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Parma_Polyhedra_Library::Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > Class Template Reference
C++ Language Interface

A generic Multiplication Floating Point Expression. More...

`#include <ppl.hh>`

Inheritance diagram for Parma_Polyhedra_Library::Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format >:
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## Public Types
typedef Floating_Point_Expression< FP_Interval_Type, FP_Format >::FP_Linear_Form | FP_Linear_Form
| Alias for the Linear_Form<FP_Interval_Type> from Floating_Point_Expression.
typedef Floating_Point_Expression< FP_Interval_Type, FP_Format >::FP_Interval_Abstract_Store | FP_Interval_Abstract_Store
| Alias for the Box<FP_Interval_Type> from Floating_Point_Expression.
typedef Floating_Point_Expression< FP_Interval_Type, FP_Format >::FP_Linear_Form_Abstract_Store | FP_Linear_Form_Abstract_Store
| Alias for the std::map<dimension_type, FP_Linear_Form> from Floating_Point_Expression.
typedef Floating_Point_Expression< FP_Interval_Type, FP_Format >::boundary_type | boundary_type
| Alias for the FP_Interval_Type::boundary_type from Floating_Point_Expression.
typedef Floating_Point_Expression< FP_Interval_Type, FP_Format >::info_type | info_type
| Alias for the FP_Interval_Type::info_type from Floating_Point_Expression.
Public Types inherited from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >
typedef Linear_Form< FP_Interval_Type > | FP_Linear_Form
| Alias for a linear form with template argument `FP_Interval_Type`.
typedef Box< FP_Interval_Type > | FP_Interval_Abstract_Store
| Alias for a map that associates a variable index to an interval. More...
typedef std::map< dimension_type, FP_Linear_Form > | FP_Linear_Form_Abstract_Store
| Alias for a map that associates a variable index to a linear form. More...
typedef FP_Interval_Type::boundary_type | boundary_type
| The floating point format used by the analyzer.
typedef FP_Interval_Type::info_type | info_type
| The interval policy used by `FP_Interval_Type`.

## Public Member Functions
bool | linearize (const FP_Interval_Abstract_Store &int_store, const FP_Linear_Form_Abstract_Store &lf_store, FP_Linear_Form &result) const
| Linearizes the expression in a given astract store. More...
void | m_swap (Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > &y)
| Swaps `*this` with `y`.
Constructors and Destructor
| Multiplication_Floating_Point_Expression (Floating_Point_Expression< FP_Interval_Type, FP_Format > *const x, Floating_Point_Expression< FP_Interval_Type, FP_Format > *const y)
| Constructor with two parameters: builds the multiplication floating point expression corresponding to `x` `y`.
| ~Multiplication_Floating_Point_Expression ()
| Destructor.
Public Member Functions inherited from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >
virtual | ~Floating_Point_Expression ()
| Destructor.

## Related Functions
(Note that these are not member functions.)
template<typename FP_Interval_Type , typename FP_Format >
void | swap (Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > &x, Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > &y)
| Swaps `x` with `y`. More...
template<typename FP_Interval_Type , typename FP_Format >
void | swap (Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > &x, Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > &y)

## Additional Inherited Members
Static Public Member Functions inherited from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >
static bool | overflows (const FP_Linear_Form &lf)
| Verifies if a given linear form overflows. More...
static void | relative_error (const FP_Linear_Form &lf, FP_Linear_Form &result)
| Computes the relative error of a given linear form. More...
static void | intervalize (const FP_Linear_Form &lf, const FP_Interval_Abstract_Store &store, FP_Interval_Type &result)
| Makes `result` become an interval that overapproximates all the possible values of `lf` in the interval abstract store `store`. More...
Static Public Attributes inherited from Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >
static FP_Interval_Type | absolute_error = compute_absolute_error()
| Absolute error. More...

## Detailed Description

### template<typename FP_Interval_Type, typename FP_Format>
class Parma_Polyhedra_Library::Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format >

A generic Multiplication Floating Point Expression.

Template type parameters

- The class template type parameter `FP_Interval_Type` represents the type of the intervals used in the abstract domain.
- The class template type parameter `FP_Format` represents the floating point format used in the concrete domain.

Linearization of multiplication floating-point expressions

Let and be two linear forms, and two sound abstract operators on linear forms such that:

Given an expression and a composite abstract store , we construct the interval linear form as follows:

.

Given an expression and a composite abstract store , we construct the interval linear form as follows:

Given an expression and a composite abstract store , we construct the interval linear form as follows:

where is the linear form computed by calling method `Floating_Point_Expression::relative_error` on , is the linear form computed by calling method `Floating_Point_Expression::intervalize` on and , and is a rounding error defined in `Floating_Point_Expression::absolute_error`.

Even though we intervalize the first operand in the above example, the actual implementation utilizes an heuristics for choosing which of the two operands must be intervalized in order to obtain the most precise result.

## Member Function Documentation

template<typename FP_Interval_Type , typename FP_Format >

bool Parma_Polyhedra_Library::Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format >::linearize | ( | const FP_Interval_Abstract_Store & | int_store,
|  | const FP_Linear_Form_Abstract_Store & | lf_store,
|  | FP_Linear_Form & | result
| ) |  | const
| virtual

Linearizes the expression in a given astract store.

Makes `result` become the linearization of `*this` in the given composite abstract store.

Parameters

  int_store | The interval abstract store.
  lf_store | The linear form abstract store.
  result | The modified linear form.

Returns
  `true` if the linearization succeeded, `false` otherwise.

Note that all variables occuring in the expressions represented by `first_operand` and `second_operand` MUST have an associated value in `int_store`. If this precondition is not met, calling the method causes an undefined behavior.

See the class description for a detailed explanation of how `result` is computed.

Implements Parma_Polyhedra_Library::Floating_Point_Expression< FP_Interval_Type, FP_Format >.

## Friends And Related Function Documentation

template<typename FP_Interval_Type , typename FP_Format >

void swap | ( | Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > & | x,
|  | Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > & | y
| ) |  |
| related

Swaps `x` with `y`.

template<typename FP_Interval_Type , typename FP_Format >

void swap | ( | Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > & | x,
|  | Multiplication_Floating_Point_Expression< FP_Interval_Type, FP_Format > & | y
| ) |  |
| related

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

- ppl.hh