [inline]

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

Exceptions:
std::invalid_argument Thrown if *this and y are dimension-incompatible.
template<typename T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::is_disjoint_from ( const Octagonal_Shape< T > &  y  )  const

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

Exceptions:
std::invalid_argument Thrown if x and y are topology-incompatible or dimension-incompatible.
template<typename T >
Poly_Con_Relation Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
Poly_Con_Relation Parma_Polyhedra_Library::Octagonal_Shape< T >::relation_with ( const Congruence cg  )  const

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

Exceptions:
std::invalid_argument Thrown if *this and cg are dimension-incompatible.
template<typename T >
Poly_Gen_Relation Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::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 $0$; 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 $1$;
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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::add_constraint ( const Constraint c  ) 

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 OS domain.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::add_constraints ( const Constraint_System cs  )  [inline]

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

Parameters:
cs The constraints that will 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 OS domain.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::add_recycled_constraints ( Constraint_System cs  )  [inline]

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

Parameters:
cs The constraint system to be added to *this. The constraints in cs 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 OS 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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::add_congruence ( const Congruence cg  ) 

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 OS domain.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 OS domain.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< 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 OS 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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::refine_with_constraint ( const Constraint c  )  [inline]

Uses a copy of constraint c to refine the system of octagonal constraints defining *this.

Parameters:
c The constraint. If it is not a octagonal constraint, it will be ignored.
Exceptions:
std::invalid_argument Thrown if *this and constraint c are dimension-incompatible.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::refine_with_congruence ( const Congruence cg  )  [inline]

Uses a copy of congruence cg to refine the system of octagonal constraints of *this.

Parameters:
cg The congruence. If it is not a octagonal equality, it will be ignored.
Exceptions:
std::invalid_argument Thrown if *this and congruence cg are dimension-incompatible.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::refine_with_constraints ( const Constraint_System cs  )  [inline]

Uses a copy of the constraints in cs to refine the system of octagonal constraints defining *this.

Parameters:
cs The constraint system to be used. Constraints that are not octagonal are ignored.
Exceptions:
std::invalid_argument Thrown if *this and cs are dimension-incompatible.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::refine_with_congruences ( const Congruence_System cgs  ) 

Uses a copy of the congruences in cgs to refine the system of octagonal constraints defining *this.

Parameters:
cgs The congruence system to be used. Congruences that are not octagonal equalities are ignored.
Exceptions:
std::invalid_argument Thrown if *this and cgs are dimension-incompatible.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::unconstrain ( Variable  var  ) 

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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::intersection_assign ( const Octagonal_Shape< T > &  y  ) 

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

Exceptions:
std::invalid_argument Thrown if *this and y are dimension-incompatible.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::upper_bound_assign ( const Octagonal_Shape< T > &  y  ) 

Assigns to *this the smallest OS that contains the convex union of *this and y.

Exceptions:
std::invalid_argument Thrown if *this and y are dimension-incompatible.
template<typename T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::upper_bound_assign_if_exact ( const Octagonal_Shape< T > &  y  ) 

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.

Implementation is based on Theorem 6.3 of [BHZ09b].

template<typename T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::integer_upper_bound_assign_if_exact ( const Octagonal_Shape< T > &  y  ) 

If the integer 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.
Note:
This operator is only available when the class template parameter T is bound to an integer datatype.
The integer upper bound of two rational OS is the smallest rational OS containing all the integral points in the two arguments. In general, the result is not an upper bound for the two input arguments, as it may cut away non-integral portions of the two rational shapes.

Implementation is based on Theorem 6.8 of [BHZ09b].

template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::difference_assign ( const Octagonal_Shape< T > &  y  ) 

Assigns to *this the smallest octagon containing the set difference of *this and y.

Exceptions:
std::invalid_argument Thrown if *this and y are dimension-incompatible.
template<typename T >
bool Parma_Polyhedra_Library::Octagonal_Shape< T >::simplify_using_context_assign ( const Octagonal_Shape< T > &  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 topology-incompatible or dimension-incompatible.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 into 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.
Exceptions:
std::invalid_argument Thrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a dimension of *this.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 into 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.
Exceptions:
std::invalid_argument Thrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a dimension of *this.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 transfer function $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym.

Parameters:
var The left hand side variable of the generalized affine transfer function.
relsym The relation symbol.
expr The numerator of the right hand side affine expression.
denominator The denominator of the right hand side affine expression.
Exceptions:
std::invalid_argument Thrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a dimension of *this or if relsym is a strict relation symbol.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 transfer function $\mathrm{lhs}' \relsym \mathrm{rhs}$, 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 or if relsym is a strict relation symbol.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 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 transfer function.
relsym The relation symbol.
expr The numerator of the right hand side affine expression.
denominator The denominator of the right hand side affine expression.
Exceptions:
std::invalid_argument Thrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a dimension of *this or if relsym is a strict relation symbol.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 or if relsym is a strict relation symbol.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::time_elapse_assign ( const Octagonal_Shape< T > &  y  )  [inline]

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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::wrap_assign ( const Variables_Set vars,
Bounded_Integer_Type_Width  w,
Bounded_Integer_Type_Representation  r,
Bounded_Integer_Type_Overflow  o,
const Constraint_System pcs = 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.
pcs Possibly null pointer to a constraint system whose variables are contained in vars. If *pcs depends on variables not in vars, the behavior is undefined. 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 *pcs.
complexity_threshold A precision parameter of the wrapping operator: higher values result in possibly improved precision.
wrap_individually true if the dimensions should be wrapped individually (something that results in much greater efficiency to the detriment of precision).
Exceptions:
std::invalid_argument Thrown if *pcs is dimension-incompatible with vars, or if *this is dimension-incompatible vars or with *pcs.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::CC76_extrapolation_assign ( const Octagonal_Shape< T > &  y,
unsigned *  tp = 0 
) [inline]

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

Parameters:
y An OS 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 T >
template<typename Iterator >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::CC76_extrapolation_assign ( const Octagonal_Shape< T > &  y,
Iterator  first,
Iterator  last,
unsigned *  tp = 0 
)

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

Parameters:
y An OS that must be contained in *this.
first An iterator that points to the first stop_point.
last An iterator that points to the last stop_point.
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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::BHMZ05_widening_assign ( const Octagonal_Shape< T > &  y,
unsigned *  tp = 0 
)

Assigns to *this the result of computing the BHMZ05-widening between *this and y.

Parameters:
y An OS 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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::limited_BHMZ05_extrapolation_assign ( const Octagonal_Shape< T > &  y,
const Constraint_System cs,
unsigned *  tp = 0 
)

Improves the result of the BHMZ05-widening computation by also enforcing those constraints in cs that are satisfied by all the points of *this.

Parameters:
y An OS that must be contained in *this.
cs The system of constraints used to improve the widened OS.
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 there is in cs a strict inequality.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::CC76_narrowing_assign ( const Octagonal_Shape< T > &  y  ) 

Restores from y the constraints of *this, lost by CC76-extrapolation applications.

Parameters:
y An OS that must contain *this.
Exceptions:
std::invalid_argument Thrown if *this and y are dimension-incompatible.
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::limited_CC76_extrapolation_assign ( const Octagonal_Shape< T > &  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 An OS that must be contained in *this.
cs The system of constraints used to improve the widened OS.
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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::add_space_dimensions_and_embed ( dimension_type  m  ) 

Adds m new dimensions and embeds the old OS 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 OS, which is characterized by a system of constraints in which the variables running through the new dimensions are not constrained. For instance, when starting from the OS $\cO \sseq \Rset^2$ and adding a third dimension, the result will be the OS

\[ \bigl\{\, (x, y, z)^\transpose \in \Rset^3 \bigm| (x, y)^\transpose \in \cO \,\bigr\}. \]

template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::add_space_dimensions_and_project ( dimension_type  m  ) 

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

Parameters:
m The number of dimensions to add.

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

\[ \bigl\{\, (x, y, 0)^\transpose \in \Rset^3 \bigm| (x, y)^\transpose \in \cO \,\bigr\}. \]

template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::concatenate_assign ( const Octagonal_Shape< T > &  y  ) 

Assigns to *this the concatenation of *this and y, taken in this order.

Exceptions:
std::length_error Thrown if the concatenation would cause the vector space to exceed dimension max_space_dimension().
template<typename T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::remove_space_dimensions ( const Variables_Set vars  ) 

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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::remove_higher_space_dimensions ( dimension_type  new_dimension  )  [inline]

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 T >
template<typename Partial_Function >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 codomain (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 codomain 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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::expand_space_dimension ( Variable  var,
dimension_type  m 
)

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 T >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
template<typename Interval_Info >
void Parma_Polyhedra_Library::Octagonal_Shape< T >::refine_fp_interval_abstract_store ( Box< Interval< T, Interval_Info > > &  store  )  const

Refines store with the constraints defining *this.

Parameters:
store The interval floating point abstract store to refine.
template<typename T >
int32_t Parma_Polyhedra_Library::Octagonal_Shape< T >::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 T >
bool operator== ( const Octagonal_Shape< T > &  x,
const Octagonal_Shape< T > &  y 
) [friend]

Returns true if and only if x and y are the same octagon.

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

template<typename T >
std::ostream & operator<< ( std::ostream &  s,
const Octagonal_Shape< T > &  x 
) [related]

Output operator.

Writes a textual representation of oct on s: false is written if oct is an empty polyhedron; true is written if oct is a universe polyhedron; a system of constraints defining oct is written otherwise, all constraints separated by ", ".

template<typename T >
bool operator!= ( const Octagonal_Shape< T > &  x,
const Octagonal_Shape< T > &  y 
) [related]

Returns true if and only if x and y are different shapes.

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

template<typename To , typename T >
bool rectilinear_distance_assign ( Checked_Number< To, Extended_Number_Policy > &  r,
const Octagonal_Shape< T > &  x,
const Octagonal_Shape< T > &  y,
Rounding_Dir  dir 
) [related]

Computes the rectilinear (or Manhattan) distance between x and y.

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>.

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 T >
bool rectilinear_distance_assign ( Checked_Number< To, Extended_Number_Policy > &  r,
const Octagonal_Shape< T > &  x,
const Octagonal_Shape< T > &  y,
Rounding_Dir  dir,
Temp &  tmp0,
Temp &  tmp1,
Temp &  tmp2 
) [related]

Computes the rectilinear (or Manhattan) distance between x and y.

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 T >
bool euclidean_distance_assign ( Checked_Number< To, Extended_Number_Policy > &  r,
const Octagonal_Shape< T > &  x,
const Octagonal_Shape< T > &  y,
Rounding_Dir  dir 
) [related]

Computes the euclidean distance between x and y.

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>.

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 T >
bool euclidean_distance_assign ( Checked_Number< To, Extended_Number_Policy > &  r,
const Octagonal_Shape< T > &  x,
const Octagonal_Shape< T > &  y,
Rounding_Dir  dir,
Temp &  tmp0,
Temp &  tmp1,
Temp &  tmp2 
) [related]

Computes the euclidean distance between x and y.

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 T >
bool l_infinity_distance_assign ( Checked_Number< To, Extended_Number_Policy > &  r,
const Octagonal_Shape< T > &  x,
const Octagonal_Shape< T > &  y,
Rounding_Dir  dir 
) [related]

Computes the $L_\infty$ distance between x and y.

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>.

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 T >
bool l_infinity_distance_assign ( Checked_Number< To, Extended_Number_Policy > &  r,
const Octagonal_Shape< T > &  x,
const Octagonal_Shape< T > &  y,
Rounding_Dir  dir,
Temp &  tmp0,
Temp &  tmp1,
Temp &  tmp2 
) [related]

Computes the $L_\infty$ distance between x and y.

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 T >
void swap ( Parma_Polyhedra_Library::Octagonal_Shape< T > &  x,
Parma_Polyhedra_Library::Octagonal_Shape< T > &  y 
) [related]

Specializes std::swap.


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