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// Copyright 2024 Cloudflare, Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
use ahash::RandomState;
use std::hash::Hash;
use std::sync::atomic::{AtomicU8, AtomicUsize, Ordering};
struct Estimator {
estimator: Box<[(Box<[AtomicU8]>, RandomState)]>,
}
impl Estimator {
fn optimal_paras(items: usize) -> (usize, usize) {
use std::cmp::max;
// derived from https://en.wikipedia.org/wiki/Count%E2%80%93min_sketch
// width = ceil(e / ε)
// depth = ceil(ln(1 − δ) / ln(1 / 2))
let error_range = 1.0 / (items as f64);
let failure_probability = 1.0 / (items as f64);
(
max((std::f64::consts::E / error_range).ceil() as usize, 16),
max((failure_probability.ln() / 0.5f64.ln()).ceil() as usize, 2),
)
}
fn optimal(items: usize) -> Self {
let (slots, hashes) = Self::optimal_paras(items);
Self::new(hashes, slots)
}
fn compact(items: usize) -> Self {
let (slots, hashes) = Self::optimal_paras(items / 100);
Self::new(hashes, slots)
}
/// Create a new `Estimator` with the given amount of hashes and columns (slots).
pub fn new(hashes: usize, slots: usize) -> Self {
let mut estimator = Vec::with_capacity(hashes);
for _ in 0..hashes {
let mut slot = Vec::with_capacity(slots);
for _ in 0..slots {
slot.push(AtomicU8::new(0));
}
estimator.push((slot.into_boxed_slice(), RandomState::new()));
}
Estimator {
estimator: estimator.into_boxed_slice(),
}
}
pub fn incr<T: Hash>(&self, key: T) -> u8 {
let mut min = u8::MAX;
for (slot, hasher) in self.estimator.iter() {
let hash = hasher.hash_one(&key) as usize;
let counter = &slot[hash % slot.len()];
let (_current, new) = incr_no_overflow(counter);
min = std::cmp::min(min, new);
}
min
}
/// Get the estimated frequency of `key`.
pub fn get<T: Hash>(&self, key: T) -> u8 {
let mut min = u8::MAX;
for (slot, hasher) in self.estimator.iter() {
let hash = hasher.hash_one(&key) as usize;
let counter = &slot[hash % slot.len()];
let current = counter.load(Ordering::Relaxed);
min = std::cmp::min(min, current);
}
min
}
/// right shift all values inside this `Estimator`.
pub fn age(&self, shift: u8) {
for (slot, _) in self.estimator.iter() {
for counter in slot.iter() {
// we don't CAS because the only update between the load and store
// is fetch_add(1), which should be fine to miss/ignore
let c = counter.load(Ordering::Relaxed);
counter.store(c >> shift, Ordering::Relaxed);
}
}
}
}
fn incr_no_overflow(var: &AtomicU8) -> (u8, u8) {
loop {
let current = var.load(Ordering::Relaxed);
if current == u8::MAX {
return (current, current);
}
let new = if current == u8::MAX - 1 {
u8::MAX
} else {
current + 1
};
if let Err(new) = var.compare_exchange(current, new, Ordering::Acquire, Ordering::Relaxed) {
// someone else beat us to it
if new == u8::MAX {
// already max
return (current, new);
} // else, try again
} else {
return (current, new);
}
}
}
// bare-minimum TinyLfu with CM-Sketch, no doorkeeper for now
pub(crate) struct TinyLfu {
estimator: Estimator,
window_counter: AtomicUsize,
window_limit: usize,
}
impl TinyLfu {
pub fn get<T: Hash>(&self, key: T) -> u8 {
self.estimator.get(key)
}
pub fn incr<T: Hash>(&self, key: T) -> u8 {
let window_size = self.window_counter.fetch_add(1, Ordering::Relaxed);
// When window_size concurrently increases, only one resets the window and age the estimator.
// > self.window_limit * 2 is a safety net in case for whatever reason window_size grows
// out of control
if window_size == self.window_limit || window_size > self.window_limit * 2 {
self.window_counter.store(0, Ordering::Relaxed);
self.estimator.age(1); // right shift 1 bit
}
self.estimator.incr(key)
}
// because we use 8-bits counters, window size can be 256 * the cache size
pub fn new(cache_size: usize) -> Self {
Self {
estimator: Estimator::optimal(cache_size),
window_counter: Default::default(),
// 8x: just a heuristic to balance the memory usage and accuracy
window_limit: cache_size * 8,
}
}
pub fn new_compact(cache_size: usize) -> Self {
Self {
estimator: Estimator::compact(cache_size),
window_counter: Default::default(),
// 8x: just a heuristic to balance the memory usage and accuracy
window_limit: cache_size * 8,
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_cmk_paras() {
let (slots, hashes) = Estimator::optimal_paras(1_000_000);
// just smoke check some standard input
assert_eq!(slots, 2718282);
assert_eq!(hashes, 20);
}
#[test]
fn test_tiny_lfu() {
let tiny = TinyLfu::new(1);
assert_eq!(tiny.get(1), 0);
assert_eq!(tiny.incr(1), 1);
assert_eq!(tiny.incr(1), 2);
assert_eq!(tiny.get(1), 2);
assert_eq!(tiny.get(2), 0);
assert_eq!(tiny.incr(2), 1);
assert_eq!(tiny.incr(2), 2);
assert_eq!(tiny.get(2), 2);
assert_eq!(tiny.incr(3), 1);
assert_eq!(tiny.incr(3), 2);
assert_eq!(tiny.incr(3), 3);
assert_eq!(tiny.incr(3), 4);
// 8 incr(), now reset
assert_eq!(tiny.incr(3), 3);
assert_eq!(tiny.incr(1), 2);
assert_eq!(tiny.incr(2), 2);
}
}
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