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//! Lookup-tables used by [`Engine`]:s.
//!
//! All tables are global and each is initialized at most once.
//!
//! # Tables
//!
//! | Table | Size | Used in encoding | Used in decoding | By engines |
//! | ------------ | ------- | ---------------- | ---------------- | ------------------ |
//! | [`Exp`] | 128 kiB | yes | yes | all |
//! | [`Log`] | 128 kiB | yes | yes | all |
//! | [`LogWalsh`] | 128 kiB | - | yes | all |
//! | [`Mul16`] | 8 MiB | yes | yes | [`NoSimd`] |
//! | [`Mul128`] | 8 MiB | yes | yes | [`Avx2`] [`Ssse3`] |
//! | [`Skew`] | 128 kiB | yes | yes | all |
//!
//! [`NoSimd`]: crate::engine::NoSimd
//! [`Avx2`]: crate::engine::Avx2
//! [`Ssse3`]: crate::engine::Ssse3
//! [`Engine`]: crate::engine
//!
use once_cell::sync::OnceCell;
use crate::engine::{
self, fwht, GfElement, CANTOR_BASIS, GF_BITS, GF_MODULUS, GF_ORDER, GF_POLYNOMIAL,
};
// ======================================================================
// TYPE ALIASES - PUBLIC
/// Used by [`Naive`] engine for multiplications
/// and by all [`Engine`]:s to initialize other tables.
///
/// [`Naive`]: crate::engine::Naive
/// [`Engine`]: crate::engine
pub type Exp = [GfElement; GF_ORDER];
/// Used by [`Naive`] engine for multiplications
/// and by all [`Engine`]:s to initialize other tables.
///
/// [`Naive`]: crate::engine::Naive
/// [`Engine`]: crate::engine
pub type Log = [GfElement; GF_ORDER];
/// Used by [`Avx2`] and [`Ssse3`] engines for multiplications.
///
/// [`Avx2`]: crate::engine::Avx2
/// [`Ssse3`]: crate::engine::Ssse3
pub type Mul128 = [Multiply128lutT; GF_ORDER];
/// Elements of the Mul128 table
#[derive(Clone, Debug)]
pub struct Multiply128lutT {
/// Lower half of GfElements
pub lo: [u128; 4],
/// Upper half of GfElements
pub hi: [u128; 4],
}
/// Used by all [`Engine`]:s in [`Engine::eval_poly`].
///
/// [`Engine`]: crate::engine
/// [`Engine::eval_poly`]: crate::engine::Engine::eval_poly
pub type LogWalsh = [GfElement; GF_ORDER];
/// Used by [`NoSimd`] engine for multiplications.
///
/// [`NoSimd`]: crate::engine::NoSimd
pub type Mul16 = [[[GfElement; 16]; 4]; GF_ORDER];
/// Used by all [`Engine`]:s for FFT and IFFT.
///
/// [`Engine`]: crate::engine
pub type Skew = [GfElement; GF_MODULUS as usize];
// ======================================================================
// ExpLog - PRIVATE
struct ExpLog {
exp: Box<Exp>,
log: Box<Log>,
}
// ======================================================================
// STATIC - PRIVATE
static EXP_LOG: OnceCell<ExpLog> = OnceCell::new();
static LOG_WALSH: OnceCell<Box<LogWalsh>> = OnceCell::new();
static MUL16: OnceCell<Box<Mul16>> = OnceCell::new();
static MUL128: OnceCell<Box<Mul128>> = OnceCell::new();
static SKEW: OnceCell<Box<Skew>> = OnceCell::new();
// ======================================================================
// FUNCTIONS - PUBLIC - math
/// Calculates `x * log_m` using [`Exp`] and [`Log`] tables.
#[inline(always)]
pub fn mul(x: GfElement, log_m: GfElement, exp: &Exp, log: &Log) -> GfElement {
if x == 0 {
0
} else {
exp[engine::add_mod(log[x as usize], log_m) as usize]
}
}
// ======================================================================
// FUNCTIONS - PUBLIC - initialize tables
/// Initializes and returns [`Exp`] and [`Log`] tables.
#[allow(clippy::needless_range_loop)]
pub fn initialize_exp_log() -> (&'static Exp, &'static Log) {
let exp_log = EXP_LOG.get_or_init(|| {
let mut exp = Box::new([0; GF_ORDER]);
let mut log = Box::new([0; GF_ORDER]);
// GENERATE LFSR TABLE
let mut state = 1;
for i in 0..GF_MODULUS {
exp[state] = i;
state <<= 1;
if state >= GF_ORDER {
state ^= GF_POLYNOMIAL;
}
}
exp[0] = GF_MODULUS;
// CONVERT TO CANTOR BASIS
log[0] = 0;
for i in 0..GF_BITS {
let width = 1usize << i;
for j in 0..width {
log[j + width] = log[j] ^ CANTOR_BASIS[i];
}
}
for i in 0..GF_ORDER {
log[i] = exp[log[i] as usize];
}
for i in 0..GF_ORDER {
exp[log[i] as usize] = i as GfElement;
}
exp[GF_MODULUS as usize] = exp[0];
ExpLog { exp, log }
});
(&exp_log.exp, &exp_log.log)
}
/// Initializes and returns [`LogWalsh`] table.
pub fn initialize_log_walsh() -> &'static LogWalsh {
LOG_WALSH.get_or_init(|| {
let (_, log) = initialize_exp_log();
let mut log_walsh: Box<LogWalsh> = Box::new([0; GF_ORDER]);
log_walsh.copy_from_slice(log.as_ref());
log_walsh[0] = 0;
fwht::fwht(log_walsh.as_mut(), GF_ORDER);
log_walsh
})
}
/// Initializes and returns [`Mul16`] table.
pub fn initialize_mul16() -> &'static Mul16 {
MUL16.get_or_init(|| {
let (exp, log) = initialize_exp_log();
let mut mul16 = vec![[[0; 16]; 4]; GF_ORDER];
for log_m in 0..=GF_MODULUS {
let lut = &mut mul16[log_m as usize];
for i in 0..16 {
lut[0][i] = mul(i as GfElement, log_m, exp, log);
lut[1][i] = mul((i << 4) as GfElement, log_m, exp, log);
lut[2][i] = mul((i << 8) as GfElement, log_m, exp, log);
lut[3][i] = mul((i << 12) as GfElement, log_m, exp, log);
}
}
mul16.into_boxed_slice().try_into().unwrap()
})
}
/// Initializes and returns [`Mul128`] table.
pub fn initialize_mul128() -> &'static Mul128 {
// Based on:
// https://github.com/catid/leopard/blob/22ddc7804998d31c8f1a2617ee720e063b1fa6cd/LeopardFF16.cpp#L375
MUL128.get_or_init(|| {
let (exp, log) = initialize_exp_log();
let mut mul128 = vec![
Multiply128lutT {
lo: [0; 4],
hi: [0; 4],
};
GF_ORDER
];
for log_m in 0..=GF_MODULUS {
for i in 0..=3 {
let mut prod_lo = [0u8; 16];
let mut prod_hi = [0u8; 16];
for x in 0..16 {
let prod = mul((x << (i * 4)) as GfElement, log_m, exp, log);
prod_lo[x] = prod as u8;
prod_hi[x] = (prod >> 8) as u8;
}
mul128[log_m as usize].lo[i] = bytemuck::cast(prod_lo);
mul128[log_m as usize].hi[i] = bytemuck::cast(prod_hi);
}
}
mul128.into_boxed_slice().try_into().unwrap()
})
}
/// Initializes and returns [`Skew`] table.
#[allow(clippy::needless_range_loop)]
pub fn initialize_skew() -> &'static Skew {
SKEW.get_or_init(|| {
let (exp, log) = initialize_exp_log();
let mut skew = Box::new([0; GF_MODULUS as usize]);
let mut temp = [0; GF_BITS - 1];
for i in 1..GF_BITS {
temp[i - 1] = 1 << i;
}
for m in 0..GF_BITS - 1 {
let step: usize = 1 << (m + 1);
skew[(1 << m) - 1] = 0;
for i in m..GF_BITS - 1 {
let s: usize = 1 << (i + 1);
let mut j = (1 << m) - 1;
while j < s {
skew[j + s] = skew[j] ^ temp[i];
j += step;
}
}
temp[m] =
GF_MODULUS - log[mul(temp[m], log[(temp[m] ^ 1) as usize], exp, log) as usize];
for i in m + 1..GF_BITS - 1 {
let sum = engine::add_mod(log[(temp[i] ^ 1) as usize], temp[m]);
temp[i] = mul(temp[i], sum, exp, log);
}
}
for i in 0..GF_MODULUS as usize {
skew[i] = log[skew[i] as usize];
}
skew
})
}