M2::ARingZZp — portable Z/p for small primes via log / exp tables. More...

#include "interface/random.h"
#include "aring.hpp"
#include "buffer.hpp"
#include "ringelem.hpp"
#include "exceptions.hpp"

Classes
class	M2::ARingZZp
	aring-style adapter for Z/p using a discrete-log (Zech) representation: every non-zero residue is its index relative to a primitive generator a. More...

Namespaces
namespace	M2

Detailed Description

M2::ARingZZp — portable Z/p for small primes via log / exp tables.

Note: AI-generated documentation. Verify against the source before relying on it.

ARingZZp is the dependency-free Z/p aring: a SimpleARing<ARingZZp> whose elements are interpreted as log indices of a chosen primitive root, with 0 reserved for the field zero and each 1 <= n <= p - 1 representing alpha^n mod p (in particular p - 1 is the representation of 1). Multiplication reduces to (a + b) mod (p - 1), inversion to p - 1 - a (negation mod p - 1), and power(a, n) to (a * n) mod (p - 1). Addition is a classical log / exp round-trip: exp_table maps the two operands back to actual residues, those are summed mod p, and log_table converts the result back to an index. log_table and exp_table are built at construction and each occupy p ints, so the pair fits comfortably in cache for the small primes M2's ZZp factory accepts (2 <= p <= 32749).

This is the only Z/p aring path with no external dependency, so it is what stripped-down or diagnostic M2 builds fall back to. The non-aring counterpart with the same table encoding is the legacy Z_mod in ZZp.hpp (typedef'd here as ring_type); the FLINT- and FFLAS-FFPACK-backed variants live in aring-zzp-flint.hpp and aring-zzp-ffpack.hpp.

See also: ZZp.hpp; aring-zzp-flint.hpp; aring-zzp-ffpack.hpp; aring.hpp

Definition in file aring-zzp.hpp.

Classes

Namespaces

Detailed Description