Integers modulo 2. More...

#include <gf2.h>

Public Types
using	Self_t = GF2
	Element type.

using	RandIter = GIV_randIter< Self_t, bool >
	Random.

Public Member Functions
Object Management
	GF2 ()
	Default constructor.

	GF2 (int p, int exp=1)
	Default constructor.

	GF2 (const GF2 &F)
	Copy constructor. More...

GF2 &	operator= (const GF2 &F)
	Assignment operator. More...

Element	minElement () const
	Accessors.

Element	maxElement () const
	Default constructor.

Residu_t	residu () const
	Access to the modulus.

Residu_t	size () const
	Default constructor.

Residu_t	characteristic () const
	Default constructor.

Residu_t	cardinality () const
	Default constructor.

template<class T >
T &	characteristic (T &p) const
	Default constructor.

template<class T >
T &	cardinality (T &p) const
	Default constructor.

Element &	init (Element &x, const int32_t &y) const
	Initialization of field base element from an Integer. More...

Element &	init (Element &x, const uint32_t &y) const
	Default constructor.

Element &	init (Element &x, const int64_t &y) const
	Default constructor.

Element &	init (Element &x, const uint64_t &y) const
	Default constructor.

Element &	init (Element &x, const float &y) const
	Default constructor.

Element &	init (Element &x, const double &y) const
	Default constructor.

Element &	init (Element &x, const Integer &y) const
	Default constructor.

Element &	init (Element &x) const
	Default constructor.

BitReference	init (BitReference x, const Integer &y=0) const
	Default constructor.

Integer &	convert (Integer &x, const Element &y) const
	Conversion of field base element to a template class T. More...

BitReference	convert (BitReference x, const Element &y) const
	Default constructor.

template<class T >
T &	convert (T &x, const Element &y) const
	Default constructor.

Element &	assign (Element &x, const Element &y) const
	Assignment of one field base element to another. More...

BitReference	assign (BitReference x, const Element &y) const
	Default constructor.

Integer &	cardinality (Integer &c) const
	Cardinality. More...

Integer &	characteristic (Integer &c) const
	Characteristic. More...

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 base elements will give undefined results.
bool	areEqual (const Element &x, const Element &y) const
	Equality of two elements. More...

bool	isZero (const Element &x) const
	Zero equality. More...

bool	isOne (const Element &x) const
	One equality. More...

bool	isUnit (const Element &x) const
	Invertibility. More...

bool	isMOne (const Element &x) const
	MOne equality. More...

Element &	add (Element &x, const Element &y, const Element &z) const
	Addition. More...

BitReference	add (BitReference x, const Element &y, const Element &z) const
	Equality of two elements. More...

Element &	sub (Element &x, const Element &y, const Element &z) const
	Subtraction. More...

BitReference	sub (BitReference x, const Element &y, const Element &z) const
	Equality of two elements. More...

Element &	mul (Element &x, const Element &y, const Element &z) const
	Multiplication. More...

BitReference	mul (BitReference x, const Element &y, const Element &z) const
	Equality of two elements. More...

Element &	div (Element &x, const Element &y, const Element &z) const
	Division. More...

BitReference	div (BitReference x, const Element &y, const Element &z) const
	Equality of two elements. More...

Element &	neg (Element &x, const Element &y) const
	Additive Inverse (Negation). More...

BitReference	neg (BitReference x, const Element &y) const
	Equality of two elements. More...

Element &	inv (Element &x, const Element &y) const
	Multiplicative Inverse. More...

BitReference	inv (BitReference x, const Element &y) const
	Equality of two elements. More...

BitReference	axpy (BitReference r, const Element &a, const Element &x, const Element &y) const
	Natural AXPY. More...

Element &	axpy (Element &r, const Element &a, const Element &x, const Element &y) const
	Equality of two elements. More...

BitReference	axmy (BitReference r, const Element &a, const Element &x, const Element &y) const
	Natural AXMY. More...

Element &	axmy (Element &r, const Element &a, const Element &x, const Element &y) const
	Equality of two elements. More...

BitReference	maxpy (BitReference r, const Element &a, const Element &x, const Element &y) const
	Natural MAXPY. More...

Element &	maxpy (Element &r, const Element &a, const Element &x, const Element &y) const
	Equality of two elements. More...

Input/Output Operations
std::ostream &	write (std::ostream &os) const
	Print field. More...

std::istream &	read (std::istream &is)
	Read field. More...

std::ostream &	write (std::ostream &os, const Element &x) const
	Print field base element. More...

std::istream &	read (std::istream &is, Element &x) const
	Read field base element. More...

std::istream &	read (std::istream &is, BitReference x) const
	Print field. More...

Inplace Arithmetic Operations
x <- x op y; x <- op x
Element &	addin (Element &x, const Element &y) const
	Inplace Addition. More...

BitReference	addin (BitReference x, const Element &y) const
	Inplace Addition. More...

Element &	subin (Element &x, const Element &y) const
	Inplace Subtraction. More...

BitReference	subin (BitReference x, const Element &y) const
	Inplace Addition. More...

Element &	mulin (Element &x, const Element &y) const
	Inplace Multiplication. More...

BitReference	mulin (BitReference x, const Element &y) const
	Inplace Addition. More...

Element &	divin (Element &x, const Element &y) const
	Inplace Division. More...

BitReference	divin (BitReference x, const Element &y) const
	Inplace Addition. More...

Element &	negin (Element &x) const
	Inplace Additive Inverse (Inplace Negation). More...

BitReference	negin (BitReference x) const
	Inplace Addition. More...

Element &	invin (Element &x) const
	Inplace Multiplicative Inverse. More...

BitReference	invin (BitReference x) const
	Inplace Addition. More...

Element &	axpyin (Element &r, const Element &a, const Element &x) const
	Inplace AXPY. More...

BitReference	axpyin (BitReference r, const Element &a, const Element &x) const
	Inplace Addition. More...

Element &	axmyin (Element &r, const Element &a, const Element &x) const
	Inplace AXMY. More...

BitReference	axmyin (BitReference r, const Element &a, const Element &x) const
	Inplace Addition. More...

Element &	maxpyin (Element &r, const Element &a, const Element &x) const
	Inplace MAXPY. More...

BitReference	maxpyin (BitReference r, const Element &a, const Element &x) const
	Inplace Addition. More...

static int	maxCardinality ()
	Inplace Addition. More...

Detailed Description

Integers modulo 2.

This is a tuned implementation of the field of integers modulo

In particular, when one constructs a VectorDomain object over this field, highly optimized bit operations will be used to make vector arithmetic very fast.

Constructor & Destructor Documentation

◆ GF2()

GF2 ( const GF2 & F )

inline

Copy constructor.

Constructs Givaro::GF2 object by copying the field. This is required to allow field objects to be passed by value into functions.

Parameters

F	Givaro::GF2 object.

Member Function Documentation

◆ operator=()

GF2& operator= ( const GF2 & F )

inline

Assignment operator.

Required by the archetype

Parameters

F	constant reference to Givaro::Modular object

Returns: reference to Givaro::Modular object for self

◆ init()

Element& init	(	Element &	x,
		const int32_t &	y
	)		const

inline

Initialization of field base element from an Integer.

Behaves like C++ allocator construct. This function assumes the output field base element x has already been constructed, but that it is not already initialized. This is not a specialization of the template function because such a specialization is not allowed inside the class declaration.

Returns: reference to field base element.

Parameters

x	field base element to contain output (reference returned).
y	Integer.

◆ convert()

Integer& convert	(	Integer &	x,
		const Element &	y
	)		const

inline

Conversion of field base element to a template class T.

This function assumes the output field base element x has already been constructed, but that it is not already initialized.

Returns: reference to template class T.

Parameters

x	template class T to contain output (reference returned).
y	constant field base element.

◆ assign()

Element& assign	(	Element &	x,
		const Element &	y
	)		const

inline

Assignment of one field base element to another.

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

Returns: reference to x

Parameters

x	field base element (reference returned).
y	field base element.

◆ cardinality()

Integer& cardinality ( Integer & c ) const

inline

Cardinality.

Return Integer representing cardinality of the domain. Returns a non-negative Integer for all domains with finite cardinality, and returns -1 to signify a domain of infinite cardinality.

Returns: Integer representing cardinality of the domain

◆ characteristic()

Integer& characteristic ( Integer & c ) const

inline

Characteristic.

Return Integer representing characteristic of the domain. Returns a positive Integer to all domains with finite characteristic, and returns 0 to signify a domain of infinite characteristic.

Returns: Integer representing characteristic of the domain.

◆ areEqual()

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

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ isZero()

bool isZero ( const Element & x ) const

inline

Zero equality.

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

Returns: boolean true if equals zero, false if not.

Parameters

x	field base element.

◆ isOne()

bool isOne ( const Element & x ) const

inline

One equality.

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

Returns: boolean true if equals one, false if not.

Parameters

x	field base element.

◆ isUnit()

bool isUnit ( const Element & x ) const

inline

Invertibility.

Test if field base element is invertible. This function assumes the field base element has already been constructed and initialized.

Returns: boolean true if equals one, false if not.

Parameters

x	field base element.

◆ isMOne()

bool isMOne ( const Element & x ) const

inline

MOne equality.

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

Returns: boolean true if equals one, false if not.

Parameters

x	field base element.

◆ write() [1/2]

std::ostream & write ( std::ostream & os ) const

inline

Print field.

Returns: output stream to which field is written.

Parameters

os	output stream to which field is written.

◆ read() [1/3]

std::istream & read ( std::istream & is )

inline

Read field.

Returns: input stream from which field is read.

Parameters

is	input stream from which field is read.

◆ write() [2/2]

std::ostream & write	(	std::ostream &	os,
		const Element &	x
	)		const

inline

Print field base element.

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

Returns: output stream to which field base element is written.

Parameters

os	output stream to which field base element is written.
x	field base element.

◆ read() [2/3]

std::istream & read	(	std::istream &	is,
		Element &	x
	)		const

inline

Read field base element.

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

Returns: input stream from which field base element is read.

Parameters

is	input stream from which field base element is read.
x	field base element.

◆ read() [3/3]

std::istream & read	(	std::istream &	is,
		BitReference	x
	)		const

inline

Print field.

Returns: output stream to which field is written.

Parameters

os	output stream to which field is written.

◆ add() [1/2]

GF2::Element & add	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Addition.

x = y + z This function assumes all the field base elements have already been constructed and initialized.

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.
z	field base element.

◆ add() [2/2]

GF2::BitReference add	(	BitReference	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ sub() [1/2]

GF2::Element & sub	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Subtraction.

x = y - z This function assumes all the field base elements have already been constructed and initialized.

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.
z	field base element.

◆ sub() [2/2]

GF2::BitReference sub	(	BitReference	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ mul() [1/2]

GF2::Element & mul	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Multiplication.

x = y * z This function assumes all the field base elements have already been constructed and initialized.

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.
z	field base element.

◆ mul() [2/2]

GF2::BitReference mul	(	BitReference	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ div() [1/2]

GF2::Element & div	(	Element &	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Division.

x = y / z This function assumes all the field base elements have already been constructed and initialized.

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.
z	field base element.

◆ div() [2/2]

GF2::BitReference div	(	BitReference	x,
		const Element &	y,
		const Element &	z
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ neg() [1/2]

GF2::Element & neg	(	Element &	x,
		const Element &	y
	)		const

inline

Additive Inverse (Negation).

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ neg() [2/2]

GF2::BitReference neg	(	BitReference	x,
		const Element &	y
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ inv() [1/2]

GF2::Element & inv	(	Element &	x,
		const Element &	y
	)		const

inline

Multiplicative Inverse.

x = 1 / y This function assumes both field base elements have already been constructed and initialized.

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ inv() [2/2]

GF2::BitReference inv	(	BitReference	x,
		const Element &	y
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ axpy() [1/2]

GF2::BitReference axpy	(	BitReference	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

Natural AXPY.

Returns: reference to r.

Parameters

r
a
x
y

◆ axpy() [2/2]

GF2::Element & axpy	(	Element &	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ axmy() [1/2]

GF2::BitReference axmy	(	BitReference	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

Natural AXMY.

Returns: reference to r.

Parameters

r
a
x
y

◆ axmy() [2/2]

GF2::Element & axmy	(	Element &	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ maxpy() [1/2]

GF2::BitReference maxpy	(	BitReference	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

Natural MAXPY.

Returns: reference to r.

Parameters

r
a
x
y

◆ maxpy() [2/2]

GF2::Element & maxpy	(	Element &	r,
		const Element &	a,
		const Element &	x,
		const Element &	y
	)		const

inline

Equality of two elements.

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

Returns: boolean true if equal, false if not.

Parameters

x	field base element
y	field base element

◆ addin() [1/2]

GF2::Element & addin	(	Element &	x,
		const Element &	y
	)		const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ addin() [2/2]

GF2::BitReference addin	(	BitReference	x,
		const Element &	y
	)		const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ subin() [1/2]

GF2::Element & subin	(	Element &	x,
		const Element &	y
	)		const

inline

Inplace Subtraction.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ subin() [2/2]

GF2::BitReference subin	(	BitReference	x,
		const Element &	y
	)		const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ mulin() [1/2]

GF2::Element & mulin	(	Element &	x,
		const Element &	y
	)		const

inline

Inplace Multiplication.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ mulin() [2/2]

GF2::BitReference mulin	(	BitReference	x,
		const Element &	y
	)		const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ divin() [1/2]

GF2::Element & divin	(	Element &	x,
		const Element &	y
	)		const

inline

Inplace Division.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ divin() [2/2]

GF2::BitReference divin	(	BitReference	x,
		const Element &	y
	)		const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ negin() [1/2]

GF2::Element & negin ( Element & x ) const

inline

Inplace Additive Inverse (Inplace Negation).

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

Returns: reference to x.

Parameters

x	field base element (reference returned).

◆ negin() [2/2]

GF2::BitReference negin ( BitReference x ) const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ invin() [1/2]

GF2::Element & invin ( Element & x ) const

inline

Inplace Multiplicative Inverse.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).

◆ invin() [2/2]

GF2::BitReference invin ( BitReference x ) const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ axpyin() [1/2]

GF2::Element & axpyin	(	Element &	r,
		const Element &	a,
		const Element &	x
	)		const

inline

Inplace AXPY.

Returns: reference to r.

Parameters

r	field element (reference returned).
a	field element.
x	field element.

◆ axpyin() [2/2]

GF2::BitReference axpyin	(	BitReference	r,
		const Element &	a,
		const Element &	x
	)		const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ axmyin() [1/2]

GF2::Element & axmyin	(	Element &	r,
		const Element &	a,
		const Element &	x
	)		const

inline

Inplace AXMY.

Returns: reference to r.

Parameters

r	field element (reference returned).
a	field element.
x	field element.

◆ axmyin() [2/2]

GF2::BitReference axmyin	(	BitReference	r,
		const Element &	a,
		const Element &	x
	)		const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ maxpyin() [1/2]

GF2::Element & maxpyin	(	Element &	r,
		const Element &	a,
		const Element &	x
	)		const

inline

Inplace MAXPY.

Returns: reference to r.

Parameters

r	field element (reference returned).
a	field element.
x	field element.

◆ maxpyin() [2/2]

GF2::BitReference maxpyin	(	BitReference	r,
		const Element &	a,
		const Element &	x
	)		const

inline

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

◆ maxCardinality()

static int maxCardinality ( )

inlinestatic

Inplace Addition.

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

Returns: reference to x.

Parameters

x	field base element (reference returned).
y	field base element.

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

gf2.h (4.2.0)
gf2.inl (4.2.0)

Public Types

Public Member Functions

Inplace Arithmetic Operations

Detailed Description

Constructor & Destructor Documentation

◆ GF2()

Member Function Documentation

◆ operator=()

◆ init()

◆ convert()

◆ assign()

◆ cardinality()

◆ characteristic()

◆ areEqual()

◆ isZero()

◆ isOne()

◆ isUnit()

◆ isMOne()

◆ write() [1/2]

◆ read() [1/3]

◆ write() [2/2]

◆ read() [2/3]

◆ read() [3/3]

◆ add() [1/2]

◆ add() [2/2]

◆ sub() [1/2]

◆ sub() [2/2]

◆ mul() [1/2]

◆ mul() [2/2]

◆ div() [1/2]

◆ div() [2/2]

◆ neg() [1/2]

◆ neg() [2/2]

◆ inv() [1/2]

◆ inv() [2/2]

◆ axpy() [1/2]

◆ axpy() [2/2]

◆ axmy() [1/2]

◆ axmy() [2/2]

◆ maxpy() [1/2]

◆ maxpy() [2/2]

◆ addin() [1/2]

◆ addin() [2/2]

◆ subin() [1/2]

◆ subin() [2/2]

◆ mulin() [1/2]

◆ mulin() [2/2]

◆ divin() [1/2]

◆ divin() [2/2]

◆ negin() [1/2]

◆ negin() [2/2]

◆ invin() [1/2]

◆ invin() [2/2]

◆ axpyin() [1/2]

◆ axpyin() [2/2]

◆ axmyin() [1/2]

◆ axmyin() [2/2]

◆ maxpyin() [1/2]

◆ maxpyin() [2/2]

◆ maxCardinality()