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PowerOfTwoModular Class Template Reference
[linbox/ring]

#include <poweroftwomodular.h>

List of all members.

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 Member Functions

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.

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
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

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.

Member Typedef Documentation

typedef Ints Element
 

Element type

Constructor & Destructor Documentation

PowerOfTwoModular (  void   )  [inline]
 

Default constructor.

Member Function Documentation

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& 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& 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.

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.

int& poweroftwo (  int &  c  )  [inline]
 

poweroftwo

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

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 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.

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

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

Does x divide y

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::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.

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.

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.

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.

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.

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& 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& 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& 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& 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& 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& 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.

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.

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& 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.

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).

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).

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:
Generated on Thu Feb 8 22:33:06 2007 for linbox by doxygen 1.3.4