# g2p
This crate can generate types that implement fast finite field arithmetic.
Many error correcting codes rely on some form of finite field of the form GF(2^p), where
p is relatively small. Similarly some cryptographic algorithms such as AES use finite field
arithmetic.
While addition and subtraction can be done quickly using just a simple XOR, multiplication is
more involved. To speed things up, you can use a precomputed table of logarithms and use the
fact that `log(a* b) = log(a) + log(b)`. Expanding back using the same base as the logarithm
gives the result for multiplication. The same method can be applied to division.
*WARNING:*
The types generated by this library are probably not suitable for cryptographic purposes, as
multiplication is not guaranteed to be constant time.
*WARNING*
Currently only small precomputed tables are supported, the compiler may hang on bigger inputs
such as for GF(65536)
[Documentation](https://docs.rs/g2p)
# Examples
```ignore
use g2p;
g2p::g2p!(GF16, 4, modulus: 0b10011);
let one: GF16 = 1.into();
let a: GF16 = 5.into();
let b: GF16 = 4.into();
let c: GF16 = 7.into();
assert_eq!(a + c, 2.into());
assert_eq!(a - c, 2.into());
assert_eq!(a * b, c);
assert_eq!(a / c, one / b);
assert_eq!(b / b, one);
```