use std::{
fmt::{Debug, Display, Formatter},
iter::{Product, Sum},
ops::{Add, AddAssign, BitXor, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
};
pub trait Field:
'static
+ Sized
+ Eq
+ PartialEq
+ Copy
+ Clone
+ Send
+ Sync
+ Debug
+ Display
+ Add<Output = Self>
+ AddAssign
+ Sub<Output = Self>
+ SubAssign
+ Div<Output = Self>
+ DivAssign
+ Mul<Output = Self>
+ MulAssign
+ Neg<Output = Self>
+ Product
+ Sum
{
const ZERO: Self;
const ONE: Self;
fn zero() -> Self {
Self::ZERO
}
fn is_zero(&self) -> bool {
*self == Self::ZERO
}
fn one() -> Self {
Self::ONE
}
fn inverse(&self) -> Self;
fn pow(self, exp: usize) -> Self;
fn square(&mut self) {
*self *= *self
}
fn idx(&self) -> usize;
}
#[derive(Debug, Clone, Copy, Eq, PartialEq)]
pub struct GF<T>(pub T);
impl<T> GF<T> {
pub fn new(inner: T) -> Self {
Self(inner)
}
}
pub type GFU8 = GF<u8>;
pub type GF256 = GFU8;
pub type GFU16 = GF<u16>;
pub type GFU32 = GF<u32>;
pub type GFU64 = GF<u64>;
pub type GFU128 = GF<u128>;
const LOGTABLE: [usize; 256] = [
512, 255, 1, 25, 2, 50, 26, 198, 3, 223, 51, 238, 27, 104, 199, 75, 4, 100, 224, 14, 52, 141,
239, 129, 28, 193, 105, 248, 200, 8, 76, 113, 5, 138, 101, 47, 225, 36, 15, 33, 53, 147, 142,
218, 240, 18, 130, 69, 29, 181, 194, 125, 106, 39, 249, 185, 201, 154, 9, 120, 77, 228, 114,
166, 6, 191, 139, 98, 102, 221, 48, 253, 226, 152, 37, 179, 16, 145, 34, 136, 54, 208, 148,
206, 143, 150, 219, 189, 241, 210, 19, 92, 131, 56, 70, 64, 30, 66, 182, 163, 195, 72, 126,
110, 107, 58, 40, 84, 250, 133, 186, 61, 202, 94, 155, 159, 10, 21, 121, 43, 78, 212, 229, 172,
115, 243, 167, 87, 7, 112, 192, 247, 140, 128, 99, 13, 103, 74, 222, 237, 49, 197, 254, 24,
227, 165, 153, 119, 38, 184, 180, 124, 17, 68, 146, 217, 35, 32, 137, 46, 55, 63, 209, 91, 149,
188, 207, 205, 144, 135, 151, 178, 220, 252, 190, 97, 242, 86, 211, 171, 20, 42, 93, 158, 132,
60, 57, 83, 71, 109, 65, 162, 31, 45, 67, 216, 183, 123, 164, 118, 196, 23, 73, 236, 127, 12,
111, 246, 108, 161, 59, 82, 41, 157, 85, 170, 251, 96, 134, 177, 187, 204, 62, 90, 203, 89, 95,
176, 156, 169, 160, 81, 11, 245, 22, 235, 122, 117, 44, 215, 79, 174, 213, 233, 230, 231, 173,
232, 116, 214, 244, 234, 168, 80, 88, 175,
];
const ALOGTABLE: [u8; 1025] = [
1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135, 19, 38, 76, 152, 45, 90, 180, 117,
234, 201, 143, 3, 6, 12, 24, 48, 96, 192, 157, 39, 78, 156, 37, 74, 148, 53, 106, 212, 181,
119, 238, 193, 159, 35, 70, 140, 5, 10, 20, 40, 80, 160, 93, 186, 105, 210, 185, 111, 222, 161,
95, 190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30, 60, 120, 240, 253, 231, 211, 187,
107, 214, 177, 127, 254, 225, 223, 163, 91, 182, 113, 226, 217, 175, 67, 134, 17, 34, 68, 136,
13, 26, 52, 104, 208, 189, 103, 206, 129, 31, 62, 124, 248, 237, 199, 147, 59, 118, 236, 197,
151, 51, 102, 204, 133, 23, 46, 92, 184, 109, 218, 169, 79, 158, 33, 66, 132, 21, 42, 84, 168,
77, 154, 41, 82, 164, 85, 170, 73, 146, 57, 114, 228, 213, 183, 115, 230, 209, 191, 99, 198,
145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255, 227, 219, 171, 75, 150, 49, 98, 196, 149,
55, 110, 220, 165, 87, 174, 65, 130, 25, 50, 100, 200, 141, 7, 14, 28, 56, 112, 224, 221, 167,
83, 166, 81, 162, 89, 178, 121, 242, 249, 239, 195, 155, 43, 86, 172, 69, 138, 9, 18, 36, 72,
144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139, 11, 22, 44, 88, 176, 125, 250, 233, 207,
131, 27, 54, 108, 216, 173, 71, 142, 1, 2, 4, 8, 16, 32, 64, 128, 29, 58, 116, 232, 205, 135,
19, 38, 76, 152, 45, 90, 180, 117, 234, 201, 143, 3, 6, 12, 24, 48, 96, 192, 157, 39, 78, 156,
37, 74, 148, 53, 106, 212, 181, 119, 238, 193, 159, 35, 70, 140, 5, 10, 20, 40, 80, 160, 93,
186, 105, 210, 185, 111, 222, 161, 95, 190, 97, 194, 153, 47, 94, 188, 101, 202, 137, 15, 30,
60, 120, 240, 253, 231, 211, 187, 107, 214, 177, 127, 254, 225, 223, 163, 91, 182, 113, 226,
217, 175, 67, 134, 17, 34, 68, 136, 13, 26, 52, 104, 208, 189, 103, 206, 129, 31, 62, 124, 248,
237, 199, 147, 59, 118, 236, 197, 151, 51, 102, 204, 133, 23, 46, 92, 184, 109, 218, 169, 79,
158, 33, 66, 132, 21, 42, 84, 168, 77, 154, 41, 82, 164, 85, 170, 73, 146, 57, 114, 228, 213,
183, 115, 230, 209, 191, 99, 198, 145, 63, 126, 252, 229, 215, 179, 123, 246, 241, 255, 227,
219, 171, 75, 150, 49, 98, 196, 149, 55, 110, 220, 165, 87, 174, 65, 130, 25, 50, 100, 200,
141, 7, 14, 28, 56, 112, 224, 221, 167, 83, 166, 81, 162, 89, 178, 121, 242, 249, 239, 195,
155, 43, 86, 172, 69, 138, 9, 18, 36, 72, 144, 61, 122, 244, 245, 247, 243, 251, 235, 203, 139,
11, 22, 44, 88, 176, 125, 250, 233, 207, 131, 27, 54, 108, 216, 173, 71, 142, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
];
impl Field for GF<u8> {
const ZERO: Self = Self(0);
const ONE: Self = Self(1);
fn inverse(&self) -> Self {
Self(ALOGTABLE[255 - (LOGTABLE[self.idx()] % 255)])
}
fn idx(&self) -> usize {
self.0 as usize
}
fn pow(self, pow: usize) -> Self {
if self.is_zero() && pow != 0 {
Self::zero()
} else {
Self(ALOGTABLE[pow*LOGTABLE[self.idx()] % 255])
}
}
}
impl MulAssign for GF<u8> {
fn mul_assign(&mut self, rhs: GF256) {
*self = GF(ALOGTABLE[(LOGTABLE[self.idx()] | 0) + (LOGTABLE[rhs.idx()] | 0)] | 0);
}
}
impl DivAssign for GF<u8> {
fn div_assign(&mut self, rhs: GF256) {
*self = GF(ALOGTABLE[LOGTABLE[self.idx()] + 255 - LOGTABLE[rhs.idx()]]);
}
}
impl<T: Display> Display for GF<T> {
fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self.0)
}
}
impl<T> Sum for GF<T>
where
Self: Field,
{
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::zero(), |a, b| a + b)
}
}
impl<T> Product for GF<T>
where
Self: Field,
{
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::one(), |a, b| a * b)
}
}
impl<T> Add for GF<T>
where
Self: AddAssign,
{
type Output = Self;
fn add(self, rhs: Self) -> Self {
let mut result = self;
result.add_assign(rhs);
result
}
}
impl<T: BitXor<Output = T> + Copy> AddAssign for GF<T> {
fn add_assign(&mut self, rhs: Self) {
*self = Self(self.0 ^ rhs.0);
}
}
impl<T> Sub for GF<T>
where
Self: SubAssign,
{
type Output = Self;
fn sub(self, rhs: Self) -> Self {
let mut result = self;
result.sub_assign(rhs);
result
}
}
impl<T: BitXor<Output = T> + Copy> SubAssign for GF<T> {
fn sub_assign(&mut self, rhs: Self) {
*self = Self(self.0 ^ rhs.0);
}
}
impl<T> Mul for GF<T>
where
Self: MulAssign,
{
type Output = Self;
fn mul(self, rhs: Self) -> Self {
let mut result = self;
result.mul_assign(rhs);
result
}
}
impl<T> Div for GF<T>
where
Self: DivAssign,
{
type Output = Self;
fn div(self, rhs: Self) -> Self {
let mut result = self;
result.div_assign(rhs);
result
}
}
impl<T> Neg for GF<T> {
type Output = Self;
fn neg(self) -> Self {
self
}
}
#[cfg(test)]
mod tests {
use crate::{Field, GF};
#[test]
fn add_sub() {
assert_eq!((GF(5) + GF(60)) - GF(5), GF(60))
}
#[test]
fn mul_div() {
assert_eq!((GF(5) * GF(60)) / GF(5), GF(60))
}
#[test]
fn pow() {
assert_eq!(GF(5).pow(0), GF(1))
}
}