#include <ppl.hh>
Public Types | |
typedef T | coefficient_type_base |
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 | |
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 | |
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, Complexity_Class complexity=ANY_COMPLEXITY) | |
Ordinary copy-constructor. | |
template<typename U > | |
BD_Shape (const BD_Shape< U > &y, Complexity_Class complexity=ANY_COMPLEXITY) | |
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 Congruence_System &cgs) | |
Builds a BDS from a system of congruences. | |
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 . | |
template<typename Interval > | |
BD_Shape (const Box< Interval > &box, Complexity_Class complexity=ANY_COMPLEXITY) | |
Builds a BDS out of a box. | |
BD_Shape (const Grid &grid, Complexity_Class complexity=ANY_COMPLEXITY) | |
Builds a BDS out of a grid. | |
template<typename U > | |
BD_Shape (const Octagonal_Shape< U > &os, Complexity_Class complexity=ANY_COMPLEXITY) | |
Builds a BDS from an octagonal shape. | |
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 ![]() *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 . | |
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 | 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 | 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 . | |
bool | is_disjoint_from (const BD_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 BDS. | |
bool | is_universe () const |
Returns true if and only if *this is a universe BDS. | |
bool | is_discrete () const |
Returns true if and only if *this is discrete. | |
bool | is_topologically_closed () const |
Returns true if and only if *this is a topologically closed subset of the vector space. | |
bool | is_bounded () const |
Returns true if and only if *this is a bounded BDS. | |
bool | contains_integer_point () const |
Returns true if and only if *this contains at least one integer point. | |
bool | constrains (Variable var) const |
Returns true if and only if var is constrained in *this . | |
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_congruence (const Congruence &cg) |
Adds a copy of congruence cg to the system of congruences of *this . | |
bool | add_congruence_and_minimize (const Congruence &cg) |
Adds a copy of congruence cg to the system of congruences of *this , minimizing the result. | |
void | add_constraints (const Constraint_System &cs) |
Adds the constraints in cs to the system of bounded differences defining *this . | |
void | add_recycled_constraints (Constraint_System &cs) |
Adds the constraints in cs to the system of constraints of *this . | |
bool | add_constraints_and_minimize (const Constraint_System &cs) |
Adds the constraints in cs to the system of bounded differences defining *this . | |
bool | add_recycled_constraints_and_minimize (Constraint_System &cs) |
Adds the constraints in cs to the system of constraints of *this , minimizing the result. | |
void | add_congruences (const Congruence_System &cgs) |
Adds to *this constraints equivalent to the congruences in cgs . | |
bool | add_congruences_and_minimize (const Congruence_System &cgs) |
Behaves as add_congruences(const Congruence_System&), but minimizes the resulting BD shape, returning false if and only if the result is empty. | |
void | add_recycled_congruences (Congruence_System &cgs) |
Adds to *this constraints equivalent to the congruences in cgs . | |
bool | add_recycled_congruences_and_minimize (Congruence_System &cgs) |
Behaves as add_recycled_congruences , but minimizes the resulting BD shape, returning false if and only if the result is empty. | |
void | refine_with_constraint (const Constraint &c) |
Uses a copy of constraint c to refine the system of bounded differences defining *this . | |
void | refine_with_congruence (const Congruence &cg) |
Uses a copy of congruence cg to refine the system of bounded differences of *this . | |
void | refine_with_constraints (const Constraint_System &cs) |
Uses a copy of the constraints in cs to refine the system of bounded differences defining *this . | |
void | refine_with_congruences (const Congruence_System &cgs) |
Uses a copy of the congruences in cgs to refine the system of bounded differences 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 &to_be_unconstrained) |
Computes the cylindrification of *this with respect to the set of space dimensions to_be_unconstrained , assigning the result to *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 | upper_bound_assign (const BD_Shape &y) |
Assigns to *this the smallest BDS containing the union of *this and y . | |
bool | upper_bound_assign_and_minimize (const BD_Shape &y) |
Assigns to *this the smallest BDS containing the convex union of *this and y . | |
bool | upper_bound_assign_if_exact (const BD_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. | |
void | difference_assign (const BD_Shape &y) |
Assigns to *this the smallest BD shape containing the set difference of *this and y . | |
bool | simplify_using_context_assign (const BD_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 affine relation ![]() ![]() 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 ![]() ![]() 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 ![]() ![]() 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 affine relation ![]() ![]() 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 ![]() | |
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 ![]() | |
void | time_elapse_assign (const BD_Shape &y) |
Assigns to *this the result of computing the time-elapse between *this and y . | |
void | topological_closure_assign () |
Assigns to *this its topological closure. | |
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 | widening_assign (const BD_Shape &y, unsigned *tp=0) |
Same as H79_widening_assign(y, tp). | |
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) |
Assigns to *this the concatenation of *this and y , taken in this order. | |
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 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 &to_be_folded, Variable var) |
Folds the space dimensions in to_be_folded into var . | |
Static Public Member Functions | |
static dimension_type | max_space_dimension () |
Returns the maximum space dimension that a BDS 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 BD_Shape< T > &x, const BD_Shape< T > &y) |
Returns true if and only if x and y are the same BDS. | |
Related Functions | |
(Note that these are not member functions.) | |
template<typename T > | |
std::ostream & | operator<< (std::ostream &s, const BD_Shape< T > &bds) |
Output operator. | |
template<typename T > | |
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. | |
template<typename To , typename T > | |
bool | rectilinear_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const BD_Shape< T > &x, const BD_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 BD_Shape< T > &x, const BD_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 BD_Shape< T > &x, const BD_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 BD_Shape< T > &x, const BD_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 BD_Shape< T > &x, const BD_Shape< T > &y, Rounding_Dir dir) |
Computes the ![]() x and y . | |
template<typename Temp , typename To , typename T > | |
bool | l_infinity_distance_assign (Checked_Number< To, Extended_Number_Policy > &r, const BD_Shape< T > &x, const BD_Shape< T > &y, Rounding_Dir dir, Temp &tmp0, Temp &tmp1, Temp &tmp2) |
Computes the ![]() x and y . | |
template<typename T > | |
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.
The domain of BD shapes 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 a bounded difference if it has the form
where and
,
,
are integer coefficients such that
, or
, or
. The user is warned that the above bounded difference 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 bounded differences.
For instance, a Constraint object encoding will be approximated by:
T
is a (bounded or unbounded) integer type;T
is the unbounded rational type mpq_class
;T
is a floating point type (having no exact representation for
On the other hand, depending from the context, a Constraint object encoding 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);
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 BD_Shape< T > & | y, | |
Complexity_Class | complexity = ANY_COMPLEXITY | |||
) | [inline] |
Ordinary copy-constructor.
The complexity argument is ignored.
Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const BD_Shape< U > & | y, | |
Complexity_Class | complexity = ANY_COMPLEXITY | |||
) | [inline, explicit] |
Builds a conservative, upward approximation of y
.
The complexity argument is ignored.
Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Constraint_System & | cs | ) | [inline, explicit] |
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 cs contains a constraint which is not optimally supported by the BD shape domain. |
Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Congruence_System & | cgs | ) | [inline, explicit] |
Builds a BDS from a system of congruences.
The BDS inherits the space dimension of cgs
cgs | A system of congruences: some elements may be safely ignored. |
Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Generator_System & | gs | ) | [inline, explicit] |
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 | |||
) | [inline, explicit] |
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
.
Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Box< Interval > & | box, | |
Complexity_Class | complexity = ANY_COMPLEXITY | |||
) | [inline, explicit] |
Builds a BDS out of a box.
The BDS inherits the space dimension of the box. The built BDS is the most precise BDS that includes the box.
box | The box representing the BDS to be built. | |
complexity | This argument is ignored as the algorithm used has polynomial complexity. |
std::length_error | Thrown if the space dimension of box exceeds the maximum allowed space dimension. |
Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Grid & | grid, | |
Complexity_Class | complexity = ANY_COMPLEXITY | |||
) | [inline, explicit] |
Builds a BDS out of a grid.
The BDS inherits the space dimension of the grid. The built BDS is the most precise BDS that includes the grid.
grid | The grid used to build the BDS. | |
complexity | This argument is ignored as the algorithm used has polynomial complexity. |
std::length_error | Thrown if the space dimension of grid exceeds the maximum allowed space dimension. |
Parma_Polyhedra_Library::BD_Shape< T >::BD_Shape | ( | const Octagonal_Shape< U > & | os, | |
Complexity_Class | complexity = ANY_COMPLEXITY | |||
) | [inline, explicit] |
Builds a BDS from an octagonal shape.
The BDS inherits the space dimension of the octagonal shape. The built BDS is the most precise BDS that includes the octagonal shape.
os | The octagonal shape used to build the BDS. | |
complexity | This argument is ignored as the algorithm used has polynomial complexity. |
std::length_error | Thrown if the space dimension of os exceeds the maximum allowed space dimension. |
bool Parma_Polyhedra_Library::BD_Shape< T >::bounds_from_above | ( | const Linear_Expression & | expr | ) | const [inline] |
Returns true
if and only if expr
is bounded from above in *this
.
std::invalid_argument | Thrown if expr and *this are dimension-incompatible. |
bool Parma_Polyhedra_Library::BD_Shape< T >::bounds_from_below | ( | const Linear_Expression & | expr | ) | const [inline] |
Returns true
if and only if expr
is bounded from below in *this
.
std::invalid_argument | Thrown if expr and *this are dimension-incompatible. |
bool Parma_Polyhedra_Library::BD_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.
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. |
std::invalid_argument | Thrown if expr and *this are dimension-incompatible. |
*this
is empty or expr
is not bounded from above, false
is returned and sup_n
, sup_d
and maximum
are left untouched.
bool Parma_Polyhedra_Library::BD_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.
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. |
std::invalid_argument | Thrown if expr and *this are dimension-incompatible. |
*this
is empty or expr
is not bounded from above, false
is returned and sup_n
, sup_d
, maximum
and g
are left untouched.
bool Parma_Polyhedra_Library::BD_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.
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. |
std::invalid_argument | Thrown if expr and *this are dimension-incompatible. |
*this
is empty or expr
is not bounded from below, false
is returned and inf_n
, inf_d
and minimum
are left untouched.
bool Parma_Polyhedra_Library::BD_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.
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. |
std::invalid_argument | Thrown if expr and *this are dimension-incompatible. |
*this
is empty or expr
is not bounded from below, false
is returned and inf_n
, inf_d
, minimum
and g
are left untouched.
bool Parma_Polyhedra_Library::BD_Shape< T >::contains | ( | const BD_Shape< T > & | y | ) | const [inline] |
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. |
bool Parma_Polyhedra_Library::BD_Shape< T >::is_disjoint_from | ( | const BD_Shape< T > & | y | ) | const [inline] |
Returns true
if and only if *this
and y
are disjoint.
std::invalid_argument | Thrown if x and y are topology-incompatible or dimension-incompatible. |
Poly_Con_Relation Parma_Polyhedra_Library::BD_Shape< T >::relation_with | ( | const Constraint & | c | ) | const [inline] |
Returns the relations holding between *this
and the constraint c
.
std::invalid_argument | Thrown if *this and constraint c are dimension-incompatible. |
Poly_Con_Relation Parma_Polyhedra_Library::BD_Shape< T >::relation_with | ( | const Congruence & | cg | ) | const [inline] |
Returns the relations holding between *this
and the congruence cg
.
std::invalid_argument | Thrown if *this and congruence cg are dimension-incompatible. |
Poly_Gen_Relation Parma_Polyhedra_Library::BD_Shape< T >::relation_with | ( | const Generator & | g | ) | const [inline] |
Returns the relations holding between *this
and the generator g
.
std::invalid_argument | Thrown if *this and generator g are dimension-incompatible. |
bool Parma_Polyhedra_Library::BD_Shape< T >::constrains | ( | Variable | var | ) | const [inline] |
Returns true
if and only if var
is constrained in *this
.
std::invalid_argument | Thrown if var is not a space dimension of *this . |
void Parma_Polyhedra_Library::BD_Shape< T >::add_constraint | ( | const Constraint & | c | ) | [inline] |
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 c is not optimally supported by the BD shape domain. |
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 c is not optimally supported by the BD shape domain. |
void Parma_Polyhedra_Library::BD_Shape< T >::add_congruence | ( | const Congruence & | cg | ) | [inline] |
Adds a copy of congruence cg
to the system of congruences of *this
.
cg | The congruence to be added. |
std::invalid_argument | Thrown if *this and congruence cg are dimension-incompatible, or cg is not optimally supported by the BD shape domain. |
bool Parma_Polyhedra_Library::BD_Shape< T >::add_congruence_and_minimize | ( | const Congruence & | cg | ) | [inline] |
Adds a copy of congruence cg
to the system of congruences of *this
, minimizing the result.
cg | The congruence to be added. |
false
if and only if the result is empty.std::invalid_argument | Thrown if *this and congruence cg are dimension-incompatible, or cg is not optimally supported by the BD shape domain. |
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 cs contains a constraint which is not optimally supported by the BD shape domain. |
void Parma_Polyhedra_Library::BD_Shape< T >::add_recycled_constraints | ( | Constraint_System & | cs | ) | [inline] |
Adds the constraints in cs
to the system of constraints of *this
.
cs | The constraint system to be added to *this . The constraints in cs may be recycled. |
std::invalid_argument | Thrown if *this and cs are dimension-incompatible, or cs contains a constraint which is not optimally supported by the BD shape domain. |
cs
upon successful or exceptional return is that it can be safely destroyed. 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. |
std::invalid_argument | Thrown if *this and cs are dimension-incompatible, or cs contains a constraint which is not optimally supported by the BD shape domain. |
bool Parma_Polyhedra_Library::BD_Shape< T >::add_recycled_constraints_and_minimize | ( | Constraint_System & | cs | ) | [inline] |
Adds the constraints in cs
to the system of constraints of *this
, minimizing the result.
false
if and only if the result is empty.cs | The constraint system to be added to *this . The constraints in cs may be recycled. |
std::invalid_argument | Thrown if *this and cs are dimension-incompatible, or cs contains a constraint which is not optimally supported by the BD shape domain. |
cs
upon successful or exceptional return is that it can be safely destroyed.void Parma_Polyhedra_Library::BD_Shape< T >::add_congruences | ( | const Congruence_System & | cgs | ) | [inline] |
Adds to *this
constraints equivalent to the congruences in cgs
.
cgs | Contains the congruences that will be added to the system of constraints of *this . |
std::invalid_argument | Thrown if *this and cgs are dimension-incompatible, or cgs contains a congruence which is not optimally supported by the BD shape domain. |
bool Parma_Polyhedra_Library::BD_Shape< T >::add_congruences_and_minimize | ( | const Congruence_System & | cgs | ) | [inline] |
Behaves as add_congruences(const Congruence_System&), but minimizes the resulting BD shape, returning false
if and only if the result is empty.
void Parma_Polyhedra_Library::BD_Shape< T >::add_recycled_congruences | ( | Congruence_System & | cgs | ) | [inline] |
Adds to *this
constraints equivalent to the congruences in cgs
.
cgs | Contains the congruences that will be added to the system of constraints of *this . Its elements may be recycled. |
std::invalid_argument | Thrown if *this and cgs are dimension-incompatible, or cgs contains a congruence which is not optimally supported by the BD shape domain. |
cgs
upon successful or exceptional return is that it can be safely destroyed. bool Parma_Polyhedra_Library::BD_Shape< T >::add_recycled_congruences_and_minimize | ( | Congruence_System & | cgs | ) | [inline] |
Behaves as add_recycled_congruences
, but minimizes the resulting BD shape, returning false
if and only if the result is empty.
void Parma_Polyhedra_Library::BD_Shape< T >::refine_with_constraint | ( | const Constraint & | c | ) | [inline] |
Uses a copy of constraint c
to refine the system of bounded differences defining *this
.
c | The constraint. If it is not a bounded difference, it will be ignored. |
std::invalid_argument | Thrown if *this and constraint c are dimension-incompatible. |
void Parma_Polyhedra_Library::BD_Shape< T >::refine_with_congruence | ( | const Congruence & | cg | ) | [inline] |
Uses a copy of congruence cg
to refine the system of bounded differences of *this
.
cg | The congruence. If it is not a bounded difference equality, it will be ignored. |
std::invalid_argument | Thrown if *this and congruence cg are dimension-incompatible. |
void Parma_Polyhedra_Library::BD_Shape< T >::refine_with_constraints | ( | const Constraint_System & | cs | ) | [inline] |
Uses a copy of the constraints in cs
to refine the system of bounded differences defining *this
.
cs | The constraint system to be used. Constraints that are not bounded differences are ignored. |
std::invalid_argument | Thrown if *this and cs are dimension-incompatible. |
void Parma_Polyhedra_Library::BD_Shape< T >::refine_with_congruences | ( | const Congruence_System & | cgs | ) | [inline] |
Uses a copy of the congruences in cgs
to refine the system of bounded differences defining *this
.
cgs | The congruence system to be used. Congruences that are not bounded difference equalities are ignored. |
std::invalid_argument | Thrown if *this and cgs are dimension-incompatible. |
void Parma_Polyhedra_Library::BD_Shape< T >::unconstrain | ( | Variable | var | ) | [inline] |
Computes the cylindrification of *this
with respect to space dimension var
, assigning the result to *this
.
var | The space dimension that will be unconstrained. |
std::invalid_argument | Thrown if var is not a space dimension of *this . |
void Parma_Polyhedra_Library::BD_Shape< T >::unconstrain | ( | const Variables_Set & | to_be_unconstrained | ) | [inline] |
Computes the cylindrification of *this
with respect to the set of space dimensions to_be_unconstrained
, assigning the result to *this
.
to_be_unconstrained | The set of space dimension that will be unconstrained. |
std::invalid_argument | Thrown if *this is dimension-incompatible with one of the Variable objects contained in to_be_removed . |
void Parma_Polyhedra_Library::BD_Shape< T >::intersection_assign | ( | const BD_Shape< T > & | y | ) | [inline] |
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 >::upper_bound_assign | ( | const BD_Shape< T > & | y | ) | [inline] |
Assigns to *this
the smallest BDS containing the union of *this
and y
.
std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
bool Parma_Polyhedra_Library::BD_Shape< T >::upper_bound_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 >::upper_bound_assign_if_exact | ( | const BD_Shape< T > & | y | ) | [inline] |
If the upper bound of *this
and y
is exact, it is assigned to *this
and true
is returned, otherwise false
is returned.
std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
void Parma_Polyhedra_Library::BD_Shape< T >::difference_assign | ( | const BD_Shape< T > & | y | ) | [inline] |
Assigns to *this
the smallest BD shape containing the set difference of *this
and y
.
std::invalid_argument | Thrown if *this and y are dimension-incompatible. |
bool Parma_Polyhedra_Library::BD_Shape< T >::simplify_using_context_assign | ( | const BD_Shape< T > & | y | ) | [inline] |
Assigns to *this
a meet-preserving simplification of *this
with respect to y
. If false
is returned, then the intersection is empty.
std::invalid_argument | Thrown if *this and y are topology-incompatible or dimension-incompatible. |
void Parma_Polyhedra_Library::BD_Shape< T >::affine_image | ( | Variable | var, | |
const Linear_Expression & | expr, | |||
Coefficient_traits::const_reference | denominator = Coefficient_one() | |||
) | [inline] |
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() | |||
) | [inline] |
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() | |||
) | [inline] |
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 | |||
) | [inline] |
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() | |||
) | [inline] |
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 >::generalized_affine_preimage | ( | const Linear_Expression & | lhs, | |
Relation_Symbol | relsym, | |||
const Linear_Expression & | rhs | |||
) | [inline] |
Assigns to *this
the preimage 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 >::bounded_affine_image | ( | Variable | var, | |
const Linear_Expression & | lb_expr, | |||
const Linear_Expression & | ub_expr, | |||
Coefficient_traits::const_reference | denominator = Coefficient_one() | |||
) | [inline] |
Assigns to *this
the image of *this
with respect to the bounded affine relation .
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). |
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 . |
void Parma_Polyhedra_Library::BD_Shape< T >::bounded_affine_preimage | ( | Variable | var, | |
const Linear_Expression & | lb_expr, | |||
const Linear_Expression & | ub_expr, | |||
Coefficient_traits::const_reference | denominator = Coefficient_one() | |||
) | [inline] |
Assigns to *this
the preimage of *this
with respect to the bounded affine relation .
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). |
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 . |
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 | |||
) | [inline] |
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 | |||
) | [inline] |
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 | |||
) | [inline] |
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 | ) | [inline] |
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 decreasing 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 | |||
) | [inline] |
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 | ) | [inline] |
Adds m
new dimensions and embeds the old BDS into the new space.
m | The number of dimensions to add. |
void Parma_Polyhedra_Library::BD_Shape< T >::add_space_dimensions_and_project | ( | dimension_type | m | ) | [inline] |
Adds m
new dimensions to the BDS and does not embed it in the new vector space.
m | The number of dimensions to add. |
void Parma_Polyhedra_Library::BD_Shape< T >::concatenate_assign | ( | const BD_Shape< T > & | y | ) | [inline] |
Assigns to *this
the concatenation of *this
and y
, taken in this order.
std::length_error | Thrown if the concatenation would cause the vector space to exceed dimension max_space_dimension() . |
void Parma_Polyhedra_Library::BD_Shape< T >::remove_space_dimensions | ( | const Variables_Set & | to_be_removed | ) | [inline] |
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 Partial_Function & | pfunc | ) | [inline] |
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
i
. If j
and true
is returned. If 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.
void Parma_Polyhedra_Library::BD_Shape< T >::expand_space_dimension | ( | Variable | var, | |
dimension_type | m | |||
) | [inline] |
Creates m
copies of the space dimension corresponding to var
.
var | The variable corresponding to the space dimension to be replicated; | |
m | The number of replicas to be created. |
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() . |
*this
has space dimension var
has space dimension m
new space dimensions void Parma_Polyhedra_Library::BD_Shape< T >::fold_space_dimensions | ( | const Variables_Set & | to_be_folded, | |
Variable | var | |||
) | [inline] |
Folds the space dimensions in to_be_folded
into var
.
to_be_folded | The set of Variable objects corresponding to the space dimensions to be folded; | |
var | The variable corresponding to the space dimension that is the destination of the folding operation. |
std::invalid_argument | Thrown if *this is dimension-incompatible with var or with one of the Variable objects contained in to_be_folded . Also thrown if var is contained in to_be_folded . |
*this
has space dimension var
has space dimension to_be_folded
is a set of variables whose maximum space dimension is also less than or equal to var
is not a member of to_be_folded
, then the space dimensions corresponding to variables in to_be_folded
are folded into the int32_t Parma_Polyhedra_Library::BD_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()
.
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.
std::ostream & operator<< | ( | std::ostream & | s, | |
const BD_Shape< T > & | c | |||
) | [related] |
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 ", ".
bool operator!= | ( | const BD_Shape< T > & | x, | |
const BD_Shape< T > & | y | |||
) | [related] |
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, | |||
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>.
bool rectilinear_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
const BD_Shape< T > & | x, | |||
const BD_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
.
bool euclidean_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
const BD_Shape< T > & | x, | |||
const BD_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>.
bool euclidean_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
const BD_Shape< T > & | x, | |||
const BD_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
.
bool l_infinity_distance_assign | ( | Checked_Number< To, Extended_Number_Policy > & | r, | |
const BD_Shape< T > & | x, | |||
const BD_Shape< T > & | y, | |||
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>.
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<Temp, 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, | |||
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
.
void swap | ( | Parma_Polyhedra_Library::BD_Shape< T > & | x, | |
Parma_Polyhedra_Library::BD_Shape< T > & | y | |||
) | [related] |
Specializes std::swap
.