Kiddo

A high-performance, flexible, ergonomic k-d tree library. Possibly the fastest k-d tree library in the world? See for yourself.

• Crate
• Documentation
• Usage
• Examples
• Benchmarks
• Change Log
• License

Kiddo is ideal for superfast spatial / geospatial lookups and nearest-neighbour / KNN queries for low-ish numbers of dimensions, where you want to ask questions such as:

• Find the nearest_n item(s) to a query point, ordered by distance;
• Find all items within a specified radius of a query point;
• Find the "best" n item(s) within a specified distance of a query point, for some definition of "best".

Kiddo provides:

• Its standard floating point k-d tree, exposed as kiddo::KdTree
• An ImmutableKdTree with space and performance advantages over the standard k-d tree, for situations where the tree does not need to be modified after creation
• Integer / fixed point support via the Fixed library;
• f16 support via the half library;
• Instant zero-copy deserialization and serialization via Rkyv (Serde still available).

Usage

Add kiddo to Cargo.toml

[dependencies]
kiddo = "5"

Add points to k-d tree and query nearest n points with distance function

use kiddo::{KdTree, SquaredEuclidean};

let entries = vec![
    [0f64, 0f64],
    [1f64, 1f64],
    [2f64, 2f64],
    [3f64, 3f64]
];

// use the kiddo::KdTree type to get up and running quickly with default settings
let mut tree: KdTree<_, 2> = (&entries).into();

// How many items are in tree?
assert_eq!(tree.size(), 4);

// find the nearest item to [0f64, 0f64].
// returns an instance of kiddo::NearestNeighbour
let nearest = tree.nearest_one::<SquaredEuclidean>(&[0f64, 0f64]);
assert_eq!(nearest.distance, 0f64);
assert_eq!(nearest.item, 0);


// find the nearest 3 items to [0f64, 0f64]
// returns a Vec of kiddo::NearestNeighbour
let nearest_n: Vec<_> = tree.nearest_n::<SquaredEuclidean>(&[0f64, 0f64], 3);
assert_eq!(
    nearest_n.iter().map(|x|(x.distance, x.item)).collect::<Vec<_>>(),
    vec![(0f64, 0), (2f64, 1), (8f64, 2)]
);

See the examples documentation for some more detailed examples.

Optional Features

The Kiddo crate exposes the following features. Any labelled as (NIGHTLY) are not available on stable Rust as they require some unstable features. You'll need to build with nightly in order to user them.

• serde - serialization / deserialization via Serde
• rkyv - zero-copy serialization / deserialization via Rkyv
• global_allocate (NIGHTLY) - When enabled Kiddo will use the unstable allocator_api feature within ImmutableKdTree to get a slight performance improvement when allocating space for leaves.
• simd (NIGHTLY) - enables some hand-written SIMD intrinsic code within ImmutableKdTree that may improve performance (currently only on the nearest_one method when using f64)
• f16 - enables usage of f16 from the half crate for float trees.
• csv and las features are only required for building some of the examples.
• tracing feature is enabled by default and adds some tracing output.
• modified_van_emde_boas: disabled by default. Enabling will switch the stem node ordering from Eytzinger to a modified Van Emde Boas ordering that may in some circumstances be slightly faster.

v5.x

Version 5 bundles a complete re-write of ImmutableKdTree alongside some rationalization of feature names and a change of type of the max_qty parameter present in some query methods from usize to NonZero<usize>.

ImmutableKdTree rewrite

Many people had previously unsuccessfully tried to use ImmutableKdTree with data containing many points that have the same value on one or more of their axes, for example point cloud data containing many points on a flat axis-aligned plane. The v5 rewrite of ImmutableKdTree experiences none of these kinds of problems and can be safely used no matter what your data looks like. Query performance is in many cases faster than the prior version, but sometimes slightly slower - your mileage may vary but differences in query performance is pretty small. Construction performance is considerably improved, with up to a 2x speedup, with the improvement becoming more pronounced as the tree size increases. Memory efficiency is slightly better also.

Modified van Emde Boas Stem Ordering

The experimental modified_van_emde_boas feature allows an alternative stem node ordering mode to be enabled. This mode is more cache-friendly. Under the standard Eytzinger ordering, a new cache line will be fetched for almost every level traversed within the stem nodes beyond the third level. The Modified van Emde Boas ordering is more cache efficient - meaning that on CPU architectures with a 64-byte cache line (ie almost all of them in servers, desktops and laptops), a cache line needs fetching only once every 3 stem levels for f64, and every 4 levels for f32. On architectures with a 128-byte cache lines (some Apple M3 and newer at the moment), this is every 4 levels for f64 and every 5 levels for f32. The downside is that logic to calculate the next stem index is significantly more complex than with the Eytzinger layout, requiring around 10 integer ops (one being a divide) vs just one integer op (a shift) for Eytzinger. Right now the performance when using modified_van_emde_boas is between 1% faster and 5% slower than standard, at least on the machines that I've tested it on. I'd love to hear how it fares on a machine with a 128-byte cache line width, if anyone cares to try it. I'm continuing to work on the performance of this and perhaps one day it may end up faster than Eytzinger if I can optimise the logic well enough - the initial implementation required 24 operations, so progress has been made.

Feature name changes

It was pointed out in #159 that it was necessary to anable both rkyv and serialize_rkyv features to use Rkyv serialization. I took the opportunity of the major version bump to rationalize the feature names to make them easier to use. serialize_rkyv has been removed and now only rkyv feature is needed to enable Rkyv serialization. serialize has been renamed to serde in line with ecosystem conventions. half has been renamed to f16 for clarity.

max_qty Changed to NonZero<usize>

It was noted by @ezrasingh that specifying max_qty as zero in version 4.2.1 alongside sorted = false resulted in a panic. Since requesting a max_qty of zero makes no sense, and to avoid adding a run-time check, the type of max_qty has been changed to NonZero<usize> to make this a compile-time check instead.

ImmutableKdTree + rkyv

The v5 ImmutableKdTree uses an Aligned Vec internally for storing stem nodes. It is not possible to zero-copy deserialize into an Aligned Vec with rkyv as there is no guarantee that the stem vec in the underlying buffer respects the alignment. As such, unfortunately this means that ImmutableKdTree itself can't be fully zero-copy serialized / deserialized, but there are some related types that are provided that allow zero-copy deserialization to be performed for all other parts of the tree except for the stems, which themselves get copied into an aligned array from the buffer. In practice this is still very fast as the stems are only a very small part of the overall tree.

See immutable-rkyv-serialize and immutable-rkyv-deserialize in the examples for how to do this.

v3.x

Version 3.x changed the distance metrics syntax, switching from function pointers to a trait-based approach that permitted some ergonomics and performance improvements. This is a breaking change though: whereas prior to v3, you may have had queries that look like this:

use kiddo::distance::squared_euclidean;
let result = kdtree.nearest_one(&[0f64, 0f64], &squared_euclidean);

Now for v3 onwards, you'll need to switch to this syntax:

use kiddo::SquaredEuclidean;
let result = kdtree.nearest_one::<SquaredEuclidean>(&[0f64, 0f64]);

V3 also introduces the ImmutableKdTree variant. Designed for use cases where all the points that you need to add to the tree are known up-front, and no modifications need to be made after the tree is initially populated. ImmutableKdTree balances and optimises the tree at construction time, ensuring much more efficient memory usage (and a correspondingly smaller size on-disk for serialized trees). Since the interior nodes of the ImmutableKdTree also take up less space in memory, more of them can fit in the CPU cache, potentially improving performance in some cases.

v2.x

Version 2.x was a complete rewrite, providing:

• a new internal architecture for much-improved performance;
• Added integer / fixed point support via the Fixed library;
• instant zero-copy deserialization and serialization via Rkyv (Serde still available).
• See the changelog for a detailed run-down on all the changes made in v2.

Benchmarks

The results of all the below benchmarks are viewable in an interactive webapp over at https://sdd.github.io/kd-tree-comparison-webapp/.

The comparative benchmark suite is located in another project, https://github.com/sdd/kd-tree-comparison.

Criterion was used to perform a series of benchmarks. We compare Kiddo v3 to:

• Kiddo v2.x
• Kiddo v1.x / v0.2.x
• FNNTW v0.2.3
• nabo-rs v0.2.1
• pykdtree v1.3.4
• sklearn.neighbours.KDTree v1.2.2
• scipy.spatial.KDTree v1.10.1

The following activities are benchmarked (where implemented):

• Construction of a k-d tree from a list of points and indexes
• Querying the nearest one, ten, or one hundred points to a given query point
• Querying all points within a set radius of a given point (both unsorted results, and results sorted by distance)
• Querying the nearest n items within a specified radius (sorted and unsorted)

Each action is benchmarked against trees that contain 100, 1,000, 10,000, 100,000, 1,000,000 and in some cases 10,000,000 nodes.

The benchmarks are repeated against 2d, 3d and 4d trees, as well as with points that are both of type f32 and of type f64, as well as a 16-bit fixed point use case for Kiddo v2.

The trees are populated with random source data whose points are all on a unit sphere. This use case is representative of common k-d tree usages in geospatial and astronomical contexts.

License

Licensed under either of

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT License (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.