package qrc

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Arithmetic over galois field GF(2⁸).

type poly = int

The type for degree 8 polynomials, using 0x1FF bits. The ith zero-based bit index represents the coefficient (0 or 1) of the ith degree variable.

type byte = int

The type for bytes, the elements of GF(2⁸).

type t

A galois field instance for a given polynomial and generator.

val create : r:poly -> g:byte -> t

create ~r ~g is a field modulo polynomial r (must be irreducible) and generator g. g is the base for exp and log.

val add : byte -> byte -> byte

add x y is y added (xored) to x.

val sub : byte -> byte -> byte

sub x y is y subtracted (xored) to x.

val exp : t -> byte -> byte

exp f x is the base g exponential g^x in f.

val log : t -> byte -> byte

log f x is y the base g logarithm of x, i.e. g^y = x. This is 255 if x = 0.

val mul : t -> byte -> byte -> byte

mul f x y multiples x by y modulo f's r polynomial.

val inv : t -> byte -> byte

inv f x is x^-1, the multiplicative inverse of x. This is 0 if x is 0.