linbox
Static Protected Member Functions
Local2_32 Struct Reference

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

#include <local2_32.h>

Inherits UnparametricField< K >.

Public Types

Common Object Interface for a LinBox Field.

These methods and member types are required of all LinBox fields.

See FieldArchetype for detailed specifications.

typedef UnparametricRandIter< K > RandIter
 Type of random field element generators.

Public Member Functions

Field Object Basics.
     
Element & inv (Element &x, const Element &y) const
 c := characteristic of this field (zero or prime).
Element & invin (Element &x) const
 c := characteristic of this field (zero or prime).
std::ostream & write (std::ostream &os) const
 c := characteristic of this field (zero or prime).
std::ostream & write (std::ostream &os, const Element &p) const
 c := characteristic of this field (zero or prime).
bool isZero (const Element &x) const
 c := characteristic of this field (zero or prime).
bool isOne (const Element &x) const
 c := characteristic of this field (zero or prime).
long unsigned int characteristic (long unsigned int &p) const
 c := characteristic of this field (zero or prime).
long unsigned int characteristic () const
 c := characteristic of this field (zero or prime).
integercharacteristic (integer &c) const
 c := characteristic of this field (zero or prime).
long unsigned int cardinality () const
 c := characteristic of this field (zero or prime).
integercardinality (integer &c) const
 c := cardinality of this field (-1 if infinite).
template<typename Src >
Element & init (Element &x, const Src &s) const
 c := characteristic of this field (zero or prime).
Element & init (Element &x) const
 c := characteristic of this field (zero or prime).
std::istream & read (std::istream &is, Element &x) const
 c := characteristic of this field (zero or prime).
std::istream & read (std::istream &is) const
 c := characteristic of this field (zero or prime).
template<typename T >
T & convert (T &x, const Element &y) const
 c := characteristic of this field (zero or prime).
Implementation-Specific Methods.

These methods are not required of all LinBox fields and are included only for the implementation of this field template.

const K & operator() (void) const
 Constant access operator.
K & operator() (void)
 Access operator.

Static Protected Member Functions

static Element & HGCD (Element &g, Element &s, const Element &a, const Element &b)
 Half GCD g = gcd (a, b).

Detailed Description

Fast arithmetic mod 2^32, including gcd.

Extend UnparametricField<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 Function Documentation

static 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.

const K& operator() ( void  ) const [inline, inherited]

Constant access operator.

Returns:
constant reference to field object
K& operator() ( void  ) [inline, inherited]

Access operator.

Returns:
reference to field object

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