rlnc 0.8.0

Random Linear Network Coding
Documentation 
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//! Following GF(2**8) logarithm and exponentiation tables are generated using
//! Python script @ https://gist.github.com/itzmeanjan/0b2ec3f378de2c2e911bd4bb5505d45a.

use rand::Rng;
use rand::distr::{Distribution, StandardUniform};
use std::ops::{Add, AddAssign, Div, Mul, Neg, Sub};

pub const GF256_ORDER: usize = u8::MAX as usize + 1;

#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
pub const GF256_BIT_WIDTH: usize = u8::BITS as usize;

#[cfg(any(target_arch = "x86", target_arch = "x86_64"))]
pub const GF256_HALF_ORDER: usize = 1usize << (GF256_BIT_WIDTH / 2);

const GF256_LOG_TABLE: [u8; GF256_ORDER] = [
    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,
];

const GF256_EXP_TABLE: [u8; 2 * GF256_ORDER - 2] = [
    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,
];

/// Gf(2^8) wrapper type.
#[derive(Default, Clone, Copy, Debug)]
pub struct Gf256 {
    val: u8,
}

impl Gf256 {
    /// Creates a new Gf256 element from a u8 value.
    pub const fn new(val: u8) -> Self {
        Gf256 { val }
    }

    /// Returns the raw u8 value of the Gf256 element.
    pub const fn get(&self) -> u8 {
        self.val
    }

    /// Returns the additive identity element (0).
    pub const fn zero() -> Self {
        Gf256::new(0)
    }

    /// Returns the multiplicative identity element (1).
    pub const fn one() -> Self {
        Gf256::new(1)
    }

    /// Returns primitive element x, for GF(2^8) field with irreducible polynomial x^8 + x^4 + x^3 + x^2 + 1.
    pub const fn primitive_element() -> Self {
        Gf256::new(2)
    }

    /// Compile-time executable multiplication of two bytes, over GF(2^8).
    pub const fn mul_const(a: u8, b: u8) -> u8 {
        if a == 0 || b == 0 {
            return 0;
        }

        let l = GF256_LOG_TABLE[a as usize] as usize;
        let r = GF256_LOG_TABLE[b as usize] as usize;

        GF256_EXP_TABLE[l + r]
    }

    /// Computes the multiplicative inverse of the element. Returns `None` for the zero element.
    pub const fn inv(self) -> Option<Self> {
        if self.val == 0 {
            return None;
        }

        Some(Gf256 {
            val: GF256_EXP_TABLE[(GF256_ORDER - 1) - GF256_LOG_TABLE[self.val as usize] as usize],
        })
    }
}

impl Add for Gf256 {
    type Output = Self;

    /// Performs addition (XOR) of two Gf256 elements.
    #[allow(clippy::suspicious_arithmetic_impl)]
    fn add(self, rhs: Self) -> Self::Output {
        Gf256 { val: self.val ^ rhs.val }
    }
}

impl AddAssign for Gf256 {
    /// Performs in-place addition i.e. compound addition operation (XOR) of two Gf256 elements.
    #[allow(clippy::suspicious_op_assign_impl)]
    fn add_assign(&mut self, rhs: Self) {
        self.val ^= rhs.val;
    }
}

impl Neg for Gf256 {
    type Output = Self;

    /// Computes the additive inverse (itself, as XOR is self-inverse).
    fn neg(self) -> Self::Output {
        Gf256 { val: self.val }
    }
}

impl Sub for Gf256 {
    type Output = Self;

    /// Performs subtraction (XOR) of two Gf256 elements.
    #[allow(clippy::suspicious_arithmetic_impl)]
    fn sub(self, rhs: Self) -> Self::Output {
        Gf256 { val: self.val ^ rhs.val }
    }
}

impl Mul for Gf256 {
    type Output = Self;

    /// Performs multiplication of two Gf256 elements using logarithm and exponentiation tables.
    fn mul(self, rhs: Self) -> Self::Output {
        Gf256 {
            val: Self::mul_const(self.val, rhs.val),
        }
    }
}

impl Div for Gf256 {
    type Output = Option<Self>;

    /// Performs division of two Gf256 elements using multiplicative inverse. Returns `None` if dividing by zero.
    #[allow(clippy::suspicious_arithmetic_impl)]
    fn div(self, rhs: Self) -> Self::Output {
        rhs.inv().map(|rhs_inv| self * rhs_inv)
    }
}

impl PartialEq for Gf256 {
    /// Checks for equality between two Gf256 elements.
    fn eq(&self, other: &Self) -> bool {
        self.val == other.val
    }
}

impl Distribution<Gf256> for StandardUniform {
    /// Samples a random Gf256 element.
    fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> Gf256 {
        Gf256 { val: rng.random() }
    }
}

#[cfg(test)]
mod test {
    use super::Gf256;
    use rand::Rng;

    #[test]
    fn prop_test_gf256_operations() {
        const NUM_TEST_ITERATIONS: usize = 100_000;

        let mut rng = rand::rng();

        (0..NUM_TEST_ITERATIONS).for_each(|_| {
            let a: Gf256 = rng.random();
            let b: Gf256 = rng.random();

            // Addition, Subtraction, Negation
            let sum = a + b;
            let diff = sum - b;

            assert_eq!(diff, a);

            // Multiplication, Division, Inversion
            let mul = a * b;
            let div = mul / b;

            if b == Gf256::zero() {
                assert_eq!(div, None);
                assert_eq!(mul, Gf256::zero());
            } else {
                assert_eq!(a, div.unwrap());
            }
        });
    }
}