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PowerOfTwoModular Class Template Reference

#include <poweroftwomodular.h>

List of all members.

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Detailed Description

template<class Ints>
class LinBox::PowerOfTwoModular< 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

Public Types
typedef Ints	Element
Public Methods
Object Management
	PowerOfTwoModular (void)
integer &	convert (integer &x, const Element &y) const
Element &	init (Element &x, const Ints &y=0) const
Element &	assign (Element &x, const Element &y) const
integer &	cardinality (integer &c) const
integer &	characteristic (integer &c) const
int &	poweroftwo (int &c)
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.
Object Management bool	areEqual (const Element &x, const Element &y) const
bool	isZero (const Element &x) const
bool	isOne (const Element &x) const
bool	isUnit (const Element &x) const
bool	isZeroDivisor (const Element &x) const
Element &	gcd_poweroftwo (Element &x, const Element &y) const
bool	doesdivide (const Element &x, const Element &y) const
int	poweroftwoinx (const Element &x) const
Element &	bezout (const Element &x, const Element &y, Element &gcd, Element &u, Element &v) const
Input/Output Operations
Arithmetic Operations std::ostream &	write (std::ostream &os) const
std::istream &	read (std::istream &is)
std::ostream &	write (std::ostream &os, const Element &x) const
std::istream &	read (std::istream &is, Element &x) const
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.
Element &	add (Element &x, const Element &y, const Element &z) const
Element &	sub (Element &x, const Element &y, const Element &z) const
Element &	mul (Element &x, const Element &y, const Element &z) const
Element &	div (Element &x, const Element &y, const Element &z) const
Element &	neg (Element &x, const Element &y) const
Element &	inv (Element &x, const Element &y) const
Element &	inv2 (Element &x, const Element &y) const
Element &	axpy (Element &r, const Element &a, const Element &x, const Element &y) const
Inplace Arithmetic Operations
x <- x op y; x <- op x
Arithmetic Operations Element &	addin (Element &x, const Element &y) const
Element &	subin (Element &x, const Element &y) const
Element &	mulin (Element &x, const Element &y) const
Element &	divin (Element &x, const Element &y) const
Element &	negin (Element &x) const
Element &	invin (Element &x) const
Element &	axpyin (Element &r, const Element &a, const Element &x) const
Protected Attributes
Element	_poweroftwo
	Private (non-static) element for modulus.

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Member Typedef Documentation

typedef Ints Element

Element type

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Constructor & Destructor Documentation

PowerOfTwoModular (  void    )  [inline]

Default constructor.

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Member Function Documentation

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.

Arithmetic Operations 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.

Object Management 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

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.

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.

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.

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

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

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.

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.

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.

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.

bool doesdivide (  const Element &    x, const Element &    y )  const [inline]

Does x divide y

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

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.

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.

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.

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).

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.

bool isUnit (  const Element &    x )  const [inline]

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.

bool isZeroDivisor (  const Element &    x )  const [inline]

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.

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.

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.

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).

int& poweroftwo (  int &    c )  [inline]

poweroftwo

int poweroftwoinx (  const Element &    x )  const [inline]

Power of two in x Input Element x = 2^n*y where y is odd Output n

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.

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.

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.

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.

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.

Arithmetic Operations 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.

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Member Data Documentation

Element _poweroftwo [protected]

Private (non-static) element for modulus.

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