Local2_32 Struct Reference

Fast arithmetic mod 2^32, including gcd. More...

#include <local2_32.h>

Inheritance diagram for Local2_32:

Public Types
enum	Exponent { _min =0 , _max =32 }
typedef Givaro::ZRing< uint32_t >::Element	Element

Public Member Functions
	Local2_32 (int p=2, int exp=32)
Element &	gcd (Element &c, const Element &a, const Element &b) const
Element &	gcdin (Element &b, const Element &a) const
Exponent &	gcdin (Exponent &k, const Element &b) const
bool	isUnit (const Element &a) const
bool	isUnit (const Exponent &a) const
bool	isZero (const Element &a) const
bool	isZero (const Exponent &a) const
Element &	mulin (Element &a, const Exponent &k) const
Element &	mulin (Element &a, const Element &b) const
Element &	axpyin (Element &r, const Element &x, const Element &y) const
Element &	divin (Element &a, const Exponent &k) const
Element &	inv (Element &a, const Element &b) const

Static Public Member Functions
static integer	maxCardinality ()

Protected Member Functions
Element &	xgcd (Element &d, Element &s, Element &t, const Element &a, const Element &b) const
Element &	HGCD (Element &g, Element &s, const Element &a, const Element &b) const
	Half GCD g = gcd (a, b).

Detailed Description

Fast arithmetic mod 2^32, including gcd.

Extend Givaro::ZRing<uint32_t> 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.

Examples

examples/smith.C.

Member Typedef Documentation

Element

typedef Givaro::ZRing<uint32_t>::Element Element

Member Enumeration Documentation

Exponent

enum Exponent

Enumerator
_min
_max

Constructor & Destructor Documentation

Local2_32()

Local2_32 ( int p = 2, int exp = 32 )

inline

Member Function Documentation

gcd()

Element & gcd ( Element & c, const Element & a, const Element & b ) const

inline

gcdin() [1/2]

Element & gcdin ( Element & b, const Element & a ) const

inline

gcdin() [2/2]

Exponent & gcdin ( Exponent & k, const Element & b ) const

inline

isUnit() [1/2]

bool isUnit ( const Element & a ) const

inline

isUnit() [2/2]

bool isUnit ( const Exponent & a ) const

inline

isZero() [1/2]

bool isZero ( const Element & a ) const

inline

isZero() [2/2]

bool isZero ( const Exponent & a ) const

inline

mulin() [1/2]

Element & mulin ( Element & a, const Exponent & k ) const

inline

mulin() [2/2]

Element & mulin ( Element & a, const Element & b ) const

inline

axpyin()

Element & axpyin ( Element & r, const Element & x, const Element & y ) const

inline

divin()

Element & divin ( Element & a, const Exponent & k ) const

inline

inv()

Element & inv ( Element & a, const Element & b ) const

inline

maxCardinality()

static integer maxCardinality ( )

inlinestatic

xgcd()

Element & xgcd ( Element & d, Element & s, Element & t, const Element & a, const Element & b ) const

inlineprotected

HGCD()

Element & HGCD ( Element & g, Element & s, const Element & a, const Element & b ) const

inlineprotected

Half GCD g = gcd (a, b).

exists t, such that: s * a + t * b = g. return g.

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

• local2_32.h