linbox
Protected Member Functions | Protected Attributes
FieldArchetype Class Reference

field specification and archetypical instance. More...

#include <archetype.h>

+ Inheritance diagram for FieldArchetype:

Public Types

Common Object Interface for a LinBox Field.

These methods are required of all LinBox fields.

typedef ElementArchetype Element
 the type in which field elements are represented.
 
typedef RandIterArchetype RandIter
 An object of this type is a generator of random field elements.
 

Public Member Functions

Arithmetic Operations

x <- y op z; x <- op y These operations require all elements, including x, to be initialized before the operation is called.

Uninitialized field elements will give undefined results.

bool areEqual (const Element &x, const Element &y) const
 Equality of two elements. More...
 
Elementadd (Element &x, const Element &y, const Element &z) const
 Addition, x <– y + z. More...
 
Elementsub (Element &x, const Element &y, const Element &z) const
 Subtraction, x <– y - z. More...
 
Elementmul (Element &x, const Element &y, const Element &z) const
 Multiplication, x <– y * z. More...
 
Elementdiv (Element &x, const Element &y, const Element &z) const
 Division, x <– y / z. More...
 
Elementneg (Element &x, const Element &y) const
 Additive Inverse (Negation), x <– - y. More...
 
Elementinv (Element &x, const Element &y) const
 Multiplicative Inverse, x <– 1 / y. More...
 
Elementaxpy (Element &r, const Element &a, const Element &x, const Element &y) const
 Field element AXPY, r <– a * x + y. More...
 
Predicates
bool isZero (const Element &x) const
 Zero equality. More...
 
bool isOne (const Element &x) const
 One equality. More...
 
bool isMOne (const Element &x) const
 MOne equality. More...
 
Inplace Arithmetic Operations

x <- x op y; x <- op x These operations require all elements, including x, to be initialized before the operation is called.

Uninitialized field elements will give undefined results.

Elementaddin (Element &x, const Element &y) const
 Inplace Addition. More...
 
Elementsubin (Element &x, const Element &y) const
 Inplace Subtraction. More...
 
Elementmulin (Element &x, const Element &y) const
 Inplace Multiplication. More...
 
Elementdivin (Element &x, const Element &y) const
 Inplace Division. More...
 
Elementnegin (Element &x) const
 Inplace Additive Inverse (Inplace Negation). More...
 
Elementinvin (Element &x) const
 Inplace Multiplicative Inverse. More...
 
Elementaxpyin (Element &r, const Element &a, const Element &x) const
 Inplace AXPY. More...
 
Input/Output Operations
std::ostream & write (std::ostream &os) const
 Print field. More...
 
std::ostream & write (std::ostream &os, const Element &x) const
 Print field element. More...
 
std::istream & read (std::istream &is, Element &x) const
 Read field element. More...
 
Implementation-Specific Methods.

These methods are not required of all LinBox\ Fields and are included only for this implementation of the archetype.

 FieldArchetype (FieldAbstract *field_ptr, ElementAbstract *elem_ptr, RandIterAbstract *randIter_ptr=0)
 Constructor. More...
 
template<class Field_qcq >
 FieldArchetype (Field_qcq *f)
 Constructor. More...
 

Protected Member Functions

template<class Field_qcq >
void constructor (FieldAbstract *trait, Field_qcq *field_ptr)
 Template method for constructing archetype from a derived class of FieldAbstract. More...
 
template<class Field_qcq >
void constructor (void *trait, Field_qcq *field_ptr)
 Template method for constructing archetype from a class not derived from FieldAbstract. More...
 
 FieldArchetype ()
 Only authorize inhertied classes to use the empty constructor.
 

Protected Attributes

FieldAbstract_field_ptr
 Pointer to FieldAbstract object. More...
 
ElementAbstract_elem_ptr
 Pointer to ElementAbstract object. More...
 
RandIterAbstract_randIter_ptr
 Pointer to RandIterAbstract object. More...
 

Object Management

Element one
 Copy constructor. More...
 
Element zero
 Copy constructor. More...
 
Element mOne
 Copy constructor. More...
 
 FieldArchetype (const FieldArchetype &F)
 Copy constructor. More...
 
 ~FieldArchetype (void)
 Destructor. More...
 
FieldArchetypeoperator= (const FieldArchetype &F)
 Assignment operator. More...
 
Elementinit (Element &x, const integer &n=0) const
 Initialization of field element from an integer. More...
 
integerconvert (integer &n, const Element &y=0) const
 Conversion of field element to an integer. More...
 
Elementassign (Element &x, const Element &y) const
 Assignment of one field element to another. More...
 
integercardinality (integer &c) const
 Cardinality. More...
 
integercharacteristic (integer &c) const
 Characteristic. More...
 

Detailed Description

field specification and archetypical instance.

The FieldArchetype and its encapsulated element class contain pointers to the FieldAbstract and its encapsulated field element, respectively. FieldAbstract then uses virtual member functions to define operations on its encapsulated field element. This field element has no knowledge of the field properties being used on it which means the field object must supply these operations.

It does not contain elements zero and one because they can be created whenever necessary, although it might be beneficial from an efficiency stand point to include them. However, because of archetype use three, the elements themselves cannot be contained, but rather pointers to them.

Constructor & Destructor Documentation

FieldArchetype ( const FieldArchetype F)
inline

Copy constructor.

Each field class is expected to provide a copy constructor. This is required to allow field objects to be passed by value into functions.

In this archetype implementation, this means copying the field to which F._field_ptr points, the element to which F._elem_ptr points, and the random element generator to which F._randIter_ptr points.

~FieldArchetype ( void  )
inline

Destructor.

This destroys the field object, but it does not destroy any field element objects.

In this archetype implementation, destruction is deletion of the field object to which _field_ptr points, the field element to which _elem_ptr points, and the random element generator to which _randIter_ptr points.

FieldArchetype ( FieldAbstract field_ptr,
ElementAbstract elem_ptr,
RandIterAbstract randIter_ptr = 0 
)
inline

Constructor.

Constructs field from pointer to FieldAbstract and its encapsulated element and random element generator. Not part of the interface. Creates new copies of field, element, and random iterator generator objects in dynamic memory.

Parameters
field_ptrpointer to FieldAbstract.
elem_ptrpointer to ElementAbstract, which is the encapsulated element of FieldAbstract.
randIter_ptrpointer to RandIterAbstract, which is the encapsulated random iterator generator of FieldAbstract.
FieldArchetype ( Field_qcq *  f)
inline

Constructor.

Constructs field from ANYTHING matching the interface using the enveloppe as a FieldAbstract and its encapsulated element and random element generator if needed.

Parameters
f

Member Function Documentation

FieldArchetype& operator= ( const FieldArchetype F)
inline

Assignment operator.

In this archetype implementation, this means copying the field to which F._field_ptr points, the element to which F._elem_ptr points, and the random element generator to which F._randIter_ptr points.

Parameters
F FieldArchetype object.
Element& init ( Element x,
const integer n = 0 
) const
inline

Initialization of field element from an integer.

x becomes the image of n under the natural map from the integers to the prime subfield. It is the result obtained from adding n 1's in the field.

This function assumes the output field element x has already been constructed, but that it is not necessarily already initialized. In this archetype implementation, this means the _elem_ptr of x exists, but that it may be the null pointer.

Returns
reference to x.
Parameters
xoutput field element.
ninput integer.
integer& convert ( integer n,
const Element y = 0 
) const
inline

Conversion of field element to an integer.

The meaning of conversion is specific to each field class. However, if x is in the prime subfield, the integer n returned is such that an init from n will reproduce x. Most often, $0 \leq n < \mathrm{characteristic}$.

Returns
reference to n.
Parameters
noutput integer.
yinput field element.
Element& assign ( Element x,
const Element y 
) const
inline

Assignment of one field element to another.

This function assumes both field elements have already been constructed and initialized.

In this archetype implementation, this means for both x and y, _elem_ptr exists and does not point to null.

Returns
reference to x
Parameters
xdestination field element.
ysource field element.
integer& cardinality ( integer c) const
inline

Cardinality.

Return c, integer representing cardinality of the field. c becomes a non-negative integer for all fields with finite cardinality, and -1 to signify a field of infinite cardinality.

integer& characteristic ( integer c) const
inline

Characteristic.

Return c, integer representing characteristic of the field (the least positive n such that the sum of n copies of x is 0 for all field elements x). c becomes a positive integer for all fields with finite characteristic, and 0 to signify a field of infinite characteristic.

bool areEqual ( const Element x,
const Element y 
) const
inline

Equality of two elements.

This function assumes both field elements have already been constructed and initialized.

In this implementation, this means for both x and y, _elem_ptr exists and does not point to null.

Returns
boolean true if equal, false if not.
Parameters
xfield element
yfield element
Element& add ( Element x,
const Element y,
const Element z 
) const
inline

Addition, x <– y + z.

This function assumes all the field elements have already been constructed and initialized.

In this implementation, this means for x, y, and z, _elem_ptr exists and does not point to null.

Returns
reference to x.
Element& sub ( Element x,
const Element y,
const Element z 
) const
inline

Subtraction, x <– y - z.

This function assumes all the field elements have already been constructed and initialized.

In this implementation, this means for x, y, and z, _elem_ptr exists and does not point to null.

Returns
reference to x.
Element& mul ( Element x,
const Element y,
const Element z 
) const
inline

Multiplication, x <– y * z.

This function assumes all the field elements have already been constructed and initialized.

In this implementation, this means for x, y, and z, _elem_ptr exists and does not point to null.

Returns
reference to x.
Element& div ( Element x,
const Element y,
const Element z 
) const
inline

Division, x <– y / z.

This function assumes all the field elements have already been constructed and initialized.

In this implementation, this means for x, y, and z, _elem_ptr exists and does not point to null.

Returns
reference to x.
Element& neg ( Element x,
const Element y 
) const
inline

Additive Inverse (Negation), x <– - y.

This function assumes both field elements have already been constructed and initialized.

In this implementation, this means for both x and y _elem_ptr exists and does not point to null.

Returns
reference to x.
Element& inv ( Element x,
const Element y 
) const
inline

Multiplicative Inverse, x <– 1 / y.

Requires that y is a unit (i.e. nonzero in a field). This function assumes both field elements have already been constructed and initialized.

In this implementation, this means for both x and y _elem_ptr exists and does not point to null.

Returns
reference to x.
Element& axpy ( Element r,
const Element a,
const Element x,
const Element y 
) const
inline

Field element AXPY, r <– a * x + y.

This function assumes all field elements have already been constructed and initialized.

Returns
reference to r.
bool isZero ( const Element x) const
inline

Zero equality.

Test if field element is equal to zero. This function assumes the field element has already been constructed and initialized.

In this implementation, this means the _elem_ptr of x exists and does not point to null.

Returns
boolean true if equals zero, false if not.
Parameters
xfield element.
bool isOne ( const Element x) const
inline

One equality.

Test if field element is equal to one. This function assumes the field element has already been constructed and initialized.

In this implementation, this means the _elem_ptr of x exists and does not point to null.

Returns
boolean true if equals one, false if not.
Parameters
xfield element.
bool isMOne ( const Element x) const
inline

MOne equality.

Test if field element is equal to one. This function assumes the field element has already been constructed and initialized.

In this implementation, this means the _elem_ptr of x exists and does not point to null.

Returns
boolean true if equals one, false if not.
Parameters
xfield element.
Element& addin ( Element x,
const Element y 
) const
inline

Inplace Addition.

x += y This function assumes both field elements have already been constructed and initialized.

In this implementation, this means for both x and y _elem_ptr exists and does not point to null.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.
Element& subin ( Element x,
const Element y 
) const
inline

Inplace Subtraction.

x -= y This function assumes both field elements have already been constructed and initialized.

In this implementation, this means for both x and y _elem_ptr exists and does not point to null.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.
Element& mulin ( Element x,
const Element y 
) const
inline

Inplace Multiplication.

x *= y This function assumes both field elements have already been constructed and initialized.

In this implementation, this means for both x and y _elem_ptr exists and does not point to null.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.
Element& divin ( Element x,
const Element y 
) const
inline

Inplace Division.

x /= y This function assumes both field elements have already been constructed and initialized.

In this implementation, this means for both x and y _elem_ptr exists and does not point to null.

Returns
reference to x.
Parameters
xfield element (reference returned).
yfield element.
Element& negin ( Element x) const
inline

Inplace Additive Inverse (Inplace Negation).

x = - x This function assumes the field element has already been constructed and initialized.

In this implementation, this means the _elem_ptr of x exists and does not point to null.

Returns
reference to x.
Parameters
xfield element (reference returned).
Element& invin ( Element x) const
inline

Inplace Multiplicative Inverse.

x = 1 / x This function assumes the field elementhas already been constructed and initialized.

In this implementation, this means the _elem_ptr of x exists and does not point to null.

Returns
reference to x.
Parameters
xfield element (reference returned).
Element& axpyin ( Element r,
const Element a,
const Element x 
) const
inline

Inplace AXPY.

r += a * x This function assumes all field elements have already been constructed and initialized.

Returns
reference to r.
Parameters
rfield element (reference returned).
afield element.
xfield element.
std::ostream& write ( std::ostream &  os) const
inline

Print field.

Returns
output stream to which field is written.
Parameters
osoutput stream to which field is written.
std::ostream& write ( std::ostream &  os,
const Element x 
) const
inline

Print field element.

This function assumes the field element has already been constructed and initialized.

In this implementation, this means for the _elem_ptr for x exists and does not point to null.

Returns
output stream to which field element is written.
Parameters
osoutput stream to which field element is written.
xfield element.
std::istream& read ( std::istream &  is,
Element x 
) const
inline

Read field element.

This function assumes the field element has already been constructed and initialized.

In this implementation, this means for the _elem_ptr for x exists and does not point to null.

Returns
input stream from which field element is read.
Parameters
isinput stream from which field element is read.
xfield element.
void constructor ( FieldAbstract trait,
Field_qcq *  field_ptr 
)
inlineprotected

Template method for constructing archetype from a derived class of FieldAbstract.

This class is needed to help the constructor differentiate between classes derived from FieldAbstract and classes that aren't. Should be called with the same argument to both parameters?

Parameters
traitpointer to FieldAbstract or class derived from it
field_ptrpointer to class derived from FieldAbstract
Bug:
leaks here (new not deleted)
void constructor ( void *  trait,
Field_qcq *  field_ptr 
)
inlineprotected

Template method for constructing archetype from a class not derived from FieldAbstract.

This class is needed to help the constructor differentiate between classes derived from FieldAbstract and classes that aren't. Should be called with the same argument to both parameters?

Parameters
traitpointer to class not derived from FieldAbstract
field_ptrpointer to class not derived from FieldAbstract

Field Documentation

Element one

Copy constructor.

Each field class is expected to provide a copy constructor. This is required to allow field objects to be passed by value into functions.

In this archetype implementation, this means copying the field to which F._field_ptr points, the element to which F._elem_ptr points, and the random element generator to which F._randIter_ptr points.

Element zero

Copy constructor.

Each field class is expected to provide a copy constructor. This is required to allow field objects to be passed by value into functions.

In this archetype implementation, this means copying the field to which F._field_ptr points, the element to which F._elem_ptr points, and the random element generator to which F._randIter_ptr points.

Element mOne

Copy constructor.

Each field class is expected to provide a copy constructor. This is required to allow field objects to be passed by value into functions.

In this archetype implementation, this means copying the field to which F._field_ptr points, the element to which F._elem_ptr points, and the random element generator to which F._randIter_ptr points.

FieldAbstract* _field_ptr
mutableprotected

Pointer to FieldAbstract object.

Not part of the interface. Included to allow for archetype use three.

ElementAbstract* _elem_ptr
mutableprotected

Pointer to ElementAbstract object.

Not part of the interface. Included to allow for archetype use three.

RandIterAbstract* _randIter_ptr
mutableprotected

Pointer to RandIterAbstract object.

Not part of the interface. Included to allow for archetype use three.


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