Local2_32 Struct Reference
[linbox/field]

#include <local2_32.h>

Inheritance diagram for Local2_32:

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Detailed Description

Fast arithmetic mod 2^32, including gcd.

Extend UnparametricField<uint32> which is a representation of Z_2^32. It is especially fast because it uses hardware arithmetic directly. This ring is a Local Principal Ideal Ring.

These needed PIR functions are added: gcdin(), isUnit(), also inv() is modified to work correctly. The type Exponent is added: more effective rep of the powers of 2, which are important because gcds are powers of 2). This entails some new versions of divin(), mulin(), isUnit().

Those are the function needed for the LocalSmith algorithm. Further appropriate PIR functions may be added later.

Public Types
typedef UnparametricField< uint32 >::Element	Element
enum	Exponent { _min = 0, _max = 32 }
Public Member Functions
	Local2_32 (int p=2, int exp=32)
Static Public Member Functions
Exponent &	gcdin (Exponent &k, const Element &b)
bool	isUnit (const Exponent &a)
bool	isZero (const Element &a)
bool	isZero (const Exponent &a)
bool	isUnit (const Element &a)
Element &	mulin (Element &a, const Exponent &k)
Element &	mulin (Element &a, const Element &b)
Element &	axpyin (Element &r, const Element &x, const Element &y)
Element &	divin (Element &a, const Exponent &k)
Element &	inv (Element &a, const Element &b)
integer	getMaxModulus ()
Static Protected Member Functions
Element &	xgcd (Element &d, Element &s, Element &t, const Element &a, const Element &b)
Element &	HGCD (Element &g, Element &s, const Element &a, const Element &b)
	Half GCD g = gcd (a, b). exists t, such that: s * a + t * b = g. return g.

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Member Typedef Documentation

typedef UnparametricField<uint32>::Element Element

The field's element type. Type K must provide a default constructor, a copy constructor, a destructor, and an assignment operator. Reimplemented from UnparametricField< uint32 >.

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Member Enumeration Documentation

enum Exponent

Enumeration values: _min  _max

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Constructor & Destructor Documentation

Local2_32 (  int  p = 2, int  exp = 32 )  [inline]

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Member Function Documentation

Exponent& gcdin (  Exponent &  k, const Element &  b )  [inline, static]

bool isUnit (  const Exponent &  a  )  [inline, static]

bool isZero (  const Element &  a  )  [inline, static]

bool isZero (  const Exponent &  a  )  [inline, static]

bool isUnit (  const Element &  a  )  [inline, static]

Element& mulin (  Element &  a, const Exponent &  k )  [inline, static]

Element& mulin (  Element &  a, const Element &  b )  [inline, static]

Element& axpyin (  Element &  r, const Element &  x, const Element &  y )  [inline, static]

Element& divin (  Element &  a, const Exponent &  k )  [inline, static]

Element& inv (  Element &  a, const Element &  b )  [inline, static]

integer getMaxModulus (   )  [inline, static]

Element& xgcd (  Element &  d, Element &  s, Element &  t, const Element &  a, const Element &  b )  [inline, static, protected]

Element& HGCD (  Element &  g, Element &  s, const Element &  a, const Element &  b )  [inline, static, protected]

Half GCD g = gcd (a, b). exists t, such that: s * a + t * b = g. return g.

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