PPL  0.12.1
Public Member Functions | Static Public Member Functions | Protected Types | Protected Member Functions | Protected Attributes | Friends | Related Functions
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R > Class Template Reference
C++ Language Interface

The partially reduced product of two abstractions. More...

#include <Partially_Reduced_Product.defs.hh>

List of all members.

Public Member Functions

 Partially_Reduced_Product (dimension_type num_dimensions=0, Degenerate_Element kind=UNIVERSE)
 Builds an object having the specified properties.
 Partially_Reduced_Product (const Congruence_System &cgs)
 Builds a pair, copying a system of congruences.
 Partially_Reduced_Product (Congruence_System &cgs)
 Builds a pair, recycling a system of congruences.
 Partially_Reduced_Product (const Constraint_System &cs)
 Builds a pair, copying a system of constraints.
 Partially_Reduced_Product (Constraint_System &cs)
 Builds a pair, recycling a system of constraints.
 Partially_Reduced_Product (const C_Polyhedron &ph, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds a product, from a C polyhedron.
 Partially_Reduced_Product (const NNC_Polyhedron &ph, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds a product, from an NNC polyhedron.
 Partially_Reduced_Product (const Grid &gr, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds a product, from a grid.
template<typename Interval >
 Partially_Reduced_Product (const Box< Interval > &box, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds a product out of a box.
template<typename U >
 Partially_Reduced_Product (const BD_Shape< U > &bd, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds a product out of a BD shape.
template<typename U >
 Partially_Reduced_Product (const Octagonal_Shape< U > &os, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds a product out of an octagonal shape.
 Partially_Reduced_Product (const Partially_Reduced_Product &y, Complexity_Class complexity=ANY_COMPLEXITY)
 Ordinary copy constructor.
template<typename E1 , typename E2 , typename S >
 Partially_Reduced_Product (const Partially_Reduced_Product< E1, E2, S > &y, Complexity_Class complexity=ANY_COMPLEXITY)
 Builds a conservative, upward approximation of y.
Partially_Reduced_Product & operator= (const Partially_Reduced_Product &y)
 The assignment operator. (*this and y can be dimension-incompatible.)
bool reduce () const
 Reduce.
Member Functions that Do Not Modify the Partially_Reduced_Product
dimension_type space_dimension () const
 Returns the dimension of the vector space enclosing *this.
dimension_type affine_dimension () const
 Returns the minimum affine dimension (see also grid affine dimension) of the components of *this.
const D1 & domain1 () const
 Returns a constant reference to the first of the pair.
const D2 & domain2 () const
 Returns a constant reference to the second of the pair.
Constraint_System constraints () const
 Returns a system of constraints which approximates *this.
Constraint_System minimized_constraints () const
 Returns a system of constraints which approximates *this, in reduced form.
Congruence_System congruences () const
 Returns a system of congruences which approximates *this.
Congruence_System minimized_congruences () const
 Returns a system of congruences which approximates *this, in reduced form.
Poly_Con_Relation relation_with (const Constraint &c) const
 Returns the relations holding between *this and c.
Poly_Con_Relation relation_with (const Congruence &cg) const
 Returns the relations holding between *this and cg.
Poly_Gen_Relation relation_with (const Generator &g) const
 Returns the relations holding between *this and g.
bool is_empty () const
 Returns true if and only if either of the components of *this are empty.
bool is_universe () const
 Returns true if and only if both of the components of *this are the universe.
bool is_topologically_closed () const
 Returns true if and only if both of the components of *this are topologically closed subsets of the vector space.
bool is_disjoint_from (const Partially_Reduced_Product &y) const
 Returns true if and only if *this and y are componentwise disjoint.
bool is_discrete () const
 Returns true if and only if a component of *this is discrete.
bool is_bounded () const
 Returns true if and only if a component of *this is bounded.
bool constrains (Variable var) const
 Returns true if and only if var is constrained in *this.
bool bounds_from_above (const Linear_Expression &expr) const
 Returns true if and only if expr is bounded in *this.
bool bounds_from_below (const Linear_Expression &expr) const
 Returns true if and only if expr is bounded 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 i *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 Partially_Reduced_Product &y) const
 Returns true if and only if each component of *this contains the corresponding component of y.
bool strictly_contains (const Partially_Reduced_Product &y) const
 Returns true if and only if each component of *this strictly contains the corresponding component of y.
bool OK () const
 Checks if all the invariants are satisfied.
Space Dimension Preserving Member Functions that May Modify the Partially_Reduced_Product
void add_constraint (const Constraint &c)
 Adds constraint c to *this.
void refine_with_constraint (const Constraint &c)
 Use the constraint c to refine *this.
void add_congruence (const Congruence &cg)
 Adds a copy of congruence cg to *this.
void refine_with_congruence (const Congruence &cg)
 Use the congruence cg to refine *this.
void add_congruences (const Congruence_System &cgs)
 Adds a copy of the congruences in cgs to *this.
void refine_with_congruences (const Congruence_System &cgs)
 Use the congruences in cgs to refine *this.
void add_recycled_congruences (Congruence_System &cgs)
 Adds the congruences in cgs to *this.
void add_constraints (const Constraint_System &cs)
 Adds a copy of the constraint system in cs to *this.
void refine_with_constraints (const Constraint_System &cs)
 Use the constraints in cs to refine *this.
void add_recycled_constraints (Constraint_System &cs)
 Adds the constraint system in cs to *this.
void unconstrain (Variable var)
 Computes the cylindrification of *this with respect to space dimension var, assigning the result to *this.
void unconstrain (const Variables_Set &vars)
 Computes the cylindrification of *this with respect to the set of space dimensions vars, assigning the result to *this.
void intersection_assign (const Partially_Reduced_Product &y)
 Assigns to *this the componentwise intersection of *this and y.
void upper_bound_assign (const Partially_Reduced_Product &y)
 Assigns to *this an upper bound of *this and y computed on the corresponding components.
bool upper_bound_assign_if_exact (const Partially_Reduced_Product &y)
 Assigns to *this an upper bound of *this and y computed on the corresponding components. If it is exact on each of the components of *this, true is returned, otherwise false is returned.
void difference_assign (const Partially_Reduced_Product &y)
 Assigns to *this an approximation of the set-theoretic difference of *this and y.
void affine_image (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
 Assigns to *this the affine image of *this under the function mapping variable var to the affine expression specified by expr and denominator.
void affine_preimage (Variable var, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
 Assigns to *this the affine preimage of *this under the function mapping variable var to the affine expression specified by expr and denominator.
void generalized_affine_image (Variable var, Relation_Symbol relsym, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
 Assigns to *this the image of *this with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym (see also generalized affine relation.)
void generalized_affine_preimage (Variable var, Relation_Symbol relsym, const Linear_Expression &expr, Coefficient_traits::const_reference denominator=Coefficient_one())
 Assigns to *this the preimage of *this with respect to the generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym. (see also generalized affine relation.)
void generalized_affine_image (const Linear_Expression &lhs, Relation_Symbol relsym, const Linear_Expression &rhs)
 Assigns to *this the image of *this with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym. (see also generalized affine relation.)
void generalized_affine_preimage (const Linear_Expression &lhs, Relation_Symbol relsym, const Linear_Expression &rhs)
 Assigns to *this the preimage of *this with respect to the generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym. (see also generalized affine relation.)
void bounded_affine_image (Variable var, const Linear_Expression &lb_expr, const Linear_Expression &ub_expr, Coefficient_traits::const_reference denominator=Coefficient_one())
 Assigns to *this the image of *this with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$.
void bounded_affine_preimage (Variable var, const Linear_Expression &lb_expr, const Linear_Expression &ub_expr, Coefficient_traits::const_reference denominator=Coefficient_one())
 Assigns to *this the preimage of *this with respect to the bounded affine relation $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$.
void time_elapse_assign (const Partially_Reduced_Product &y)
 Assigns to *this the result of computing the time-elapse between *this and y. (See also time-elapse.)
void topological_closure_assign ()
 Assigns to *this its topological closure.
void widening_assign (const Partially_Reduced_Product &y, unsigned *tp=NULL)
 Assigns to *this the result of computing the "widening" between *this and y.
void drop_some_non_integer_points (Complexity_Class complexity=ANY_COMPLEXITY)
 Possibly tightens *this by dropping some points with non-integer coordinates.
void drop_some_non_integer_points (const Variables_Set &vars, Complexity_Class complexity=ANY_COMPLEXITY)
 Possibly tightens *this by dropping some points with non-integer coordinates for the space dimensions corresponding to vars.
Member Functions that May Modify the Dimension of the Vector Space
void add_space_dimensions_and_embed (dimension_type m)
 Adds m new space dimensions and embeds the components of *this in the new vector space.
void add_space_dimensions_and_project (dimension_type m)
 Adds m new space dimensions and does not embed the components in the new vector space.
void concatenate_assign (const Partially_Reduced_Product &y)
 Assigns to the first (resp., second) component of *this the "concatenation" of the first (resp., second) components of *this and y, taken in this order. See also Concatenating Polyhedra.
void remove_space_dimensions (const Variables_Set &vars)
 Removes all the specified dimensions from the vector space.
void remove_higher_space_dimensions (dimension_type new_dimension)
 Removes the higher dimensions of the vector space so that the resulting space will have dimension new_dimension.
template<typename Partial_Function >
void map_space_dimensions (const Partial_Function &pfunc)
 Remaps the dimensions of the vector space according to a partial function.
void expand_space_dimension (Variable var, dimension_type m)
 Creates m copies of the space dimension corresponding to var.
void fold_space_dimensions (const Variables_Set &vars, Variable dest)
 Folds the space dimensions in vars into dest.
Miscellaneous Member Functions
 ~Partially_Reduced_Product ()
 Destructor.
void m_swap (Partially_Reduced_Product &y)
 Swaps *this with product y. (*this and y can be dimension-incompatible.)
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.

Static Public Member Functions

static dimension_type max_space_dimension ()
 Returns the maximum space dimension this product can handle.

Protected Types

typedef D1 Domain1
 The type of the first component.
typedef D2 Domain2
 The type of the second component.

Protected Member Functions

void clear_reduced_flag () const
 Clears the reduced flag.
void set_reduced_flag () const
 Sets the reduced flag.
bool is_reduced () const
 Return true if and only if the reduced flag is set.

Protected Attributes

D1 d1
 The first component.
D2 d2
 The second component.
bool reduced
 Flag to record whether the components are reduced with respect to each other and the reduction class.

Friends

bool operator== (const Partially_Reduced_Product< D1, D2, R > &x, const Partially_Reduced_Product< D1, D2, R > &y)
std::ostream & Parma_Polyhedra_Library::IO_Operators::operator<< (std::ostream &s, const Partially_Reduced_Product< D1, D2, R > &dp)

Related Functions

(Note that these are not member functions.)

template<typename D1 , typename D2 , typename R >
std::ostream & operator<< (std::ostream &s, const Partially_Reduced_Product< D1, D2, R > &dp)
 Output operator.
template<typename D1 , typename D2 , typename R >
void swap (Partially_Reduced_Product< D1, D2, R > &x, Partially_Reduced_Product< D1, D2, R > &y)
 Swaps x with y.
template<typename D1 , typename D2 , typename R >
bool operator== (const Partially_Reduced_Product< D1, D2, R > &x, const Partially_Reduced_Product< D1, D2, R > &y)
 Returns true if and only if the components of x and y are pairwise equal.
template<typename D1 , typename D2 , typename R >
bool operator!= (const Partially_Reduced_Product< D1, D2, R > &x, const Partially_Reduced_Product< D1, D2, R > &y)
 Returns true if and only if the components of x and y are not pairwise equal.
template<typename D1 , typename D2 , typename R >
bool operator== (const Partially_Reduced_Product< D1, D2, R > &x, const Partially_Reduced_Product< D1, D2, R > &y)
template<typename D1 , typename D2 , typename R >
bool operator!= (const Partially_Reduced_Product< D1, D2, R > &x, const Partially_Reduced_Product< D1, D2, R > &y)
template<typename D1 , typename D2 , typename R >
std::ostream & operator<< (std::ostream &s, const Partially_Reduced_Product< D1, D2, R > &dp)
template<typename D1 , typename D2 , typename R >
void swap (Partially_Reduced_Product< D1, D2, R > &x, Partially_Reduced_Product< D1, D2, R > &y)

Detailed Description

template<typename D1, typename D2, typename R>
class Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >

The partially reduced product of two abstractions.

Warning:
At present, the supported instantiations for the two domain templates D1 and D2 are the simple pointset domains: C_Polyhedron, NNC_Polyhedron, Grid, Octagonal_Shape<T>, BD_Shape<T>, Box<T>.

An object of the class Partially_Reduced_Product<D1, D2, R> represents the (partially reduced) product of two pointset domains D1 and D2 where the form of any reduction is defined by the reduction class R.

Suppose $D_1$ and $D_2$ are two abstract domains with concretization functions: $\fund{\gamma_1}{D_1}{\Rset^n}$ and $\fund{\gamma_2}{D_2}{\Rset^n}$, respectively.

The partially reduced product $D = D_1 \times D_2$, for any reduction class R, has a concretization $\fund{\gamma}{D}{\Rset^n}$ where, if $d = (d_1, d_2) \in D$

\[ \gamma(d) = \gamma_1(d_1) \inters \gamma_2(d_2). \]

The operations are defined to be the result of applying the corresponding operations on each of the components provided the product is already reduced by the reduction method defined by R. In particular, if R is the No_Reduction<D1, D2> class, then the class Partially_Reduced_Product<D1, D2, R> domain is the direct product as defined in [CC79].

How the results on the components are interpreted and combined depend on the specific test. For example, the test for emptiness will first make sure the product is reduced (using the reduction method provided by R if it is not already known to be reduced) and then test if either component is empty; thus, if R defines no reduction between its components and $d = (G, P) \in (\Gset \times \Pset)$ is a direct product in one dimension where $G$ denotes the set of numbers that are integral multiples of 3 while $P$ denotes the set of numbers between 1 and 2, then an operation that tests for emptiness should return false. However, the test for the universe returns true if and only if the test is_universe() on both components returns true.

In all the examples it is assumed that the template R is the No_Reduction<D1, D2> class and that variables x and y are defined (where they are used) as follows: 
  Variable x(0);
  Variable y(1);
Example 1
The following code builds a direct product of a Grid and NNC Polyhedron, corresponding to the positive even integer pairs in $\Rset^2$, given as a system of congruences: 
  Congruence_System cgs;
  cgs.insert((x %= 0) / 2);
  cgs.insert((y %= 0) / 2);
  Partially_Reduced_Product<Grid, NNC_Polyhedron, No_Reduction<D1, D2> >
    dp(cgs);
  dp.add_constraint(x >= 0);
  dp.add_constraint(y >= 0);
Example 2
The following code builds the same product in $\Rset^2$: 
  Partially_Reduced_Product<Grid, NNC_Polyhedron, No_Reduction<D1, D2> > dp(2);
  dp.add_constraint(x >= 0);
  dp.add_constraint(y >= 0);
  dp.add_congruence((x %= 0) / 2);
  dp.add_congruence((y %= 0) / 2);
Example 3
The following code will write "dp is empty": 
  Partially_Reduced_Product<Grid, NNC_Polyhedron, No_Reduction<D1, D2> > dp(1);
  dp.add_congruence((x %= 0) / 2);
  dp.add_congruence((x %= 1) / 2);
  if (dp.is_empty())
    cout << "dp is empty." << endl;
  else
    cout << "dp is not empty." << endl;
Example 4
The following code will write "dp is not empty": 
  Partially_Reduced_Product<Grid, NNC_Polyhedron, No_Reduction<D1, D2> > dp(1);
  dp.add_congruence((x %= 0) / 2);
  dp.add_constraint(x >= 1);
  dp.add_constraint(x <= 1);
  if (dp.is_empty())
    cout << "dp is empty." << endl;
  else
    cout << "dp is not empty." << endl;

Definition at line 418 of file Partially_Reduced_Product.defs.hh.

Member Typedef Documentation

template<typename D1, typename D2, typename R>
typedef D1 Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Domain1
protected

The type of the first component.

Definition at line 1623 of file Partially_Reduced_Product.defs.hh.

template<typename D1, typename D2, typename R>
typedef D2 Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Domain2
protected

The type of the second component.

Definition at line 1626 of file Partially_Reduced_Product.defs.hh.

Constructor & Destructor Documentation

template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( dimension_type  num_dimensions = 0,
Degenerate_Element  kind = UNIVERSE 
)
inlineexplicit

Builds an object having the specified properties.

Parameters:
num_dimensionsThe number of dimensions of the vector space enclosing the pair;
kindSpecifies whether a universe or an empty pair has to be built.
Exceptions:
std::length_errorThrown if num_dimensions exceeds the maximum allowed space dimension.

Definition at line 46 of file Partially_Reduced_Product.inlines.hh.

  : d1(num_dimensions, kind),
    d2(num_dimensions, kind) {
  set_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const Congruence_System &  cgs)
inlineexplicit

Builds a pair, copying a system of congruences.

The pair inherits the space dimension of the congruence system.

Parameters:
cgsThe system of congruences to be approximated by the pair.
Exceptions:
std::length_errorThrown if num_dimensions exceeds the maximum allowed space dimension.

Definition at line 56 of file Partially_Reduced_Product.inlines.hh.

  : d1(cgs), d2(cgs) {
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( Congruence_System &  cgs)
inlineexplicit

Builds a pair, recycling a system of congruences.

The pair inherits the space dimension of the congruence system.

Parameters:
cgsThe system of congruences to be approximates by the pair. Its data-structures may be recycled to build the pair.
Exceptions:
std::length_errorThrown if num_dimensions exceeds the maximum allowed space dimension.

Definition at line 64 of file Partially_Reduced_Product.inlines.hh.

  : d1(const_cast<const Congruence_System&>(cgs)), d2(cgs) {
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const Constraint_System &  cs)
inlineexplicit

Builds a pair, copying a system of constraints.

The pair inherits the space dimension of the constraint system.

Parameters:
csThe system of constraints to be approximated by the pair.
Exceptions:
std::length_errorThrown if num_dimensions exceeds the maximum allowed space dimension.

Definition at line 72 of file Partially_Reduced_Product.inlines.hh.

  : d1(cs), d2(cs) {
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( Constraint_System &  cs)
inlineexplicit

Builds a pair, recycling a system of constraints.

The pair inherits the space dimension of the constraint system.

Parameters:
csThe system of constraints to be approximated by the pair.
Exceptions:
std::length_errorThrown if the space dimension of cs exceeds the maximum allowed space dimension.

Definition at line 80 of file Partially_Reduced_Product.inlines.hh.

  : d1(const_cast<const Constraint_System&>(cs)), d2(cs) {
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const C_Polyhedron &  ph,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inlineexplicit

Builds a product, from a C polyhedron.

Builds a product containing ph using algorithms whose complexity does not exceed the one specified by complexity. If complexity is ANY_COMPLEXITY, then the built product is the smallest one containing ph. The product inherits the space dimension of the polyhedron.

Parameters:
phThe polyhedron to be approximated by the product.
complexityThe complexity that will not be exceeded.
Exceptions:
std::length_errorThrown if the space dimension of ph exceeds the maximum allowed space dimension.

Definition at line 88 of file Partially_Reduced_Product.inlines.hh.

  : d1(ph, complexity), d2(ph, complexity) {
  set_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const NNC_Polyhedron &  ph,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inlineexplicit

Builds a product, from an NNC polyhedron.

Builds a product containing ph using algorithms whose complexity does not exceed the one specified by complexity. If complexity is ANY_COMPLEXITY, then the built product is the smallest one containing ph. The product inherits the space dimension of the polyhedron.

Parameters:
phThe polyhedron to be approximated by the product.
complexityThe complexity that will not be exceeded.
Exceptions:
std::length_errorThrown if the space dimension of ph exceeds the maximum allowed space dimension.

Definition at line 97 of file Partially_Reduced_Product.inlines.hh.

  : d1(ph, complexity), d2(ph, complexity) {
  set_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const Grid &  gr,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inlineexplicit

Builds a product, from a grid.

Builds a product containing gr. The product inherits the space dimension of the grid.

Parameters:
grThe grid to be approximated by the product.
complexityThe complexity is ignored.
Exceptions:
std::length_errorThrown if the space dimension of gr exceeds the maximum allowed space dimension.

Definition at line 106 of file Partially_Reduced_Product.inlines.hh.

  : d1(gr), d2(gr) {
  set_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
template<typename Interval >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const Box< Interval > &  box,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inline

Builds a product out of a box.

Builds a product containing box. The product inherits the space dimension of the box.

Parameters:
boxThe box representing the pair to be built.
complexityThe complexity is ignored.
Exceptions:
std::length_errorThrown if the space dimension of box exceeds the maximum allowed space dimension.

Definition at line 115 of file Partially_Reduced_Product.inlines.hh.

  : d1(box), d2(box) {
  set_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
template<typename U >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const BD_Shape< U > &  bd,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inline

Builds a product out of a BD shape.

Builds a product containing bd. The product inherits the space dimension of the BD shape.

Parameters:
bdThe BD shape representing the product to be built.
complexityThe complexity is ignored.
Exceptions:
std::length_errorThrown if the space dimension of bd exceeds the maximum allowed space dimension.

Definition at line 124 of file Partially_Reduced_Product.inlines.hh.

  : d1(bd), d2(bd) {
  set_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
template<typename U >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const Octagonal_Shape< U > &  os,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inline

Builds a product out of an octagonal shape.

Builds a product containing os. The product inherits the space dimension of the octagonal shape.

Parameters:
osThe octagonal shape representing the product to be built.
complexityThe complexity is ignored.
Exceptions:
std::length_errorThrown if the space dimension of os exceeds the maximum allowed space dimension.

Definition at line 133 of file Partially_Reduced_Product.inlines.hh.

  : d1(os), d2(os) {
  set_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const Partially_Reduced_Product< D1, D2, R > &  y,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inline

Ordinary copy constructor.

Definition at line 141 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduced.

  : d1(y.d1), d2(y.d2) {
  reduced = y.reduced;
}
template<typename D1 , typename D2 , typename R >
template<typename E1 , typename E2 , typename S >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product ( const Partially_Reduced_Product< E1, E2, S > &  y,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inlineexplicit

Builds a conservative, upward approximation of y.

The complexity argument is ignored.

Definition at line 151 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::domain1(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::domain2(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::intersection_assign().

  : d1(y.space_dimension()), d2(y.space_dimension()) {
  Partially_Reduced_Product<D1, D2, R> pg1(y.domain1(), complexity);
  Partially_Reduced_Product<D1, D2, R> pg2(y.domain2(), complexity);
  pg1.intersection_assign(pg2);
  m_swap(pg1);
  /* Even if y is reduced, the built product may not be reduced as
     the reduction method may have changed (i.e., S != R). */
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::~Partially_Reduced_Product ( )
inline

Destructor.

Definition at line 165 of file Partially_Reduced_Product.inlines.hh.

                                                                 {
}

Member Function Documentation

template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::add_congruence ( const Congruence &  cg)
inline

Adds a copy of congruence cg to *this.

Exceptions:
std::invalid_argumentThrown if *this and congruence cg are dimension-incompatible.

Definition at line 399 of file Partially_Reduced_Product.inlines.hh.

                                                                         {
  d1.add_congruence(cg);
  d2.add_congruence(cg);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::add_congruences ( const Congruence_System &  cgs)
inline

Adds a copy of the congruences in cgs to *this.

Parameters:
cgsThe congruence system to be added.
Exceptions:
std::invalid_argumentThrown if *this and cgs are dimension-incompatible.

Definition at line 434 of file Partially_Reduced_Product.inlines.hh.

                                              {
  d1.add_congruences(cgs);
  d2.add_congruences(cgs);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::add_constraint ( const Constraint &  c)
inline

Adds constraint c to *this.

Exceptions:
std::invalid_argumentThrown if *this and c are dimension-incompatible.

Definition at line 383 of file Partially_Reduced_Product.inlines.hh.

                                                                        {
  d1.add_constraint(c);
  d2.add_constraint(c);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::add_constraints ( const Constraint_System &  cs)
inline

Adds a copy of the constraint system in cs to *this.

Parameters:
csThe constraint system to be added.
Exceptions:
std::invalid_argumentThrown if *this and cs are dimension-incompatible.

Definition at line 416 of file Partially_Reduced_Product.inlines.hh.

                                             {
  d1.add_constraints(cs);
  d2.add_constraints(cs);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::add_recycled_congruences ( Congruence_System &  cgs)

Adds the congruences in cgs to *this.

Parameters:
cgsThe congruence system to be added that may be recycled.
Exceptions:
std::invalid_argumentThrown if *this and cs are dimension-incompatible.
Warning:
The only assumption that can be made about cgs upon successful or exceptional return is that it can be safely destroyed.

Definition at line 115 of file Partially_Reduced_Product.templates.hh.

                                                 {
  if (d1.can_recycle_congruence_systems()) {
    d2.refine_with_congruences(cgs);
    d1.add_recycled_congruences(cgs);
  }
  else
    if (d2.can_recycle_congruence_systems()) {
      d1.refine_with_congruences(cgs);
      d2.add_recycled_congruences(cgs);
    }
    else {
      d1.add_congruences(cgs);
      d2.add_congruences(cgs);
    }
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::add_recycled_constraints ( Constraint_System &  cs)

Adds the constraint system in cs to *this.

Parameters:
csThe constraint system to be added that may be recycled.
Exceptions:
std::invalid_argumentThrown if *this and cs are dimension-incompatible.
Warning:
The only assumption that can be made about cs upon successful or exceptional return is that it can be safely destroyed.

Definition at line 95 of file Partially_Reduced_Product.templates.hh.

                                                {
  if (d1.can_recycle_constraint_systems()) {
    d2.refine_with_constraints(cs);
    d1.add_recycled_constraints(cs);
  }
  else
    if (d2.can_recycle_constraint_systems()) {
      d1.refine_with_constraints(cs);
      d2.add_recycled_constraints(cs);
    }
    else {
      d1.add_constraints(cs);
      d2.add_constraints(cs);
    }
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::add_space_dimensions_and_embed ( dimension_type  m)
inline

Adds m new space dimensions and embeds the components of *this in the new vector space.

Parameters:
mThe number of dimensions to add.
Exceptions:
std::length_errorThrown if adding m new space dimensions would cause the vector space to exceed dimension max_space_dimension().

Definition at line 579 of file Partially_Reduced_Product.inlines.hh.

                                                 {
  d1.add_space_dimensions_and_embed(m);
  d2.add_space_dimensions_and_embed(m);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::add_space_dimensions_and_project ( dimension_type  m)
inline

Adds m new space dimensions and does not embed the components in the new vector space.

Parameters:
mThe number of space dimensions to add.
Exceptions:
std::length_errorThrown if adding m new space dimensions would cause the vector space to exceed dimension max_space_dimension().

Definition at line 587 of file Partially_Reduced_Product.inlines.hh.

                                                   {
  d1.add_space_dimensions_and_project(m);
  d2.add_space_dimensions_and_project(m);
}
template<typename D1 , typename D2 , typename R >
dimension_type Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::affine_dimension ( ) const
inline

Returns the minimum affine dimension (see also grid affine dimension) of the components of *this.

Definition at line 189 of file Partially_Reduced_Product.inlines.hh.

                                                             {
  reduce();
  const dimension_type d1_dim = d1.affine_dimension();
  const dimension_type d2_dim = d2.affine_dimension();
  return std::min(d1_dim, d2_dim);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 to the affine expression specified by expr and denominator.

Parameters:
varThe variable to which the affine expression is assigned;
exprThe numerator of the affine expression;
denominatorThe denominator of the affine expression (optional argument with default value 1).
Exceptions:
std::invalid_argumentThrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a space dimension of *this.

Definition at line 264 of file Partially_Reduced_Product.inlines.hh.

                                                              {
  d1.affine_image(var, expr, denominator);
  d2.affine_image(var, expr, denominator);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 to the affine expression specified by expr and denominator.

Parameters:
varThe variable to which the affine expression is substituted;
exprThe numerator of the affine expression;
denominatorThe denominator of the affine expression (optional argument with default value 1).
Exceptions:
std::invalid_argumentThrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a space dimension of *this.

Definition at line 275 of file Partially_Reduced_Product.inlines.hh.

                                                                 {
  d1.affine_preimage(var, expr, denominator);
  d2.affine_preimage(var, expr, denominator);
  clear_reduced_flag();
}
template<typename D1, typename D2, typename R>
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::ascii_dump ( ) const

Writes to std::cerr an ASCII representation of *this.

template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::ascii_dump ( std::ostream &  s) const
inline

Writes to s an ASCII representation of *this.

Definition at line 698 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Implementation::BD_Shapes::no, and Parma_Polyhedra_Library::Implementation::BD_Shapes::yes.

                                                                    {
  const char yes = '+';
  const char no = '-';
  s << "Partially_Reduced_Product\n";
  s << (reduced ? yes : no) << "reduced\n";
  s << "Domain 1:\n";
  d1.ascii_dump(s);
  s << "Domain 2:\n";
  d2.ascii_dump(s);
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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.

Definition at line 434 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Implementation::BD_Shapes::no, and Parma_Polyhedra_Library::Implementation::BD_Shapes::yes.

                                                              {
  const char yes = '+';
  const char no = '-';
  std::string str;
  if (!(s >> str) || str != "Partially_Reduced_Product")
    return false;
  if (!(s >> str)
      || (str[0] != yes && str[0] != no)
      || str.substr(1) != "reduced")
    return false;
  reduced = (str[0] == yes);
  if (!(s >> str) || str != "Domain")
    return false;
  if (!(s >> str) || str != "1:")
    return false;
  if (!d1.ascii_load(s))
    return false;
  if (!(s >> str) || str != "Domain")
    return false;
  if (!(s >> str) || str != "2:")
    return false;
  return d2.ascii_load(s);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$.

Parameters:
varThe variable updated by the affine relation;
lb_exprThe numerator of the lower bounding affine expression;
ub_exprThe numerator of the upper bounding affine expression;
denominatorThe (common) denominator for the lower and upper bounding affine expressions (optional argument with default value 1).
Exceptions:
std::invalid_argumentThrown 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.

Definition at line 333 of file Partially_Reduced_Product.inlines.hh.

                                                                      {
  d1.bounded_affine_image(var, lb_expr, ub_expr, denominator);
  d2.bounded_affine_image(var, lb_expr, ub_expr, denominator);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 $\frac{\mathrm{lb\_expr}}{\mathrm{denominator}} \leq \mathrm{var}' \leq \frac{\mathrm{ub\_expr}}{\mathrm{denominator}}$.

Parameters:
varThe variable updated by the affine relation;
lb_exprThe numerator of the lower bounding affine expression;
ub_exprThe numerator of the upper bounding affine expression;
denominatorThe (common) denominator for the lower and upper bounding affine expressions (optional argument with default value 1).
Exceptions:
std::invalid_argumentThrown 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.

Definition at line 345 of file Partially_Reduced_Product.inlines.hh.

                                                                         {
  d1.bounded_affine_preimage(var, lb_expr, ub_expr, denominator);
  d2.bounded_affine_preimage(var, lb_expr, ub_expr, denominator);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::bounds_from_above ( const Linear_Expression &  expr) const
inline

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

This method is the same as bounds_from_below.

Exceptions:
std::invalid_argumentThrown if expr and *this are dimension-incompatible.

Definition at line 540 of file Partially_Reduced_Product.inlines.hh.

                                                       {
  reduce();
  return d1.bounds_from_above(expr) || d2.bounds_from_above(expr);
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::bounds_from_below ( const Linear_Expression &  expr) const
inline

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

This method is the same as bounds_from_above.

Exceptions:
std::invalid_argumentThrown if expr and *this are dimension-incompatible.

Definition at line 548 of file Partially_Reduced_Product.inlines.hh.

                                                       {
  reduce();
  return d1.bounds_from_below(expr) || d2.bounds_from_below(expr);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::clear_reduced_flag ( ) const
inlineprotected

Clears the reduced flag.

Definition at line 684 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduced.

Referenced by Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::OK().

                                                               {
  const_cast<Partially_Reduced_Product&>(*this).reduced = false;
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::concatenate_assign ( const Partially_Reduced_Product< D1, D2, R > &  y)
inline

Assigns to the first (resp., second) component of *this the "concatenation" of the first (resp., second) components of *this and y, taken in this order. See also Concatenating Polyhedra.

Exceptions:
std::length_errorThrown if the concatenation would cause the vector space to exceed dimension max_space_dimension().

Definition at line 595 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_reduced().

                                                       {
  d1.concatenate_assign(y.d1);
  d2.concatenate_assign(y.d2);
  if (!is_reduced() || !y.is_reduced())
    clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Congruence_System Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::congruences ( ) const

Returns a system of congruences which approximates *this.

Definition at line 69 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Congruence_System::begin(), Parma_Polyhedra_Library::Congruence_System::end(), and Parma_Polyhedra_Library::Congruence_System::insert().

                                                        {
  reduce();
  Congruence_System cgs = d2.congruences();
  const Congruence_System& cgs1 = d1.congruences();
  for (Congruence_System::const_iterator i = cgs1.begin(),
         cgs_end = cgs1.end(); i != cgs_end; ++i)
    cgs.insert(*i);
  return cgs;
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::constrains ( Variable  var) const
inline

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

Exceptions:
std::invalid_argumentThrown if var is not a space dimension of *this.

Definition at line 555 of file Partially_Reduced_Product.inlines.hh.

                                                                   {
  reduce();
  return d1.constrains(var) || d2.constrains(var);
}
template<typename D1 , typename D2 , typename R >
Constraint_System Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::constraints ( ) const

Returns a system of constraints which approximates *this.

Definition at line 38 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Constraint_System::begin(), Parma_Polyhedra_Library::Constraint_System::end(), and Parma_Polyhedra_Library::Constraint_System::insert().

                                                        {
  reduce();
  Constraint_System cs = d2.constraints();
  const Constraint_System& cs1 = d1.constraints();
  for (Constraint_System::const_iterator i = cs1.begin(),
         cs_end = cs1.end(); i != cs_end; ++i)
    cs.insert(*i);
  return cs;
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::contains ( const Partially_Reduced_Product< D1, D2, R > &  y) const
inline

Returns true if and only if each component of *this contains the corresponding component of y.

Exceptions:
std::invalid_argumentThrown if *this and y are dimension-incompatible.

Definition at line 647 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                                   {
  reduce();
  y.reduce();
  return d1.contains(y.d1) && d2.contains(y.d2);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::difference_assign ( const Partially_Reduced_Product< D1, D2, R > &  y)
inline

Assigns to *this an approximation of the set-theoretic difference of *this and y.

Exceptions:
std::invalid_argumentThrown if *this and y are dimension-incompatible.

Definition at line 225 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                                      {
  reduce();
  y.reduce();
  d1.difference_assign(y.d1);
  d2.difference_assign(y.d2);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
const D1 & Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::domain1 ( ) const
inline

Returns a constant reference to the first of the pair.

Definition at line 482 of file Partially_Reduced_Product.inlines.hh.

Referenced by Parma_Polyhedra_Library::Box< ITV >::Box(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product().

                                                    {
  reduce();
  return d1;
}
template<typename D1 , typename D2 , typename R >
const D2 & Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::domain2 ( ) const
inline

Returns a constant reference to the second of the pair.

Definition at line 489 of file Partially_Reduced_Product.inlines.hh.

Referenced by Parma_Polyhedra_Library::Box< ITV >::Box(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product().

                                                    {
  reduce();
  return d2;
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::drop_some_non_integer_points ( Complexity_Class  complexity = ANY_COMPLEXITY)
inline

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

Parameters:
complexityThe maximal complexity of any algorithms used.
Note:
Currently there is no optimality guarantee, not even if complexity is ANY_COMPLEXITY.

Definition at line 452 of file Partially_Reduced_Product.inlines.hh.

                                                          {
  reduce();
  d1.drop_some_non_integer_points(complexity);
  d2.drop_some_non_integer_points(complexity);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::drop_some_non_integer_points ( const Variables_Set &  vars,
Complexity_Class  complexity = ANY_COMPLEXITY 
)
inline

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

Parameters:
varsPoints with non-integer coordinates for these variables/space-dimensions can be discarded.
complexityThe maximal complexity of any algorithms used.
Note:
Currently there is no optimality guarantee, not even if complexity is ANY_COMPLEXITY.

Definition at line 462 of file Partially_Reduced_Product.inlines.hh.

                                                                 {
  reduce();
  d1.drop_some_non_integer_points(vars, complexity);
  d2.drop_some_non_integer_points(vars, complexity);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::expand_space_dimension ( Variable  var,
dimension_type  m 
)
inline

Creates m copies of the space dimension corresponding to var.

Parameters:
varThe variable corresponding to the space dimension to be replicated;
mThe number of replicas to be created.
Exceptions:
std::invalid_argumentThrown if var does not correspond to a dimension of the vector space.
std::length_errorThrown if adding m new space dimensions would cause the vector space to exceed dimension max_space_dimension().

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

Definition at line 630 of file Partially_Reduced_Product.inlines.hh.

                                                       {
  d1.expand_space_dimension(var, m);
  d2.expand_space_dimension(var, m);
}
template<typename D1 , typename D2 , typename R >
memory_size_type Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::external_memory_in_bytes ( ) const
inline

Returns the size in bytes of the memory managed by *this.

Definition at line 170 of file Partially_Reduced_Product.inlines.hh.

                                                                     {
  return d1.external_memory_in_bytes() + d2.external_memory_in_bytes();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::fold_space_dimensions ( const Variables_Set &  vars,
Variable  dest 
)
inline

Folds the space dimensions in vars into dest.

Parameters:
varsThe set of Variable objects corresponding to the space dimensions to be folded;
destThe variable corresponding to the space dimension that is the destination of the folding operation.
Exceptions:
std::invalid_argumentThrown if *this is dimension-incompatible with dest or with one of the Variable objects contained in vars. Also thrown if dest is contained in vars.

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

Definition at line 638 of file Partially_Reduced_Product.inlines.hh.

                                       {
  d1.fold_space_dimensions(vars, dest);
  d2.fold_space_dimensions(vars, dest);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym (see also generalized affine relation.)

Parameters:
varThe left hand side variable of the generalized affine relation;
relsymThe relation symbol;
exprThe numerator of the right hand side affine expression;
denominatorThe denominator of the right hand side affine expression (optional argument with default value 1).
Exceptions:
std::invalid_argumentThrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a space dimension of *this or if *this is a C_Polyhedron and relsym is a strict relation symbol.

Definition at line 286 of file Partially_Reduced_Product.inlines.hh.

                                                                          {
  d1.generalized_affine_image(var, relsym, expr, denominator);
  d2.generalized_affine_image(var, relsym, expr, denominator);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym. (see also generalized affine relation.)

Parameters:
lhsThe left hand side affine expression;
relsymThe relation symbol;
rhsThe right hand side affine expression.
Exceptions:
std::invalid_argumentThrown if *this is dimension-incompatible with lhs or rhs or if *this is a C_Polyhedron and relsym is a strict relation symbol.

Definition at line 310 of file Partially_Reduced_Product.inlines.hh.

                                                         {
  d1.generalized_affine_image(lhs, relsym, rhs);
  d2.generalized_affine_image(lhs, relsym, rhs);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 generalized affine relation $\mathrm{var}' \relsym \frac{\mathrm{expr}}{\mathrm{denominator}}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym. (see also generalized affine relation.)

Parameters:
varThe left hand side variable of the generalized affine relation;
relsymThe relation symbol;
exprThe numerator of the right hand side affine expression;
denominatorThe denominator of the right hand side affine expression (optional argument with default value 1).
Exceptions:
std::invalid_argumentThrown if denominator is zero or if expr and *this are dimension-incompatible or if var is not a space dimension of *this or if *this is a C_Polyhedron and relsym is a strict relation symbol.

Definition at line 298 of file Partially_Reduced_Product.inlines.hh.

                                                                             {
  d1.generalized_affine_preimage(var, relsym, expr, denominator);
  d2.generalized_affine_preimage(var, relsym, expr, denominator);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 generalized affine relation $\mathrm{lhs}' \relsym \mathrm{rhs}$, where $\mathord{\relsym}$ is the relation symbol encoded by relsym. (see also generalized affine relation.)

Parameters:
lhsThe left hand side affine expression;
relsymThe relation symbol;
rhsThe right hand side affine expression.
Exceptions:
std::invalid_argumentThrown if *this is dimension-incompatible with lhs or rhs or if *this is a C_Polyhedron and relsym is a strict relation symbol.

Definition at line 321 of file Partially_Reduced_Product.inlines.hh.

                                                            {
  d1.generalized_affine_preimage(lhs, relsym, rhs);
  d2.generalized_affine_preimage(lhs, relsym, rhs);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
int32_t Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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().

Definition at line 711 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::hash_code_from_dimension().

                                                      {
  return hash_code_from_dimension(space_dimension());
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::intersection_assign ( const Partially_Reduced_Product< D1, D2, R > &  y)
inline

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

Exceptions:
std::invalid_argumentThrown if *this and y are dimension-incompatible.

Definition at line 216 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2.

Referenced by Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product().

                                                        {
  d1.intersection_assign(y.d1);
  d2.intersection_assign(y.d2);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_bounded ( ) const
inline

Returns true if and only if a component of *this is bounded.

Definition at line 532 of file Partially_Reduced_Product.inlines.hh.

                                                       {
  reduce();
  return d1.is_bounded() || d2.is_bounded();
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_discrete ( ) const
inline

Returns true if and only if a component of *this is discrete.

Definition at line 525 of file Partially_Reduced_Product.inlines.hh.

                                                        {
  reduce();
  return d1.is_discrete() || d2.is_discrete();
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_disjoint_from ( const Partially_Reduced_Product< D1, D2, R > &  y) const
inline

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

Exceptions:
std::invalid_argumentThrown if x and y are dimension-incompatible.

Definition at line 517 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                                           {
  reduce();
  y.reduce();
  return d1.is_disjoint_from(y.d1) || d2.is_disjoint_from(y.d2);
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_empty ( ) const
inline

Returns true if and only if either of the components of *this are empty.

Definition at line 496 of file Partially_Reduced_Product.inlines.hh.

Referenced by Parma_Polyhedra_Library::Pointset_Powerset< PSET >::Pointset_Powerset().

                                                     {
  reduce();
  return d1.is_empty() || d2.is_empty();
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_reduced ( ) const
inlineprotected

Return true if and only if the reduced flag is set.

Definition at line 678 of file Partially_Reduced_Product.inlines.hh.

Referenced by Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::concatenate_assign(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                                       {
  return reduced;
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_topologically_closed ( ) const
inline

Returns true if and only if both of the components of *this are topologically closed subsets of the vector space.

Definition at line 509 of file Partially_Reduced_Product.inlines.hh.

                                                                    {
  reduce();
  return d1.is_topologically_closed() && d2.is_topologically_closed();
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_universe ( ) const
inline

Returns true if and only if both of the components of *this are the universe.

Definition at line 503 of file Partially_Reduced_Product.inlines.hh.

                                                        {
  return d1.is_universe() && d2.is_universe();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::m_swap ( Partially_Reduced_Product< D1, D2, R > &  y)
inline

Swaps *this with product y. (*this and y can be dimension-incompatible.)

Definition at line 374 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduced, and Parma_Polyhedra_Library::swap().

Referenced by Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::swap().

                                                                         {
  using std::swap;
  swap(d1, y.d1);
  swap(d2, y.d2);
  swap(reduced, y.reduced);
}
template<typename D1 , typename D2 , typename R >
template<typename Partial_Function >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::map_space_dimensions ( const Partial_Function &  pfunc)
inline

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

If pfunc maps only some of the dimensions of *this then the rest will be projected away.

If the highest dimension mapped to by pfunc is higher than the highest dimension in *this then the number of dimensions in *this will be increased to the highest dimension mapped to by pfunc.

Parameters:
pfuncThe partial function specifying the destiny of each space dimension.

The template class Partial_Function must provide the following methods. 

      bool has_empty_codomain() const

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

      dimension_type max_in_codomain() const

returns the maximum value that belongs to the codomain of the partial function. The max_in_codomain() method is called at most once. 

      bool maps(dimension_type i, dimension_type& j) const

Let $f$ be the represented function and $k$ be the value of i. If $f$ is defined in $k$, then $f(k)$ is assigned to j and true is returned. If $f$ is undefined in $k$, then false is returned. This method is called at most $n$ times, where $n$ is the dimension of the vector space enclosing *this.

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

Definition at line 622 of file Partially_Reduced_Product.inlines.hh.

                                                    {
  d1.map_space_dimensions(pfunc);
  d2.map_space_dimensions(pfunc);
}
template<typename D1 , typename D2 , typename R >
dimension_type Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::max_space_dimension ( )
inlinestatic

Returns the maximum space dimension this product can handle.

Definition at line 37 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::max_space_dimension().

                                                          {
  return (D1::max_space_dimension() < D2::max_space_dimension())
    ? D1::max_space_dimension()
    : D2::max_space_dimension();
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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.

Parameters:
exprThe linear expression to be maximized subject to *this;
sup_nThe numerator of the supremum value;
sup_dThe denominator of the supremum value;
maximumtrue if the supremum value can be reached in this.
Exceptions:
std::invalid_argumentThrown if expr and *this are dimension-incompatible.

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

Definition at line 199 of file Partially_Reduced_Product.templates.hh.

References PPL_DIRTY_TEMP_COEFFICIENT.

                                {
  reduce();

  if (is_empty())
    return false;

  PPL_DIRTY_TEMP_COEFFICIENT(sup1_n);
  PPL_DIRTY_TEMP_COEFFICIENT(sup1_d);
  PPL_DIRTY_TEMP_COEFFICIENT(sup2_n);
  PPL_DIRTY_TEMP_COEFFICIENT(sup2_d);
  bool maximum1;
  bool maximum2;
  bool r1 = d1.maximize(expr, sup1_n, sup1_d, maximum1);
  bool r2 = d2.maximize(expr, sup2_n, sup2_d, maximum2);
  // If neither is bounded from above, return false.
  if (!r1 && !r2)
    return false;
  // If only d2 is bounded from above, then use the values for d2.
  if (!r1) {
    sup_n = sup2_n;
    sup_d = sup2_d;
    maximum = maximum2;
    return true;
  }
  // If only d1 is bounded from above, then use the values for d1.
  if (!r2) {
    sup_n = sup1_n;
    sup_d = sup1_d;
    maximum = maximum1;
    return true;
  }
  // If both d1 and d2 are bounded from above, then use the minimum values.
  if (sup2_d * sup1_n >= sup1_d * sup2_n) {
    sup_n = sup1_n;
    sup_d = sup1_d;
    maximum = maximum1;
  }
  else {
    sup_n = sup2_n;
    sup_d = sup2_d;
    maximum = maximum2;
  }
  return true;
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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.

Parameters:
exprThe linear expression to be maximized subject to *this;
sup_nThe numerator of the supremum value;
sup_dThe denominator of the supremum value;
maximumtrue if the supremum value can be reached in this.
gWhen maximization succeeds, will be assigned the point or closure point where expr reaches its supremum value.
Exceptions:
std::invalid_argumentThrown if expr and *this are dimension-incompatible.

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

Definition at line 302 of file Partially_Reduced_Product.templates.hh.

References PPL_ASSERT, and PPL_DIRTY_TEMP_COEFFICIENT.

                               {
  reduce();

  if (is_empty())
    return false;
  PPL_ASSERT(reduced);

  PPL_DIRTY_TEMP_COEFFICIENT(sup1_n);
  PPL_DIRTY_TEMP_COEFFICIENT(sup1_d);
  PPL_DIRTY_TEMP_COEFFICIENT(sup2_n);
  PPL_DIRTY_TEMP_COEFFICIENT(sup2_d);
  bool maximum1;
  bool maximum2;
  Generator g1(point());
  Generator g2(point());
  bool r1 = d1.maximize(expr, sup1_n, sup1_d, maximum1, g1);
  bool r2 = d2.maximize(expr, sup2_n, sup2_d, maximum2, g2);
  // If neither is bounded from above, return false.
  if (!r1 && !r2)
    return false;
  // If only d2 is bounded from above, then use the values for d2.
  if (!r1) {
    sup_n = sup2_n;
    sup_d = sup2_d;
    maximum = maximum2;
    g = g2;
    return true;
  }
  // If only d1 is bounded from above, then use the values for d1.
  if (!r2) {
    sup_n = sup1_n;
    sup_d = sup1_d;
    maximum = maximum1;
    g = g1;
    return true;
  }
  // If both d1 and d2 are bounded from above, then use the minimum values.
  if (sup2_d * sup1_n >= sup1_d * sup2_n) {
    sup_n = sup1_n;
    sup_d = sup1_d;
    maximum = maximum1;
    g = g1;
  }
  else {
    sup_n = sup2_n;
    sup_d = sup2_d;
    maximum = maximum2;
    g = g2;
  }
  return true;
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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 i *this, in which case the infimum value is computed.

Parameters:
exprThe linear expression to be minimized subject to *this;
inf_nThe numerator of the infimum value;
inf_dThe denominator of the infimum value;
minimumtrue if the infimum value can be reached in this.
Exceptions:
std::invalid_argumentThrown if expr and *this are dimension-incompatible.

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

Definition at line 250 of file Partially_Reduced_Product.templates.hh.

References PPL_ASSERT, and PPL_DIRTY_TEMP_COEFFICIENT.

                                {
  reduce();

  if (is_empty())
    return false;
  PPL_ASSERT(reduced);

  PPL_DIRTY_TEMP_COEFFICIENT(inf1_n);
  PPL_DIRTY_TEMP_COEFFICIENT(inf1_d);
  PPL_DIRTY_TEMP_COEFFICIENT(inf2_n);
  PPL_DIRTY_TEMP_COEFFICIENT(inf2_d);
  bool minimum1;
  bool minimum2;
  bool r1 = d1.minimize(expr, inf1_n, inf1_d, minimum1);
  bool r2 = d2.minimize(expr, inf2_n, inf2_d, minimum2);
  // If neither is bounded from below, return false.
  if (!r1 && !r2)
    return false;
  // If only d2 is bounded from below, then use the values for d2.
  if (!r1) {
    inf_n = inf2_n;
    inf_d = inf2_d;
    minimum = minimum2;
    return true;
  }
  // If only d1 is bounded from below, then use the values for d1.
  if (!r2) {
    inf_n = inf1_n;
    inf_d = inf1_d;
    minimum = minimum1;
    return true;
  }
  // If both d1 and d2 are bounded from below, then use the minimum values.
  if (inf2_d * inf1_n <= inf1_d * inf2_n) {
    inf_n = inf1_n;
    inf_d = inf1_d;
    minimum = minimum1;
  }
  else {
    inf_n = inf2_n;
    inf_d = inf2_d;
    minimum = minimum2;
  }
  return true;
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::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.

Parameters:
exprThe linear expression to be minimized subject to *this;
inf_nThe numerator of the infimum value;
inf_dThe denominator of the infimum value;
minimumtrue if the infimum value can be reached in this.
gWhen minimization succeeds, will be assigned the point or closure point where expr reaches its infimum value.
Exceptions:
std::invalid_argumentThrown if expr and *this are dimension-incompatible.

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

Definition at line 361 of file Partially_Reduced_Product.templates.hh.

References PPL_ASSERT, and PPL_DIRTY_TEMP_COEFFICIENT.

                               {
  reduce();

  if (is_empty())
    return false;
  PPL_ASSERT(reduced);

  PPL_DIRTY_TEMP_COEFFICIENT(inf1_n);
  PPL_DIRTY_TEMP_COEFFICIENT(inf1_d);
  PPL_DIRTY_TEMP_COEFFICIENT(inf2_n);
  PPL_DIRTY_TEMP_COEFFICIENT(inf2_d);
  bool minimum1;
  bool minimum2;
  Generator g1(point());
  Generator g2(point());
  bool r1 = d1.minimize(expr, inf1_n, inf1_d, minimum1, g1);
  bool r2 = d2.minimize(expr, inf2_n, inf2_d, minimum2, g2);
  // If neither is bounded from below, return false.
  if (!r1 && !r2)
    return false;
  // If only d2 is bounded from below, then use the values for d2.
  if (!r1) {
    inf_n = inf2_n;
    inf_d = inf2_d;
    minimum = minimum2;
    g = g2;
    return true;
  }
  // If only d1 is bounded from below, then use the values for d1.
  if (!r2) {
    inf_n = inf1_n;
    inf_d = inf1_d;
    minimum = minimum1;
    g = g1;
    return true;
  }
  // If both d1 and d2 are bounded from below, then use the minimum values.
  if (inf2_d * inf1_n <= inf1_d * inf2_n) {
    inf_n = inf1_n;
    inf_d = inf1_d;
    minimum = minimum1;
    g = g1;
  }
  else {
    inf_n = inf2_n;
    inf_d = inf2_d;
    minimum = minimum2;
    g = g2;
  }
  return true;
}
template<typename D1 , typename D2 , typename R >
Congruence_System Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::minimized_congruences ( ) const

Returns a system of congruences which approximates *this, in reduced form.

Definition at line 81 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Congruence_System::begin(), Parma_Polyhedra_Library::Congruence_System::end(), Parma_Polyhedra_Library::Congruence_System::insert(), and Parma_Polyhedra_Library::Grid::minimized_congruences().

                                                                  {
  reduce();
  Congruence_System cgs = d2.congruences();
  const Congruence_System& cgs1 = d1.congruences();
  for (Congruence_System::const_iterator i = cgs1.begin(),
         cgs_end = cgs1.end(); i != cgs_end; ++i)
    cgs.insert(*i);
  Grid gr(cgs);
  return gr.minimized_congruences();
}
template<typename D1 , typename D2 , typename R >
Constraint_System Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::minimized_constraints ( ) const

Returns a system of constraints which approximates *this, in reduced form.

Definition at line 50 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Constraint_System::begin(), Parma_Polyhedra_Library::Constraint_System::end(), Parma_Polyhedra_Library::Constraint_System::has_strict_inequalities(), Parma_Polyhedra_Library::Constraint_System::insert(), and Parma_Polyhedra_Library::Polyhedron::minimized_constraints().

                                                                  {
  reduce();
  Constraint_System cs = d2.constraints();
  const Constraint_System& cs1 = d1.constraints();
  for (Constraint_System::const_iterator i = cs1.begin(),
         cs_end = cs1.end(); i != cs_end; ++i)
    cs.insert(*i);
  if (cs.has_strict_inequalities()) {
    NNC_Polyhedron ph(cs);
    return ph.minimized_constraints();
  }
  else {
    C_Polyhedron ph(cs);
    return ph.minimized_constraints();
  }
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::OK ( ) const
inline

Checks if all the invariants are satisfied.

Definition at line 419 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::clear_reduced_flag(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                               {
  if (reduced) {
    Partially_Reduced_Product<D1, D2, R> dp1 = *this;
    Partially_Reduced_Product<D1, D2, R> dp2 = *this;
    /* Force dp1 reduction */
    dp1.clear_reduced_flag();
    dp1.reduce();
    if (dp1 != dp2)
      return false;
  }
  return d1.OK() && d2.OK();
}
template<typename D1 , typename D2 , typename R >
Partially_Reduced_Product< D1, D2, R > & Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator= ( const Partially_Reduced_Product< D1, D2, R > &  y)
inline

The assignment operator. (*this and y can be dimension-incompatible.)

Definition at line 473 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduced.

                                              {
  d1 = y.d1;
  d2 = y.d2;
  reduced = y.reduced;
  return *this;
}
template<typename D1, typename D2, typename R>
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::print ( ) const

Prints *this to std::cerr using operator<<.

template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce ( ) const
inline

Reduce.

Definition at line 665 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_reduced().

Referenced by Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::contains(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::difference_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_disjoint_from(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::OK(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator==(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::strictly_contains(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::time_elapse_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::upper_bound_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::upper_bound_assign_if_exact(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::widening_assign().

                                                   {
  Partially_Reduced_Product& dp
    = const_cast<Partially_Reduced_Product&>(*this);
  if (dp.is_reduced())
    return false;
  R r;
  r.product_reduce(dp.d1, dp.d2);
  set_reduced_flag();
  return true;
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::refine_with_congruence ( const Congruence &  cg)
inline

Use the congruence cg to refine *this.

Parameters:
cgThe congruence to be used for refinement.
Exceptions:
std::invalid_argumentThrown if *this and cg are dimension-incompatible.

Definition at line 407 of file Partially_Reduced_Product.inlines.hh.

                                                                                 {
  d1.refine_with_congruence(cg);
  d2.refine_with_congruence(cg);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::refine_with_congruences ( const Congruence_System &  cgs)
inline

Use the congruences in cgs to refine *this.

Parameters:
cgsThe congruences to be used for refinement.
Exceptions:
std::invalid_argumentThrown if *this and cgs are dimension-incompatible.

Definition at line 443 of file Partially_Reduced_Product.inlines.hh.

                                                      {
  d1.refine_with_congruences(cgs);
  d2.refine_with_congruences(cgs);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::refine_with_constraint ( const Constraint &  c)
inline

Use the constraint c to refine *this.

Parameters:
cThe constraint to be used for refinement.
Exceptions:
std::invalid_argumentThrown if *this and c are dimension-incompatible.

Definition at line 391 of file Partially_Reduced_Product.inlines.hh.

                                                                                {
  d1.refine_with_constraint(c);
  d2.refine_with_constraint(c);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::refine_with_constraints ( const Constraint_System &  cs)
inline

Use the constraints in cs to refine *this.

Parameters:
csThe constraints to be used for refinement.
Exceptions:
std::invalid_argumentThrown if *this and cs are dimension-incompatible.

Definition at line 425 of file Partially_Reduced_Product.inlines.hh.

                                                     {
  d1.refine_with_constraints(cs);
  d2.refine_with_constraints(cs);
  clear_reduced_flag();
}
template<typename D1 , typename D2 , typename R >
Poly_Con_Relation Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::relation_with ( const Constraint &  c) const

Returns the relations holding between *this and c.

Definition at line 147 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Poly_Con_Relation::implies(), Parma_Polyhedra_Library::Poly_Con_Relation::is_disjoint(), Parma_Polyhedra_Library::Poly_Con_Relation::is_included(), Parma_Polyhedra_Library::Poly_Con_Relation::nothing(), and Parma_Polyhedra_Library::Poly_Con_Relation::saturates().

                                         {
  reduce();
  Poly_Con_Relation relation1 = d1.relation_with(c);
  Poly_Con_Relation relation2 = d2.relation_with(c);

  Poly_Con_Relation result = Poly_Con_Relation::nothing();

  if (relation1.implies(Poly_Con_Relation::is_included()))
    result = result && Poly_Con_Relation::is_included();
  else if (relation2.implies(Poly_Con_Relation::is_included()))
    result = result && Poly_Con_Relation::is_included();
  if (relation1.implies(Poly_Con_Relation::saturates()))
    result = result && Poly_Con_Relation::saturates();
  else if (relation2.implies(Poly_Con_Relation::saturates()))
    result = result && Poly_Con_Relation::saturates();
  if (relation1.implies(Poly_Con_Relation::is_disjoint()))
    result = result && Poly_Con_Relation::is_disjoint();
  else if (relation2.implies(Poly_Con_Relation::is_disjoint()))
    result = result && Poly_Con_Relation::is_disjoint();

  return result;
}
template<typename D1 , typename D2 , typename R >
Poly_Con_Relation Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::relation_with ( const Congruence &  cg) const

Returns the relations holding between *this and cg.

Definition at line 173 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Poly_Con_Relation::implies(), Parma_Polyhedra_Library::Poly_Con_Relation::is_disjoint(), Parma_Polyhedra_Library::Poly_Con_Relation::is_included(), Parma_Polyhedra_Library::Poly_Con_Relation::nothing(), and Parma_Polyhedra_Library::Poly_Con_Relation::saturates().

                                          {
  reduce();
  Poly_Con_Relation relation1 = d1.relation_with(cg);
  Poly_Con_Relation relation2 = d2.relation_with(cg);

  Poly_Con_Relation result = Poly_Con_Relation::nothing();

  if (relation1.implies(Poly_Con_Relation::is_included()))
    result = result && Poly_Con_Relation::is_included();
  else if (relation2.implies(Poly_Con_Relation::is_included()))
    result = result && Poly_Con_Relation::is_included();
  if (relation1.implies(Poly_Con_Relation::saturates()))
    result = result && Poly_Con_Relation::saturates();
  else if (relation2.implies(Poly_Con_Relation::saturates()))
    result = result && Poly_Con_Relation::saturates();
  if (relation1.implies(Poly_Con_Relation::is_disjoint()))
    result = result && Poly_Con_Relation::is_disjoint();
  else if (relation2.implies(Poly_Con_Relation::is_disjoint()))
    result = result && Poly_Con_Relation::is_disjoint();

  return result;
}
template<typename D1 , typename D2 , typename R >
Poly_Gen_Relation Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::relation_with ( const Generator &  g) const

Returns the relations holding between *this and g.

Definition at line 135 of file Partially_Reduced_Product.templates.hh.

References Parma_Polyhedra_Library::Poly_Gen_Relation::nothing(), and Parma_Polyhedra_Library::Poly_Gen_Relation::subsumes().

                                        {
  reduce();
  if (Poly_Gen_Relation::nothing() == d1.relation_with(g)
      || Poly_Gen_Relation::nothing() == d2.relation_with(g))
    return Poly_Gen_Relation::nothing();
  else
    return Poly_Gen_Relation::subsumes();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::remove_higher_space_dimensions ( dimension_type  new_dimension)
inline

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

Exceptions:
std::invalid_argumentThrown if new_dimensions is greater than the space dimension of *this.

Definition at line 613 of file Partially_Reduced_Product.inlines.hh.

                                                             {
  d1.remove_higher_space_dimensions(new_dimension);
  d2.remove_higher_space_dimensions(new_dimension);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::remove_space_dimensions ( const Variables_Set &  vars)
inline

Removes all the specified dimensions from the vector space.

Parameters:
varsThe set of Variable objects corresponding to the space dimensions to be removed.
Exceptions:
std::invalid_argumentThrown if *this is dimension-incompatible with one of the Variable objects contained in vars.

Definition at line 605 of file Partially_Reduced_Product.inlines.hh.

                                                   {
  d1.remove_space_dimensions(vars);
  d2.remove_space_dimensions(vars);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::set_reduced_flag ( ) const
inlineprotected

Sets the reduced flag.

Definition at line 690 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduced.

                                                             {
  const_cast<Partially_Reduced_Product&>(*this).reduced = true;
}
template<typename D1 , typename D2 , typename R >
dimension_type Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::space_dimension ( ) const
inline

Returns the dimension of the vector space enclosing *this.

Definition at line 182 of file Partially_Reduced_Product.inlines.hh.

References PPL_ASSERT.

Referenced by Parma_Polyhedra_Library::Box< ITV >::Box().

                                                            {
  PPL_ASSERT(d1.space_dimension() == d2.space_dimension());
  return d1.space_dimension();
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::strictly_contains ( const Partially_Reduced_Product< D1, D2, R > &  y) const
inline

Returns true if and only if each component of *this strictly contains the corresponding component of y.

Exceptions:
std::invalid_argumentThrown if *this and y are dimension-incompatible.

Definition at line 656 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                                            {
  reduce();
  y.reduce();
  return (d1.contains(y.d1) && d2.strictly_contains(y.d2))
    || (d2.contains(y.d2) && d1.strictly_contains(y.d1));
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::time_elapse_assign ( const Partially_Reduced_Product< D1, D2, R > &  y)
inline

Assigns to *this the result of computing the time-elapse between *this and y. (See also time-elapse.)

Exceptions:
std::invalid_argumentThrown if *this and y are dimension-incompatible.

Definition at line 357 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, PPL_ASSERT_HEAVY, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                                       {
  reduce();
  y.reduce();
  d1.time_elapse_assign(y.d1);
  d2.time_elapse_assign(y.d2);
  PPL_ASSERT_HEAVY(OK());
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::topological_closure_assign ( )
inline

Assigns to *this its topological closure.

Definition at line 367 of file Partially_Reduced_Product.inlines.hh.

                                                                 {
  d1.topological_closure_assign();
  d2.topological_closure_assign();
}
template<typename D1 , typename D2 , typename R >
memory_size_type Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::total_memory_in_bytes ( ) const
inline

Returns the total size in bytes of the memory occupied by *this.

Definition at line 176 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::external_memory_in_bytes().

                                                                  {
  return sizeof(*this) + external_memory_in_bytes();
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::unconstrain ( Variable  var)
inline

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

Parameters:
varThe space dimension that will be unconstrained.
Exceptions:
std::invalid_argumentThrown if var is not a space dimension of *this.

Definition at line 199 of file Partially_Reduced_Product.inlines.hh.

                                {
  reduce();
  d1.unconstrain(var);
  d2.unconstrain(var);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::unconstrain ( const Variables_Set &  vars)
inline

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

Parameters:
varsThe set of space dimension that will be unconstrained.
Exceptions:
std::invalid_argumentThrown if *this is dimension-incompatible with one of the Variable objects contained in vars.

Definition at line 207 of file Partially_Reduced_Product.inlines.hh.

                                                                           {
  reduce();
  d1.unconstrain(vars);
  d2.unconstrain(vars);
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::upper_bound_assign ( const Partially_Reduced_Product< D1, D2, R > &  y)
inline

Assigns to *this an upper bound of *this and y computed on the corresponding components.

Exceptions:
std::invalid_argumentThrown if *this and y are dimension-incompatible.

Definition at line 236 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                                       {
  reduce();
  y.reduce();
  d1.upper_bound_assign(y.d1);
  d2.upper_bound_assign(y.d2);
}
template<typename D1 , typename D2 , typename R >
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::upper_bound_assign_if_exact ( const Partially_Reduced_Product< D1, D2, R > &  y)
inline

Assigns to *this an upper bound of *this and y computed on the corresponding components. If it is exact on each of the components of *this, true is returned, otherwise false is returned.

Exceptions:
std::invalid_argumentThrown if *this and y are dimension-incompatible.

Definition at line 246 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce(), and Parma_Polyhedra_Library::swap().

                                                                {
  reduce();
  y.reduce();
  D1 d1_copy = d1;
  bool ub_exact = d1_copy.upper_bound_assign_if_exact(y.d1);
  if (!ub_exact)
    return false;
  ub_exact = d2.upper_bound_assign_if_exact(y.d2);
  if (!ub_exact)
    return false;
  using std::swap;
  swap(d1, d1_copy);
  return true;
}
template<typename D1 , typename D2 , typename R >
void Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::widening_assign ( const Partially_Reduced_Product< D1, D2, R > &  y,
unsigned *  tp = NULL 
)
inline

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

This widening uses either the congruence or generator systems depending on which of the systems describing x and y are up to date and minimized.

Parameters:
yA product that must be contained in *this;
tpAn optional pointer to an unsigned variable storing the number of available tokens (to be used when applying the widening with tokens delay technique).
Exceptions:
std::invalid_argumentThrown if *this and y are dimension-incompatible.

Definition at line 563 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                {
  // FIXME(0.10.1): In general this is _NOT_ a widening since the reduction
  //        may mean that the sequence does not satisfy the ascending
  //        chain condition.
  //        However, for the direct, smash and constraints product
  //        it may be ok - but this still needs checking.
  reduce();
  y.reduce();
  d1.widening_assign(y.d1, tp);
  d2.widening_assign(y.d2, tp);
}

Friends And Related Function Documentation

template<typename D1 , typename D2 , typename R >
bool operator!= ( const Partially_Reduced_Product< D1, D2, R > &  x,
const Partially_Reduced_Product< D1, D2, R > &  y 
)
related

Returns true if and only if the components of x and y are not pairwise equal.

Note that x and y may be dimension-incompatible: in those cases, the value true is returned.

template<typename D1 , typename D2 , typename R >
bool operator!= ( const Partially_Reduced_Product< D1, D2, R > &  x,
const Partially_Reduced_Product< D1, D2, R > &  y 
)
related

Definition at line 728 of file Partially_Reduced_Product.inlines.hh.

                                                          {
  return !(x == y);
}
template<typename D1 , typename D2 , typename R >
std::ostream & operator<< ( std::ostream &  s,
const Partially_Reduced_Product< D1, D2, R > &  dp 
)
related

Output operator.

Writes a textual representation of dp on s.

template<typename D1 , typename D2 , typename R >
std::ostream & operator<< ( std::ostream &  s,
const Partially_Reduced_Product< D1, D2, R > &  dp 
)
related

Definition at line 736 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2.

                                                                         {
  return s << "Domain 1:\n"
           << dp.d1
           << "Domain 2:\n"
           << dp.d2;
}
template<typename D1 , typename D2 , typename R >
bool operator== ( const Partially_Reduced_Product< D1, D2, R > &  x,
const Partially_Reduced_Product< D1, D2, R > &  y 
)
related

Returns true if and only if the components of x and y are pairwise equal.

Note that x and y may be dimension-incompatible: in those cases, the value false is returned.

template<typename D1 , typename D2 , typename R >
bool operator== ( const Partially_Reduced_Product< D1, D2, R > &  x,
const Partially_Reduced_Product< D1, D2, R > &  y 
)
related

Definition at line 718 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1, Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2, and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce().

                                                          {
  x.reduce();
  y.reduce();
  return x.d1 == y.d1 && x.d2 == y.d2;
}
template<typename D1, typename D2, typename R>
bool operator== ( const Partially_Reduced_Product< D1, D2, R > &  x,
const Partially_Reduced_Product< D1, D2, R > &  y 
)
friend
template<typename D1, typename D2, typename R>
std::ostream& Parma_Polyhedra_Library::IO_Operators::operator<< ( std::ostream &  s,
const Partially_Reduced_Product< D1, D2, R > &  dp 
)
friend
template<typename D1 , typename D2 , typename R >
void swap ( Partially_Reduced_Product< D1, D2, R > &  x,
Partially_Reduced_Product< D1, D2, R > &  y 
)
related

Swaps x with y.

template<typename D1 , typename D2 , typename R >
void swap ( Partially_Reduced_Product< D1, D2, R > &  x,
Partially_Reduced_Product< D1, D2, R > &  y 
)
related

Definition at line 805 of file Partially_Reduced_Product.inlines.hh.

References Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::m_swap().

                                              {
  x.m_swap(y);
}

Member Data Documentation

template<typename D1, typename D2, typename R>
D1 Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d1
protected

The first component.

Definition at line 1629 of file Partially_Reduced_Product.defs.hh.

Referenced by Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::concatenate_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::contains(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::difference_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::intersection_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_disjoint_from(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::m_swap(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator<<(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator=(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator==(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::strictly_contains(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::time_elapse_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::upper_bound_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::upper_bound_assign_if_exact(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::widening_assign().

template<typename D1, typename D2, typename R>
D2 Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::d2
protected

The second component.

Definition at line 1632 of file Partially_Reduced_Product.defs.hh.

Referenced by Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::concatenate_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::contains(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::difference_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::intersection_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::is_disjoint_from(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::m_swap(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator<<(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator=(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator==(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduce(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::strictly_contains(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::time_elapse_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::upper_bound_assign(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::upper_bound_assign_if_exact(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::widening_assign().

template<typename D1, typename D2, typename R>
bool Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::reduced
protected

Flag to record whether the components are reduced with respect to each other and the reduction class.

Definition at line 1648 of file Partially_Reduced_Product.defs.hh.

Referenced by Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::clear_reduced_flag(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::m_swap(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::operator=(), Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::Partially_Reduced_Product(), and Parma_Polyhedra_Library::Partially_Reduced_Product< D1, D2, R >::set_reduced_flag().

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