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Implement basic arithmetic on symbols

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Christopher Berner 2019-01-24 18:50:15 -08:00
parent 8009b07fd3
commit 8773208cc1
2 changed files with 203 additions and 0 deletions
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1
src/lib.rs
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mod systematic_constants;
mod rng;
mod symbol;
mod base;
mod encoder;
mod decoder;

202
src/symbol.rs Normal file
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use std::ops::Add;
use std::ops::Mul;
use std::ops::Div;
// As defined in section 5.7.3
const OCT_EXP: [u8; 510] = [
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];
// As defined in section 5.7.4, but with a prepended zero to make this zero indexed
const OCT_LOG: [u8; 256] = [
0, 0, 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];
#[derive(Clone, Debug, PartialEq)]
pub struct Symbol {
pub value: Vec<u8>
}
impl Add for Symbol {
type Output = Symbol;
fn add(self, other: Symbol) -> Symbol {
let mut result = Vec::with_capacity(self.value.len());
for i in 0..self.value.len() {
// As defined in section 5.7.2, addition on octets is implemented as bitxor
result.push(self.value[i] ^ other.value[i]);
}
Symbol {
value: result
}
}
}
impl Mul for Symbol {
type Output = Symbol;
fn mul(self, other: Symbol) -> Symbol {
let mut result = Vec::with_capacity(self.value.len());
for i in 0..self.value.len() {
// As defined in section 5.7.2, multiplication is implemented via the tables above
if self.value[i] == 0 || other.value[i] == 0 {
result.push(0);
}
else {
let log_u = OCT_LOG[self.value[i] as usize] as usize;
let log_v = OCT_LOG[other.value[i] as usize] as usize;
result.push(OCT_EXP[log_u + log_v]);
}
}
Symbol {
value: result
}
}
}
impl Div for Symbol {
type Output = Symbol;
fn div(self, rhs: Symbol) -> Symbol {
let mut result = Vec::with_capacity(self.value.len());
for i in 0..self.value.len() {
assert_ne!(0, rhs.value[i]);
// As defined in section 5.7.2, division is implemented via the tables above
if self.value[i] == 0 {
result.push(0);
}
else {
let log_u = OCT_LOG[self.value[i] as usize] as usize;
let log_v = OCT_LOG[rhs.value[i] as usize] as usize;
result.push(OCT_EXP[255 + log_u - log_v]);
}
}
Symbol {
value: result
}
}
}
#[cfg(test)]
mod tests {
extern crate rand;
use symbol::tests::rand::Rng;
use symbol::Symbol;
#[test]
fn addition() {
let elements = 4;
let mut data: Vec<u8> = vec![0; elements];
for i in 0..elements {
data[i] = rand::thread_rng().gen();
}
let symbol = Symbol {
value: data
};
let symbol2 = symbol.clone();
let zero = Symbol {
value: vec![0, 0, 0, 0]
};
// See section 5.7.2. u is its own additive inverse
assert_eq!(zero, symbol + symbol2);
}
#[test]
fn multiplication_identity() {
let elements = 4;
let mut data: Vec<u8> = vec![0; elements];
for i in 0..elements {
data[i] = rand::thread_rng().gen();
}
let symbol = Symbol {
value: data
};
let one = Symbol {
value: vec![1, 1, 1, 1]
};
assert_eq!(symbol, symbol.clone() * one);
}
#[test]
fn multiplicative_inverse() {
let elements = 4;
let mut data: Vec<u8> = vec![0; elements];
for i in 0..elements {
data[i] = rand::thread_rng().gen();
}
let symbol = Symbol {
value: data
};
let one = Symbol {
value: vec![1, 1, 1, 1]
};
assert_eq!(one.clone(), symbol.clone() * (one.clone() / symbol.clone()));
}
#[test]
fn division() {
let elements = 4;
let mut data: Vec<u8> = vec![0; elements];
for i in 0..elements {
data[i] = rand::thread_rng().gen();
}
let symbol = Symbol {
value: data
};
let symbol2 = symbol.clone();
let one = Symbol {
value: vec![1, 1, 1, 1]
};
assert_eq!(one, symbol / symbol2);
}
}