#distances #ann #algorithm #distance


some distances used in Ann related crates

3 releases

0.1.2 May 13, 2024
0.1.1 Apr 29, 2024
0.1.0 Apr 29, 2024

#1204 in Algorithms

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748 downloads per month
Used in 6 crates (2 directly)


1.5K SLoC


This crate provides distances computations used in some related crates hnsw_rs, annembed and coreset

All distances implement the trait Distance:

pub trait Distance<T: Send + Sync> {  
    fn eval(&self, va: &[T], vb: &[T]) -> f32;


The crate provides:

  • usual distances as L1, L2, Cosine, Jaccard, Hamming for vectors of standard numeric types, Levenshtein distance on u16.

  • Hellinger distance and Jeffreys divergence between probability distributions (f32 and f64). It must be noted that the Jeffreys divergence (a symetrized Kullback-Leibler divergence) do not satisfy the triangle inequality. (Neither Cosine distance !).

  • Jensen-Shannon distance between probability distributions (f32 and f64). It is defined as the square root of the Jensen-Shannon divergence and is a bounded metric. See Nielsen F. in Entropy 2019, 21(5), 485.

  • A Trait to enable the user to implement its own distances. It takes as data slices of types T satisfying T:Serialize+Clone+Send+Sync. It is also possible to use C extern functions or closures.

  • Simd implementation is provided for the most often used case.


Simd support is provided with the simdeez crate on Intel and partial implementation with std::simd for general case.



  • The simd provided by the simdeez crate is accessible with the feature "simdeez_f" for x86_64 processors. Compile with cargo build --release --features "simdeez_f" .... To compile this crate on a M1 chip just do not activate this feature.

  • It is nevertheless possible to experiment with std::simd. Compiling with the feature stdsimd (cargo build --release --features "stdsimd"), activates the portable_simd feature on rust nightly. This requires nightly compiler. Only the Hamming distance with the u32x16 and u64x8 types and DistL1,DistL2 and DistDot on f32*16 are provided for now.

Benchmarks and Examples

The speed is illustated in the hnsw_rs, annembed crates


Petter Egesund added the DistLevenshtein distance.


Licensed under either of

at your option.


~112K SLoC