Public Types | |
| typedef T | base_type |
| The numeric base type upon which bounded differences are built. | |
| typedef N | coefficient_type |
| The (extended) numeric type of the inhomogeneous term of the inequalities defining a BDS. | |
Public Member Functions | |
Constructors, Assignment, Swap and Destructor | |
| BD_Shape (dimension_type num_dimensions=0, Degenerate_Element kind=UNIVERSE) | |
| Builds a universe or empty BDS of the specified space dimension. | |
| BD_Shape (const BD_Shape &y) | |
| Ordinary copy-constructor. | |
| template<typename U> | |
| BD_Shape (const BD_Shape< U > &y) | |
Builds a conservative, upward approximation of y. | |
| BD_Shape (const Constraint_System &cs) | |
Builds a BDS from the system of constraints cs. | |
| BD_Shape (const Generator_System &gs) | |
Builds a BDS from the system of generators gs. | |
| BD_Shape (const Polyhedron &ph, Complexity_Class complexity=ANY_COMPLEXITY) | |
Builds a BDS from the polyhedron ph. | |
| BD_Shape & | operator= (const BD_Shape &y) |
The assignment operator (*this and y can be dimension-incompatible). | |
| void | swap (BD_Shape &y) |
Swaps *this with y (*this and y can be dimension-incompatible). | |
| ~BD_Shape () | |
| Destructor. | |
Member Functions that Do Not Modify the BD_Shape | |
| 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. | |
| Constraint_System | constraints () const |
Returns a system of constraints defining *this. | |
| Constraint_System | minimized_constraints () const |
Returns a minimized system of constraints defining *this. | |
| bool | contains (const BD_Shape &y) const |
Returns true if and only if *this contains y. | |
| bool | strictly_contains (const BD_Shape &y) const |
Returns true if and only if *this strictly contains y. | |
| Poly_Con_Relation | relation_with (const Constraint &c) const |
Returns the relations holding between *this and the constraint c. | |
| 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 BDS. | |
| bool | is_universe () const |
Returns true if and only if *this is a universe BDS. | |
| bool | OK () const |
Returns true if and only if *this satisfies all its invariants. | |
Space-Dimension Preserving Member Functions that May Modify the BD_Shape | |
| void | add_constraint (const Constraint &c) |
Adds a copy of constraint c to the system of bounded differences defining *this. | |
| bool | add_constraint_and_minimize (const Constraint &c) |
Adds a copy of constraint c to the system of bounded differences defining *this. | |
| void | add_constraints (const Constraint_System &cs) |
Adds the constraints in cs to the system of bounded differences defining *this. | |
| bool | add_constraints_and_minimize (const Constraint_System &cs) |
Adds the constraints in cs to the system of bounded differences defining *this. | |
| void | intersection_assign (const BD_Shape &y) |
Assigns to *this the intersection of *this and y. | |
| bool | intersection_assign_and_minimize (const BD_Shape &y) |
Assigns to *this the intersection of *this and y. | |
| void | bds_hull_assign (const BD_Shape &y) |
Assigns to *this the smallest BDS containing the convex union of *this and y. | |
| bool | bds_hull_assign_and_minimize (const BD_Shape &y) |
Assigns to *this the smallest BDS containing the convex union of *this and y. | |
| void | upper_bound_assign (const BD_Shape &y) |
| Same as bds_hull_assign. | |
| bool | bds_hull_assign_if_exact (const BD_Shape &y) |
If the bds-hull of *this and y is exact, it is assigned to *this and true is returned, otherwise false is returned. | |
| bool | upper_bound_assign_if_exact (const BD_Shape &y) |
| Same as bds_hull_assign_if_exact. | |
| void | bds_difference_assign (const BD_Shape &y) |
Assigns to *this the poly-difference of *this and y. | |
| void | difference_assign (const BD_Shape &y) |
| Same as bds_difference_assign. | |
| 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 affine relation , where 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 affine relation , where is the relation symbol encoded by relsym. | |
| 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 , where is the relation symbol encoded by relsym. | |
| void | time_elapse_assign (const BD_Shape &y) |
Assigns to *this the result of computing the time-elapse between *this and y. | |
| void | CC76_extrapolation_assign (const BD_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 BD_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 BD_Shape &y, unsigned *tp=0) |
Assigns to *this the result of computing the BHMZ05-widening of *this and y. | |
| void | limited_BHMZ05_extrapolation_assign (const BD_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 BD_Shape &y) |
Assigns to *this the result of restoring in y the constraints of *this that were lost by CC76-extrapolation applications. | |
| void | limited_CC76_extrapolation_assign (const BD_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. | |
| void | H79_widening_assign (const BD_Shape &y, unsigned *tp=0) |
Assigns to *this the result of computing the H79-widening between *this and y. | |
| void | limited_H79_extrapolation_assign (const BD_Shape &y, const Constraint_System &cs, unsigned *tp=0) |
Improves the result of the H79-widening 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 BDS into the new space. | |
| void | add_space_dimensions_and_project (dimension_type m) |
Adds m new dimensions to the BDS and does not embed it in the new vector space. | |
| void | concatenate_assign (const BD_Shape &y) |
Seeing a BDS 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. | |
| void | remove_space_dimensions (const Variables_Set &to_be_removed) |
| 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 PartialFunction> | |
| void | map_space_dimensions (const PartialFunction &pfunc) |
| Remaps the dimensions of the vector space according to a partial function. | |
Static Public Member Functions | |
| static dimension_type | max_space_dimension () |
| Returns the maximum space dimension that a BDS can handle. | |
Friends | |
| std::ostream & | operator<< (std::ostream &s, const BD_Shape< T > &c) |
| Output operator. | |
Related Functions | |
| (Note that these are not member functions.) | |
| bool | operator== (const BD_Shape< T > &x, const BD_Shape< T > &y) |
Returns true if and only if x and y are the same BDS. | |
| bool | operator!= (const BD_Shape< T > &x, const BD_Shape< T > &y) |
Returns true if and only if x and y aren't the same BDS. | |
| bool | rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const BD_Shape< T > &x, const BD_Shape< T > &y, const Rounding_Dir dir) |
Computes the rectilinear (or Manhattan) distance between x and y. | |
| bool | rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const BD_Shape< T > &x, const BD_Shape< T > &y, const Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2) |
Computes the rectilinear (or Manhattan) distance between x and y. | |
| bool | euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const BD_Shape< T > &x, const BD_Shape< T > &y, const Rounding_Dir dir) |
Computes the euclidean distance between x and y. | |
| bool | euclidean_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const BD_Shape< T > &x, const BD_Shape< T > &y, const Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2) |
Computes the euclidean distance between x and y. | |
| bool | l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const BD_Shape< T > &x, const BD_Shape< T > &y, const Rounding_Dir dir) |
Computes the distance between x and y. | |
| bool | l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const BD_Shape< T > &x, const BD_Shape< T > &y, const Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2) |
Computes the distance between x and y. | |
| void | swap (Parma_Polyhedra_Library::BD_Shape< T > &x, Parma_Polyhedra_Library::BD_Shape< T > &y) |
Specializes std::swap. | |
The class template BD_Shape<T> allows for the efficient representation of a restricted kind of topologically closed convex polyhedra called bounded difference shapes (BDSs, for short). The name comes from the fact that the closed affine half-spaces that characterize the polyhedron can be expressed by constraints of the form
or
, where the inhomogeneous term
is a rational number.
Based on the class template type parameter T, a family of extended numbers is built and used to approximate the inhomogeneous term of bounded differences. These extended numbers provide a representation for the value
, as well as rounding-aware implementations for several arithmetic functions. The value of the type parameter T may be one of the following:
int32_t or int64_t);float or double);mpz_class or mpq_class).The user interface for BDSs is meant to be as similar as possible to the one developed for the polyhedron class C_Polyhedron. At the interface level, bounded differences are specified using objects of type Constraint: such a constraint is a bounded difference if it is of the form
where
and
,
,
are integer coefficients such that
, or
, or
. The user is warned that the above Constraint object will be mapped into a correct approximation that, depending on the expressive power of the chosen template argument T, may loose some precision. In particular, constraint objects that do not encode a bounded difference will be simply (and safely) ignored.
For instance, a Constraint object encoding
will be approximated by:
, if T is a (bounded or unbounded) integer type;
, if T is the unbounded rational type mpq_class;
, where
, if T is a floating point type (having no exact representation for
).
On the other hand, a Constraint object encoding
will be safely ignored in all of the above cases.
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);
, given as a system of constraints: Constraint_System cs;
cs.insert(x >= 0);
cs.insert(x <= 1);
cs.insert(y >= 0);
cs.insert(y <= 1);
cs.insert(z >= 0);
cs.insert(z <= 1);
BD_Shape<T> bd(cs);
Constraint_System cs;
cs.insert(x >= 0);
cs.insert(x <= 1);
cs.insert(y >= 0);
cs.insert(y <= 1);
cs.insert(z >= 0);
cs.insert(z <= 1);
cs.insert(x + y <= 0); // 7
cs.insert(x - z + x >= 0); // 8
cs.insert(3*z - y <= 1); // 9
BD_Shape<T> bd(cs);
| Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | dimension_type | num_dimensions = 0, |
|
| Degenerate_Element | kind = UNIVERSE | |||
| ) | [inline, explicit] |
Builds a universe or empty BDS of the specified space dimension.
| num_dimensions | The number of dimensions of the vector space enclosing the BDS; | |
| kind | Specifies whether the universe or the empty BDS has to be built. |
| Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Constraint_System & | cs | ) | [inline] |
Builds a BDS from the system of constraints cs.
The BDS inherits the space dimension of cs.
| cs | A system of constraints: constraints that are not bounded differences are ignored (even though they may have contributed to the space dimension). |
| std::invalid_argument | Thrown if the system of constraints cs contains strict inequalities. |
| Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Generator_System & | gs | ) |
Builds a BDS from the system of generators gs.
Builds the smallest BDS containing the polyhedron defined by gs. The BDS inherits the space dimension of gs.
| std::invalid_argument | Thrown if the system of generators is not empty but has no points. |
| Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Polyhedron & | ph, | |
| Complexity_Class | complexity = ANY_COMPLEXITY | |||
| ) |
Builds a BDS from the polyhedron ph.
Builds a BDS containing ph using algorithms whose complexity does not exceed the one specified by complexity. If complexity is ANY_COMPLEXITY, then the BDS built is the smallest one containing ph.
| bool Parma_Polyhedra_Library::BD_Shape< T >::contains | ( | const BD_Shape< T > & | y | ) | const |
Returns true if and only if *this contains y.
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| bool Parma_Polyhedra_Library::BD_Shape< T >::strictly_contains | ( | const BD_Shape< T > & | y | ) | const [inline] |
Returns true if and only if *this strictly contains y.
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| Poly_Con_Relation Parma_Polyhedra_Library::BD_Shape< T >::relation_with | ( | const Constraint & | c | ) | const |
Returns the relations holding between *this and the constraint c.
| std::invalid_argument | Thrown if *this and constraint c are dimension-incompatible or if c is a strict inequality or if c is not a bounded difference constraint. |
| Poly_Gen_Relation Parma_Polyhedra_Library::BD_Shape< T >::relation_with | ( | const Generator & | g | ) | const |
Returns the relations holding between *this and the generator g.
| std::invalid_argument | Thrown if *this and generator g are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::add_constraint | ( | const Constraint & | c | ) |
Adds a copy of constraint c to the system of bounded differences defining *this.
| c | The constraint to be added. If it is not a bounded difference, it will be simply ignored. |
| std::invalid_argument | Thrown if *this and constraint c are dimension-incompatible, or if c is a strict inequality. |
| bool Parma_Polyhedra_Library::BD_Shape< T >::add_constraint_and_minimize | ( | const Constraint & | c | ) | [inline] |
Adds a copy of constraint c to the system of bounded differences defining *this.
false if and only if the result is empty.| c | The constraint to be added. If it is not a bounded difference, it will be simply ignored. |
| std::invalid_argument | Thrown if *this and constraint c are dimension-incompatible, or if c is a strict inequality. |
| void Parma_Polyhedra_Library::BD_Shape< T >::add_constraints | ( | const Constraint_System & | cs | ) | [inline] |
Adds the constraints in cs to the system of bounded differences defining *this.
| cs | The constraints that will be added. Constraints that are not bounded differences will be simply ignored. |
| std::invalid_argument | Thrown if *this and cs are dimension-incompatible, or if cs contains a strict inequality. |
| bool Parma_Polyhedra_Library::BD_Shape< T >::add_constraints_and_minimize | ( | const Constraint_System & | cs | ) | [inline] |
Adds the constraints in cs to the system of bounded differences defining *this.
false if and only if the result is empty.| cs | The constraints that will be added. Constraints that are not bounded differences will be simply ignored. |
| std::invalid_argument | Thrown if *this and cs are dimension-incompatible, or if cs contains a strict inequality. |
| void Parma_Polyhedra_Library::BD_Shape< T >::intersection_assign | ( | const BD_Shape< T > & | y | ) |
Assigns to *this the intersection of *this and y.
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| bool Parma_Polyhedra_Library::BD_Shape< T >::intersection_assign_and_minimize | ( | const BD_Shape< T > & | y | ) | [inline] |
Assigns to *this the intersection of *this and y.
false if and only if the result is empty.| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::bds_hull_assign | ( | const BD_Shape< T > & | y | ) |
Assigns to *this the smallest BDS containing the convex union of *this and y.
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| bool Parma_Polyhedra_Library::BD_Shape< T >::bds_hull_assign_and_minimize | ( | const BD_Shape< T > & | y | ) | [inline] |
Assigns to *this the smallest BDS containing the convex union of *this and y.
false if and only if the result is empty.| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| bool Parma_Polyhedra_Library::BD_Shape< T >::bds_hull_assign_if_exact | ( | const BD_Shape< T > & | y | ) | [inline] |
If the bds-hull of *this and y is exact, it is assigned to *this and true is returned, otherwise false is returned.
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::bds_difference_assign | ( | const BD_Shape< T > & | y | ) |
Assigns to *this the poly-difference of *this and y.
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_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.
| var | The variable to which the affine expression is assigned. | |
| expr | The numerator of the affine expression. | |
| denominator | The denominator of the affine expression. |
| 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. |
| void Parma_Polyhedra_Library::BD_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.
| var | The variable to which the affine expression is substituted. | |
| expr | The numerator of the affine expression. | |
| denominator | The denominator of the affine expression. |
| 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. |
| void Parma_Polyhedra_Library::BD_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 affine relation
, where
is the relation symbol encoded by relsym.
| 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. |
| 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. |
| void Parma_Polyhedra_Library::BD_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 affine relation
, where
is the relation symbol encoded by relsym.
| lhs | The left hand side affine expression. | |
| relsym | The relation symbol. | |
| rhs | The right hand side affine expression. |
| std::invalid_argument | Thrown if *this is dimension-incompatible with lhs or rhs or if relsym is a strict relation symbol. |
| void Parma_Polyhedra_Library::BD_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
, where
is the relation symbol encoded by relsym.
| 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. |
| 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. |
| void Parma_Polyhedra_Library::BD_Shape< T >::time_elapse_assign | ( | const BD_Shape< T > & | y | ) | [inline] |
Assigns to *this the result of computing the time-elapse between *this and y.
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::CC76_extrapolation_assign | ( | const BD_Shape< T > & | y, | |
| unsigned * | tp = 0 | |||
| ) | [inline] |
Assigns to *this the result of computing the CC76-extrapolation between *this and y.
| y | A BDS 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). |
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::CC76_extrapolation_assign | ( | const BD_Shape< T > & | y, | |
| Iterator | first, | |||
| Iterator | last, | |||
| unsigned * | tp = 0 | |||
| ) |
Assigns to *this the result of computing the CC76-extrapolation between *this and y.
| y | A BDS that must be contained in *this. | |
| first | An iterator referencing the first stop-point. | |
| last | An iterator referencing one past 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). |
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::BHMZ05_widening_assign | ( | const BD_Shape< T > & | y, | |
| unsigned * | tp = 0 | |||
| ) |
Assigns to *this the result of computing the BHMZ05-widening of *this and y.
| y | A BDS 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). |
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::limited_BHMZ05_extrapolation_assign | ( | const BD_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.
| y | A BDS that must be contained in *this. | |
| cs | The system of constraints used to improve the widened BDS. | |
| 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). |
| std::invalid_argument | Thrown if *this, y and cs are dimension-incompatible or if cs contains a strict inequality. |
| void Parma_Polyhedra_Library::BD_Shape< T >::CC76_narrowing_assign | ( | const BD_Shape< T > & | y | ) |
Assigns to *this the result of restoring in y the constraints of *this that were lost by CC76-extrapolation applications.
| y | A BDS that must contain *this. |
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
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 descreasing iteration sequence). Hence, the call x.CC76_narrowing_assign(y) will assign to x the result of the computation
. | void Parma_Polyhedra_Library::BD_Shape< T >::limited_CC76_extrapolation_assign | ( | const BD_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.
| y | A BDS that must be contained in *this. | |
| cs | The system of constraints used to improve the widened BDS. | |
| 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). |
| std::invalid_argument | Thrown if *this, y and cs are dimension-incompatible or if cs contains a strict inequality. |
| void Parma_Polyhedra_Library::BD_Shape< T >::H79_widening_assign | ( | const BD_Shape< T > & | y, | |
| unsigned * | tp = 0 | |||
| ) | [inline] |
Assigns to *this the result of computing the H79-widening between *this and y.
| y | A BDS 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). |
| std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::limited_H79_extrapolation_assign | ( | const BD_Shape< T > & | y, | |
| const Constraint_System & | cs, | |||
| unsigned * | tp = 0 | |||
| ) | [inline] |
Improves the result of the H79-widening computation by also enforcing those constraints in cs that are satisfied by all the points of *this.
| y | A BDS that must be contained in *this. | |
| cs | The system of constraints used to improve the widened BDS. | |
| 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). |
| std::invalid_argument | Thrown if *this, y and cs are dimension-incompatible. |
| void Parma_Polyhedra_Library::BD_Shape< T >::add_space_dimensions_and_embed | ( | dimension_type | m | ) |
Adds m new dimensions and embeds the old BDS into the new space.
| m | The number of dimensions to add. |
and adding a third dimension, the result will be the BDS
| void Parma_Polyhedra_Library::BD_Shape< T >::add_space_dimensions_and_project | ( | dimension_type | m | ) |
Adds m new dimensions to the BDS and does not embed it in the new vector space.
| m | The number of dimensions to add. |
and adding a third dimension, the result will be the BDS
| void Parma_Polyhedra_Library::BD_Shape< T >::concatenate_assign | ( | const BD_Shape< T > & | y | ) |
Seeing a BDS 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
and
be the BDSs corresponding, on entry, to *this and y, respectively. Upon successful completion, *this will represent the BDS
such that
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.
| void Parma_Polyhedra_Library::BD_Shape< T >::remove_space_dimensions | ( | const Variables_Set & | to_be_removed | ) |
| void Parma_Polyhedra_Library::BD_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.
| std::invalid_argument | Thrown if new_dimension is greater than the space dimension of *this. |
| void Parma_Polyhedra_Library::BD_Shape< T >::map_space_dimensions | ( | const PartialFunction & | pfunc | ) |
Remaps the dimensions of the vector space according to a partial function.
| pfunc | The partial function specifying the destiny of each dimension. |
bool has_empty_codomain() const
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
bool maps(dimension_type i, dimension_type& j) const
be the represented function and
be the value of i. If
is defined in
, then
is assigned to j and true is returned. If
is undefined in
, 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.
| std::ostream & operator<< | ( | std::ostream & | s, | |
| const BD_Shape< T > & | c | |||
| ) | [friend] |
Output operator.
Writes a textual representation of bds on s: false is written if bds is an empty polyhedron; true is written if bds is the universe polyhedron; a system of constraints defining bds is written otherwise, all constraints separated by ", ".
Returns true if and only if x and y are the same BDS.
Note that x and y may be dimension-incompatible shapes: in this case, the value false is returned.
Returns true if and only if x and y aren't the same BDS.
Note that x and y may be dimension-incompatible shapes: in this case, the value true is returned.
| bool rectilinear_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
| const BD_Shape< T > & | x, | |||
| const BD_Shape< T > & | y, | |||
| const 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>.
| bool rectilinear_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
| const BD_Shape< T > & | x, | |||
| const BD_Shape< T > & | y, | |||
| const 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.
| bool euclidean_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
| const BD_Shape< T > & | x, | |||
| const BD_Shape< T > & | y, | |||
| const 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>.
| bool euclidean_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
| const BD_Shape< T > & | x, | |||
| const BD_Shape< T > & | y, | |||
| const 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.
| bool l_infinity_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
| const BD_Shape< T > & | x, | |||
| const BD_Shape< T > & | y, | |||
| const Rounding_Dir | dir | |||
| ) | [related] |
Computes the
distance between x and y.
If the
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>.
| bool l_infinity_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
| const BD_Shape< T > & | x, | |||
| const BD_Shape< T > & | y, | |||
| const Rounding_Dir | dir, | |||
| Temp & | tmp0, | |||
| Temp & | tmp1, | |||
| Temp & | tmp2 | |||
| ) | [related] |
Computes the
distance between x and y.
If the
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.
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