polars_utils/
cardinality_sketch.rs

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1use crate::algebraic_ops::alg_add_f64;
2
3// Computes 2^-n by directly subtracting from the IEEE754 double exponent.
4fn inv_pow2(n: u8) -> f64 {
5    let base = f64::to_bits(1.0);
6    f64::from_bits(base - ((n as u64) << 52))
7}
8
9/// HyperLogLog in Practice: Algorithmic Engineering of
10/// a State of The Art Cardinality Estimation Algorithm
11/// Stefan Heule, Marc Nunkesser, Alexander Hall
12///
13/// We use m = 256 which gives a relative error of ~6.5% of the cardinality
14/// estimate. We don't bother with stuffing the counts in 6 bits, byte access is
15/// fast.
16///
17/// The bias correction described in the paper is not implemented, so this is
18/// somewhere in between HyperLogLog and HyperLogLog++.
19#[derive(Clone)]
20pub struct CardinalitySketch {
21    buckets: Box<[u8; 256]>,
22}
23
24impl Default for CardinalitySketch {
25    fn default() -> Self {
26        Self::new()
27    }
28}
29
30impl CardinalitySketch {
31    pub fn new() -> Self {
32        Self {
33            // This compiles to alloc_zeroed directly.
34            buckets: vec![0u8; 256].into_boxed_slice().try_into().unwrap(),
35        }
36    }
37
38    /// Add a new hash to the sketch.
39    pub fn insert(&mut self, mut h: u64) {
40        const ARBITRARY_ODD: u64 = 0x902813a5785dc787;
41        // We multiply by this arbitrarily chosen odd number and then take the
42        // top bits to ensure the sketch is influenced by all bits of the hash.
43        h = h.wrapping_mul(ARBITRARY_ODD);
44        let idx = (h >> 56) as usize;
45        let p = 1 + (h << 8).leading_zeros() as u8;
46        self.buckets[idx] = self.buckets[idx].max(p);
47    }
48
49    pub fn combine(&mut self, other: &CardinalitySketch) {
50        *self.buckets = std::array::from_fn(|i| std::cmp::max(self.buckets[i], other.buckets[i]));
51    }
52
53    pub fn estimate(&self) -> usize {
54        let m = 256.0;
55        let alpha_m = 0.7123 / (1.0 + 1.079 / m);
56
57        let mut sum = 0.0;
58        let mut num_zero = 0;
59        for x in self.buckets.iter() {
60            sum = alg_add_f64(sum, inv_pow2(*x));
61            num_zero += (*x == 0) as usize;
62        }
63
64        let est = (alpha_m * m * m) / sum;
65        let corr_est = if est <= 5.0 / 2.0 * m && num_zero != 0 {
66            // Small cardinality estimate, full 64-bit logarithm is overkill.
67            m * (m as f32 / num_zero as f32).ln() as f64
68        } else {
69            est
70        };
71
72        corr_est as usize
73    }
74}
polars_utils/cardinality_sketch.rs

polars_utils/
cardinality_sketch.rs
