linbox
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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. | |
std::istream & | read (std::istream &is) |
Builds this field to have characteristic q and cardinality qe. | |
std::istream & | read (std::istream &s, Element &a) const |
Builds this field to have characteristic q and cardinality qe. | |
template<typename Src > | |
Element & | init (Element &x, const Src &s) const |
Builds this field to have characteristic q and cardinality qe. | |
Element & | init (Element &x) const |
Builds this field to have characteristic q and cardinality qe. | |
template<typename T > | |
T & | convert (T &x, const Element &y) const |
Builds this field to have characteristic q and cardinality qe. | |
integer & | cardinality (integer &c) const |
Builds this field to have characteristic q and cardinality qe. | |
integer & | characteristic (integer &c) const |
Builds this field to have characteristic q and cardinality qe. | |
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). | |
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.
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inlinestaticprotected |
Half GCD g = gcd (a, b).
exists t, such that: s * a + t * b = g. return g.
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inlineinherited |
Builds this field to have characteristic q and cardinality qe.
This constructor must be defined in a specialization.
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inlineinherited |
Builds this field to have characteristic q and cardinality qe.
This constructor must be defined in a specialization.
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inlineinherited |
Builds this field to have characteristic q and cardinality qe.
This constructor must be defined in a specialization.
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inlineinherited |
Builds this field to have characteristic q and cardinality qe.
This constructor must be defined in a specialization.
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inlineinherited |
Builds this field to have characteristic q and cardinality qe.
This constructor must be defined in a specialization.
Builds this field to have characteristic q and cardinality qe.
This constructor must be defined in a specialization.
Builds this field to have characteristic q and cardinality qe.
This constructor must be defined in a specialization.
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inlineinherited |
Constant access operator.
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inlineinherited |
Access operator.