#![allow(clippy::wrong_self_convention, clippy::suspicious_arithmetic_impl)]
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
#[repr(transparent)]
pub struct Gf256(pub u8);
impl Gf256 {
#[inline]
pub fn zero() -> Gf256 {
Gf256(0)
}
#[inline]
pub fn one() -> Gf256 {
Gf256(1)
}
#[inline]
pub fn as_slice(s: &[u8]) -> &[Gf256] {
unsafe { std::slice::from_raw_parts(s.as_ptr() as *const Gf256, s.len()) }
}
#[inline]
pub fn as_slice_mut(s: &mut [u8]) -> &mut [Gf256] {
unsafe { std::slice::from_raw_parts_mut(s.as_mut_ptr() as *mut Gf256, s.len()) }
}
#[inline]
pub fn to_bytes(s: &[Gf256]) -> &[u8] {
unsafe { std::slice::from_raw_parts(s.as_ptr() as *const u8, s.len()) }
}
#[inline]
pub fn to_bytes_mut(s: &mut [Gf256]) -> &mut [u8] {
unsafe { std::slice::from_raw_parts_mut(s.as_mut_ptr() as *mut u8, s.len()) }
}
pub fn add_mul_slice(res: &mut [Self], a: &[Self], b: Self) {
assert_eq!(res.len(), a.len());
for (res, &a) in res.iter_mut().zip(a) {
*res += a * b;
}
}
pub fn exp(power: usize) -> Gf256 {
Gf256(GF256_EXP[power % 255])
}
pub fn log(self) -> Option<usize> {
if self.0 != 0 {
Some(GF256_LOG[self.0 as usize] as usize)
} else {
None
}
}
}
static GF256_EXP: [u8; 255] = [
0x01, 0x03, 0x05, 0x0f, 0x11, 0x33, 0x55, 0xff, 0x1a, 0x2e, 0x72, 0x96, 0xa1, 0xf8, 0x13, 0x35,
0x5f, 0xe1, 0x38, 0x48, 0xd8, 0x73, 0x95, 0xa4, 0xf7, 0x02, 0x06, 0x0a, 0x1e, 0x22, 0x66, 0xaa,
0xe5, 0x34, 0x5c, 0xe4, 0x37, 0x59, 0xeb, 0x26, 0x6a, 0xbe, 0xd9, 0x70, 0x90, 0xab, 0xe6, 0x31,
0x53, 0xf5, 0x04, 0x0c, 0x14, 0x3c, 0x44, 0xcc, 0x4f, 0xd1, 0x68, 0xb8, 0xd3, 0x6e, 0xb2, 0xcd,
0x4c, 0xd4, 0x67, 0xa9, 0xe0, 0x3b, 0x4d, 0xd7, 0x62, 0xa6, 0xf1, 0x08, 0x18, 0x28, 0x78, 0x88,
0x83, 0x9e, 0xb9, 0xd0, 0x6b, 0xbd, 0xdc, 0x7f, 0x81, 0x98, 0xb3, 0xce, 0x49, 0xdb, 0x76, 0x9a,
0xb5, 0xc4, 0x57, 0xf9, 0x10, 0x30, 0x50, 0xf0, 0x0b, 0x1d, 0x27, 0x69, 0xbb, 0xd6, 0x61, 0xa3,
0xfe, 0x19, 0x2b, 0x7d, 0x87, 0x92, 0xad, 0xec, 0x2f, 0x71, 0x93, 0xae, 0xe9, 0x20, 0x60, 0xa0,
0xfb, 0x16, 0x3a, 0x4e, 0xd2, 0x6d, 0xb7, 0xc2, 0x5d, 0xe7, 0x32, 0x56, 0xfa, 0x15, 0x3f, 0x41,
0xc3, 0x5e, 0xe2, 0x3d, 0x47, 0xc9, 0x40, 0xc0, 0x5b, 0xed, 0x2c, 0x74, 0x9c, 0xbf, 0xda, 0x75,
0x9f, 0xba, 0xd5, 0x64, 0xac, 0xef, 0x2a, 0x7e, 0x82, 0x9d, 0xbc, 0xdf, 0x7a, 0x8e, 0x89, 0x80,
0x9b, 0xb6, 0xc1, 0x58, 0xe8, 0x23, 0x65, 0xaf, 0xea, 0x25, 0x6f, 0xb1, 0xc8, 0x43, 0xc5, 0x54,
0xfc, 0x1f, 0x21, 0x63, 0xa5, 0xf4, 0x07, 0x09, 0x1b, 0x2d, 0x77, 0x99, 0xb0, 0xcb, 0x46, 0xca,
0x45, 0xcf, 0x4a, 0xde, 0x79, 0x8b, 0x86, 0x91, 0xa8, 0xe3, 0x3e, 0x42, 0xc6, 0x51, 0xf3, 0x0e,
0x12, 0x36, 0x5a, 0xee, 0x29, 0x7b, 0x8d, 0x8c, 0x8f, 0x8a, 0x85, 0x94, 0xa7, 0xf2, 0x0d, 0x17,
0x39, 0x4b, 0xdd, 0x7c, 0x84, 0x97, 0xa2, 0xfd, 0x1c, 0x24, 0x6c, 0xb4, 0xc7, 0x52, 0xf6,
];
static GF256_LOG: [u8; 256] = [
0x00, 0x00, 0x19, 0x01, 0x32, 0x02, 0x1a, 0xc6, 0x4b, 0xc7, 0x1b, 0x68, 0x33, 0xee, 0xdf, 0x03,
0x64, 0x04, 0xe0, 0x0e, 0x34, 0x8d, 0x81, 0xef, 0x4c, 0x71, 0x08, 0xc8, 0xf8, 0x69, 0x1c, 0xc1,
0x7d, 0xc2, 0x1d, 0xb5, 0xf9, 0xb9, 0x27, 0x6a, 0x4d, 0xe4, 0xa6, 0x72, 0x9a, 0xc9, 0x09, 0x78,
0x65, 0x2f, 0x8a, 0x05, 0x21, 0x0f, 0xe1, 0x24, 0x12, 0xf0, 0x82, 0x45, 0x35, 0x93, 0xda, 0x8e,
0x96, 0x8f, 0xdb, 0xbd, 0x36, 0xd0, 0xce, 0x94, 0x13, 0x5c, 0xd2, 0xf1, 0x40, 0x46, 0x83, 0x38,
0x66, 0xdd, 0xfd, 0x30, 0xbf, 0x06, 0x8b, 0x62, 0xb3, 0x25, 0xe2, 0x98, 0x22, 0x88, 0x91, 0x10,
0x7e, 0x6e, 0x48, 0xc3, 0xa3, 0xb6, 0x1e, 0x42, 0x3a, 0x6b, 0x28, 0x54, 0xfa, 0x85, 0x3d, 0xba,
0x2b, 0x79, 0x0a, 0x15, 0x9b, 0x9f, 0x5e, 0xca, 0x4e, 0xd4, 0xac, 0xe5, 0xf3, 0x73, 0xa7, 0x57,
0xaf, 0x58, 0xa8, 0x50, 0xf4, 0xea, 0xd6, 0x74, 0x4f, 0xae, 0xe9, 0xd5, 0xe7, 0xe6, 0xad, 0xe8,
0x2c, 0xd7, 0x75, 0x7a, 0xeb, 0x16, 0x0b, 0xf5, 0x59, 0xcb, 0x5f, 0xb0, 0x9c, 0xa9, 0x51, 0xa0,
0x7f, 0x0c, 0xf6, 0x6f, 0x17, 0xc4, 0x49, 0xec, 0xd8, 0x43, 0x1f, 0x2d, 0xa4, 0x76, 0x7b, 0xb7,
0xcc, 0xbb, 0x3e, 0x5a, 0xfb, 0x60, 0xb1, 0x86, 0x3b, 0x52, 0xa1, 0x6c, 0xaa, 0x55, 0x29, 0x9d,
0x97, 0xb2, 0x87, 0x90, 0x61, 0xbe, 0xdc, 0xfc, 0xbc, 0x95, 0xcf, 0xcd, 0x37, 0x3f, 0x5b, 0xd1,
0x53, 0x39, 0x84, 0x3c, 0x41, 0xa2, 0x6d, 0x47, 0x14, 0x2a, 0x9e, 0x5d, 0x56, 0xf2, 0xd3, 0xab,
0x44, 0x11, 0x92, 0xd9, 0x23, 0x20, 0x2e, 0x89, 0xb4, 0x7c, 0xb8, 0x26, 0x77, 0x99, 0xe3, 0xa5,
0x67, 0x4a, 0xed, 0xde, 0xc5, 0x31, 0xfe, 0x18, 0x0d, 0x63, 0x8c, 0x80, 0xc0, 0xf7, 0x70, 0x07,
];
impl Add<Gf256> for Gf256 {
type Output = Self;
#[inline]
fn add(self, rhs: Gf256) -> Self::Output {
Gf256(self.0 ^ rhs.0)
}
}
impl AddAssign<Gf256> for Gf256 {
#[inline]
fn add_assign(&mut self, rhs: Gf256) {
*self = *self + rhs;
}
}
impl Sub<Gf256> for Gf256 {
type Output = Gf256;
#[inline]
fn sub(self, rhs: Gf256) -> Self::Output {
Gf256(self.0 ^ rhs.0)
}
}
impl SubAssign<Gf256> for Gf256 {
#[inline]
fn sub_assign(&mut self, rhs: Gf256) {
*self = *self - rhs;
}
}
impl Mul<Gf256> for Gf256 {
type Output = Gf256;
fn mul(self, rhs: Gf256) -> Self::Output {
if let Some(log1) = self.log() {
if let Some(log2) = rhs.log() {
return Gf256::exp(log1 + log2);
}
}
Gf256(0)
}
}
impl MulAssign<Gf256> for Gf256 {
fn mul_assign(&mut self, rhs: Gf256) {
*self = *self * rhs;
}
}
impl Div<Gf256> for Gf256 {
type Output = Gf256;
fn div(self, rhs: Gf256) -> Self::Output {
let log2 = rhs.log().expect("division by zero");
if let Some(log1) = self.log() {
return Gf256::exp(log1 + 255 - log2);
}
Gf256(0)
}
}
impl DivAssign<Gf256> for Gf256 {
fn div_assign(&mut self, rhs: Gf256) {
*self = *self / rhs;
}
}
#[cfg(test)]
mod tests {
#![allow(clippy::eq_op)]
use super::*;
use quickcheck::*;
impl Arbitrary for Gf256 {
fn arbitrary<G: Gen>(gen: &mut G) -> Gf256 {
Gf256(u8::arbitrary(gen))
}
}
mod addition {
use super::*;
quickcheck! {
fn law_associativity(a: Gf256, b: Gf256, c: Gf256) -> bool {
(a + b) + c == a + (b + c)
}
fn law_commutativity(a: Gf256, b: Gf256) -> bool {
a + b == b + a
}
fn law_distributivity(a: Gf256, b: Gf256, c: Gf256) -> bool {
a * (b + c) == a * b + a * c
}
fn law_identity(a: Gf256) -> bool {
a + Gf256::zero() == a && Gf256::zero() + a == a
}
fn law_inverses(a: Gf256) -> bool {
a + (Gf256::zero() - a) == Gf256::zero() && (Gf256::zero() - a) + a == Gf256::zero()
}
}
}
mod multiplication {
use super::*;
quickcheck! {
fn law_associativity(a: Gf256, b: Gf256, c: Gf256) -> bool {
(a * b) * c == a * (b * c)
}
fn law_commutativity(a: Gf256, b: Gf256) -> bool {
a * b == b * a
}
fn law_distributivity(a: Gf256, b: Gf256, c: Gf256) -> bool {
(a + b) * c == a * c + b * c
}
fn law_identity(a: Gf256) -> bool {
a * Gf256::one() == a && Gf256::one() * a == a
}
fn law_inverses(a: Gf256) -> TestResult {
if a == Gf256::zero() {
return TestResult::discard();
}
let left = a * (Gf256::one() / a) == Gf256::one();
let right = (Gf256::one() / a) * a == Gf256::one();
TestResult::from_bool(left && right)
}
}
}
}