PPL 0.12
|
A linear congruence. More...
#include <ppl.hh>
Inherits Parma_Polyhedra_Library::Dense_Row.
Public Member Functions | |
Congruence (const Congruence &cg) | |
Ordinary copy constructor. | |
Congruence (const Constraint &c) | |
Copy-constructs (modulo 0) from equality constraint c . | |
~Congruence () | |
Destructor. | |
Congruence & | operator= (const Congruence &cg) |
Assignment operator. | |
dimension_type | space_dimension () const |
Returns the dimension of the vector space enclosing *this . | |
Coefficient_traits::const_reference | coefficient (Variable v) const |
Returns the coefficient of v in *this . | |
Coefficient_traits::const_reference | inhomogeneous_term () const |
Returns the inhomogeneous term of *this . | |
Coefficient_traits::const_reference | modulus () const |
Returns a const reference to the modulus of *this . | |
Congruence & | operator/= (Coefficient_traits::const_reference k) |
Multiplies k into the modulus of *this . | |
bool | is_tautological () const |
Returns true if and only if *this is a tautology (i.e., an always true congruence). | |
bool | is_inconsistent () const |
Returns true if and only if *this is inconsistent (i.e., an always false congruence). | |
bool | is_proper_congruence () const |
Returns true if the modulus is greater than zero. | |
bool | is_equality () const |
Returns true if *this is an equality. | |
bool | is_equal_at_dimension (dimension_type dim, const Congruence &cg) const |
Returns true if *this is equal to cg in dimension dim . | |
memory_size_type | total_memory_in_bytes () const |
Returns a lower bound to the total size in bytes of the memory occupied by *this . | |
memory_size_type | external_memory_in_bytes () const |
Returns the size in bytes of the memory managed by *this . | |
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 of the internal representation of *this . | |
void | m_swap (Congruence &y) |
Swaps *this with y . | |
bool | OK () const |
Checks if all the invariants are satisfied. | |
Static Public Member Functions | |
static dimension_type | max_space_dimension () |
Returns the maximum space dimension a Congruence can handle. | |
static void | initialize () |
Initializes the class. | |
static void | finalize () |
Finalizes the class. | |
static const Congruence & | zero_dim_integrality () |
Returns a reference to the true (zero-dimension space) congruence ![]() | |
static const Congruence & | zero_dim_false () |
Returns a reference to the false (zero-dimension space) congruence ![]() | |
static Congruence | create (const Linear_Expression &e1, const Linear_Expression &e2) |
Returns the congruence ![]() | |
static Congruence | create (const Linear_Expression &e, Coefficient_traits::const_reference n) |
Returns the congruence ![]() | |
static Congruence | create (Coefficient_traits::const_reference n, const Linear_Expression &e) |
Returns the congruence ![]() | |
Protected Member Functions | |
void | sign_normalize () |
Normalizes the signs. | |
void | normalize () |
Normalizes signs and the inhomogeneous term. | |
void | strong_normalize () |
Calls normalize, then divides out common factors. | |
Friends | |
Congruence | operator/ (const Congruence &cg, Coefficient_traits::const_reference k) |
Returns a copy of cg , multiplying k into the copy's modulus. | |
Congruence | operator/ (const Constraint &c, Coefficient_traits::const_reference m) |
Creates a congruence from c , with m as the modulus. | |
bool | operator== (const Congruence &x, const Congruence &y) |
Returns true if and only if x and y are equivalent. | |
bool | operator!= (const Congruence &x, const Congruence &y) |
Returns false 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 &c) |
Output operators. | |
void | swap (Congruence &x, Congruence &y) |
Swaps x with y . | |
Congruence | operator%= (const Linear_Expression &e1, const Linear_Expression &e2) |
Returns the congruence ![]() | |
Congruence | operator%= (const Linear_Expression &e, Coefficient_traits::const_reference n) |
Returns the congruence ![]() |
A linear congruence.
An object of the class Congruence is a congruence:
where is the dimension of the space,
is the integer coefficient of variable
,
is the integer inhomogeneous term and
is the integer modulus; if
, then
represents the equality congruence
and, if
, then the congruence
is said to be a proper congruence.
%=
' to a pair of linear expressions. Congruences with modulus m
are typically constructed by building a congruence m
using the modulus symbol is `/
'.The space dimension of a congruence is defined as the maximum space dimension of the arguments of its constructor.
x
, y
and z
are defined as follows: Variable x(0); Variable y(1); Variable z(2);
Congruence eq_cg((3*x + 5*y - z %= 0) / 0);
Congruence mod1_cg(4*x %= 2*y - 13);
Congruence mod2_cg((4*x %= 2*y - 13) / 2);
Congruence false_cg = Congruence::zero_dim_false();
Congruence false_cg1((Linear_Expression::zero() %= 1) / 0); Congruence false_cg2((Linear_Expression::zero() %= 1) / 2);
Congruence false_cg3((0*z %= 1) / 0);
e
and modulus m
(in this case m
but where the linear expression is Congruence cg1((x - 5*y + 3*z %= 4) / 5); cout << "Congruence cg1: " << cg1 << endl; const Coefficient& m = cg1.modulus(); if (m == 0) cout << "Congruence cg1 is an equality." << endl; else { Linear_Expression e; for (dimension_type i = cg1.space_dimension(); i-- > 0; ) e += 2 * cg1.coefficient(Variable(i)) * Variable(i); e += 2 * cg1.inhomogeneous_term(); Congruence cg2((e %= 0) / m); cout << "Congruence cg2: " << cg2 << endl; }
Congruence cg1: A - 5*B + 3*C %= 4 / 5 Congruence cg2: 2*A - 10*B + 6*C %= 8 / 5
Parma_Polyhedra_Library::Congruence::Congruence | ( | const Constraint & | c | ) | [explicit] |
Copy-constructs (modulo 0) from equality constraint c
.
std::invalid_argument | Thrown if c is an inequality. |
Coefficient_traits::const_reference Parma_Polyhedra_Library::Congruence::coefficient | ( | Variable | v | ) | const [inline] |
Returns the coefficient of v
in *this
.
std::invalid_argument | thrown if the index of v is greater than or equal to the space dimension of *this . |
Congruence & Parma_Polyhedra_Library::Congruence::operator/= | ( | Coefficient_traits::const_reference | k | ) | [inline] |
Multiplies k
into the modulus of *this
.
If called with *this
representing the congruence , then it returns with *this representing the congruence
.
bool Parma_Polyhedra_Library::Congruence::is_tautological | ( | ) | const |
Returns true
if and only if *this
is a tautology (i.e., an always true congruence).
A tautological congruence has one the following two forms:
bool Parma_Polyhedra_Library::Congruence::is_inconsistent | ( | ) | const |
Returns true
if and only if *this
is inconsistent (i.e., an always false congruence).
An inconsistent congruence has one of the following two forms:
bool Parma_Polyhedra_Library::Congruence::is_proper_congruence | ( | ) | const [inline] |
Returns true
if the modulus is greater than zero.
A congruence with a modulus of 0 is a linear equality.
bool Parma_Polyhedra_Library::Congruence::is_equality | ( | ) | const [inline] |
Returns true
if *this
is an equality.
A modulus of zero denotes a linear equality.
void Parma_Polyhedra_Library::Congruence::sign_normalize | ( | ) | [protected] |
Normalizes the signs.
The signs of the coefficients and the inhomogeneous term are normalized, leaving the first non-zero homogeneous coefficient positive.
void Parma_Polyhedra_Library::Congruence::normalize | ( | ) | [protected] |
Normalizes signs and the inhomogeneous term.
Applies sign_normalize, then reduces the inhomogeneous term to the smallest possible positive number.
void Parma_Polyhedra_Library::Congruence::strong_normalize | ( | ) | [protected] |
Calls normalize, then divides out common factors.
Strongly normalized Congruences have equivalent semantics if and only if they have the same syntax (as output by operator<<).
Congruence operator/ | ( | const Congruence & | cg, |
Coefficient_traits::const_reference | k | ||
) | [friend] |
Returns a copy of cg
, multiplying k
into the copy's modulus.
If cg
represents the congruence , then the result represents the congruence
.
Congruence operator/ | ( | const Constraint & | c, |
Coefficient_traits::const_reference | m | ||
) | [friend] |
Creates a congruence from c
, with m
as the modulus.
bool operator== | ( | const Congruence & | x, |
const Congruence & | y | ||
) | [friend] |
Returns true
if and only if x
and y
are equivalent.
bool operator!= | ( | const Congruence & | x, |
const Congruence & | y | ||
) | [friend] |
Returns false
if and only if x
and y
are equivalent.
std::ostream & operator<< | ( | std::ostream & | s, |
const Congruence & | c | ||
) | [related] |
Output operators.
void swap | ( | Congruence & | x, |
Congruence & | y | ||
) | [related] |
Swaps x
with y
.
Congruence operator%= | ( | const Linear_Expression & | e1, |
const Linear_Expression & | e2 | ||
) | [related] |
Returns the congruence .
Congruence operator%= | ( | const Linear_Expression & | e, |
Coefficient_traits::const_reference | n | ||
) | [related] |
Returns the congruence .