#include <Powerset.defs.hh>
Public Types | |
typedef Sequence::size_type | size_type |
typedef Sequence::value_type | value_type |
typedef omega_iterator | iterator |
Alias for a read-only bidirectional iterator on the disjuncts of a Powerset element. | |
typedef omega_const_iterator | const_iterator |
A bidirectional const_iterator on the disjuncts of a Powerset element. | |
typedef std::reverse_iterator < iterator > | reverse_iterator |
The reverse iterator type built from Powerset::iterator. | |
typedef std::reverse_iterator < const_iterator > | const_reverse_iterator |
The reverse iterator type built from Powerset::const_iterator. | |
Public Member Functions | |
Constructors and Destructor | |
Powerset () | |
Default constructor: builds the bottom of the powerset constraint system (i.e., the empty powerset). | |
Powerset (const Powerset &y) | |
Copy constructor. | |
Powerset (const D &d) | |
If d is not bottom, builds a powerset containing only d . Builds the empty powerset otherwise. | |
~Powerset () | |
Destructor. | |
Member Functions that Do Not Modify the Powerset Element | |
bool | definitely_entails (const Powerset &y) const |
Returns true if *this definitely entails y . Returns false if *this may not entail y (i.e., if *this does not entail y or if entailment could not be decided). | |
bool | is_top () const |
Returns true if and only if *this is the top element of the powerset constraint system (i.e., it represents the universe). | |
bool | is_bottom () const |
Returns true if and only if *this is the bottom element of the powerset constraint system (i.e., it represents the empty set). | |
memory_size_type | total_memory_in_bytes () const |
Returns a lower bound to the total size in bytes of the memory occupied by *this . | |
memory_size_type | external_memory_in_bytes () const |
Returns a lower bound to the size in bytes of the memory managed by *this . | |
bool | OK (bool disallow_bottom=false) const |
Checks if all the invariants are satisfied. | |
Member Functions for the Direct Manipulation of Disjuncts | |
void | omega_reduce () const |
Drops from the sequence of disjuncts in *this all the non-maximal elements so that *this is non-redundant. | |
size_type | size () const |
Returns the number of disjuncts. | |
bool | empty () const |
Returns true if and only if there are no disjuncts. | |
iterator | begin () |
Returns an iterator pointing to the first disjunct, if *this is not empty; otherwise, returns the past-the-end iterator. | |
iterator | end () |
Returns the past-the-end iterator. | |
const_iterator | begin () const |
Returns a const_iterator pointing to the first disjunct, if *this is not empty; otherwise, returns the past-the-end const_iterator. | |
const_iterator | end () const |
Returns the past-the-end const_iterator. | |
reverse_iterator | rbegin () |
Returns a reverse_iterator pointing to the last disjunct, if *this is not empty; otherwise, returns the before-the-start reverse_iterator. | |
reverse_iterator | rend () |
Returns the before-the-start reverse_iterator. | |
const_reverse_iterator | rbegin () const |
Returns a const_reverse_iterator pointing to the last disjunct, if *this is not empty; otherwise, returns the before-the-start const_reverse_iterator. | |
const_reverse_iterator | rend () const |
Returns the before-the-start const_reverse_iterator. | |
void | add_disjunct (const D &d) |
Adds to *this the disjunct d . | |
iterator | drop_disjunct (iterator position) |
Drops the disjunct in *this pointed to by position , returning an iterator to the disjunct following position . | |
void | drop_disjuncts (iterator first, iterator last) |
Drops all the disjuncts from first to last (excluded). | |
void | clear () |
Drops all the disjuncts, making *this an empty powerset. | |
Member Functions that May Modify the Powerset Element | |
Powerset & | operator= (const Powerset &y) |
The assignment operator. | |
void | swap (Powerset &y) |
Swaps *this with y . | |
void | least_upper_bound_assign (const Powerset &y) |
Assigns to *this the least upper bound of *this and y . | |
void | upper_bound_assign (const Powerset &y) |
Assigns to *this an upper bound of *this and y . | |
void | meet_assign (const Powerset &y) |
Assigns to *this the meet of *this and y . | |
void | collapse () |
If *this is not empty (i.e., it is not the bottom element), it is reduced to a singleton obtained by computing an upper-bound of all the disjuncts. | |
Protected Types | |
typedef std::list< D > | Sequence |
A powerset is implemented as a sequence of elements. | |
typedef Sequence::iterator | Sequence_iterator |
Alias for the low-level iterator on the disjuncts. | |
typedef Sequence::const_iterator | Sequence_const_iterator |
Alias for the low-level const_iterator on the disjuncts. | |
Protected Member Functions | |
bool | is_omega_reduced () const |
Returns true if and only if *this does not contain non-maximal elements. | |
void | collapse (unsigned max_disjuncts) |
Upon return, *this will contain at most max_disjuncts elements; the set of disjuncts in positions greater than or equal to max_disjuncts , will be replaced at that position by their upper-bound. | |
iterator | add_non_bottom_disjunct (const D &d, iterator first, iterator last) |
Adds to *this the disjunct d , assuming d is not the bottom element and ensuring partial Omega-reduction. | |
void | add_non_bottom_disjunct (const D &d) |
Adds to *this the disjunct d , assuming d is not the bottom element. | |
template<typename Binary_Operator_Assign> | |
void | pairwise_apply_assign (const Powerset &y, Binary_Operator_Assign op_assign) |
Assigns to *this the result of applying op_assign pairwise to the elements in *this and y . | |
Protected Attributes | |
Sequence | sequence |
The sequence container holding powerset's elements. | |
bool | reduced |
If true , *this is Omega-reduced. | |
Private Member Functions | |
bool | check_omega_reduced () const |
Does the hard work of checking whether *this contains non-maximal elements and returns true if and only if it does not. | |
void | collapse (Sequence_iterator sink) |
Replaces the disjunct *sink by an upper bound of itself and all the disjuncts following it. | |
Related Functions | |
(Note that these are not member functions.) | |
template<typename D> | |
bool | operator== (const Powerset< D > &x, const Powerset< D > &y) |
Returns true if and only if x and y are equivalent. | |
template<typename D> | |
bool | operator!= (const Powerset< D > &x, const Powerset< D > &y) |
Returns true if and only if x and y are not equivalent. | |
template<typename D> | |
std::ostream & | operator<< (std::ostream &s, const Powerset< D > &x) |
Output operator. | |
template<typename D> | |
void | swap (Parma_Polyhedra_Library::Powerset< D > &x, Parma_Polyhedra_Library::Powerset< D > &y) |
Specializes std::swap . | |
Classes | |
class | omega_const_iterator |
A const_iterator on the disjuncts of a Powerset element. More... | |
class | omega_iterator |
An iterator on the disjuncts of a Powerset element. More... |
This class offers a generic implementation of a powerset domain as defined in Section The Powerset Construction.
Besides invoking the available methods on the disjuncts of a Powerset, this class also provides bidirectional iterators that allow for a direct inspection of these disjuncts. For a consistent handling of Omega-reduction, all the iterators are read-only, meaning that the disjuncts cannot be overwritten. Rather, by using the class iterator
, it is possible to drop one or more disjuncts (possibly so as to later add back modified versions). As an example of iterator usage, the following templatic function drops from powerset ps
all the disjuncts that would have become redundant by the addition of an external element d
.
template <typename D> void drop_subsumed(Powerset<D>& ps, const D& d) { for (typename Powerset<D>::iterator i = ps.begin(), ps_end = ps.end(), i != ps_end; ) if (i->definitely_entails(d)) i = ps.drop_disjunct(i); else ++i; }
The template class D must provide the following methods.
Returns a lower bound on the total size in bytes of the memory occupied by the instance of D.bool is_top() const
true
if and only if the instance of D is the top element of the domain. bool is_bottom() const
true
if and only if the instance of D is the bottom element of the domain. bool definitely_entails(const D& y) const
true
if the instance of D definitely entails y
. Returns false
if the instance may not entail y
(i.e., if the instance does not entail y
or if entailment could not be decided). void upper_bound_assign(const D& y)
y
. void meet_assign(const D& y)
y
. bool OK() const
true
if the instance of D is in a consistent state, else returns false
.The following operators on the template class D must be defined.
operator<<(std::ostream& s, const D& x)
s
. operator==(const D& x, const D& y)
true
if and only if x
and y
are equivalent D's. operator!=(const D& x, const D& y)
true
if and only if x
and y
are different D's.
Definition at line 144 of file Powerset.defs.hh.
typedef std::list<D> Parma_Polyhedra_Library::Powerset< D >::Sequence [protected] |
A powerset is implemented as a sequence of elements.
The particular sequence employed must support efficient deletion in any position and efficient back insertion.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 218 of file Powerset.defs.hh.
typedef Sequence::iterator Parma_Polyhedra_Library::Powerset< D >::Sequence_iterator [protected] |
Alias for the low-level iterator on the disjuncts.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 221 of file Powerset.defs.hh.
typedef Sequence::const_iterator Parma_Polyhedra_Library::Powerset< D >::Sequence_const_iterator [protected] |
Alias for the low-level const_iterator on the disjuncts.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 224 of file Powerset.defs.hh.
typedef Sequence::size_type Parma_Polyhedra_Library::Powerset< D >::size_type |
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 234 of file Powerset.defs.hh.
typedef Sequence::value_type Parma_Polyhedra_Library::Powerset< D >::value_type |
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 235 of file Powerset.defs.hh.
typedef omega_iterator Parma_Polyhedra_Library::Powerset< D >::iterator |
Alias for a read-only bidirectional iterator on the disjuncts of a Powerset element.
By using this iterator type, the disjuncts cannot be overwritten, but they can be removed using methods drop_disjunct(iterator position)
and drop_disjuncts(iterator first, iterator last)
, while still ensuring a correct handling of Omega-reduction.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 238 of file Powerset.defs.hh.
typedef omega_const_iterator Parma_Polyhedra_Library::Powerset< D >::const_iterator |
A bidirectional const_iterator on the disjuncts of a Powerset element.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 252 of file Powerset.defs.hh.
typedef std::reverse_iterator<iterator> Parma_Polyhedra_Library::Powerset< D >::reverse_iterator |
The reverse iterator type built from Powerset::iterator.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 255 of file Powerset.defs.hh.
typedef std::reverse_iterator<const_iterator> Parma_Polyhedra_Library::Powerset< D >::const_reverse_iterator |
The reverse iterator type built from Powerset::const_iterator.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 257 of file Powerset.defs.hh.
Parma_Polyhedra_Library::Powerset< D >::Powerset | ( | ) | [inline] |
Default constructor: builds the bottom of the powerset constraint system (i.e., the empty powerset).
Definition at line 302 of file Powerset.inlines.hh.
Parma_Polyhedra_Library::Powerset< D >::Powerset | ( | const Powerset< D > & | y | ) | [inline] |
Parma_Polyhedra_Library::Powerset< D >::Powerset | ( | const D & | d | ) | [inline, explicit] |
If d
is not bottom, builds a powerset containing only d
. Builds the empty powerset otherwise.
Definition at line 308 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::OK(), and Parma_Polyhedra_Library::Powerset< D >::sequence.
00309 : sequence(), reduced(true) { 00310 if (!d.is_bottom()) 00311 sequence.push_back(d); 00312 assert(OK()); 00313 }
Parma_Polyhedra_Library::Powerset< D >::~Powerset | ( | ) | [inline] |
bool Parma_Polyhedra_Library::Powerset< D >::definitely_entails | ( | const Powerset< D > & | y | ) | const [inline] |
Returns true
if *this
definitely entails y
. Returns false
if *this
may not entail y
(i.e., if *this
does not entail y
or if entailment could not be decided).
Definition at line 170 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin(), and Parma_Polyhedra_Library::Powerset< D >::end().
00170 { 00171 const Powerset<D>& x = *this; 00172 bool found = true; 00173 for (const_iterator xi = x.begin(), 00174 x_end = x.end(); found && xi != x_end; ++xi) { 00175 found = false; 00176 for (const_iterator yi = y.begin(), 00177 y_end = y.end(); !found && yi != y_end; ++yi) 00178 found = (*xi).definitely_entails(*yi); 00179 } 00180 return found; 00181 }
bool Parma_Polyhedra_Library::Powerset< D >::is_top | ( | ) | const [inline] |
Returns true
if and only if *this
is the top element of the powerset constraint system (i.e., it represents the universe).
Definition at line 343 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Powerset< D >::end(), and Parma_Polyhedra_Library::Powerset< D >::omega_reduce().
00343 { 00344 // Must perform omega-reduction for correctness. 00345 omega_reduce(); 00346 const_iterator xi = begin(); 00347 const_iterator x_end = end(); 00348 return xi != x_end && xi->is_top() && ++xi == x_end; 00349 }
bool Parma_Polyhedra_Library::Powerset< D >::is_bottom | ( | ) | const [inline] |
Returns true
if and only if *this
is the bottom element of the powerset constraint system (i.e., it represents the empty set).
Definition at line 353 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::empty(), and Parma_Polyhedra_Library::Powerset< D >::omega_reduce().
Referenced by Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::map_space_dimensions().
00353 { 00354 // Must perform omega-reduction for correctness. 00355 omega_reduce(); 00356 return empty(); 00357 }
memory_size_type Parma_Polyhedra_Library::Powerset< D >::total_memory_in_bytes | ( | ) | const [inline] |
Returns a lower bound to the total size in bytes of the memory occupied by *this
.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 380 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::external_memory_in_bytes().
00380 { 00381 return sizeof(*this) + external_memory_in_bytes(); 00382 }
memory_size_type Parma_Polyhedra_Library::Powerset< D >::external_memory_in_bytes | ( | ) | const [inline] |
Returns a lower bound to the size in bytes of the memory managed by *this
.
Reimplemented in Parma_Polyhedra_Library::Polyhedra_Powerset< PH >.
Definition at line 264 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin(), and Parma_Polyhedra_Library::Powerset< D >::end().
Referenced by Parma_Polyhedra_Library::Powerset< D >::total_memory_in_bytes().
00264 { 00265 memory_size_type bytes = 0; 00266 for (const_iterator xi = begin(), x_end = end(); xi != x_end; ++xi) { 00267 bytes += xi->total_memory_in_bytes(); 00268 // We assume there is at least a forward and a backward link, and 00269 // that the pointers implementing them are at least the size of 00270 // pointers to `D'. 00271 bytes += 2*sizeof(D*); 00272 } 00273 return bytes; 00274 }
bool Parma_Polyhedra_Library::Powerset< D >::OK | ( | bool | disallow_bottom = false |
) | const [inline] |
Checks if all the invariants are satisfied.
Definition at line 278 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Powerset< D >::check_omega_reduced(), Parma_Polyhedra_Library::Powerset< D >::end(), and Parma_Polyhedra_Library::Powerset< D >::reduced.
Referenced by Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Powerset< D >::omega_reduce(), and Parma_Polyhedra_Library::Powerset< D >::Powerset().
00278 { 00279 for (const_iterator xi = begin(), x_end = end(); xi != x_end; ++xi) { 00280 if (!xi->OK()) 00281 return false; 00282 if (disallow_bottom && xi->is_bottom()) { 00283 #ifndef NDEBUG 00284 std::cerr << "Bottom element in powerset!" 00285 << std::endl; 00286 #endif 00287 return false; 00288 } 00289 } 00290 if (reduced && !check_omega_reduced()) { 00291 #ifndef NDEBUG 00292 std::cerr << "Powerset claims to be reduced, but it is not!" 00293 << std::endl; 00294 #endif 00295 return false; 00296 } 00297 return true; 00298 }
void Parma_Polyhedra_Library::Powerset< D >::omega_reduce | ( | ) | const [inline] |
Drops from the sequence of disjuncts in *this
all the non-maximal elements so that *this
is non-redundant.
This method is declared const
because, even though Omega-reduction may change the syntactic representation of *this
, its semantics will be unchanged.
Definition at line 58 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::abandon_expensive_computations, Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Powerset< D >::drop_disjunct(), Parma_Polyhedra_Library::Powerset< D >::end(), Parma_Polyhedra_Library::Powerset< D >::OK(), and Parma_Polyhedra_Library::Powerset< D >::reduced.
Referenced by Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::concatenate_assign(), Parma_Polyhedra_Library::Powerset< D >::is_bottom(), Parma_Polyhedra_Library::Powerset< D >::is_top(), Parma_Polyhedra_Library::Powerset< D >::least_upper_bound_assign(), Parma_Polyhedra_Library::Powerset< D >::operator==(), Parma_Polyhedra_Library::Powerset< D >::pairwise_apply_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::pairwise_reduce(), and Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::poly_difference_assign().
00058 { 00059 if (reduced) 00060 return; 00061 00062 Powerset& x = const_cast<Powerset&>(*this); 00063 // First remove all bottom elements. 00064 for (iterator xi = x.begin(), x_end = x.end(); xi != x_end; ) 00065 if (xi->is_bottom()) 00066 xi = x.drop_disjunct(xi); 00067 else 00068 ++xi; 00069 // Then remove non-maximal elements. 00070 for (iterator xi = x.begin(); xi != x.end(); ) { 00071 const D& xv = *xi; 00072 bool dropping_xi = false; 00073 for (iterator yi = x.begin(); yi != x.end(); ) 00074 if (xi == yi) 00075 ++yi; 00076 else { 00077 const D& yv = *yi; 00078 if (yv.definitely_entails(xv)) 00079 yi = x.drop_disjunct(yi); 00080 else if (xv.definitely_entails(yv)) { 00081 dropping_xi = true; 00082 break; 00083 } 00084 else 00085 ++yi; 00086 } 00087 if (dropping_xi) 00088 xi = x.drop_disjunct(xi); 00089 else 00090 ++xi; 00091 if (abandon_expensive_computations && xi != x.end()) { 00092 // Hurry up! 00093 x.collapse(xi.base); 00094 break; 00095 } 00096 } 00097 reduced = true; 00098 assert(OK()); 00099 }
Powerset< D >::size_type Parma_Polyhedra_Library::Powerset< D >::size | ( | ) | const [inline] |
Returns the number of disjuncts.
Definition at line 251 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::ascii_dump(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BGP99_heuristics_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BHZ03_widening_assign(), Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Powerset< D >::operator==(), and Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::pairwise_reduce().
00251 { 00252 return sequence.size(); 00253 }
bool Parma_Polyhedra_Library::Powerset< D >::empty | ( | ) | const [inline] |
Returns true
if and only if there are no disjuncts.
Definition at line 257 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraint_and_minimize(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraints_and_minimize(), Parma_Polyhedra_Library::Powerset< D >::collapse(), and Parma_Polyhedra_Library::Powerset< D >::is_bottom().
00257 { 00258 return sequence.empty(); 00259 }
Powerset< D >::iterator Parma_Polyhedra_Library::Powerset< D >::begin | ( | ) | [inline] |
Returns an iterator pointing to the first disjunct, if *this
is not empty; otherwise, returns the past-the-end iterator.
Definition at line 203 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::ascii_dump(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BGP99_heuristics_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BHZ03_widening_assign(), Parma_Polyhedra_Library::Powerset< D >::check_omega_reduced(), Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::collect_certificates(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::concatenate_assign(), Parma_Polyhedra_Library::Powerset< D >::definitely_entails(), Parma_Polyhedra_Library::Powerset< D >::external_memory_in_bytes(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::geometrically_covers(), Parma_Polyhedra_Library::Powerset< D >::is_top(), Parma_Polyhedra_Library::Powerset< D >::least_upper_bound_assign(), Parma_Polyhedra_Library::Powerset< D >::OK(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::OK(), Parma_Polyhedra_Library::Powerset< D >::omega_reduce(), Parma_Polyhedra_Library::Powerset< D >::operator==(), Parma_Polyhedra_Library::Powerset< D >::pairwise_apply_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::pairwise_reduce(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::poly_difference_assign(), and Parma_Polyhedra_Library::Powerset< D >::rend().
00203 { 00204 return sequence.begin(); 00205 }
Powerset< D >::iterator Parma_Polyhedra_Library::Powerset< D >::end | ( | ) | [inline] |
Returns the past-the-end iterator.
Definition at line 209 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::ascii_dump(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BGP99_heuristics_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BHZ03_widening_assign(), Parma_Polyhedra_Library::Powerset< D >::check_omega_reduced(), Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::collect_certificates(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::concatenate_assign(), Parma_Polyhedra_Library::Powerset< D >::definitely_entails(), Parma_Polyhedra_Library::Powerset< D >::external_memory_in_bytes(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::geometrically_covers(), Parma_Polyhedra_Library::Powerset< D >::is_top(), Parma_Polyhedra_Library::Powerset< D >::least_upper_bound_assign(), Parma_Polyhedra_Library::Powerset< D >::OK(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::OK(), Parma_Polyhedra_Library::Powerset< D >::omega_reduce(), Parma_Polyhedra_Library::Powerset< D >::operator==(), Parma_Polyhedra_Library::Powerset< D >::pairwise_apply_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::pairwise_reduce(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::poly_difference_assign(), and Parma_Polyhedra_Library::Powerset< D >::rbegin().
00209 { 00210 return sequence.end(); 00211 }
Powerset< D >::const_iterator Parma_Polyhedra_Library::Powerset< D >::begin | ( | ) | const [inline] |
Returns a const_iterator pointing to the first disjunct, if *this
is not empty; otherwise, returns the past-the-end const_iterator.
Definition at line 215 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::sequence.
00215 { 00216 return sequence.begin(); 00217 }
Powerset< D >::const_iterator Parma_Polyhedra_Library::Powerset< D >::end | ( | ) | const [inline] |
Returns the past-the-end const_iterator.
Definition at line 221 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::sequence.
00221 { 00222 return sequence.end(); 00223 }
Powerset< D >::reverse_iterator Parma_Polyhedra_Library::Powerset< D >::rbegin | ( | ) | [inline] |
Returns a reverse_iterator pointing to the last disjunct, if *this
is not empty; otherwise, returns the before-the-start reverse_iterator.
Definition at line 227 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::end().
00227 { 00228 return reverse_iterator(end()); 00229 }
Powerset< D >::reverse_iterator Parma_Polyhedra_Library::Powerset< D >::rend | ( | ) | [inline] |
Returns the before-the-start reverse_iterator.
Definition at line 233 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin().
00233 { 00234 return reverse_iterator(begin()); 00235 }
Powerset< D >::const_reverse_iterator Parma_Polyhedra_Library::Powerset< D >::rbegin | ( | ) | const [inline] |
Returns a const_reverse_iterator pointing to the last disjunct, if *this
is not empty; otherwise, returns the before-the-start const_reverse_iterator.
Definition at line 239 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::end().
00239 { 00240 return const_reverse_iterator(end()); 00241 }
Powerset< D >::const_reverse_iterator Parma_Polyhedra_Library::Powerset< D >::rend | ( | ) | const [inline] |
Returns the before-the-start const_reverse_iterator.
Definition at line 245 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin().
00245 { 00246 return const_reverse_iterator(begin()); 00247 }
void Parma_Polyhedra_Library::Powerset< D >::add_disjunct | ( | const D & | d | ) | [inline] |
Adds to *this
the disjunct d
.
Definition at line 329 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct().
00329 { 00330 if (!d.is_bottom()) 00331 add_non_bottom_disjunct(d); 00332 }
Powerset< D >::iterator Parma_Polyhedra_Library::Powerset< D >::drop_disjunct | ( | iterator | position | ) | [inline] |
Drops the disjunct in *this
pointed to by position
, returning an iterator to the disjunct following position
.
Definition at line 263 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::omega_iterator::base, and Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct(), Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Powerset< D >::omega_reduce(), and Parma_Polyhedra_Library::Powerset< D >::operator==().
00263 { 00264 return sequence.erase(position.base); 00265 }
void Parma_Polyhedra_Library::Powerset< D >::drop_disjuncts | ( | iterator | first, | |
iterator | last | |||
) | [inline] |
Drops all the disjuncts from first
to last
(excluded).
Definition at line 269 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::omega_iterator::base, and Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Powerset< D >::collapse().
00269 { 00270 sequence.erase(first.base, last.base); 00271 }
void Parma_Polyhedra_Library::Powerset< D >::clear | ( | ) | [inline] |
Drops all the disjuncts, making *this
an empty powerset.
Definition at line 275 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::sequence.
00275 { 00276 sequence.clear(); 00277 }
Powerset< D > & Parma_Polyhedra_Library::Powerset< D >::operator= | ( | const Powerset< D > & | y | ) | [inline] |
The assignment operator.
Definition at line 287 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::reduced, and Parma_Polyhedra_Library::Powerset< D >::sequence.
void Parma_Polyhedra_Library::Powerset< D >::swap | ( | Powerset< D > & | y | ) | [inline] |
Swaps *this
with y
.
Definition at line 295 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::reduced, and Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Powerset< D >::swap().
void Parma_Polyhedra_Library::Powerset< D >::least_upper_bound_assign | ( | const Powerset< D > & | y | ) | [inline] |
Assigns to *this
the least upper bound of *this
and y
.
Definition at line 230 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct(), Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Powerset< D >::end(), and Parma_Polyhedra_Library::Powerset< D >::omega_reduce().
Referenced by Parma_Polyhedra_Library::Powerset< D >::upper_bound_assign().
00230 { 00231 // Ensure omega-reduction here, since what follows has quadratic complexity. 00232 omega_reduce(); 00233 y.omega_reduce(); 00234 iterator old_begin = begin(); 00235 iterator old_end = end(); 00236 for (const_iterator i = y.begin(), y_end = y.end(); i != y_end; ++i) 00237 old_begin = add_non_bottom_disjunct(*i, old_begin, old_end); 00238 }
void Parma_Polyhedra_Library::Powerset< D >::upper_bound_assign | ( | const Powerset< D > & | y | ) | [inline] |
Assigns to *this
an upper bound of *this
and y
.
The result will be the least upper bound of *this
and y
.
Definition at line 374 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::least_upper_bound_assign().
00374 { 00375 least_upper_bound_assign(y); 00376 }
void Parma_Polyhedra_Library::Powerset< D >::meet_assign | ( | const Powerset< D > & | y | ) | [inline] |
Assigns to *this
the meet of *this
and y
.
Definition at line 368 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::pairwise_apply_assign().
00368 { 00369 pairwise_apply_assign(y, std::mem_fun_ref(&D::meet_assign)); 00370 }
void Parma_Polyhedra_Library::Powerset< D >::collapse | ( | ) | [inline] |
If *this
is not empty (i.e., it is not the bottom element), it is reduced to a singleton obtained by computing an upper-bound of all the disjuncts.
Definition at line 361 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::empty(), and Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BGP99_extrapolation_assign(), Parma_Polyhedra_Library::Powerset< D >::collapse(), and Parma_Polyhedra_Library::Powerset< D >::omega_reduce().
bool Parma_Polyhedra_Library::Powerset< D >::is_omega_reduced | ( | ) | const [inline, protected] |
Returns true
if and only if *this
does not contain non-maximal elements.
Definition at line 141 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::check_omega_reduced(), and Parma_Polyhedra_Library::Powerset< D >::reduced.
Referenced by Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BGP99_heuristics_assign(), Parma_Polyhedra_Library::Powerset< D >::collapse(), and Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::collect_certificates().
00141 { 00142 if (!reduced && check_omega_reduced()) 00143 reduced = true; 00144 return reduced; 00145 }
void Parma_Polyhedra_Library::Powerset< D >::collapse | ( | unsigned | max_disjuncts | ) | [inline, protected] |
Upon return, *this
will contain at most max_disjuncts
elements; the set of disjuncts in positions greater than or equal to max_disjuncts
, will be replaced at that position by their upper-bound.
Definition at line 103 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::omega_iterator::base, Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Powerset< D >::is_omega_reduced(), Parma_Polyhedra_Library::Powerset< D >::OK(), Parma_Polyhedra_Library::Powerset< D >::omega_reduce(), and Parma_Polyhedra_Library::Powerset< D >::size().
00103 { 00104 assert(max_disjuncts > 0); 00105 // Omega-reduce before counting the number of disjuncts. 00106 omega_reduce(); 00107 size_type n = size(); 00108 if (n > max_disjuncts) { 00109 // Let `i' point to the last disjunct that will survive. 00110 iterator i = begin(); 00111 std::advance(i, max_disjuncts-1); 00112 // This disjunct will be assigned an upper-bound of itself and of 00113 // all the disjuncts that follow. 00114 collapse(i.base); 00115 } 00116 assert(OK()); 00117 assert(is_omega_reduced()); 00118 }
Powerset< D >::iterator Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct | ( | const D & | d, | |
iterator | first, | |||
iterator | last | |||
) | [inline, protected] |
Adds to *this
the disjunct d
, assuming d
is not the bottom element and ensuring partial Omega-reduction.
If d
is not the bottom element and is not Omega-redundant with respect to elements in positions between first
and last
, all elements in these positions that would be made Omega-redundant by the addition of d
are dropped and d
is added to the reduced sequence.
Definition at line 149 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::drop_disjunct(), and Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Powerset< D >::add_disjunct(), Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BGP99_heuristics_assign(), Parma_Polyhedra_Library::Powerset< D >::least_upper_bound_assign(), and Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::pairwise_reduce().
00151 { 00152 for (iterator xi = first; xi != last; ) { 00153 const D& xv = *xi; 00154 if (d.definitely_entails(xv)) 00155 return first; 00156 else if (xv.definitely_entails(d)) { 00157 if (xi == first) 00158 ++first; 00159 xi = drop_disjunct(xi); 00160 } 00161 else 00162 ++xi; 00163 } 00164 sequence.push_back(d); 00165 return first; 00166 }
void Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct | ( | const D & | d | ) | [inline, protected] |
Adds to *this
the disjunct d
, assuming d
is not the bottom element.
Definition at line 322 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct(), Parma_Polyhedra_Library::Powerset< D >::begin(), and Parma_Polyhedra_Library::Powerset< D >::end().
00322 { 00323 assert(!d.is_bottom()); 00324 add_non_bottom_disjunct(d, begin(), end()); 00325 }
void Parma_Polyhedra_Library::Powerset< D >::pairwise_apply_assign | ( | const Powerset< D > & | y, | |
Binary_Operator_Assign | op_assign | |||
) | [inline, protected] |
Assigns to *this
the result of applying op_assign
pairwise to the elements in *this
and y
.
The elements of the powerset result are obtained by applying op_assign
to each pair of elements whose components are drawn from *this
and y
, respectively.
Definition at line 209 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Powerset< D >::end(), Parma_Polyhedra_Library::Powerset< D >::omega_reduce(), Parma_Polyhedra_Library::Powerset< D >::reduced, and Parma_Polyhedra_Library::Powerset< D >::sequence.
Referenced by Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::intersection_assign(), Parma_Polyhedra_Library::Powerset< D >::meet_assign(), and Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::time_elapse_assign().
00210 { 00211 // Ensure omega-reduction here, since what follows has quadratic complexity. 00212 omega_reduce(); 00213 y.omega_reduce(); 00214 Sequence new_sequence; 00215 for (const_iterator xi = begin(), x_end = end(), 00216 y_begin = y.begin(), y_end = y.end(); xi != x_end; ++xi) 00217 for (const_iterator yi = y_begin; yi != y_end; ++yi) { 00218 D zi = *xi; 00219 op_assign(zi, *yi); 00220 if (!zi.is_bottom()) 00221 new_sequence.push_back(zi); 00222 } 00223 // Put the new sequence in place. 00224 std::swap(sequence, new_sequence); 00225 reduced = false; 00226 }
bool Parma_Polyhedra_Library::Powerset< D >::check_omega_reduced | ( | ) | const [inline, private] |
Does the hard work of checking whether *this
contains non-maximal elements and returns true
if and only if it does not.
Definition at line 122 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin(), and Parma_Polyhedra_Library::Powerset< D >::end().
Referenced by Parma_Polyhedra_Library::Powerset< D >::is_omega_reduced(), and Parma_Polyhedra_Library::Powerset< D >::OK().
00122 { 00123 for (const_iterator x_begin = begin(), x_end = end(), 00124 xi = x_begin; xi != x_end; ++xi) { 00125 const D& xv = *xi; 00126 if (xv.is_bottom()) 00127 return false; 00128 for (const_iterator yi = x_begin; yi != x_end; ++yi) { 00129 if (xi == yi) 00130 continue; 00131 const D& yv = *yi; 00132 if (xv.definitely_entails(yv) || yv.definitely_entails(xv)) 00133 return false; 00134 } 00135 } 00136 return true; 00137 }
void Parma_Polyhedra_Library::Powerset< D >::collapse | ( | Sequence_iterator | sink | ) | [inline, private] |
Replaces the disjunct *sink
by an upper bound of itself and all the disjuncts following it.
Definition at line 34 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Powerset< D >::drop_disjunct(), Parma_Polyhedra_Library::Powerset< D >::drop_disjuncts(), Parma_Polyhedra_Library::Powerset< D >::end(), Parma_Polyhedra_Library::Powerset< D >::OK(), and Parma_Polyhedra_Library::Powerset< D >::sequence.
00034 { 00035 assert(sink != sequence.end()); 00036 D& d = *sink; 00037 iterator x_sink = sink; 00038 iterator next_x_sink = x_sink; 00039 ++next_x_sink; 00040 iterator x_end = end(); 00041 for (const_iterator xi = next_x_sink; xi != x_end; ++xi) 00042 d.upper_bound_assign(*xi); 00043 // Drop the surplus disjuncts. 00044 drop_disjuncts(next_x_sink, x_end); 00045 00046 // Ensure omega-reduction. 00047 for (iterator xi = begin(); xi != x_sink; ) 00048 if (xi->definitely_entails(d)) 00049 xi = drop_disjunct(xi); 00050 else 00051 ++xi; 00052 00053 assert(OK()); 00054 }
Returns true
if and only if x
and y
are equivalent.
Definition at line 186 of file Powerset.templates.hh.
References Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Powerset< D >::drop_disjunct(), Parma_Polyhedra_Library::Powerset< D >::end(), Parma_Polyhedra_Library::Powerset< D >::omega_reduce(), and Parma_Polyhedra_Library::Powerset< D >::size().
00186 { 00187 x.omega_reduce(); 00188 y.omega_reduce(); 00189 if (x.size() != y.size()) 00190 return false; 00191 // Take a copy of `y' and work with it. 00192 Powerset<D> yy = y; 00193 for (typename Powerset<D>::const_iterator xi = x.begin(), 00194 x_end = x.end(); xi != x_end; ++xi) { 00195 typename Powerset<D>::iterator yyi = yy.begin(); 00196 typename Powerset<D>::iterator yy_end = yy.end(); 00197 yyi = std::find(yyi, yy_end, *xi); 00198 if (yyi == yy_end) 00199 return false; 00200 else 00201 yy.drop_disjunct(yyi); 00202 } 00203 return true; 00204 }
Returns true
if and only if x
and y
are not equivalent.
Definition at line 337 of file Powerset.inlines.hh.
std::ostream & operator<< | ( | std::ostream & | s, | |
const Powerset< D > & | x | |||
) | [related] |
Output operator.
Definition at line 245 of file Powerset.templates.hh.
00245 { 00246 if (x.is_bottom()) 00247 s << "false"; 00248 else if (x.is_top()) 00249 s << "true"; 00250 else 00251 for (typename Powerset<D>::const_iterator i = x.begin(), 00252 x_end = x.end(); i != x_end; ) { 00253 s << "{ " << *i++ << " }"; 00254 if (i != x_end) 00255 s << ", "; 00256 } 00257 return s; 00258 }
void swap | ( | Parma_Polyhedra_Library::Powerset< D > & | x, | |
Parma_Polyhedra_Library::Powerset< D > & | y | |||
) | [related] |
Specializes std::swap
.
Definition at line 392 of file Powerset.inlines.hh.
References Parma_Polyhedra_Library::Powerset< D >::swap().
00393 { 00394 x.swap(y); 00395 }
Sequence Parma_Polyhedra_Library::Powerset< D >::sequence [protected] |
The sequence container holding powerset's elements.
Definition at line 227 of file Powerset.defs.hh.
Referenced by Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraint(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraint_and_minimize(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraints(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraints_and_minimize(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_disjunct(), Parma_Polyhedra_Library::Powerset< D >::add_non_bottom_disjunct(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_space_dimensions_and_embed(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_space_dimensions_and_project(), Parma_Polyhedra_Library::Powerset< D >::begin(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::BGP99_heuristics_assign(), Parma_Polyhedra_Library::Powerset< D >::clear(), Parma_Polyhedra_Library::Powerset< D >::collapse(), Parma_Polyhedra_Library::Powerset< D >::drop_disjunct(), Parma_Polyhedra_Library::Powerset< D >::drop_disjuncts(), Parma_Polyhedra_Library::Powerset< D >::empty(), Parma_Polyhedra_Library::Powerset< D >::end(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::map_space_dimensions(), Parma_Polyhedra_Library::Powerset< D >::operator=(), Parma_Polyhedra_Library::Powerset< D >::pairwise_apply_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::pairwise_reduce(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::poly_difference_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::Polyhedra_Powerset(), Parma_Polyhedra_Library::Powerset< D >::Powerset(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::remove_higher_space_dimensions(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::remove_space_dimensions(), Parma_Polyhedra_Library::Powerset< D >::size(), and Parma_Polyhedra_Library::Powerset< D >::swap().
bool Parma_Polyhedra_Library::Powerset< D >::reduced [mutable, protected] |
If true
, *this
is Omega-reduced.
Definition at line 230 of file Powerset.defs.hh.
Referenced by Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraint(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraint_and_minimize(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraints(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_constraints_and_minimize(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::add_disjunct(), Parma_Polyhedra_Library::Powerset< D >::is_omega_reduced(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::map_space_dimensions(), Parma_Polyhedra_Library::Powerset< D >::OK(), Parma_Polyhedra_Library::Powerset< D >::omega_reduce(), Parma_Polyhedra_Library::Powerset< D >::operator=(), Parma_Polyhedra_Library::Powerset< D >::pairwise_apply_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::poly_difference_assign(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::Polyhedra_Powerset(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::remove_higher_space_dimensions(), Parma_Polyhedra_Library::Polyhedra_Powerset< PH >::remove_space_dimensions(), and Parma_Polyhedra_Library::Powerset< D >::swap().