Ring of elements modulo some power of two. More...

#include <poweroftwomodular.h>

Data Structures
struct	RandIter
	Random iterator generator type. More...

Public Types
typedef Ints	Element
	Element type.

Public Member Functions
Object Management
	PowerOfTwoGivaro::Modular (void)
	Default constructor.

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

Element &	init (Element &x, const Ints &y=0) const
	Initialization of field base element from an integer. More...

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

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

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

int &	poweroftwo (int &c)
	poweroftwo

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
	isUnit. More...

bool	isZeroDivisor (const Element &x) const
	isZeroDivisor. More...

Element &	gcd_poweroftwo (Element &x, const Element &y) const
	Gcd with 2^_poweroftwo . More...

bool	doesdivide (const Element &x, const Element &y) const
	Does x divide y.

int	poweroftwoinx (const Element &x) const
	Power of two in x Input Element x = 2^n*y where y is odd Output n.

Element &	bezout (const Element &x, const Element &y, Element &gcd, Element &u, Element &v) const
	bezout. More...

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

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

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

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

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

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

Element &	inv2 (Element &x, const Element &y) const
	Multiplicative Inverse 2. More...

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

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

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

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

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

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

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

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

Protected Attributes
Element	_poweroftwo
	Private (non-static) element for modulus.

Detailed Description

template<class Ints>
class LinBox::PowerOfTwoGivaro::Modular< Ints >

Ring of elements modulo some power of two.

Parameters

element	Element type, e.g. long or integer
Intermediate	Type to use for intermediate computations. This should be a data type that can support integers twice the length of the maximal modulus used

Member Function Documentation

§ 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.

§ init()

Element& init	(	Element &	x,
		const Ints &	y = `0`
	)		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.

§ 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

isUnit.

Parameters

x

§ isZeroDivisor()

bool isZeroDivisor ( const Element & x ) const

inline

isZeroDivisor.

Parameters

x

§ gcd_poweroftwo()

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

inline

Gcd with 2^_poweroftwo .

Valid for Ints up to 32 bits Specialization is required for bigger Ints

Parameters

x
y

§ bezout()

Element& bezout	(	const Element &	x,
		const Element &	y,
		Element &	gcd,
		Element &	u,
		Element &	v
	)		const

inline

bezout.

Parameters

x,y
gcd
u,v

§ 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() [1/2]

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() [2/2]

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

inline

Read field base element.

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.

§ add()

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.

§ sub()

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.

§ mul()

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.

§ div()

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. This fonction assumes that x divides y. That can be verified by using doesdivide(x,y)

Returns: reference to x.

Parameters

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

§ neg()

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.

§ inv()

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. This function assumes that y is odd (ie 1/y exists)

Returns: reference to x.

Parameters

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

§ inv2()

Element& inv2	(	Element &	x,
		const Element &	y
	)		const

inline

Multiplicative Inverse 2.

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.

§ axpy()

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

inline

Natural AXPY.

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

Returns: reference to r.

Parameters

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

§ addin()

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.

§ subin()

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.

§ mulin()

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.

§ divin()

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.

§ negin()

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).

§ invin()

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).

§ axpyin()

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. Purely virtual

Returns: reference to r.

Parameters

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

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

poweroftwomodular.h

Data Structures

Public Types

Public Member Functions

Protected Attributes

Detailed Description

template<class Ints> class LinBox::PowerOfTwoGivaro::Modular< Ints >

Member Function Documentation

§ convert()

§ init()

§ assign()

§ cardinality()

§ characteristic()

§ areEqual()

§ isZero()

§ isOne()

§ isUnit()

§ isZeroDivisor()

§ gcd_poweroftwo()

§ bezout()

§ write() [1/2]

§ read() [1/2]

§ write() [2/2]

§ read() [2/2]

§ add()

§ sub()

§ mul()

§ div()

§ neg()

§ inv()

§ inv2()

§ axpy()

§ addin()

§ subin()

§ mulin()

§ divin()

§ negin()

§ invin()

§ axpyin()

template<class Ints>
class LinBox::PowerOfTwoGivaro::Modular< Ints >