knn: Move NearestNeighbor interfaces to a submodule

7 files changed, 523 insertions, 508 deletions

diff --git a/src/distance.rs b/src/distance.rs
index e44ed03..680f11f 100644
--- a/src/distance.rs
+++ b/src/distance.rs
@@ -108,7 +108,7 @@ impl<T: Value> Distance for T {
 /// With those implementations available, you could use a [`NearestNeighbors<Gps, PointOfInterest>`]
 /// instance to find the closest point(s) of interest to any GPS location.
 ///
-/// [`NearestNeighbors<Gps, PointOfInterest>`]: super::NearestNeighbors
+/// [`NearestNeighbors<Gps, PointOfInterest>`]: crate::knn::NearestNeighbors
 pub trait Proximity<T: ?Sized = Self> {
     /// The type that represents distances.
     type Distance: Distance;
diff --git a/src/exhaustive.rs b/src/exhaustive.rs
index 442850c..f0abf9c 100644
--- a/src/exhaustive.rs
+++ b/src/exhaustive.rs
@@ -1,7 +1,7 @@
-//! Exhaustive nearest neighbor search.
+//! [Exhaustive nearest neighbor search](https://en.wikipedia.org/wiki/Nearest_neighbor_search#Linear_search).
 
 use crate::distance::Proximity;
-use crate::{ExactNeighbors, NearestNeighbors, Neighborhood};
+use crate::knn::{ExactNeighbors, NearestNeighbors, Neighborhood};
 
 use std::iter::FromIterator;
 
@@ -118,7 +118,7 @@ impl<K: Proximity<V>, V> ExactNeighbors<K, V> for ExhaustiveSearch<V> {}
 pub mod tests {
     use super::*;
 
-    use crate::tests::test_exact_neighbors;
+    use crate::knn::tests::test_exact_neighbors;
 
     #[test]
     fn test_exhaustive_index() {
diff --git a/src/kd.rs b/src/kd.rs
index d37321e..bf6b7c6 100644
--- a/src/kd.rs
+++ b/src/kd.rs
@@ -3,8 +3,8 @@
 use crate::coords::Coordinates;
 use crate::distance::Proximity;
 use crate::lp::Minkowski;
+use crate::knn::{ExactNeighbors, NearestNeighbors, Neighborhood};
 use crate::util::Ordered;
-use crate::{ExactNeighbors, NearestNeighbors, Neighborhood};
 
 use num_traits::Signed;
 
@@ -541,7 +541,7 @@ where
 mod tests {
     use super::*;
 
-    use crate::tests::test_exact_neighbors;
+    use crate::knn::tests::test_exact_neighbors;
 
     #[test]
     fn test_kd_tree() {
diff --git a/src/knn.rs b/src/knn.rs
new file mode 100644
index 0000000..1cc1f39
--- /dev/null
+++ b/src/knn.rs
@@ -0,0 +1,491 @@
+//! [Nearest neighbor search](https://en.wikipedia.org/wiki/Nearest_neighbor_search) interfaces.
+
+use crate::distance::{Distance, Proximity};
+
+use std::convert::TryInto;
+
+/// A nearest neighbor.
+#[derive(Clone, Copy, Debug)]
+pub struct Neighbor<V, D> {
+    /// The neighbor itself.
+    pub item: V,
+    /// The distance from the target to this neighbor.
+    pub distance: D,
+}
+
+impl<V, D> Neighbor<V, D> {
+    /// Create a new Neighbor.
+    pub fn new(item: V, distance: D) -> Self {
+        Self { item, distance }
+    }
+}
+
+impl<V1, D1, V2, D2> PartialEq<Neighbor<V2, D2>> for Neighbor<V1, D1>
+where
+    V1: PartialEq<V2>,
+    D1: PartialEq<D2>,
+{
+    fn eq(&self, other: &Neighbor<V2, D2>) -> bool {
+        self.item == other.item && self.distance == other.distance
+    }
+}
+
+/// Accumulates nearest neighbor search results.
+///
+/// Type parameters:
+///
+/// * `K`: The type of the search target (the "key" type)
+/// * `V`: The type of neighbors this contains (the "value" type)
+///
+/// Neighborhood implementations keep track of the current search radius and accumulate the results,
+/// work which would otherwise have to be duplicated for every nearest neighbor search algorithm.
+/// They also serve as a customization point, allowing for functionality to be injected into any
+/// [NearestNeighbors] implementation (for example, filtering the result set or limiting the number
+/// of neighbors considered).
+pub trait Neighborhood<K: Proximity<V>, V> {
+    /// Returns the target of the nearest neighbor search.
+    fn target(&self) -> K;
+
+    /// Check whether a distance is within the current search radius.
+    fn contains<D>(&self, distance: D) -> bool
+    where
+        D: PartialOrd<K::Distance>;
+
+    /// Consider a new candidate neighbor.
+    ///
+    /// Returns `self.target().distance(item)`.
+    fn consider(&mut self, item: V) -> K::Distance;
+}
+
+/// A [Neighborhood] with at most one result.
+#[derive(Debug)]
+struct SingletonNeighborhood<K, V, D> {
+    /// The search target.
+    target: K,
+    /// The current threshold distance.
+    threshold: Option<D>,
+    /// The current nearest neighbor, if any.
+    neighbor: Option<Neighbor<V, D>>,
+}
+
+impl<K, V, D> SingletonNeighborhood<K, V, D> {
+    /// Create a new singleton neighborhood.
+    ///
+    /// * `target`: The search target.
+    /// * `threshold`: The maximum allowable distance.
+    fn new(target: K, threshold: Option<D>) -> Self {
+        Self {
+            target,
+            threshold,
+            neighbor: None,
+        }
+    }
+
+    /// Convert this result into an optional neighbor.
+    fn into_option(self) -> Option<Neighbor<V, D>> {
+        self.neighbor
+    }
+}
+
+impl<K, V> Neighborhood<K, V> for SingletonNeighborhood<K, V, K::Distance>
+where
+    K: Copy + Proximity<V>,
+{
+    fn target(&self) -> K {
+        self.target
+    }
+
+    fn contains<D>(&self, distance: D) -> bool
+    where
+        D: PartialOrd<K::Distance>,
+    {
+        self.threshold.map_or(true, |t| distance <= t)
+    }
+
+    fn consider(&mut self, item: V) -> K::Distance {
+        let distance = self.target.distance(&item);
+
+        if self.contains(distance) {
+            self.threshold = Some(distance);
+            self.neighbor = Some(Neighbor::new(item, distance));
+        }
+
+        distance
+    }
+}
+
+/// A [Neighborhood] of up to `k` results, using a binary heap.
+#[derive(Debug)]
+struct HeapNeighborhood<'a, K, V, D> {
+    /// The target of the nearest neighbor search.
+    target: K,
+    /// The number of nearest neighbors to find.
+    k: usize,
+    /// The current threshold distance to the farthest result.
+    threshold: Option<D>,
+    /// A max-heap of the best candidates found so far.
+    heap: &'a mut Vec<Neighbor<V, D>>,
+}
+
+impl<'a, K, V, D: Distance> HeapNeighborhood<'a, K, V, D> {
+    /// Create a new HeapNeighborhood.
+    ///
+    /// * `target`: The search target.
+    /// * `k`: The maximum number of nearest neighbors to find.
+    /// * `threshold`: The maximum allowable distance.
+    /// * `heap`: The vector of neighbors to use as the heap.
+    fn new(
+        target: K,
+        k: usize,
+        mut threshold: Option<D>,
+        heap: &'a mut Vec<Neighbor<V, D>>,
+    ) -> Self {
+        // A descending array is also a max-heap
+        heap.reverse();
+
+        if k > 0 && heap.len() == k {
+            let distance = heap[0].distance;
+            if threshold.map_or(true, |t| distance <= t) {
+                threshold = Some(distance);
+            }
+        }
+
+        Self {
+            target,
+            k,
+            threshold,
+            heap,
+        }
+    }
+
+    /// Push a new element into the heap.
+    fn push(&mut self, item: Neighbor<V, D>) {
+        let mut i = self.heap.len();
+        self.heap.push(item);
+
+        while i > 0 {
+            let parent = (i - 1) / 2;
+            if self.heap[i].distance > self.heap[parent].distance {
+                self.heap.swap(i, parent);
+                i = parent;
+            } else {
+                break;
+            }
+        }
+    }
+
+    /// Restore the heap property by lowering the root.
+    fn sink_root(&mut self, len: usize) {
+        let mut i = 0;
+        let dist = self.heap[i].distance;
+
+        loop {
+            let mut child = 2 * i + 1;
+            let right = child + 1;
+            if right < len && self.heap[child].distance < self.heap[right].distance {
+                child = right;
+            }
+
+            if child < len && dist < self.heap[child].distance {
+                self.heap.swap(i, child);
+                i = child;
+            } else {
+                break;
+            }
+        }
+    }
+
+    /// Replace the root of the heap with a new element.
+    fn replace_root(&mut self, item: Neighbor<V, D>) {
+        self.heap[0] = item;
+        self.sink_root(self.heap.len());
+    }
+
+    /// Sort the heap from smallest to largest distance.
+    fn sort(&mut self) {
+        for i in (0..self.heap.len()).rev() {
+            self.heap.swap(0, i);
+            self.sink_root(i);
+        }
+    }
+}
+
+impl<'a, K, V> Neighborhood<K, V> for HeapNeighborhood<'a, K, V, K::Distance>
+where
+    K: Copy + Proximity<V>,
+{
+    fn target(&self) -> K {
+        self.target
+    }
+
+    fn contains<D>(&self, distance: D) -> bool
+    where
+        D: PartialOrd<K::Distance>,
+    {
+        self.k > 0 && self.threshold.map_or(true, |t| distance <= t)
+    }
+
+    fn consider(&mut self, item: V) -> K::Distance {
+        let distance = self.target.distance(&item);
+
+        if self.contains(distance) {
+            let neighbor = Neighbor::new(item, distance);
+
+            if self.heap.len() < self.k {
+                self.push(neighbor);
+            } else {
+                self.replace_root(neighbor);
+            }
+
+            if self.heap.len() == self.k {
+                self.threshold = Some(self.heap[0].distance);
+            }
+        }
+
+        distance
+    }
+}
+
+/// A [nearest neighbor search] index.
+///
+/// Type parameters:
+///
+/// * `K`: The type of the search target (the "key" type)
+/// * `V`: The type of the returned neighbors (the "value" type)
+///
+/// In general, exact nearest neighbor searches may be prohibitively expensive due to the [curse of
+/// dimensionality].  Therefore, NearestNeighbor implementations are allowed to give approximate
+/// results.  The marker trait [ExactNeighbors] denotes implementations which are guaranteed to give
+/// exact results.
+///
+/// [nearest neighbor search]: https://en.wikipedia.org/wiki/Nearest_neighbor_search
+/// [curse of dimensionality]: https://en.wikipedia.org/wiki/Curse_of_dimensionality
+pub trait NearestNeighbors<K: Proximity<V>, V = K> {
+    /// Returns the nearest neighbor to `target` (or `None` if this index is empty).
+    fn nearest(&self, target: &K) -> Option<Neighbor<&V, K::Distance>> {
+        self.search(SingletonNeighborhood::new(target, None))
+            .into_option()
+    }
+
+    /// Returns the nearest neighbor to `target` within the distance `threshold`, if one exists.
+    fn nearest_within<D>(&self, target: &K, threshold: D) -> Option<Neighbor<&V, K::Distance>>
+    where
+        D: TryInto<K::Distance>,
+    {
+        if let Ok(distance) = threshold.try_into() {
+            self.search(SingletonNeighborhood::new(target, Some(distance)))
+                .into_option()
+        } else {
+            None
+        }
+    }
+
+    /// Returns the up to `k` nearest neighbors to `target`.
+    ///
+    /// The result will be sorted from nearest to farthest.
+    fn k_nearest(&self, target: &K, k: usize) -> Vec<Neighbor<&V, K::Distance>> {
+        let mut neighbors = Vec::with_capacity(k);
+        self.merge_k_nearest(target, k, &mut neighbors);
+        neighbors
+    }
+
+    /// Returns the up to `k` nearest neighbors to `target` within the distance `threshold`.
+    ///
+    /// The result will be sorted from nearest to farthest.
+    fn k_nearest_within<D>(
+        &self,
+        target: &K,
+        k: usize,
+        threshold: D,
+    ) -> Vec<Neighbor<&V, K::Distance>>
+    where
+        D: TryInto<K::Distance>,
+    {
+        let mut neighbors = Vec::with_capacity(k);
+        self.merge_k_nearest_within(target, k, threshold, &mut neighbors);
+        neighbors
+    }
+
+    /// Merges up to `k` nearest neighbors into an existing sorted vector.
+    fn merge_k_nearest<'v>(
+        &'v self,
+        target: &K,
+        k: usize,
+        neighbors: &mut Vec<Neighbor<&'v V, K::Distance>>,
+    ) {
+        self.search(HeapNeighborhood::new(target, k, None, neighbors))
+            .sort();
+    }
+
+    /// Merges up to `k` nearest neighbors within the `threshold` into an existing sorted vector.
+    fn merge_k_nearest_within<'v, D>(
+        &'v self,
+        target: &K,
+        k: usize,
+        threshold: D,
+        neighbors: &mut Vec<Neighbor<&'v V, K::Distance>>,
+    ) where
+        D: TryInto<K::Distance>,
+    {
+        if let Ok(distance) = threshold.try_into() {
+            self.search(HeapNeighborhood::new(target, k, Some(distance), neighbors))
+                .sort();
+        }
+    }
+
+    /// Search for nearest neighbors and add them to a neighborhood.
+    fn search<'k, 'v, N>(&'v self, neighborhood: N) -> N
+    where
+        K: 'k,
+        V: 'v,
+        N: Neighborhood<&'k K, &'v V>;
+}
+
+/// Marker trait for [NearestNeighbors] implementations that always return exact results.
+pub trait ExactNeighbors<K: Proximity<V>, V = K>: NearestNeighbors<K, V> {}
+
+#[cfg(test)]
+pub mod tests {
+    use super::*;
+
+    use crate::euclid::{Euclidean, EuclideanDistance};
+    use crate::exhaustive::ExhaustiveSearch;
+
+    use rand::prelude::*;
+
+    use std::iter::FromIterator;
+
+    type Point = Euclidean<[f32; 3]>;
+
+    /// Test an [ExactNeighbors] implementation.
+    pub fn test_exact_neighbors<T, F>(from_iter: F)
+    where
+        T: ExactNeighbors<Point>,
+        F: Fn(Vec<Point>) -> T,
+    {
+        test_empty(&from_iter);
+        test_pythagorean(&from_iter);
+        test_random_points(&from_iter);
+    }
+
+    fn test_empty<T, F>(from_iter: &F)
+    where
+        T: NearestNeighbors<Point>,
+        F: Fn(Vec<Point>) -> T,
+    {
+        let points = Vec::new();
+        let index = from_iter(points);
+        let target = Euclidean([0.0, 0.0, 0.0]);
+        assert_eq!(index.nearest(&target), None);
+        assert_eq!(index.nearest_within(&target, 1.0), None);
+        assert!(index.k_nearest(&target, 0).is_empty());
+        assert!(index.k_nearest(&target, 3).is_empty());
+        assert!(index.k_nearest_within(&target, 0, 1.0).is_empty());
+        assert!(index.k_nearest_within(&target, 3, 1.0).is_empty());
+    }
+
+    fn test_pythagorean<T, F>(from_iter: &F)
+    where
+        T: NearestNeighbors<Point>,
+        F: Fn(Vec<Point>) -> T,
+    {
+        let points = vec![
+            Euclidean([3.0, 4.0, 0.0]),
+            Euclidean([5.0, 0.0, 12.0]),
+            Euclidean([0.0, 8.0, 15.0]),
+            Euclidean([1.0, 2.0, 2.0]),
+            Euclidean([2.0, 3.0, 6.0]),
+            Euclidean([4.0, 4.0, 7.0]),
+        ];
+        let index = from_iter(points);
+        let target = Euclidean([0.0, 0.0, 0.0]);
+
+        assert_eq!(
+            index.nearest(&target).expect("No nearest neighbor found"),
+            Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0)
+        );
+
+        assert_eq!(index.nearest_within(&target, 2.0), None);
+        assert_eq!(
+            index.nearest_within(&target, 4.0).expect("No nearest neighbor found within 4.0"),
+            Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0)
+        );
+
+        assert!(index.k_nearest(&target, 0).is_empty());
+        assert_eq!(
+            index.k_nearest(&target, 3),
+            vec![
+                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
+                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
+                Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), 7.0),
+            ]
+        );
+
+        assert!(index.k_nearest(&target, 0).is_empty());
+        assert_eq!(
+            index.k_nearest_within(&target, 3, 6.0),
+            vec![
+                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
+                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
+            ]
+        );
+        assert_eq!(
+            index.k_nearest_within(&target, 3, 8.0),
+            vec![
+                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
+                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
+                Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), 7.0),
+            ]
+        );
+
+        let mut neighbors = Vec::new();
+        index.merge_k_nearest(&target, 3, &mut neighbors);
+        assert_eq!(
+            neighbors,
+            vec![
+                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
+                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
+                Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), 7.0),
+            ]
+        );
+
+        neighbors = vec![
+            Neighbor::new(&target, EuclideanDistance::from_squared(0.0)),
+            Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), EuclideanDistance::from_squared(25.0)),
+            Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), EuclideanDistance::from_squared(49.0)),
+        ];
+        index.merge_k_nearest_within(&target, 3, 4.0, &mut neighbors);
+        assert_eq!(
+            neighbors,
+            vec![
+                Neighbor::new(&target, 0.0),
+                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
+                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
+            ]
+        );
+    }
+
+    fn test_random_points<T, F>(from_iter: &F)
+    where
+        T: NearestNeighbors<Point>,
+        F: Fn(Vec<Point>) -> T,
+    {
+        let mut points = Vec::new();
+        for _ in 0..256 {
+            points.push(Euclidean([random(), random(), random()]));
+        }
+
+        let index = from_iter(points.clone());
+        let eindex = ExhaustiveSearch::from_iter(points.clone());
+
+        let target = Euclidean([random(), random(), random()]);
+
+        assert_eq!(
+            index.k_nearest(&target, 3),
+            eindex.k_nearest(&target, 3),
+            "target: {:?}, points: {:#?}",
+            target,
+            points,
+        );
+    }
+}
diff --git a/src/lib.rs b/src/lib.rs
index 6402da2..1e77f6b 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -46,7 +46,6 @@
 //!
 //!     # use acap::euclid::Euclidean;
 //!     use acap::vp::VpTree;
-//!     use acap::NearestNeighbors;
 //!
 //!     let tree = VpTree::balanced(vec![
 //!         Euclidean([3, 4]),
@@ -61,7 +60,8 @@
 //!
 //!     # use acap::euclid::Euclidean;
 //!     # use acap::vp::VpTree;
-//!     # use acap::NearestNeighbors;
+//!     use acap::knn::NearestNeighbors;
+//!
 //!     # let tree = VpTree::balanced(
 //!     #     vec![Euclidean([3, 4]), Euclidean([5, 12]), Euclidean([8, 15]), Euclidean([7, 24])]
 //!     # );
@@ -87,8 +87,8 @@
 //! nearest neighbor index instead of having it hold the data itself:
 //!
 //!     use acap::euclid::Euclidean;
+//!     use acap::knn::NearestNeighbors;
 //!     use acap::vp::VpTree;
-//!     use acap::NearestNeighbors;
 //!
 //!     let points = vec![
 //!         Euclidean([3, 4]),
@@ -107,17 +107,20 @@
 //! See the [`Proximity`] documentation.
 //!
 //! [nearest neighbor search]: https://en.wikipedia.org/wiki/Nearest_neighbor_search
-//! [`distance()`]: Proximity#tymethod.distance
-//! [`value()`]: Distance#method.value
-//! [coordinates]: Coordinates
+//! [`distance()`]: distance::Proximity#tymethod.distance
+//! [`value()`]: distance::Distance#method.value
+//! [coordinates]: coords::Coordinates
 //! [Euclidean distance]: https://en.wikipedia.org/wiki/Euclidean_distance
-//! [many different similarity search data structures]: NearestNeighbors#implementors
+//! [`NearestNeighbors`]: knn::NearestNeighbors
+//! [many different similarity search data structures]: knn::NearestNeighbors#implementors
 //! [vantage-point tree]: https://en.wikipedia.org/wiki/Vantage-point_tree
 //! [`VpTree`]: vp::VpTree
-//! [`nearest()`]: NearestNeighbors#method.nearest
-//! [`k_nearest()`]: NearestNeighbors#method.k_nearest
-//! [`nearest_within()`]: NearestNeighbors#method.nearest_within
-//! [`k_nearest_within()`]: NearestNeighbors#method.k_nearest_within
+//! [`Neighbor`]: knn::Neighbor
+//! [`nearest()`]: knn::NearestNeighbors#method.nearest
+//! [`k_nearest()`]: knn::NearestNeighbors#method.k_nearest
+//! [`nearest_within()`]: knn::NearestNeighbors#method.nearest_within
+//! [`k_nearest_within()`]: knn::NearestNeighbors#method.k_nearest_within
+//! [`ExactNeighbors`]: knn::ExactNeighbors
 
 pub mod chebyshev;
 pub mod coords;
@@ -127,6 +130,7 @@ pub mod euclid;
 pub mod exhaustive;
 pub mod hamming;
 pub mod kd;
+pub mod knn;
 pub mod lp;
 pub mod taxi;
 pub mod vp;
@@ -136,490 +140,4 @@ mod util;
 pub use coords::Coordinates;
 pub use distance::{Distance, Metric, Proximity};
 pub use euclid::{euclidean_distance, Euclidean, EuclideanDistance};
-
-use std::convert::TryInto;
-
-/// A nearest neighbor.
-#[derive(Clone, Copy, Debug)]
-pub struct Neighbor<V, D> {
-    /// The neighbor itself.
-    pub item: V,
-    /// The distance from the target to this neighbor.
-    pub distance: D,
-}
-
-impl<V, D> Neighbor<V, D> {
-    /// Create a new Neighbor.
-    pub fn new(item: V, distance: D) -> Self {
-        Self { item, distance }
-    }
-}
-
-impl<V1, D1, V2, D2> PartialEq<Neighbor<V2, D2>> for Neighbor<V1, D1>
-where
-    V1: PartialEq<V2>,
-    D1: PartialEq<D2>,
-{
-    fn eq(&self, other: &Neighbor<V2, D2>) -> bool {
-        self.item == other.item && self.distance == other.distance
-    }
-}
-
-/// Accumulates nearest neighbor search results.
-///
-/// Type parameters:
-///
-/// * `K`: The type of the search target (the "key" type)
-/// * `V`: The type of neighbors this contains (the "value" type)
-///
-/// Neighborhood implementations keep track of the current search radius and accumulate the results,
-/// work which would otherwise have to be duplicated for every nearest neighbor search algorithm.
-/// They also serve as a customization point, allowing for functionality to be injected into any
-/// [NearestNeighbors] implementation (for example, filtering the result set or limiting the number
-/// of neighbors considered).
-pub trait Neighborhood<K: Proximity<V>, V> {
-    /// Returns the target of the nearest neighbor search.
-    fn target(&self) -> K;
-
-    /// Check whether a distance is within the current search radius.
-    fn contains<D>(&self, distance: D) -> bool
-    where
-        D: PartialOrd<K::Distance>;
-
-    /// Consider a new candidate neighbor.
-    ///
-    /// Returns `self.target().distance(item)`.
-    fn consider(&mut self, item: V) -> K::Distance;
-}
-
-/// A [Neighborhood] with at most one result.
-#[derive(Debug)]
-struct SingletonNeighborhood<K, V, D> {
-    /// The search target.
-    target: K,
-    /// The current threshold distance.
-    threshold: Option<D>,
-    /// The current nearest neighbor, if any.
-    neighbor: Option<Neighbor<V, D>>,
-}
-
-impl<K, V, D> SingletonNeighborhood<K, V, D> {
-    /// Create a new singleton neighborhood.
-    ///
-    /// * `target`: The search target.
-    /// * `threshold`: The maximum allowable distance.
-    fn new(target: K, threshold: Option<D>) -> Self {
-        Self {
-            target,
-            threshold,
-            neighbor: None,
-        }
-    }
-
-    /// Convert this result into an optional neighbor.
-    fn into_option(self) -> Option<Neighbor<V, D>> {
-        self.neighbor
-    }
-}
-
-impl<K, V> Neighborhood<K, V> for SingletonNeighborhood<K, V, K::Distance>
-where
-    K: Copy + Proximity<V>,
-{
-    fn target(&self) -> K {
-        self.target
-    }
-
-    fn contains<D>(&self, distance: D) -> bool
-    where
-        D: PartialOrd<K::Distance>,
-    {
-        self.threshold.map_or(true, |t| distance <= t)
-    }
-
-    fn consider(&mut self, item: V) -> K::Distance {
-        let distance = self.target.distance(&item);
-
-        if self.contains(distance) {
-            self.threshold = Some(distance);
-            self.neighbor = Some(Neighbor::new(item, distance));
-        }
-
-        distance
-    }
-}
-
-/// A [Neighborhood] of up to `k` results, using a binary heap.
-#[derive(Debug)]
-struct HeapNeighborhood<'a, K, V, D> {
-    /// The target of the nearest neighbor search.
-    target: K,
-    /// The number of nearest neighbors to find.
-    k: usize,
-    /// The current threshold distance to the farthest result.
-    threshold: Option<D>,
-    /// A max-heap of the best candidates found so far.
-    heap: &'a mut Vec<Neighbor<V, D>>,
-}
-
-impl<'a, K, V, D: Distance> HeapNeighborhood<'a, K, V, D> {
-    /// Create a new HeapNeighborhood.
-    ///
-    /// * `target`: The search target.
-    /// * `k`: The maximum number of nearest neighbors to find.
-    /// * `threshold`: The maximum allowable distance.
-    /// * `heap`: The vector of neighbors to use as the heap.
-    fn new(
-        target: K,
-        k: usize,
-        mut threshold: Option<D>,
-        heap: &'a mut Vec<Neighbor<V, D>>,
-    ) -> Self {
-        // A descending array is also a max-heap
-        heap.reverse();
-
-        if k > 0 && heap.len() == k {
-            let distance = heap[0].distance;
-            if threshold.map_or(true, |t| distance <= t) {
-                threshold = Some(distance);
-            }
-        }
-
-        Self {
-            target,
-            k,
-            threshold,
-            heap,
-        }
-    }
-
-    /// Push a new element into the heap.
-    fn push(&mut self, item: Neighbor<V, D>) {
-        let mut i = self.heap.len();
-        self.heap.push(item);
-
-        while i > 0 {
-            let parent = (i - 1) / 2;
-            if self.heap[i].distance > self.heap[parent].distance {
-                self.heap.swap(i, parent);
-                i = parent;
-            } else {
-                break;
-            }
-        }
-    }
-
-    /// Restore the heap property by lowering the root.
-    fn sink_root(&mut self, len: usize) {
-        let mut i = 0;
-        let dist = self.heap[i].distance;
-
-        loop {
-            let mut child = 2 * i + 1;
-            let right = child + 1;
-            if right < len && self.heap[child].distance < self.heap[right].distance {
-                child = right;
-            }
-
-            if child < len && dist < self.heap[child].distance {
-                self.heap.swap(i, child);
-                i = child;
-            } else {
-                break;
-            }
-        }
-    }
-
-    /// Replace the root of the heap with a new element.
-    fn replace_root(&mut self, item: Neighbor<V, D>) {
-        self.heap[0] = item;
-        self.sink_root(self.heap.len());
-    }
-
-    /// Sort the heap from smallest to largest distance.
-    fn sort(&mut self) {
-        for i in (0..self.heap.len()).rev() {
-            self.heap.swap(0, i);
-            self.sink_root(i);
-        }
-    }
-}
-
-impl<'a, K, V> Neighborhood<K, V> for HeapNeighborhood<'a, K, V, K::Distance>
-where
-    K: Copy + Proximity<V>,
-{
-    fn target(&self) -> K {
-        self.target
-    }
-
-    fn contains<D>(&self, distance: D) -> bool
-    where
-        D: PartialOrd<K::Distance>,
-    {
-        self.k > 0 && self.threshold.map_or(true, |t| distance <= t)
-    }
-
-    fn consider(&mut self, item: V) -> K::Distance {
-        let distance = self.target.distance(&item);
-
-        if self.contains(distance) {
-            let neighbor = Neighbor::new(item, distance);
-
-            if self.heap.len() < self.k {
-                self.push(neighbor);
-            } else {
-                self.replace_root(neighbor);
-            }
-
-            if self.heap.len() == self.k {
-                self.threshold = Some(self.heap[0].distance);
-            }
-        }
-
-        distance
-    }
-}
-
-/// A [nearest neighbor search] index.
-///
-/// Type parameters:
-///
-/// * `K`: The type of the search target (the "key" type)
-/// * `V`: The type of the returned neighbors (the "value" type)
-///
-/// In general, exact nearest neighbor searches may be prohibitively expensive due to the [curse of
-/// dimensionality].  Therefore, NearestNeighbor implementations are allowed to give approximate
-/// results.  The marker trait [ExactNeighbors] denotes implementations which are guaranteed to give
-/// exact results.
-///
-/// [nearest neighbor search]: https://en.wikipedia.org/wiki/Nearest_neighbor_search
-/// [curse of dimensionality]: https://en.wikipedia.org/wiki/Curse_of_dimensionality
-pub trait NearestNeighbors<K: Proximity<V>, V = K> {
-    /// Returns the nearest neighbor to `target` (or `None` if this index is empty).
-    fn nearest(&self, target: &K) -> Option<Neighbor<&V, K::Distance>> {
-        self.search(SingletonNeighborhood::new(target, None))
-            .into_option()
-    }
-
-    /// Returns the nearest neighbor to `target` within the distance `threshold`, if one exists.
-    fn nearest_within<D>(&self, target: &K, threshold: D) -> Option<Neighbor<&V, K::Distance>>
-    where
-        D: TryInto<K::Distance>,
-    {
-        if let Ok(distance) = threshold.try_into() {
-            self.search(SingletonNeighborhood::new(target, Some(distance)))
-                .into_option()
-        } else {
-            None
-        }
-    }
-
-    /// Returns the up to `k` nearest neighbors to `target`.
-    ///
-    /// The result will be sorted from nearest to farthest.
-    fn k_nearest(&self, target: &K, k: usize) -> Vec<Neighbor<&V, K::Distance>> {
-        let mut neighbors = Vec::with_capacity(k);
-        self.merge_k_nearest(target, k, &mut neighbors);
-        neighbors
-    }
-
-    /// Returns the up to `k` nearest neighbors to `target` within the distance `threshold`.
-    ///
-    /// The result will be sorted from nearest to farthest.
-    fn k_nearest_within<D>(
-        &self,
-        target: &K,
-        k: usize,
-        threshold: D,
-    ) -> Vec<Neighbor<&V, K::Distance>>
-    where
-        D: TryInto<K::Distance>,
-    {
-        let mut neighbors = Vec::with_capacity(k);
-        self.merge_k_nearest_within(target, k, threshold, &mut neighbors);
-        neighbors
-    }
-
-    /// Merges up to `k` nearest neighbors into an existing sorted vector.
-    fn merge_k_nearest<'v>(
-        &'v self,
-        target: &K,
-        k: usize,
-        neighbors: &mut Vec<Neighbor<&'v V, K::Distance>>,
-    ) {
-        self.search(HeapNeighborhood::new(target, k, None, neighbors))
-            .sort();
-    }
-
-    /// Merges up to `k` nearest neighbors within the `threshold` into an existing sorted vector.
-    fn merge_k_nearest_within<'v, D>(
-        &'v self,
-        target: &K,
-        k: usize,
-        threshold: D,
-        neighbors: &mut Vec<Neighbor<&'v V, K::Distance>>,
-    ) where
-        D: TryInto<K::Distance>,
-    {
-        if let Ok(distance) = threshold.try_into() {
-            self.search(HeapNeighborhood::new(target, k, Some(distance), neighbors))
-                .sort();
-        }
-    }
-
-    /// Search for nearest neighbors and add them to a neighborhood.
-    fn search<'k, 'v, N>(&'v self, neighborhood: N) -> N
-    where
-        K: 'k,
-        V: 'v,
-        N: Neighborhood<&'k K, &'v V>;
-}
-
-/// Marker trait for [NearestNeighbors] implementations that always return exact results.
-pub trait ExactNeighbors<K: Proximity<V>, V = K>: NearestNeighbors<K, V> {}
-
-#[cfg(test)]
-pub mod tests {
-    use super::*;
-
-    use crate::exhaustive::ExhaustiveSearch;
-
-    use rand::prelude::*;
-
-    use std::iter::FromIterator;
-
-    type Point = Euclidean<[f32; 3]>;
-
-    /// Test an [ExactNeighbors] implementation.
-    pub fn test_exact_neighbors<T, F>(from_iter: F)
-    where
-        T: ExactNeighbors<Point>,
-        F: Fn(Vec<Point>) -> T,
-    {
-        test_empty(&from_iter);
-        test_pythagorean(&from_iter);
-        test_random_points(&from_iter);
-    }
-
-    fn test_empty<T, F>(from_iter: &F)
-    where
-        T: NearestNeighbors<Point>,
-        F: Fn(Vec<Point>) -> T,
-    {
-        let points = Vec::new();
-        let index = from_iter(points);
-        let target = Euclidean([0.0, 0.0, 0.0]);
-        assert_eq!(index.nearest(&target), None);
-        assert_eq!(index.nearest_within(&target, 1.0), None);
-        assert!(index.k_nearest(&target, 0).is_empty());
-        assert!(index.k_nearest(&target, 3).is_empty());
-        assert!(index.k_nearest_within(&target, 0, 1.0).is_empty());
-        assert!(index.k_nearest_within(&target, 3, 1.0).is_empty());
-    }
-
-    fn test_pythagorean<T, F>(from_iter: &F)
-    where
-        T: NearestNeighbors<Point>,
-        F: Fn(Vec<Point>) -> T,
-    {
-        let points = vec![
-            Euclidean([3.0, 4.0, 0.0]),
-            Euclidean([5.0, 0.0, 12.0]),
-            Euclidean([0.0, 8.0, 15.0]),
-            Euclidean([1.0, 2.0, 2.0]),
-            Euclidean([2.0, 3.0, 6.0]),
-            Euclidean([4.0, 4.0, 7.0]),
-        ];
-        let index = from_iter(points);
-        let target = Euclidean([0.0, 0.0, 0.0]);
-
-        assert_eq!(
-            index.nearest(&target).expect("No nearest neighbor found"),
-            Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0)
-        );
-
-        assert_eq!(index.nearest_within(&target, 2.0), None);
-        assert_eq!(
-            index.nearest_within(&target, 4.0).expect("No nearest neighbor found within 4.0"),
-            Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0)
-        );
-
-        assert!(index.k_nearest(&target, 0).is_empty());
-        assert_eq!(
-            index.k_nearest(&target, 3),
-            vec![
-                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
-                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
-                Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), 7.0),
-            ]
-        );
-
-        assert!(index.k_nearest(&target, 0).is_empty());
-        assert_eq!(
-            index.k_nearest_within(&target, 3, 6.0),
-            vec![
-                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
-                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
-            ]
-        );
-        assert_eq!(
-            index.k_nearest_within(&target, 3, 8.0),
-            vec![
-                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
-                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
-                Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), 7.0),
-            ]
-        );
-
-        let mut neighbors = Vec::new();
-        index.merge_k_nearest(&target, 3, &mut neighbors);
-        assert_eq!(
-            neighbors,
-            vec![
-                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
-                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
-                Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), 7.0),
-            ]
-        );
-
-        neighbors = vec![
-            Neighbor::new(&target, EuclideanDistance::from_squared(0.0)),
-            Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), EuclideanDistance::from_squared(25.0)),
-            Neighbor::new(&Euclidean([2.0, 3.0, 6.0]), EuclideanDistance::from_squared(49.0)),
-        ];
-        index.merge_k_nearest_within(&target, 3, 4.0, &mut neighbors);
-        assert_eq!(
-            neighbors,
-            vec![
-                Neighbor::new(&target, 0.0),
-                Neighbor::new(&Euclidean([1.0, 2.0, 2.0]), 3.0),
-                Neighbor::new(&Euclidean([3.0, 4.0, 0.0]), 5.0),
-            ]
-        );
-    }
-
-    fn test_random_points<T, F>(from_iter: &F)
-    where
-        T: NearestNeighbors<Point>,
-        F: Fn(Vec<Point>) -> T,
-    {
-        let mut points = Vec::new();
-        for _ in 0..256 {
-            points.push(Euclidean([random(), random(), random()]));
-        }
-
-        let index = from_iter(points.clone());
-        let eindex = ExhaustiveSearch::from_iter(points.clone());
-
-        let target = Euclidean([random(), random(), random()]);
-
-        assert_eq!(
-            index.k_nearest(&target, 3),
-            eindex.k_nearest(&target, 3),
-            "target: {:?}, points: {:#?}",
-            target,
-            points,
-        );
-    }
-}
+pub use knn::{ExactNeighbors, NearestNeighbors, Neighbor};
diff --git a/src/util.rs b/src/util.rs
index f838a9b..0979782 100644
--- a/src/util.rs
+++ b/src/util.rs
@@ -3,7 +3,7 @@
 use std::cmp::Ordering;
 
 /// A wrapper that converts a partial ordering into a total one by panicking.
-#[derive(Clone, Copy, Debug, PartialEq, PartialOrd)]
+#[derive(Clone, Copy, Debug, PartialOrd)]
 pub struct Ordered<T>(T);
 
 impl<T> Ordered<T> {
@@ -25,7 +25,13 @@ impl<T: PartialOrd> Ord for Ordered<T> {
     }
 }
 
-impl<T: PartialEq> Eq for Ordered<T> {}
+impl<T: PartialOrd> PartialEq for Ordered<T> {
+    fn eq(&self, other: &Self) -> bool {
+        self.cmp(other) == Ordering::Equal
+    }
+}
+
+impl<T: PartialOrd> Eq for Ordered<T> {}
 
 #[cfg(test)]
 mod tests {
diff --git a/src/vp.rs b/src/vp.rs
index e0b218f..a5859ae 100644
--- a/src/vp.rs
+++ b/src/vp.rs
@@ -1,8 +1,8 @@
 //! [Vantage-point trees](https://en.wikipedia.org/wiki/Vantage-point_tree).
 
 use crate::distance::{Distance, DistanceValue, Metric, Proximity};
+use crate::knn::{ExactNeighbors, NearestNeighbors, Neighborhood};
 use crate::util::Ordered;
-use crate::{ExactNeighbors, NearestNeighbors, Neighborhood};
 
 use num_traits::zero;
 
@@ -620,7 +620,7 @@ where
 mod tests {
     use super::*;
 
-    use crate::tests::test_exact_neighbors;
+    use crate::knn::tests::test_exact_neighbors;
 
     #[test]
     fn test_vp_tree() {