Line data Source code
1 : use std::hash::Hash;
2 :
3 : /// estimator of hash jobs per second.
4 : /// <https://en.wikipedia.org/wiki/Count%E2%80%93min_sketch>
5 : pub(crate) struct CountMinSketch {
6 : // one for each depth
7 : hashers: Vec<ahash::RandomState>,
8 : width: usize,
9 : depth: usize,
10 : // buckets, width*depth
11 : buckets: Vec<u32>,
12 : }
13 :
14 : impl CountMinSketch {
15 : /// Given parameters (ε, δ),
16 : /// set width = ceil(e/ε)
17 : /// set depth = ceil(ln(1/δ))
18 : ///
19 : /// guarantees:
20 : /// actual <= estimate
21 : /// estimate <= actual + ε * N with probability 1 - δ
22 : /// where N is the cardinality of the stream
23 18 : pub(crate) fn with_params(epsilon: f64, delta: f64) -> Self {
24 18 : CountMinSketch::new(
25 18 : (std::f64::consts::E / epsilon).ceil() as usize,
26 18 : (1.0_f64 / delta).ln().ceil() as usize,
27 18 : )
28 18 : }
29 :
30 18 : fn new(width: usize, depth: usize) -> Self {
31 18 : Self {
32 18 : #[cfg(test)]
33 18 : hashers: (0..depth)
34 72 : .map(|i| {
35 72 : // digits of pi for good randomness
36 72 : ahash::RandomState::with_seeds(
37 72 : 314159265358979323,
38 72 : 84626433832795028,
39 72 : 84197169399375105,
40 72 : 82097494459230781 + i as u64,
41 72 : )
42 72 : })
43 18 : .collect(),
44 18 : #[cfg(not(test))]
45 18 : hashers: (0..depth).map(|_| ahash::RandomState::new()).collect(),
46 0 : width,
47 0 : depth,
48 0 : buckets: vec![0; width * depth],
49 0 : }
50 0 : }
51 :
52 227175 : pub(crate) fn inc_and_return<T: Hash>(&mut self, t: &T, x: u32) -> u32 {
53 227175 : let mut min = u32::MAX;
54 795123 : for row in 0..self.depth {
55 795123 : let col = (self.hashers[row].hash_one(t) as usize) % self.width;
56 795123 :
57 795123 : let row = &mut self.buckets[row * self.width..][..self.width];
58 795123 : row[col] = row[col].saturating_add(x);
59 795123 : min = std::cmp::min(min, row[col]);
60 795123 : }
61 227175 : min
62 227175 : }
63 :
64 0 : pub(crate) fn reset(&mut self) {
65 0 : self.buckets.clear();
66 0 : self.buckets.resize(self.width * self.depth, 0);
67 0 : }
68 : }
69 :
70 : #[cfg(test)]
71 : mod tests {
72 : use rand::rngs::StdRng;
73 : use rand::seq::SliceRandom;
74 : use rand::{Rng, SeedableRng};
75 :
76 : use super::CountMinSketch;
77 :
78 8 : fn eval_precision(n: usize, p: f64, q: f64) -> usize {
79 8 : // fixed value of phi for consistent test
80 8 : let mut rng = StdRng::seed_from_u64(16180339887498948482);
81 8 :
82 8 : #[allow(non_snake_case)]
83 8 : let mut N = 0;
84 8 :
85 8 : let mut ids = vec![];
86 8 :
87 4400 : for _ in 0..n {
88 4400 : // number to insert at once
89 4400 : let n = rng.gen_range(1..4096);
90 4400 : // number of insert operations
91 4400 : let m = rng.gen_range(1..100);
92 4400 :
93 4400 : let id = uuid::Builder::from_random_bytes(rng.gen()).into_uuid();
94 4400 : ids.push((id, n, m));
95 4400 :
96 4400 : // N = sum(actual)
97 4400 : N += n * m;
98 4400 : }
99 :
100 : // q% of counts will be within p of the actual value
101 8 : let mut sketch = CountMinSketch::with_params(p / N as f64, 1.0 - q);
102 8 :
103 8 : // insert a bunch of entries in a random order
104 8 : let mut ids2 = ids.clone();
105 800 : while !ids2.is_empty() {
106 792 : ids2.shuffle(&mut rng);
107 222768 : ids2.retain_mut(|id| {
108 222768 : sketch.inc_and_return(&id.0, id.1);
109 222768 : id.2 -= 1;
110 222768 : id.2 > 0
111 222768 : });
112 : }
113 :
114 8 : let mut within_p = 0;
115 4408 : for (id, n, m) in ids {
116 4400 : let actual = n * m;
117 4400 : let estimate = sketch.inc_and_return(&id, 0);
118 4400 :
119 4400 : // This estimate has the guarantee that actual <= estimate
120 4400 : assert!(actual <= estimate);
121 :
122 : // This estimate has the guarantee that estimate <= actual + εN with probability 1 - δ.
123 : // ε = p / N, δ = 1 - q;
124 : // therefore, estimate <= actual + p with probability q.
125 4400 : if estimate as f64 <= actual as f64 + p {
126 4384 : within_p += 1;
127 4384 : }
128 : }
129 8 : within_p
130 8 : }
131 :
132 : #[test]
133 1 : fn precision() {
134 1 : assert_eq!(eval_precision(100, 100.0, 0.99), 100);
135 1 : assert_eq!(eval_precision(1000, 100.0, 0.99), 1000);
136 1 : assert_eq!(eval_precision(100, 4096.0, 0.99), 100);
137 1 : assert_eq!(eval_precision(1000, 4096.0, 0.99), 1000);
138 :
139 : // seems to be more precise than the literature indicates?
140 : // probably numbers are too small to truly represent the probabilities.
141 1 : assert_eq!(eval_precision(100, 4096.0, 0.90), 100);
142 1 : assert_eq!(eval_precision(1000, 4096.0, 0.90), 1000);
143 1 : assert_eq!(eval_precision(100, 4096.0, 0.1), 96);
144 1 : assert_eq!(eval_precision(1000, 4096.0, 0.1), 988);
145 1 : }
146 :
147 : // returns memory usage in bytes, and the time complexity per insert.
148 4 : fn eval_cost(p: f64, q: f64) -> (usize, usize) {
149 4 : #[allow(non_snake_case)]
150 4 : // N = sum(actual)
151 4 : // Let's assume 1021 samples, all of 4096
152 4 : let N = 1021 * 4096;
153 4 : let sketch = CountMinSketch::with_params(p / N as f64, 1.0 - q);
154 4 :
155 4 : let memory = size_of::<u32>() * sketch.buckets.len();
156 4 : let time = sketch.depth;
157 4 : (memory, time)
158 4 : }
159 :
160 : #[test]
161 1 : fn memory_usage() {
162 1 : assert_eq!(eval_cost(100.0, 0.99), (2273580, 5));
163 1 : assert_eq!(eval_cost(4096.0, 0.99), (55520, 5));
164 1 : assert_eq!(eval_cost(4096.0, 0.90), (33312, 3));
165 1 : assert_eq!(eval_cost(4096.0, 0.1), (11104, 1));
166 1 : }
167 : }
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