PPL 1.2

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Parma_Polyhedra_Library Namespace Reference

The entire library is confined to this namespace. More...

## Namespaces
| IO_Operators
| All input/output operators are confined to this namespace.

## Classes
class | Approximable_Reference
| A concrete expression representing a reference to some approximable. More...
class | Approximable_Reference_Common
| Base class for references to some approximable. More...
class | BD_Shape
| A bounded difference shape. More...
class | BHRZ03_Certificate
| The convergence certificate for the BHRZ03 widening operator. More...
class | Binary_Operator
| A binary operator applied to two concrete expressions. More...
class | Binary_Operator_Common
| Base class for binary operator applied to two concrete expressions. More...
class | Box
| A not necessarily closed, iso-oriented hyperrectangle. More...
class | C_Polyhedron
| A closed convex polyhedron. More...
class | Cast_Floating_Point_Expression
| A generic Cast Floating Point Expression. More...
class | Cast_Operator
| A cast operator converting one concrete expression to some type. More...
class | Cast_Operator_Common
| Base class for cast operator concrete expressions. More...
class | Checked_Number
| A wrapper for numeric types implementing a given policy. More...
class | Concrete_Expression
| The base class of all concrete expressions. More...
class | Concrete_Expression_Common
| Base class for all concrete expressions. More...
class | Concrete_Expression_Type
| The type of a concrete expression. More...
class | Congruence
| A linear congruence. More...
class | Congruence_System
| A system of congruences. More...
class | Congruences_Reduction
| This class provides the reduction method for the Congruences_Product domain. More...
class | Constant_Floating_Point_Expression
| A generic Constant Floating Point Expression. More...
class | Constraint
| A linear equality or inequality. More...
class | Constraint_System
| A system of constraints. More...
class | Constraint_System_const_iterator
| An iterator over a system of constraints. More...
class | Constraints_Reduction
| This class provides the reduction method for the Constraints_Product domain. More...
class | Determinate
| A wrapper for PPL pointsets, providing them with a determinate constraint system interface, as defined in [Bag98]. More...
class | Difference_Floating_Point_Expression
| A generic Difference Floating Point Expression. More...
class | Division_Floating_Point_Expression
| A generic Division Floating Point Expression. More...
class | Domain_Product
| This class is temporary and will be removed when template typedefs will be supported in C++. More...
class | Floating_Point_Constant
| A floating-point constant concrete expression. More...
class | Floating_Point_Constant_Common
| Base class for floating-point constant concrete expression. More...
class | Floating_Point_Expression
class | FP_Oracle
| An abstract class to be implemented by an external analyzer such as ECLAIR in order to provide to the PPL the necessary information for performing the analysis of floating point computations. More...
class | Generator
| A line, ray, point or closure point. More...
class | Generator_System
| A system of generators. More...
class | Generator_System_const_iterator
| An iterator over a system of generators. More...
class | GMP_Integer
| Unbounded integers as provided by the GMP library. More...
class | Grid
| A grid. More...
class | Grid_Certificate
| The convergence certificate for the Grid widening operator. More...
class | Grid_Generator
| A grid line, parameter or grid point. More...
class | Grid_Generator_System
| A system of grid generators. More...
class | H79_Certificate
| A convergence certificate for the H79 widening operator. More...
class | Integer_Constant
| An integer constant concrete expression. More...
class | Integer_Constant_Common
| Base class for integer constant concrete expressions. More...
class | Interval
| A generic, not necessarily closed, possibly restricted interval. More...
class | Linear_Expression
| A linear expression. More...
class | Linear_Form
| A linear form with interval coefficients. More...
class | MIP_Problem
| A Mixed Integer (linear) Programming problem. More...
class | Multiplication_Floating_Point_Expression
| A generic Multiplication Floating Point Expression. More...
class | NNC_Polyhedron
| A not necessarily closed convex polyhedron. More...
class | No_Reduction
| This class provides the reduction method for the Direct_Product domain. More...
class | Octagonal_Shape
| An octagonal shape. More...
class | Opposite_Floating_Point_Expression
| A generic Opposite Floating Point Expression. More...
class | Partially_Reduced_Product
| The partially reduced product of two abstractions. More...
class | PIP_Decision_Node
| A tree node representing a decision in the space of solutions. More...
class | PIP_Problem
| A Parametric Integer (linear) Programming problem. More...
class | PIP_Solution_Node
| A tree node representing part of the space of solutions. More...
class | PIP_Tree_Node
| A node of the PIP solution tree. More...
class | Pointset_Powerset
| The powerset construction instantiated on PPL pointset domains. More...
class | Poly_Con_Relation
| The relation between a polyhedron and a constraint. More...
class | Poly_Gen_Relation
| The relation between a polyhedron and a generator. More...
class | Polyhedron
| The base class for convex polyhedra. More...
class | Powerset
| The powerset construction on a base-level domain. More...
struct | Recycle_Input
| A tag class. More...
struct | Select_Temp_Boundary_Type
| Helper class to select the appropriate numerical type to perform boundary computations so as to reduce the chances of overflow without incurring too much overhead. More...
class | Shape_Preserving_Reduction
| This class provides the reduction method for the Shape_Preserving_Product domain. More...
class | Smash_Reduction
| This class provides the reduction method for the Smash_Product domain. More...
class | Sum_Floating_Point_Expression
| A generic Sum Floating Point Expression. More...
class | Threshold_Watcher
| A class of watchdogs controlling the exceeding of a threshold. More...
class | Throwable
| User objects the PPL can throw. More...
class | Unary_Operator
| A unary operator applied to one concrete expression. More...
class | Unary_Operator_Common
| Base class for unary operator applied to one concrete expression. More...
class | Variable
| A dimension of the vector space. More...
class | Variable_Floating_Point_Expression
| A generic Variable Floating Point Expression. More...
class | Variables_Set
| An std::set of variables' indexes. More...
class | Watchdog
| A watchdog timer. More...

## Typedefs
typedef size_t | dimension_type
| An unsigned integral type for representing space dimensions. More...
typedef size_t | memory_size_type
| An unsigned integral type for representing memory size in bytes. More...
typedef int | Concrete_Expression_Kind
| Encodes the kind of concrete expression. More...
typedef int | Concrete_Expression_BOP
| Encodes a binary operator of concrete expressions. More...
typedef int | Concrete_Expression_UOP
| Encodes a unary operator of concrete expressions. More...
typedef PPL_COEFFICIENT_TYPE | Coefficient
| An alias for easily naming the type of PPL coefficients. More...

## Enumerations
enum | Result_Class { VC_NORMAL, VC_MINUS_INFINITY, VC_PLUS_INFINITY, VC_NAN }
enum | Result_Relation { VR_EMPTY, VR_EQ, VR_LT, VR_GT, VR_NE, VR_LE, VR_GE, VR_LGE }
enum | Result { V_EMPTY, V_EQ, V_LT, V_GT, V_NE, V_LE, V_GE, V_LGE, V_OVERFLOW, V_LT_INF, V_GT_SUP, V_LT_PLUS_INFINITY, V_GT_MINUS_INFINITY, V_EQ_MINUS_INFINITY, V_EQ_PLUS_INFINITY, V_NAN, V_CVT_STR_UNK, V_DIV_ZERO, V_INF_ADD_INF, V_INF_DIV_INF, V_INF_MOD, V_INF_MUL_ZERO, V_INF_SUB_INF, V_MOD_ZERO, V_SQRT_NEG, V_UNKNOWN_NEG_OVERFLOW, V_UNKNOWN_POS_OVERFLOW, V_UNREPRESENTABLE }
| Possible outcomes of a checked arithmetic computation. More...
enum | Rounding_Dir { ROUND_DOWN, ROUND_UP, ROUND_IGNORE , ROUND_NOT_NEEDED , ROUND_STRICT_RELATION }
| Rounding directions for arithmetic computations. More...
enum | Degenerate_Element { UNIVERSE, EMPTY }
| Kinds of degenerate abstract elements. More...
enum | Relation_Symbol { EQUAL, LESS_THAN, LESS_OR_EQUAL, GREATER_THAN, GREATER_OR_EQUAL, NOT_EQUAL }
| Relation symbols. More...
enum | Complexity_Class { POLYNOMIAL_COMPLEXITY, SIMPLEX_COMPLEXITY, ANY_COMPLEXITY }
| Complexity pseudo-classes. More...
enum | Optimization_Mode { MINIMIZATION, MAXIMIZATION }
| Possible optimization modes. More...
enum | Bounded_Integer_Type_Width { BITS_8, BITS_16, BITS_32, BITS_64, BITS_128 }
enum | Bounded_Integer_Type_Representation { UNSIGNED, SIGNED_2_COMPLEMENT }
enum | Bounded_Integer_Type_Overflow { OVERFLOW_WRAPS, OVERFLOW_UNDEFINED, OVERFLOW_IMPOSSIBLE }
enum | Representation { DENSE, SPARSE }
enum | Floating_Point_Format { IEEE754_HALF, IEEE754_SINGLE, IEEE754_DOUBLE, IEEE754_QUAD, INTEL_DOUBLE_EXTENDED, IBM_SINGLE, IBM_DOUBLE }
enum | PIP_Problem_Status { UNFEASIBLE_PIP_PROBLEM, OPTIMIZED_PIP_PROBLEM }
| Possible outcomes of the PIP_Problem solver. More...
enum | MIP_Problem_Status { UNFEASIBLE_MIP_PROBLEM, UNBOUNDED_MIP_PROBLEM, OPTIMIZED_MIP_PROBLEM }
| Possible outcomes of the MIP_Problem solver. More...

## Functions
dimension_type | not_a_dimension ()
| Returns a value that does not designate a valid dimension.
unsigned | irrational_precision ()
| Returns the precision parameter used for irrational calculations.
void | set_irrational_precision (const unsigned p)
| Sets the precision parameter used for irrational calculations. More...
void | set_rounding_for_PPL ()
| Sets the FPU rounding mode so that the PPL abstractions based on floating point numbers work correctly. More...
void | restore_pre_PPL_rounding ()
| Sets the FPU rounding mode as it was before initialization of the PPL. More...
void | initialize ()
| Initializes the library.
void | finalize ()
| Finalizes the library.
Coefficient_traits::const_reference | Coefficient_zero ()
| Returns a const reference to a Coefficient with value 0.
Coefficient_traits::const_reference | Coefficient_one ()
| Returns a const reference to a Coefficient with value 1.
dimension_type | max_space_dimension ()
| Returns the maximum space dimension this library can handle.
Library Version Control Functions
unsigned | version_major ()
| Returns the major number of the PPL version.
unsigned | version_minor ()
| Returns the minor number of the PPL version.
unsigned | version_revision ()
| Returns the revision number of the PPL version.
unsigned | version_beta ()
| Returns the beta number of the PPL version.
const char * | version ()
| Returns a character string containing the PPL version.
const char * | banner ()
| Returns a character string containing the PPL banner. More...
Functions Inspecting and/or Combining Result Values
Result | operator& (Result x, Result y)
Result | operator| (Result x, Result y)
Result | operator- (Result x, Result y)
Result_Class | result_class (Result r)
Result_Relation | result_relation (Result r)
Result | result_relation_class (Result r)
Functions Controlling Floating Point Unit
void | fpu_initialize_control_functions ()
| Initializes the FPU control functions.
fpu_rounding_direction_type | fpu_get_rounding_direction ()
| Returns the current FPU rounding direction.
void | fpu_set_rounding_direction (fpu_rounding_direction_type dir)
| Sets the FPU rounding direction to `dir`.
fpu_rounding_control_word_type | fpu_save_rounding_direction (fpu_rounding_direction_type dir)
| Sets the FPU rounding direction to `dir` and returns the rounding control word previously in use.
fpu_rounding_control_word_type | fpu_save_rounding_direction_reset_inexact (fpu_rounding_direction_type dir)
| Sets the FPU rounding direction to `dir`, clears the inexact computation status, and returns the rounding control word previously in use.
void | fpu_restore_rounding_direction (fpu_rounding_control_word_type w)
| Restores the FPU rounding rounding control word to `cw`.
void | fpu_reset_inexact ()
| Clears the inexact computation status.
int | fpu_check_inexact ()
| Queries the inexact computation status. More...
Functions Inspecting and/or Combining Rounding_Dir Values
Rounding_Dir | operator& (Rounding_Dir x, Rounding_Dir y)
Rounding_Dir | operator| (Rounding_Dir x, Rounding_Dir y)
Rounding_Dir | inverse (Rounding_Dir dir)
Rounding_Dir | round_dir (Rounding_Dir dir)
bool | round_down (Rounding_Dir dir)
bool | round_up (Rounding_Dir dir)
bool | round_ignore (Rounding_Dir dir)
bool | round_not_needed (Rounding_Dir dir)
bool | round_not_requested (Rounding_Dir dir)
bool | round_direct (Rounding_Dir dir)
bool | round_inverse (Rounding_Dir dir)
bool | round_strict_relation (Rounding_Dir dir)
fpu_rounding_direction_type | round_fpu_dir (Rounding_Dir dir)
Functions for the Synthesis of Linear Rankings
template<typename PSET >
bool | termination_test_MS (const PSET &pset)
template<typename PSET >
bool | termination_test_MS_2 (const PSET &pset_before, const PSET &pset_after)
template<typename PSET >
bool | one_affine_ranking_function_MS (const PSET &pset, Generator &mu)
template<typename PSET >
bool | one_affine_ranking_function_MS_2 (const PSET &pset_before, const PSET &pset_after, Generator &mu)
template<typename PSET >
void | all_affine_ranking_functions_MS (const PSET &pset, C_Polyhedron &mu_space)
template<typename PSET >
void | all_affine_ranking_functions_MS_2 (const PSET &pset_before, const PSET &pset_after, C_Polyhedron &mu_space)
template<typename PSET >
void | all_affine_quasi_ranking_functions_MS (const PSET &pset, C_Polyhedron &decreasing_mu_space, C_Polyhedron &bounded_mu_space)
template<typename PSET >
void | all_affine_quasi_ranking_functions_MS_2 (const PSET &pset_before, const PSET &pset_after, C_Polyhedron &decreasing_mu_space, C_Polyhedron &bounded_mu_space)
template<typename PSET >
bool | termination_test_PR (const PSET &pset)
template<typename PSET >
bool | termination_test_PR_2 (const PSET &pset_before, const PSET &pset_after)
template<typename PSET >
bool | one_affine_ranking_function_PR (const PSET &pset, Generator &mu)
template<typename PSET >
bool | one_affine_ranking_function_PR_2 (const PSET &pset_before, const PSET &pset_after, Generator &mu)
template<typename PSET >
void | all_affine_ranking_functions_PR (const PSET &pset, NNC_Polyhedron &mu_space)
template<typename PSET >
void | all_affine_ranking_functions_PR_2 (const PSET &pset_before, const PSET &pset_after, NNC_Polyhedron &mu_space)

## Variables
const Throwable *volatile | abandon_expensive_computations
| A pointer to an exception object. More...

## Detailed Description

The entire library is confined to this namespace.

## Typedef Documentation

typedef int Parma_Polyhedra_Library::Concrete_Expression_Kind

Encodes the kind of concrete expression.

The values should be defined by the particular instance and uniquely identify one of: Binary_Operator, Unary_Operator, Cast_Operator, Integer_Constant, Floating_Point_Constant, or Approximable_Reference. For example, the Binary_Operator kind integer constant should be defined by an instance as the member `Binary_Operator<T>::KIND`.

typedef int Parma_Polyhedra_Library::Concrete_Expression_BOP

Encodes a binary operator of concrete expressions.

The values should be uniquely defined by the particular instance and named: ADD, SUB, MUL, DIV, REM, BAND, BOR, BXOR, LSHIFT, RSHIFT.

typedef int Parma_Polyhedra_Library::Concrete_Expression_UOP

Encodes a unary operator of concrete expressions.

The values should be uniquely defined by the particular instance and named: PLUS, MINUS, BNOT.

## Enumeration Type Documentation

enum Parma_Polyhedra_Library::Result_Class

Enumerator
VC_NORMAL | Representable number result class.
VC_MINUS_INFINITY | Negative infinity result class.
VC_PLUS_INFINITY | Positive infinity result class.
VC_NAN | Not a number result class.

enum Parma_Polyhedra_Library::Result_Relation

Enumerator
VR_EMPTY | No values satisfies the relation.
VR_EQ | Equal. This need to be accompanied by a value.
VR_LT | Less than. This need to be accompanied by a value.
VR_GT | Greater than. This need to be accompanied by a value.
VR_NE | Not equal. This need to be accompanied by a value.
VR_LE | Less or equal. This need to be accompanied by a value.
VR_GE | Greater or equal. This need to be accompanied by a value.
VR_LGE | All values satisfy the relation.

## Function Documentation

const char* Parma_Polyhedra_Library::banner | ( |  | ) |

Returns a character string containing the PPL banner.

The banner provides information about the PPL version, the licensing, the lack of any warranty whatsoever, the C++ compiler used to build the library, where to report bugs and where to look for further information.

int Parma_Polyhedra_Library::fpu_check_inexact | ( |  | ) |
| inline

Queries the inexact computation status.

Returns 0 if the computation was definitely exact, 1 if it was definitely inexact, -1 if definite exactness information is unavailable.

void Parma_Polyhedra_Library::set_irrational_precision | ( | const unsigned | p | ) |
| inline

Sets the precision parameter used for irrational calculations.

The lesser between numerator and denominator is limited to 2**`p`.

If `p` is less than or equal to `INT_MAX`, sets the precision parameter used for irrational calculations to `p`.

Exceptions

  std::invalid_argument | Thrown if `p` is greater than `INT_MAX`.

void Parma_Polyhedra_Library::set_rounding_for_PPL | ( |  | ) |
| inline

Sets the FPU rounding mode so that the PPL abstractions based on floating point numbers work correctly.

This is performed automatically at initialization-time. Calling this function is needed only if restore_pre_PPL_rounding() has been previously called.

void Parma_Polyhedra_Library::restore_pre_PPL_rounding | ( |  | ) |
| inline

Sets the FPU rounding mode as it was before initialization of the PPL.

This is important if the application uses floating-point computations outside the PPL. It is crucial when the application uses functions from a mathematical library that are not guaranteed to work correctly under all rounding modes.

After calling this function it is absolutely necessary to call set_rounding_for_PPL() before using any PPL abstractions based on floating point numbers. This is performed automatically at finalization-time.