Parma_Polyhedra_Library::Congruence_System Class Reference
[C++ Language Interface]

A system of congruences. More...

#include <Congruence_System.defs.hh>

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List of all members.

Public Member Functions

 Congruence_System ()
 Default constructor: builds an empty system of congruences.
 Congruence_System (const Congruence &cg)
 Builds the singleton system containing only congruence cg.
 Congruence_System (const Constraint &c)
 If c represents the constraint $ e_1 = e_2 $, builds the singleton system containing only constraint $ e_1 = e_2 \pmod{0}$.
 Congruence_System (const Constraint_System &cs)
 Builds a system containing copies of any equalities in cs.
 Congruence_System (const Congruence_System &cgs)
 Ordinary copy-constructor.
 ~Congruence_System ()
 Destructor.
Congruence_System & operator= (const Congruence_System &cgs)
 Assignment operator.
dimension_type space_dimension () const
 Returns the dimension of the vector space enclosing *this.
bool is_equal_to (const Congruence_System &cgs) const
 Returns true if and only if *this is exactly equal to cgs.
bool has_linear_equalities () const
 Returns true if and only if *this contains one or more linear equalities.
void clear ()
 Removes all the congruences and sets the space dimension to 0.
void insert (const Congruence &cg)
 Inserts in *this a copy of the congruence cg, increasing the number of space dimensions if needed.
void insert (const Constraint &c)
 Inserts in *this a copy of the equality constraint c, seen as a modulo 0 congruence, increasing the number of space dimensions if needed.
void insert (const Congruence_System &cgs)
 Inserts in *this a copy of the congruences in cgs, increasing the number of space dimensions if needed.
void recycling_insert (Congruence_System &cgs)
 Inserts into *this the congruences in cgs, increasing the number of space dimensions if needed.
const_iterator begin () const
 Returns the const_iterator pointing to the first congruence, if this is not empty; otherwise, returns the past-the-end const_iterator.
const_iterator end () const
 Returns the past-the-end const_iterator.
bool OK () const
 Checks if all the invariants are satisfied.
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) 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.
dimension_type num_equalities () const
 Returns the number of equalities.
dimension_type num_proper_congruences () const
 Returns the number of proper congruences.
void swap (Congruence_System &cgs)
 Swaps *this with y.
void add_unit_rows_and_columns (dimension_type dims)
 Adds dims rows and dims columns of zeroes to the matrix, initializing the added rows as in the unit congruence system.
void concatenate (const Congruence_System &cgs)
 Concatenates copies of the congruences from cgs onto *this.

Static Public Member Functions

static dimension_type max_space_dimension ()
 Returns the maximum space dimension a Congruence_System can handle.
static const Congruence_System & zero_dim_empty ()
 Returns the system containing only Congruence::zero_dim_false().

Protected Member Functions

bool satisfies_all_congruences (const Grid_Generator &g) const
 Returns true if g satisfies all the congruences.

Private Member Functions

void normalize_moduli ()
 Adjusts all expressions to have the same moduli.
bool increase_space_dimension (const dimension_type new_space_dim)
 Increase the number of space dimensions to new_space_dim.
void insert_verbatim (const Congruence &cg)
 Inserts in *this an exact copy of the congruence cg, increasing the number of space dimensions if needed.
Congruence & operator[] (dimension_type k)
 Returns the k- th congruence of the system.
const Congruence & operator[] (dimension_type k) const
 Returns a constant reference to the k- th congruence of the system.
bool has_a_free_dimension () const
 Returns true if and only if any of the dimensions in *this is free of constraint.
void affine_preimage (dimension_type v, const Linear_Expression &expr, Coefficient_traits::const_reference denominator)
 Substitutes a given column of coefficients by a given affine expression.
void resize_no_copy (dimension_type new_n_rows, dimension_type new_n_columns)
 Resizes the system without worrying about the old contents.

Friends

class const_iterator
class Grid
class Grid_Certificate
void swap (Parma_Polyhedra_Library::Congruence_System &x, Parma_Polyhedra_Library::Congruence_System &y)
 Specializes std::swap.
bool operator== (const Congruence_System &x, const Congruence_System &y)
 Returns true if and only if x and y are equivalent.

Related Functions

(Note that these are not member functions.)

std::ostream & operator<< (std::ostream &s, const Congruence_System &cgs)
 Output operator.

Classes

class  const_iterator
 An iterator over a system of congruences. More...

Detailed Description

A system of congruences.

An object of the class Congruence_System is a system of congruences, i.e., a multiset of objects of the class Congruence. When inserting congruences in a system, space dimensions are automatically adjusted so that all the congruences in the system are defined on the same vector space.

In all the examples it is assumed that variables x and y are defined as follows: 
  Variable x(0);
  Variable y(1);
Example 1
The following code builds a system of congruences corresponding to an integer grid in $\Rset^2$: 
  Congruence_System cgs;
  cgs.insert(x %= 0);
  cgs.insert(y %= 0);
Note that: the congruence system is created with space dimension zero; the first and second congruence insertions increase the space dimension to $1$ and $2$, respectively.
Example 2
By adding to the congruence system of the previous example, the congruence $x + y = 1 \pmod{2}$: 
  cgs.insert((x + y %= 1) / 2);
we obtain the grid containing just those integral points where the sum of the x and y values is odd.
Example 3
The following code builds a system of congruences corresponding to the grid in $\Zset^2$ containing just the integral points on the x axis: 
  Congruence_System cgs;
  cgs.insert(x %= 0);
  cgs.insert((y %= 0) / 0);
Note:
After inserting a multiset of congruences in a congruence system, there are no guarantees that an exact copy of them can be retrieved: in general, only an equivalent congruence system will be available, where original congruences may have been reordered, removed (if they are trivial, duplicate or implied by other congruences), linearly combined, etc.

Definition at line 127 of file Congruence_System.defs.hh.

Constructor & Destructor Documentation

Parma_Polyhedra_Library::Congruence_System::Congruence_System (  )  [inline]

Default constructor: builds an empty system of congruences.

Definition at line 31 of file Congruence_System.inlines.hh.

00032   : Matrix(0, 2) {
00033 }

Parma_Polyhedra_Library::Congruence_System::Congruence_System ( const Congruence &  cg  )  [inline, explicit]

Builds the singleton system containing only congruence cg.

Definition at line 36 of file Congruence_System.inlines.hh.

References insert().

00037   : Matrix(0, 2) {
00038   insert(cg);
00039 }

Parma_Polyhedra_Library::Congruence_System::Congruence_System ( const Constraint &  c  )  [inline, explicit]

If c represents the constraint $ e_1 = e_2 $, builds the singleton system containing only constraint $ e_1 = e_2 \pmod{0}$.

Exceptions:
std::invalid_argument Thrown if c is not an equality constraint.

Definition at line 42 of file Congruence_System.inlines.hh.

References insert().

00043   : Matrix(0, 2) {
00044   insert(c);
00045 }

Parma_Polyhedra_Library::Congruence_System::Congruence_System ( const Constraint_System &  cs  )  [explicit]

Builds a system containing copies of any equalities in cs.

Definition at line 40 of file Congruence_System.cc.

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

00041   : Matrix(0, 2) {
00042   for (Constraint_System::const_iterator i = cs.begin(),
00043          cs_end = cs.end(); i != cs_end; ++i)
00044     if (i->is_equality())
00045       insert(*i);
00046 }

Parma_Polyhedra_Library::Congruence_System::Congruence_System ( const Congruence_System &  cgs  )  [inline]

Ordinary copy-constructor.

Definition at line 48 of file Congruence_System.inlines.hh.

00049   : Matrix(cs) {
00050 }

Parma_Polyhedra_Library::Congruence_System::~Congruence_System (  )  [inline]

Destructor.

Definition at line 53 of file Congruence_System.inlines.hh.

00053                                       {
00054 }

Member Function Documentation

Congruence_System & Parma_Polyhedra_Library::Congruence_System::operator= ( const Congruence_System &  cgs  )  [inline]

Assignment operator.

Definition at line 57 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::operator=().

00057                                                        {
00058   Matrix::operator=(y);
00059   return *this;
00060 }

dimension_type Parma_Polyhedra_Library::Congruence_System::max_space_dimension (  )  [inline, static]

Returns the maximum space dimension a Congruence_System can handle.

Definition at line 73 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::max_num_columns().

Referenced by Parma_Polyhedra_Library::Grid::max_space_dimension().

00073                                        {
00074   return Matrix::max_num_columns() - 2;
00075 }

dimension_type Parma_Polyhedra_Library::Congruence_System::space_dimension (  )  const [inline]

Returns the dimension of the vector space enclosing *this.

Definition at line 78 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::num_columns().

Referenced by Parma_Polyhedra_Library::Polyhedron::add_congruences(), Parma_Polyhedra_Library::Grid::add_congruences(), Parma_Polyhedra_Library::Grid::add_recycled_congruences(), Parma_Polyhedra_Library::Grid::add_recycled_congruences_and_minimize(), affine_preimage(), concatenate(), Parma_Polyhedra_Library::Grid::construct(), Parma_Polyhedra_Library::Grid::Grid(), has_a_free_dimension(), increase_space_dimension(), Parma_Polyhedra_Library::Grid::limited_extrapolation_assign(), Parma_Polyhedra_Library::Grid::OK(), satisfies_all_congruences(), Parma_Polyhedra_Library::Grid::select_wider_congruences(), Parma_Polyhedra_Library::Polyhedron::throw_dimension_incompatible(), and Parma_Polyhedra_Library::Grid::throw_dimension_incompatible().

00078                                          {
00079   return Matrix::num_columns() - 2;
00080 }

bool Parma_Polyhedra_Library::Congruence_System::is_equal_to ( const Congruence_System &  cgs  )  const

Returns true if and only if *this is exactly equal to cgs.

Definition at line 224 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::num_columns(), and Parma_Polyhedra_Library::Matrix::num_rows().

Referenced by Parma_Polyhedra_Library::Grid::OK().

00224                                                                     {
00225   if (num_rows() != cgs.num_rows())
00226     return false;
00227 
00228   for (dimension_type row = 0; row < cgs.num_rows(); ++row)
00229     for (dimension_type col = 0; col < cgs.num_columns(); ++col) {
00230       if (operator[](row)[col] == cgs[row][col])
00231         continue;
00232       return false;
00233     }
00234   return true;
00235 }

bool Parma_Polyhedra_Library::Congruence_System::has_linear_equalities (  )  const

Returns true if and only if *this contains one or more linear equalities.

Definition at line 238 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::num_columns(), and Parma_Polyhedra_Library::Matrix::num_rows().

00238                                                   {
00239   const Congruence_System& cgs = *this;
00240   dimension_type modulus_index = cgs.num_columns() - 1;
00241   for (dimension_type i = cgs.num_rows(); i-- > 0; )
00242     if (cgs[i][modulus_index] == 0)
00243       return true;
00244   return false;
00245 }

void Parma_Polyhedra_Library::Congruence_System::clear (  )  [inline]

Removes all the congruences and sets the space dimension to 0.

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 83 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::add_zero_columns(), and Parma_Polyhedra_Library::Matrix::clear().

Referenced by Parma_Polyhedra_Library::Grid::set_zero_dim_univ().

00083                          {
00084   Matrix::clear();
00085   add_zero_columns(2);          // Modulus and constant term.
00086 }

void Parma_Polyhedra_Library::Congruence_System::insert ( const Congruence &  cg  )  [inline]

Inserts in *this a copy of the congruence cg, increasing the number of space dimensions if needed.

The copy of cg will be strongly normalized after being inserted.

Definition at line 89 of file Congruence_System.inlines.hh.

References insert_verbatim(), OK(), operator[](), and Parma_Polyhedra_Library::Matrix::rows.

Referenced by Parma_Polyhedra_Library::Grid::add_congruence(), Congruence_System(), Parma_Polyhedra_Library::Grid::Grid(), Parma_Polyhedra_Library::Grid::intersection_assign(), Parma_Polyhedra_Library::Grid::limited_extrapolation_assign(), and Parma_Polyhedra_Library::Grid::select_wider_congruences().

00089                                               {
00090   insert_verbatim(cg);
00091   static_cast<Congruence&>(operator[](rows.size()-1)).strong_normalize();
00092   assert(OK());
00093 }

void Parma_Polyhedra_Library::Congruence_System::insert ( const Constraint &  c  ) 

Inserts in *this a copy of the equality constraint c, seen as a modulo 0 congruence, increasing the number of space dimensions if needed.

The modulo 0 congruence will be strongly normalized after being inserted.

Exceptions:
std::invalid_argument Thrown if c is a relation.

Definition at line 98 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::add_recycled_row(), Parma_Polyhedra_Library::Matrix::add_zero_columns(), Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), OK(), operator[](), Parma_Polyhedra_Library::Matrix::row_capacity, Parma_Polyhedra_Library::Matrix::rows, Parma_Polyhedra_Library::Constraint::space_dimension(), and Parma_Polyhedra_Library::Matrix::swap_columns().

00098                                                 {
00099   dimension_type cg_size = c.space_dimension() + 2;
00100   const dimension_type old_num_columns = num_columns();
00101   if (cg_size < old_num_columns) {
00102     // Create a congruence of the required size from `c'.
00103     Congruence cg(c, old_num_columns, row_capacity);
00104     add_recycled_row(cg);
00105   }
00106   else {
00107     if (cg_size > old_num_columns) {
00108       // Resize the system, if necessary.
00109       add_zero_columns(cg_size - old_num_columns);
00110       if (num_rows() != 0)
00111         // Move the moduli to the last column.
00112         swap_columns(old_num_columns - 1, cg_size - 1);
00113     }
00114     Congruence cg(c, cg_size, row_capacity);
00115     add_recycled_row(cg);
00116   }
00117   operator[](rows.size()-1).strong_normalize();
00118 
00119   assert(OK());
00120 }

void Parma_Polyhedra_Library::Congruence_System::insert ( const Congruence_System &  cgs  ) 

Inserts in *this a copy of the congruences in cgs, increasing the number of space dimensions if needed.

The inserted copies will be strongly normalized.

Definition at line 154 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::add_zero_rows(), Parma_Polyhedra_Library::Matrix::add_zero_rows_and_columns(), Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), OK(), Parma_Polyhedra_Library::Matrix::row_capacity, Parma_Polyhedra_Library::Matrix::row_size, and Parma_Polyhedra_Library::Matrix::swap_columns().

00154                                                        {
00155   Congruence_System& x = *this;
00156 
00157   const dimension_type x_n_rows = x.num_rows();
00158   const dimension_type y_n_rows = y.num_rows();
00159   const dimension_type old_n_cols = x.num_columns();
00160   const dimension_type y_n_cols = y.num_columns();
00161   // Grow to the required size.
00162   if (old_n_cols >= y_n_cols)
00163     add_zero_rows(y_n_rows, Row::Flags());
00164   else {
00165     add_zero_rows_and_columns(y_n_rows,
00166                               y_n_cols - old_n_cols,
00167                               Row::Flags());
00168     // Swap the modulus column into the new last column.
00169     swap_columns(old_n_cols - 1, num_columns() - 1);
00170   }
00171 
00172   // Copy the rows of `y', forcing size and capacity.
00173   const dimension_type x_mod_index = x.num_columns() - 1;
00174   const dimension_type y_mod_index = y_n_cols - 1;
00175   for (dimension_type i = y_n_rows; i-- > 0; ) {
00176     Row copy(y[i], x.row_size, x.row_capacity);
00177     // Swap the modulus to the correct column.
00178     std::swap(copy[x_mod_index], copy[y_mod_index]);
00179     std::swap(copy, x[x_n_rows+i]);
00180   }
00181   assert(OK());
00182 }

void Parma_Polyhedra_Library::Congruence_System::recycling_insert ( Congruence_System &  cgs  ) 

Inserts into *this the congruences in cgs, increasing the number of space dimensions if needed.

Definition at line 123 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::add_zero_rows(), Parma_Polyhedra_Library::Matrix::add_zero_rows_and_columns(), Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), OK(), operator[](), and Parma_Polyhedra_Library::Matrix::swap_columns().

Referenced by Parma_Polyhedra_Library::Grid::add_recycled_congruences(), and Parma_Polyhedra_Library::Grid::add_recycled_congruences_and_minimize().

00123                                                              {
00124   const dimension_type old_num_rows = num_rows();
00125   const dimension_type cgs_num_rows = cgs.num_rows();
00126   const dimension_type old_num_cols = num_columns();
00127   dimension_type cgs_num_cols = cgs.num_columns();
00128   if (old_num_cols >= cgs_num_cols)
00129     add_zero_rows(cgs_num_rows, Row::Flags());
00130   else {
00131     add_zero_rows_and_columns(cgs_num_rows,
00132                               cgs_num_cols - old_num_cols,
00133                               Row::Flags());
00134     // Swap the modulus column into the new last column.
00135     swap_columns(old_num_cols - 1, num_columns() - 1);
00136   }
00137   --cgs_num_cols; // Convert to modulus index.
00138   const dimension_type mod_index = num_columns() - 1;
00139   for (dimension_type i = cgs_num_rows; i-- > 0; ) {
00140     // Swap one coefficient at a time into the newly added rows, instead
00141     // of swapping each entire row.  This ensures that the added rows
00142     // have the same capacities as the existing rows.
00143     Congruence& new_cg = operator[](old_num_rows + i);
00144     Congruence& old_cg = cgs[i];
00145     for (dimension_type j = cgs_num_cols; j-- > 0; )
00146       std::swap(new_cg[j], old_cg[j]);
00147     std::swap(new_cg[mod_index], old_cg[cgs_num_cols]); // Modulus.
00148   }
00149 
00150   assert(OK());
00151 }

const Congruence_System & Parma_Polyhedra_Library::Congruence_System::zero_dim_empty (  )  [inline, static]

Returns the system containing only Congruence::zero_dim_false().

Definition at line 102 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Congruence::zero_dim_false().

00102                                   {
00103   static const Congruence_System zdf(Congruence::zero_dim_false());
00104   return zdf;
00105 }

Congruence_System::const_iterator Parma_Polyhedra_Library::Congruence_System::begin (  )  const [inline]

Returns the const_iterator pointing to the first congruence, if this is not empty; otherwise, returns the past-the-end const_iterator.

Reimplemented from Parma_Polyhedra_Library::Matrix.

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

References Parma_Polyhedra_Library::Matrix::begin().

Referenced by Parma_Polyhedra_Library::Polyhedron::add_congruences(), Parma_Polyhedra_Library::Grid::add_recycled_congruences(), Parma_Polyhedra_Library::Grid::add_recycled_congruences_and_minimize(), Parma_Polyhedra_Library::Grid::expand_space_dimension(), Parma_Polyhedra_Library::Grid::grid_difference_assign(), and operator<<().

00170                                {
00171   const_iterator i(Matrix::begin(), *this);
00172   i.skip_forward();
00173   return i;
00174 }

Congruence_System::const_iterator Parma_Polyhedra_Library::Congruence_System::end (  )  const [inline]

Returns the past-the-end const_iterator.

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 177 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::end().

Referenced by Parma_Polyhedra_Library::Polyhedron::add_congruences(), Parma_Polyhedra_Library::Grid::add_recycled_congruences(), Parma_Polyhedra_Library::Grid::add_recycled_congruences_and_minimize(), Parma_Polyhedra_Library::Grid::expand_space_dimension(), Parma_Polyhedra_Library::Grid::grid_difference_assign(), and operator<<().

00177                              {
00178   const const_iterator i(Matrix::end(), *this);
00179   return i;
00180 }

bool Parma_Polyhedra_Library::Congruence_System::OK (  )  const

Checks if all the invariants are satisfied.

Returns true if and only if *this is a valid Matrix, each row in the system is a valid Congruence and the number of columns is consistent with the number of congruences.

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 428 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), Parma_Polyhedra_Library::Congruence::OK(), and Parma_Polyhedra_Library::Matrix::OK().

Referenced by ascii_load(), increase_space_dimension(), insert(), insert_verbatim(), normalize_moduli(), Parma_Polyhedra_Library::Grid::OK(), recycling_insert(), and Parma_Polyhedra_Library::Grid::simplify().

00428                                {
00429   // A Congruence_System must be a valid Matrix.
00430   if (!Matrix::OK())
00431     return false;
00432 
00433   if (num_rows()) {
00434     if (num_columns() < 2) {
00435 #ifndef NDEBUG
00436       std::cerr << "Congruence_System has rows and fewer than two columns."
00437                 << std::endl;
00438 #endif
00439       return false;
00440     }
00441   }
00442 
00443   // Checking each congruence in the system.
00444   const Congruence_System& x = *this;
00445   for (dimension_type i = num_rows(); i-- > 0; ) {
00446     const Congruence& cg = x[i];
00447     if (!cg.OK())
00448       return false;
00449   }
00450 
00451   // All checks passed.
00452   return true;
00453 }

void Parma_Polyhedra_Library::Congruence_System::ascii_dump (  )  const

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

Reimplemented from Parma_Polyhedra_Library::Matrix.

Referenced by Parma_Polyhedra_Library::Grid::ascii_dump(), ascii_dump(), Parma_Polyhedra_Library::Grid::conversion(), Parma_Polyhedra_Library::Grid::OK(), and Parma_Polyhedra_Library::Grid::simplify().

void Parma_Polyhedra_Library::Congruence_System::ascii_dump ( std::ostream &  s  )  const

Writes to s an ASCII representation of *this.

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 392 of file Congruence_System.cc.

References ascii_dump(), Parma_Polyhedra_Library::Matrix::num_columns(), and Parma_Polyhedra_Library::Matrix::num_rows().

00392                                                     {
00393   const Congruence_System& x = *this;
00394   dimension_type x_num_rows = x.num_rows();
00395   dimension_type x_num_columns = x.num_columns();
00396   s << x_num_rows << " x " << x_num_columns
00397     << std::endl;
00398   if (x_num_rows && x_num_columns)
00399     for (dimension_type i = 0; i < x_num_rows; ++i)
00400       x[i].ascii_dump(s);
00401 }

void Parma_Polyhedra_Library::Congruence_System::print (  )  const

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

Reimplemented from Parma_Polyhedra_Library::Matrix.

bool Parma_Polyhedra_Library::Congruence_System::ascii_load ( std::istream &  s  ) 

Loads from s an ASCII representation (as produced by ascii_dump) and sets *this accordingly. Returns true if successful, false otherwise.

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 406 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::num_rows(), OK(), and resize_no_copy().

Referenced by Parma_Polyhedra_Library::Grid::ascii_load().

00406                                               {
00407   std::string str;
00408   dimension_type nrows;
00409   dimension_type ncols;
00410   if (!(s >> nrows))
00411     return false;
00412   if (!(s >> str))
00413     return false;
00414   if (!(s >> ncols))
00415     return false;
00416   resize_no_copy(nrows, ncols);
00417 
00418   Congruence_System& x = *this;
00419   for (dimension_type i = 0; i < x.num_rows(); ++i)
00420     x[i].ascii_load(s);
00421 
00422   // Check for well-formedness.
00423   assert(OK());
00424   return true;
00425 }

memory_size_type Parma_Polyhedra_Library::Congruence_System::total_memory_in_bytes (  )  const [inline]

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

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 193 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Checked::total_memory_in_bytes().

00193                                                {
00194   return Matrix::total_memory_in_bytes();
00195 }

memory_size_type Parma_Polyhedra_Library::Congruence_System::external_memory_in_bytes (  )  const [inline]

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

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 188 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Checked::external_memory_in_bytes().

Referenced by Parma_Polyhedra_Library::Grid::external_memory_in_bytes().

00188                                                   {
00189   return Matrix::external_memory_in_bytes();
00190 }

PPL::dimension_type Parma_Polyhedra_Library::Congruence_System::num_equalities (  )  const

Returns the number of equalities.

Definition at line 255 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::num_rows().

Referenced by Parma_Polyhedra_Library::Grid_Certificate::Grid_Certificate(), Parma_Polyhedra_Library::Grid::quick_equivalence_test(), and Parma_Polyhedra_Library::Grid::widening_assign().

00255                                            {
00256   const Congruence_System& cgs = *this;
00257   dimension_type n = 0;
00258   for (dimension_type i = num_rows(); i-- > 0 ; )
00259     if (cgs[i].is_equality())
00260       ++n;
00261   return n;
00262 }

PPL::dimension_type Parma_Polyhedra_Library::Congruence_System::num_proper_congruences (  )  const

Returns the number of proper congruences.

Definition at line 265 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Congruence::is_proper_congruence(), and Parma_Polyhedra_Library::Matrix::num_rows().

Referenced by Parma_Polyhedra_Library::Grid_Certificate::Grid_Certificate().

00265                                                    {
00266   const Congruence_System& cgs = *this;
00267   dimension_type n = 0;
00268   for (dimension_type i = num_rows(); i-- > 0 ; ) {
00269     const Congruence& cg = cgs[i];
00270     if (cg.is_proper_congruence())
00271       ++n;
00272   }
00273   return n;
00274 }

void Parma_Polyhedra_Library::Congruence_System::swap ( Congruence_System &  cgs  )  [inline]

Swaps *this with y.

Definition at line 183 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::swap().

Referenced by Parma_Polyhedra_Library::Grid::Grid().

00183                                             {
00184   Matrix::swap(y);
00185 }

void Parma_Polyhedra_Library::Congruence_System::add_unit_rows_and_columns ( dimension_type  dims  ) 

Adds dims rows and dims columns of zeroes to the matrix, initializing the added rows as in the unit congruence system.

Parameters:
dims The number of rows and columns to be added: must be strictly positive.
Turns the $r \times c$ matrix $A$ into the $(r+dims) \times (c+dims)$ matrix $\bigl({0 \atop A}{B \atop A}\bigr)$ where $B$ is the $dims \times dims$ unit matrix of the form $\bigl({0 \atop 1}{1 \atop 0}\bigr)$. The matrix is expanded avoiding reallocation whenever possible.

Definition at line 490 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::add_zero_rows_and_columns(), Parma_Polyhedra_Library::Linear_Row::LINE_OR_EQUALITY, Parma_Polyhedra_Library::NECESSARILY_CLOSED, Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), and Parma_Polyhedra_Library::Matrix::swap_columns().

Referenced by Parma_Polyhedra_Library::Grid::add_space_dimensions(), and Parma_Polyhedra_Library::Grid::add_space_dimensions_and_project().

00490                                                                    {
00491   assert(num_columns() > 0);
00492   dimension_type col = num_columns() - 1;
00493   dimension_type old_num_rows = num_rows();
00494   add_zero_rows_and_columns(dims, dims,
00495                             Linear_Row::Flags(NECESSARILY_CLOSED,
00496                                               Linear_Row::LINE_OR_EQUALITY));
00497   // Swap the modulus column into the new last column.
00498   swap_columns(col, col + dims);
00499 
00500   // Swap the added columns to the front of the matrix.
00501   for (dimension_type row = old_num_rows; row-- > 0; )
00502     std::swap(operator[](row), operator[](row + dims));
00503 
00504   col += dims - 1;
00505   // Set the diagonal element of each added row.
00506   for (dimension_type row = 0; row < dims; ++row)
00507     const_cast<Coefficient&>(operator[](row)[col - row]) = 1;
00508 }

void Parma_Polyhedra_Library::Congruence_System::concatenate ( const Congruence_System &  cgs  ) 

Concatenates copies of the congruences from cgs onto *this.

The matrix for the new system of congruences is obtained by leaving the old system in the upper left-hand side and placing the congruences of cgs in the lower right-hand side, and padding with zeroes.

Definition at line 511 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::add_zero_rows_and_columns(), increase_space_dimension(), Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), operator[](), and space_dimension().

Referenced by Parma_Polyhedra_Library::Grid::concatenate_assign().

00511                                                                     {
00512   // TODO: this implementation is just an executable specification.
00513   Congruence_System cgs = const_cgs;
00514 
00515   dimension_type added_rows = cgs.num_rows();
00516   dimension_type added_columns = cgs.space_dimension();
00517 
00518   if (added_rows == 0) {
00519     increase_space_dimension(space_dimension() + added_columns);
00520     return;
00521   }
00522 
00523   dimension_type old_num_rows = num_rows();
00524   dimension_type old_modi = num_columns() - 1;
00525   dimension_type old_space_dim = space_dimension();
00526 
00527   add_zero_rows_and_columns(added_rows, added_columns,
00528                             Row::Flags());
00529 
00530   dimension_type cgs_num_columns = cgs.num_columns();
00531   dimension_type modi = num_columns() - 1;
00532 
00533   // Swap the modulus and the new last column, in the old rows.
00534   for (dimension_type i = 0; i < old_num_rows; ++i) {
00535     Congruence& cg = operator[](i);
00536     std::swap(cg[old_modi], cg[modi]);
00537   }
00538 
00539   // Move the congruences into *this from `cgs', shifting the
00540   // coefficients along into the appropriate columns.
00541   for (dimension_type i = added_rows; i-- > 0; ) {
00542     Congruence& cg_old = cgs[i];
00543     Congruence& cg_new = operator[](old_num_rows + i);
00544     // The inhomogeneous term is moved to the same column.
00545     std::swap(cg_new[0], cg_old[0]);
00546     // All homogeneous terms are shifted by `space_dim' columns.
00547     for (dimension_type j = 1; j < cgs_num_columns; ++j)
00548       std::swap(cg_old[j], cg_new[old_space_dim + j]);
00549   }
00550 }

bool Parma_Polyhedra_Library::Congruence_System::satisfies_all_congruences ( const Grid_Generator &  g  )  const [protected]

Returns true if g satisfies all the congruences.

Definition at line 278 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Scalar_Products::assign(), Parma_Polyhedra_Library::Grid_Generator::divisor(), Parma_Polyhedra_Library::Congruence::is_equality(), Parma_Polyhedra_Library::Grid_Generator::is_line(), Parma_Polyhedra_Library::Congruence::modulus(), space_dimension(), Parma_Polyhedra_Library::Grid_Generator::space_dimension(), and TEMP_INTEGER.

Referenced by Parma_Polyhedra_Library::Grid::is_included_in(), Parma_Polyhedra_Library::Grid::is_universe(), and Parma_Polyhedra_Library::Grid::relation_with().

00278                                                          {
00279   assert(g.space_dimension() <= space_dimension());
00280 
00281   const Congruence_System& cgs = *this;
00282   TEMP_INTEGER(sp);
00283   if (g.is_line())
00284     for (dimension_type i = cgs.num_rows(); i-- > 0; ) {
00285       const Congruence& cg = cgs[i];
00286       Scalar_Products::assign(sp, g, cg);
00287       if (sp != 0)
00288         return false;
00289     }
00290   else {
00291     const Coefficient& divisor = g.divisor();
00292     for (dimension_type i = cgs.num_rows(); i-- > 0; ) {
00293       const Congruence& cg = cgs[i];
00294       Scalar_Products::assign(sp, g, cg);
00295       if (cg.is_equality()) {
00296         if (sp != 0)
00297           return false;
00298       }
00299       else if (sp % (cg.modulus() * divisor) != 0)
00300         return false;
00301     }
00302   }
00303   return true;
00304 }

void Parma_Polyhedra_Library::Congruence_System::normalize_moduli (  )  [private]

Adjusts all expressions to have the same moduli.

Definition at line 185 of file Congruence_System.cc.

References Parma_Polyhedra_Library::lcm_assign(), Parma_Polyhedra_Library::Congruence::modulus(), Parma_Polyhedra_Library::Matrix::num_rows(), OK(), operator[](), Parma_Polyhedra_Library::Matrix::row_size, Parma_Polyhedra_Library::Row::size(), and TEMP_INTEGER.

Referenced by Parma_Polyhedra_Library::Grid::construct(), and Parma_Polyhedra_Library::Grid::simplify().

00185                                        {
00186   dimension_type row = num_rows();
00187   if (row > 0) {
00188     // Calculate the LCM of all the moduli.
00189     TEMP_INTEGER(lcm);
00190     // Find last proper congruence.
00191     while (true) {
00192       lcm = operator[](--row).modulus();
00193       if (lcm > 0)
00194         break;
00195       if (row == 0)
00196         // All rows are equalities.
00197         return;
00198     }
00199     while (row > 0) {
00200       TEMP_INTEGER(modulus);
00201       modulus = operator[](--row).modulus();
00202       if (modulus > 0)
00203         lcm_assign(lcm, lcm, modulus);
00204     }
00205 
00206     // Represent every row using the LCM as the modulus.
00207     dimension_type row_size = operator[](0).size();
00208     for (dimension_type row = num_rows(); row-- > 0; ) {
00209       TEMP_INTEGER(modulus);
00210       modulus = operator[](row).modulus();
00211       if (modulus <= 0 || modulus == lcm)
00212         continue;
00213       TEMP_INTEGER(factor);
00214       factor = lcm / modulus;
00215       for (dimension_type col = row_size; col-- > 0; )
00216         operator[](row)[col] *= factor;
00217       operator[](row)[row_size-1] = lcm;
00218     }
00219   }
00220   assert(OK());
00221 }

bool Parma_Polyhedra_Library::Congruence_System::increase_space_dimension ( const dimension_type  new_space_dim  )  [private]

Increase the number of space dimensions to new_space_dim.

new_space_dim must at least equal to the current space dimension.

Definition at line 50 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::add_zero_columns(), Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), OK(), space_dimension(), and Parma_Polyhedra_Library::Matrix::swap_columns().

Referenced by concatenate(), Parma_Polyhedra_Library::Grid::Grid(), Parma_Polyhedra_Library::Grid::minimized_congruences(), and Parma_Polyhedra_Library::Grid::set_empty().

00050                                                              {
00051   assert(space_dimension() <= new_space_dim);
00052 
00053   dimension_type cols_to_add = new_space_dim - space_dimension();
00054 
00055   if (cols_to_add)
00056     if (num_rows()) {
00057       dimension_type old_num_cols = num_columns();
00058       add_zero_columns(cols_to_add);
00059       // Move the moduli.
00060       swap_columns(num_columns() - 1, old_num_cols - 1);
00061     }
00062     else
00063       // Empty system.
00064       add_zero_columns(cols_to_add);
00065 
00066   assert(OK());
00067   return true;
00068 }

void Parma_Polyhedra_Library::Congruence_System::insert_verbatim ( const Congruence &  cg  )  [private]

Inserts in *this an exact copy of the congruence cg, increasing the number of space dimensions if needed.

This method inserts a copy of cg in the given form, instead of first strong normalizing cg as insert would do.

Definition at line 71 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::add_recycled_row(), Parma_Polyhedra_Library::Matrix::add_row(), Parma_Polyhedra_Library::Matrix::add_zero_columns(), Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), OK(), Parma_Polyhedra_Library::Matrix::row_capacity, Parma_Polyhedra_Library::Row::size(), and Parma_Polyhedra_Library::Matrix::swap_columns().

Referenced by Parma_Polyhedra_Library::Grid::expand_space_dimension(), and insert().

00071                                                           {
00072   const dimension_type old_num_columns = num_columns();
00073   const dimension_type cg_size = cg.size();
00074 
00075   if (cg_size > old_num_columns) {
00076     // Resize the system, if necessary.
00077     add_zero_columns(cg_size - old_num_columns);
00078     if (num_rows() != 0)
00079       // Move the moduli to the last column.
00080       swap_columns(old_num_columns - 1, cg_size - 1);
00081     add_row(cg);
00082   }
00083   else if (cg_size < old_num_columns) {
00084     // Create a resized copy of `cg'.
00085     Congruence rc(cg, old_num_columns, row_capacity);
00086     // Move the modulus to its place.
00087     std::swap(rc[cg_size - 1], rc[old_num_columns - 1]);
00088     add_recycled_row(rc);
00089   }
00090   else
00091     // Here cg_size == old_num_columns.
00092     add_row(cg);
00093 
00094   assert(OK());
00095 }

Congruence & Parma_Polyhedra_Library::Congruence_System::operator[] ( dimension_type  k  )  [inline, private]

Returns the k- th congruence of the system.

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 63 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::operator[]().

Referenced by concatenate(), has_a_free_dimension(), insert(), normalize_moduli(), and recycling_insert().

00063                                                     {
00064   return static_cast<Congruence&>(Matrix::operator[](k));
00065 }

const Congruence & Parma_Polyhedra_Library::Congruence_System::operator[] ( dimension_type  k  )  const [inline, private]

Returns a constant reference to the k- th congruence of the system.

Reimplemented from Parma_Polyhedra_Library::Matrix.

Definition at line 68 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::operator[]().

00068                                                           {
00069   return static_cast<const Congruence&>(Matrix::operator[](k));
00070 }

bool Parma_Polyhedra_Library::Congruence_System::has_a_free_dimension (  )  const [private]

Returns true if and only if any of the dimensions in *this is free of constraint.

Any equality or proper congruence affecting a dimension constrains that dimension.

This method assumes the system is in minimal form.

Definition at line 307 of file Congruence_System.cc.

References Parma_Polyhedra_Library::Matrix::num_rows(), operator[](), and space_dimension().

Referenced by Parma_Polyhedra_Library::Grid::is_discrete().

00307                                                  {
00308   // Search for a dimension that is free of any congruence or equality
00309   // constraint.  Assumes a minimized system.
00310   dimension_type space_dim = space_dimension();
00311   std::vector<bool> free_dim(space_dim, true);
00312   dimension_type free_dims = space_dim;
00313   for (dimension_type row = num_rows(); row-- > 0; ) {
00314     const Congruence& cg = operator[](row);
00315     for (dimension_type dim = 0; dim < space_dim; ++dim)
00316       if (free_dim[dim] && cg[dim+1] != 0) {
00317         if (--free_dims == 0) {
00318           // All dimensions are constrained.
00319 #ifndef NDEBUG
00320           free_dim[dim] = false;
00321           // Check that there are free_dims dimensions marked free
00322           // in free_dim.
00323           dimension_type count = 0;
00324           for (dimension_type dim = 0; dim < space_dim; ++dim)
00325             count += free_dim[dim];
00326           assert(count == free_dims);
00327 #endif
00328           return true;
00329         }
00330         free_dim[dim] = false;
00331       }
00332   }
00333   // At least one dimension is free of constraint.
00334   return false;
00335 }

void Parma_Polyhedra_Library::Congruence_System::affine_preimage ( dimension_type  v,
const Linear_Expression &  expr,
Coefficient_traits::const_reference  denominator 
) [private]

Substitutes a given column of coefficients by a given affine expression.

Parameters:
v Index of the column to which the affine transformation is substituted;
expr The numerator of the affine transformation: $\sum_{i = 0}^{n - 1} a_i x_i + b$;
denominator The denominator of the affine transformation.
We allow affine transformations (see the Section Operations on Rational Grids) to have rational coefficients. Since the coefficients of linear expressions are integers we also provide an integer denominator that will be used as denominator of the affine transformation. The denominator is required to be a positive integer and its default value is 1.

The affine transformation substitutes the matrix of congruences by a new matrix whose elements ${a'}_{ij}$ are built from the old one $a_{ij}$ as follows:

\[ {a'}_{ij} = \begin{cases} a_{ij} * \mathrm{denominator} + a_{iv} * \mathrm{expr}[j] \quad \text{for } j \neq v; \\ \mathrm{expr}[v] * a_{iv} \quad \text{for } j = v. \end{cases} \]

expr is a constant parameter and unaltered by this computation.

Definition at line 339 of file Congruence_System.cc.

References Parma_Polyhedra_Library::add_mul_assign(), Parma_Polyhedra_Library::Matrix::num_columns(), Parma_Polyhedra_Library::Matrix::num_rows(), Parma_Polyhedra_Library::Row::size(), Parma_Polyhedra_Library::Linear_Expression::space_dimension(), and space_dimension().

Referenced by Parma_Polyhedra_Library::Grid::affine_image(), and Parma_Polyhedra_Library::Grid::affine_preimage().

00341                                                                {
00342   // `v' is the index of a column corresponding to a "user" variable
00343   // (i.e., it cannot be the inhomogeneous term).
00344   assert(v > 0 && v <= space_dimension());
00345   assert(expr.space_dimension() <= space_dimension());
00346   assert(denominator > 0);
00347 
00348   const dimension_type n_columns = num_columns();
00349   const dimension_type n_rows = num_rows();
00350   const dimension_type expr_size = expr.size();
00351   const bool not_invertible = (v >= expr_size || expr[v] == 0);
00352   Congruence_System& x = *this;
00353 
00354   if (denominator == 1)
00355     // Optimized computation only considering columns having indexes <
00356     // expr_size.
00357     for (dimension_type i = n_rows; i-- > 0; ) {
00358       Congruence& row = x[i];
00359       Coefficient& row_v = row[v];
00360       if (row_v != 0) {
00361         for (dimension_type j = expr_size; j-- > 0; )
00362           if (j != v)
00363             // row[j] = row[j] + row_v * expr[j]
00364             add_mul_assign(row[j], row_v, expr[j]);
00365         if (not_invertible)
00366           row_v = 0;
00367         else
00368           row_v *= expr[v];
00369       }
00370     }
00371   else
00372     for (dimension_type i = n_rows; i-- > 0; ) {
00373       Congruence& row = x[i];
00374       Coefficient& row_v = row[v];
00375       if (row_v != 0) {
00376         for (dimension_type j = n_columns; j-- > 0; )
00377           if (j != v) {
00378             Coefficient& row_j = row[j];
00379             row_j *= denominator;
00380             if (j < expr_size)
00381               add_mul_assign(row_j, row_v, expr[j]);
00382           }
00383         if (not_invertible)
00384           row_v = 0;
00385         else
00386           row_v *= expr[v];
00387       }
00388     }
00389 }

void Parma_Polyhedra_Library::Congruence_System::resize_no_copy ( dimension_type  new_n_rows,
dimension_type  new_n_columns 
) [inline, private]

Resizes the system without worrying about the old contents.

Parameters:
new_n_rows The number of rows of the resized system;
new_n_columns The number of columns of the resized system.
The system is expanded to the specified dimensions avoiding reallocation whenever possible. The contents of the original system is lost.

Definition at line 96 of file Congruence_System.inlines.hh.

References Parma_Polyhedra_Library::Matrix::resize_no_copy().

Referenced by ascii_load(), and Parma_Polyhedra_Library::Grid::conversion().

00097                                                                       {
00098   Matrix::resize_no_copy(new_n_rows, new_n_columns, Row::Flags());
00099 }

Friends And Related Function Documentation

friend class const_iterator [friend]

Definition at line 392 of file Congruence_System.defs.hh.

friend class Grid [friend]

Definition at line 394 of file Congruence_System.defs.hh.

friend class Grid_Certificate [friend]

Definition at line 395 of file Congruence_System.defs.hh.

void swap ( Parma_Polyhedra_Library::Congruence_System &  x,
Parma_Polyhedra_Library::Congruence_System &  y 
) [friend]

Specializes std::swap.

Definition at line 204 of file Congruence_System.inlines.hh.

00205                                                   {
00206   x.swap(y);
00207 }

bool operator== ( const Congruence_System &  x,
const Congruence_System &  y 
) [friend]

Returns true if and only if x and y are equivalent.

Definition at line 474 of file Congruence_System.cc.

00474                                                                       {
00475   if (x.num_columns() == y.num_columns()) {
00476     dimension_type num_rows = x.num_rows();
00477     if (num_rows == y.num_rows()) {
00478       while (num_rows--) {
00479         if (x[num_rows] == y[num_rows])
00480           continue;
00481         return false;
00482       }
00483       return true;
00484     }
00485   }
00486   return false;
00487 }

std::ostream & operator<< ( std::ostream &  s,
const Congruence_System &  cgs 
) [related]

Output operator.

Writes true if cgs is empty. Otherwise, writes on s the congruences of cgs, all in one row and separated by ", ".

Definition at line 457 of file Congruence_System.cc.

References begin(), end(), and Parma_Polyhedra_Library::Congruence::strong_normalize().

00457                                                                        {
00458   Congruence_System::const_iterator i = cgs.begin();
00459   const Congruence_System::const_iterator cgs_end = cgs.end();
00460   if (i == cgs_end)
00461     return s << "true";
00462   while (true) {
00463     Congruence cg = *i++;
00464     cg.strong_normalize();
00465     s << cg;
00466     if (i == cgs_end)
00467       return s;
00468     s << ", ";
00469   }
00470 }

The documentation for this class was generated from the following files:
Generated on Wed Jul 16 22:55:47 2008 for PPL by  doxygen 1.5.6