hermes_core/structures/vector/ivf/

routing.rs

//! Metric-agnostic IVF routing primitives.
//!
//! Quantizers provide metric-specific centroid scores. This module owns the
//! topology-independent parts: flat/two-level policy, bounded beam sizing,
//! deterministic top selection, and the versioned probe plan shared by every
//! segment participating in one query.

use std::cmp::Reverse;
use std::collections::BinaryHeap;
use std::sync::Arc;

use crate::dsl::IvfRoutingMode;
use rand::prelude::*;
use serde::{Deserialize, Serialize};

/// Automatic routing switches to a centroid graph at this leaf count.
///
/// Float centroids are wide (a 768-dim leaf is 3 KiB), so a flat pass over them
/// gets expensive at far fewer leaves than for packed binary codes. This value
/// is the historical one and is *not* backed by a crossover measurement; see
/// [`BINARY_HNSW_AUTO_THRESHOLD`] for the measured binary counterpart, and
/// measure the float case the same way before changing this.
pub const HNSW_AUTO_THRESHOLD: usize = 4_096;

/// Automatic routing switch for packed binary centroids.
///
/// A base-layer search with beam `ef` and degree `2 * HNSW_M` touches on the
/// order of `ef * 2M` adjacency slots, so below roughly that many leaves it
/// visits the whole codebook anyway — by random access with heap traffic, and
/// approximately, where the flat pass is one sequential SIMD scan that is
/// *exact*. Measured on 2,560-bit binary centroids at `nprobe = 64`
/// (`benches/binary_vectors.rs`, `binary_routing_crossover`, aarch64/NEON):
///
/// | leaves | flat probe | graph probe |
/// |-------:|-----------:|------------:|
/// |  4,096 |    28.6 µs |    116.3 µs |
/// | 16,384 |   126.0 µs |    212.9 µs |
/// | 32,768 |   249.3 µs |    255.1 µs |
/// | 65,536 |   513.3 µs |    444.6 µs |
///
/// The graph only starts paying off past ~32k leaves, so that is the switch.
/// Explicit `hnsw` routing is still honoured at any size.
///
/// Hierarchical *training* has its own threshold — see
/// [`HIERARCHICAL_TRAINING_THRESHOLD`] — because O(N·K) seeding becomes
/// unaffordable long before graph routing becomes profitable.
pub const BINARY_HNSW_AUTO_THRESHOLD: usize = 32_768;

/// Codebook size past which coarse training becomes hierarchical.
///
/// Direct k-means/k-majority seeding costs one full pass over the sample per
/// centroid; beyond a few thousand centroids that dominates training, so large
/// codebooks train as `sqrt(K)` parents plus per-parent child codebooks
/// regardless of which router is used at query time.
pub const HIERARCHICAL_TRAINING_THRESHOLD: usize = 4_096;

/// Extra leaf coverage requested from the parent level. A beam of four times
/// the minimum parent count avoids the recall cliff of greedy one-parent
/// hierarchical routing while keeping parent/leaf scoring sublinear.
const PARENT_BEAM_OVERSAMPLE: usize = 4;
/// Construction assignments become permanent, so inspect multiple populated
/// parent cells even when the query-time leaf budget fits under one parent.
const MIN_BUILD_PARENT_BEAM: usize = 4;

const HNSW_M: usize = 32;
const HNSW_EF_CONSTRUCTION: usize = 200;
const HNSW_QUERY_OVERSAMPLE: usize = 4;
const HNSW_MIN_EF_SEARCH: usize = 128;
/// Index construction happens once per vector generation and can afford a
/// wider centroid search than latency-sensitive queries. Keeping the budgets
/// separate prevents an approximate query-router miss from permanently
/// assigning a vector to a needlessly distant leaf.
const HNSW_BUILD_OVERSAMPLE: usize = 8;
/// Floor for the construction beam.
///
/// This is a *floor*, so it is what single-candidate assignment actually pays:
/// every vector in a rebuilt segment routes with `take = 1`. Recall@1 against
/// exact centroid assignment saturates well before 512 at `M = 32` — see
/// `hnsw_build_beam_recall_saturates_before_the_floor` — while the cost is
/// linear in the beam, so a 512 floor spent ~4x the distance work of a 128 one
/// for no measurable assignment gain. Multi-candidate build routing still
/// widens through `HNSW_BUILD_OVERSAMPLE`.
pub(crate) const HNSW_MIN_EF_BUILD: usize = 128;

/// Neighbour lists are capped at `2 * HNSW_M`; one stack block therefore covers
/// a whole expansion, letting the batched distance form run without touching
/// the allocator.
const NEIGHBOR_BLOCK: usize = HNSW_M * 4;

/// Distance from one query to graph nodes.
///
/// Float centroids vectorise across the dimension, so the pairwise form is
/// already efficient there. Binary centroids are single-row popcounts: scoring
/// a whole neighbour list per call is what keeps the SIMD kernel fed and pays
/// the `#[target_feature]` dispatch once per expansion instead of per node.
pub trait QueryDistance {
    fn distance(&self, node: u32) -> f32;

    /// Score a whole neighbour list. Defaults to repeated pairwise calls.
    fn distances(&self, nodes: &[u32], out: &mut [f32]) {
        debug_assert_eq!(nodes.len(), out.len());
        for (slot, &node) in out.iter_mut().zip(nodes) {
            *slot = self.distance(node);
        }
    }
}

impl<F: Fn(u32) -> f32> QueryDistance for F {
    #[inline]
    fn distance(&self, node: u32) -> f32 {
        self(node)
    }
}

/// Distance between two graph nodes, used while constructing the graph.
pub trait PairDistance {
    fn distance(&self, left: u32, right: u32) -> f32;

    /// Score `left` against a whole node list. Defaults to pairwise calls.
    fn distances_from(&self, left: u32, rights: &[u32], out: &mut [f32]) {
        debug_assert_eq!(rights.len(), out.len());
        for (slot, &right) in out.iter_mut().zip(rights) {
            *slot = self.distance(left, right);
        }
    }
}

impl<F: Fn(u32, u32) -> f32> PairDistance for F {
    #[inline]
    fn distance(&self, left: u32, right: u32) -> f32 {
        self(left, right)
    }
}

/// One inserted node's view of a [`PairDistance`], so construction reuses the
/// same batched search as queries.
struct PairQueryDistance<'a, P: ?Sized> {
    pair: &'a P,
    left: u32,
}

impl<P: PairDistance + ?Sized> QueryDistance for PairQueryDistance<'_, P> {
    #[inline]
    fn distance(&self, node: u32) -> f32 {
        self.pair.distance(self.left, node)
    }

    #[inline]
    fn distances(&self, nodes: &[u32], out: &mut [f32]) {
        self.pair.distances_from(self.left, nodes, out);
    }
}

#[derive(Clone, Copy, Debug)]
struct GraphCandidate {
    node: u32,
    distance: f32,
}

impl PartialEq for GraphCandidate {
    fn eq(&self, other: &Self) -> bool {
        self.node == other.node && self.distance.to_bits() == other.distance.to_bits()
    }
}

impl Eq for GraphCandidate {}

impl PartialOrd for GraphCandidate {
    fn partial_cmp(&self, other: &Self) -> Option<std::cmp::Ordering> {
        Some(self.cmp(other))
    }
}

impl Ord for GraphCandidate {
    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
        self.distance
            .total_cmp(&other.distance)
            .then_with(|| self.node.cmp(&other.node))
    }
}

struct VisitedNodes {
    epochs: Vec<u32>,
    current: u32,
}

impl VisitedNodes {
    fn new(nodes: usize) -> Self {
        Self {
            epochs: vec![0; nodes],
            current: 0,
        }
    }

    fn reset(&mut self) {
        self.current = self.current.wrapping_add(1);
        if self.current == 0 {
            self.epochs.fill(0);
            self.current = 1;
        }
    }

    fn ensure_nodes(&mut self, nodes: usize) {
        if self.epochs.len() < nodes {
            self.epochs.resize(nodes, 0);
        }
    }

    fn insert(&mut self, node: u32) -> bool {
        let slot = &mut self.epochs[node as usize];
        if *slot == self.current {
            false
        } else {
            *slot = self.current;
            true
        }
    }
}

struct HnswQueryScratch {
    visited: VisitedNodes,
    candidates: BinaryHeap<Reverse<GraphCandidate>>,
    best: BinaryHeap<GraphCandidate>,
    ordered: Vec<GraphCandidate>,
    /// Unvisited neighbours of the node being expanded, plus their distances,
    /// so one expansion is one batched distance call.
    pending: Vec<u32>,
    pending_distances: Vec<f32>,
}

impl HnswQueryScratch {
    fn new() -> Self {
        Self {
            visited: VisitedNodes::new(0),
            candidates: BinaryHeap::new(),
            best: BinaryHeap::new(),
            ordered: Vec::new(),
            pending: Vec::new(),
            pending_distances: Vec::new(),
        }
    }
}

thread_local! {
    /// Segment construction routes millions of vectors through the same graph.
    /// Retaining scratch per worker avoids zeroing the visited bitmap and
    /// reallocating both heaps for every assignment.
    static HNSW_QUERY_SCRATCH: std::cell::RefCell<HnswQueryScratch> =
        std::cell::RefCell::new(HnswQueryScratch::new());
}

/// Compact, centroid-free HNSW topology. Node IDs are global leaf IDs, so the
/// graph shares the quantizer's existing centroid matrix rather than storing a
/// second copy of every vector.
#[derive(Debug, Clone, Serialize, Deserialize)]
pub struct HnswRoutingGraph {
    m: u16,
    ef_construction: u32,
    entry_point: u32,
    max_level: u8,
    node_levels: Vec<u8>,
    /// Per-node ranges into `level_offsets`; each node owns level_count + 1
    /// offsets so every adjacency is a direct pair of indexed loads.
    node_offsets: Vec<u32>,
    level_offsets: Vec<u32>,
    neighbors: Vec<u32>,
}

impl HnswRoutingGraph {
    pub fn build(node_count: usize, distance: impl PairDistance, seed: u64) -> Self {
        assert!(node_count > 0 && node_count <= u32::MAX as usize);
        let mut rng = rand::rngs::StdRng::seed_from_u64(seed);
        let level_multiplier = 1.0 / (HNSW_M as f64).ln();
        let node_levels: Vec<u8> = (0..node_count)
            .map(|_| {
                let uniform = rng.random::<f64>().clamp(f64::MIN_POSITIVE, 1.0);
                (-uniform.ln() * level_multiplier).floor().min(31.0) as u8
            })
            .collect();
        let mut insertion_order: Vec<u32> = (0..node_count as u32).collect();
        insertion_order.shuffle(&mut rng);
        let mut links: Vec<Vec<Vec<u32>>> = node_levels
            .iter()
            .map(|&level| vec![Vec::new(); level as usize + 1])
            .collect();
        let mut visited = VisitedNodes::new(node_count);
        let mut entry_point = insertion_order[0];
        let mut max_level = node_levels[entry_point as usize];

        for &node in insertion_order.iter().skip(1) {
            let node_level = node_levels[node as usize];
            let mut entry = entry_point;
            let node_distance = PairQueryDistance {
                pair: &distance,
                left: node,
            };

            for level in ((node_level as usize + 1)..=max_level as usize).rev() {
                entry = greedy_search_level(&links, entry, level, &node_distance);
            }

            for level in (0..=usize::min(node_level as usize, max_level as usize)).rev() {
                let candidates = search_graph_layer(
                    &links,
                    entry,
                    level,
                    HNSW_EF_CONSTRUCTION,
                    &node_distance,
                    &mut visited,
                );
                if let Some(best) = candidates.first() {
                    entry = best.node;
                }
                let max_connections = if level == 0 { HNSW_M * 2 } else { HNSW_M };
                let selected =
                    select_diverse_neighbors(node, candidates, max_connections, &distance);
                links[node as usize][level] = selected.clone();
                for neighbor in selected {
                    let adjacency = &mut links[neighbor as usize][level];
                    if !adjacency.contains(&node) {
                        adjacency.push(node);
                    }
                    if adjacency.len() > max_connections {
                        let candidates = adjacency
                            .iter()
                            .copied()
                            .map(|candidate| GraphCandidate {
                                node: candidate,
                                distance: distance.distance(neighbor, candidate),
                            })
                            .collect();
                        *adjacency = select_diverse_neighbors(
                            neighbor,
                            candidates,
                            max_connections,
                            &distance,
                        );
                    }
                }
            }

            if node_level > max_level {
                entry_point = node;
                max_level = node_level;
            }
        }

        Self::compact(
            HNSW_M,
            HNSW_EF_CONSTRUCTION,
            entry_point,
            max_level,
            node_levels,
            links,
        )
    }

    fn compact(
        m: usize,
        ef_construction: usize,
        entry_point: u32,
        max_level: u8,
        node_levels: Vec<u8>,
        links: Vec<Vec<Vec<u32>>>,
    ) -> Self {
        let mut node_offsets = Vec::with_capacity(links.len() + 1);
        let level_count: usize = links.iter().map(|levels| levels.len() + 1).sum();
        let neighbor_count: usize = links
            .iter()
            .flat_map(|levels| levels.iter())
            .map(Vec::len)
            .sum();
        let mut level_offsets = Vec::with_capacity(level_count);
        let mut neighbors = Vec::with_capacity(neighbor_count);
        for levels in links {
            node_offsets.push(level_offsets.len() as u32);
            for mut adjacency in levels {
                adjacency.sort_unstable();
                adjacency.dedup();
                level_offsets.push(neighbors.len() as u32);
                neighbors.extend(adjacency);
            }
            level_offsets.push(neighbors.len() as u32);
        }
        node_offsets.push(level_offsets.len() as u32);
        Self {
            m: m as u16,
            ef_construction: ef_construction as u32,
            entry_point,
            max_level,
            node_levels,
            node_offsets,
            level_offsets,
            neighbors,
        }
    }

    #[inline]
    pub fn neighbors(&self, node: u32, level: usize) -> &[u32] {
        if (self.node_levels[node as usize] as usize) < level {
            return &[];
        }
        let offset_index = self.node_offsets[node as usize] as usize + level;
        let start = self.level_offsets[offset_index] as usize;
        let end = self.level_offsets[offset_index + 1] as usize;
        &self.neighbors[start..end]
    }

    pub fn search(&self, query_distance: impl QueryDistance, take: usize) -> Vec<u32> {
        let take = take.min(self.node_levels.len());
        if take == 0 {
            return Vec::new();
        }
        let ef_search = take
            .saturating_mul(HNSW_QUERY_OVERSAMPLE)
            .max(HNSW_MIN_EF_SEARCH)
            .min(self.node_levels.len());
        self.search_with_budget(query_distance, take, ef_search)
    }

    /// Higher-recall centroid search used only while constructing postings.
    pub(crate) fn search_for_build(
        &self,
        query_distance: impl QueryDistance,
        take: usize,
    ) -> Vec<u32> {
        let take = take.min(self.node_levels.len());
        if take == 0 {
            return Vec::new();
        }
        self.search_with_budget(query_distance, take, self.build_budget(take))
    }

    /// Single nearest node, for the assignment of one vector to one leaf.
    ///
    /// Construction routes every vector in a segment through here, so it avoids
    /// both the result `Vec` and the full ranking of the beam that
    /// [`Self::search_for_build`] needs — the minimum of the bounded heap is
    /// the same node the ranked list would have put first.
    pub(crate) fn search_best_for_build(&self, query_distance: impl QueryDistance) -> Option<u32> {
        if self.node_levels.is_empty() {
            return None;
        }
        let ef_search = self.build_budget(1);
        let mut entry = self.entry_point;
        for level in (1..=self.max_level as usize).rev() {
            entry = greedy_search_compact(self, entry, level, &query_distance);
        }
        HNSW_QUERY_SCRATCH.with(|scratch| {
            let mut scratch = scratch.borrow_mut();
            search_compact_layer_reusing(self, entry, ef_search, &query_distance, &mut scratch);
            Some(
                scratch
                    .best
                    .iter()
                    .min()
                    .map_or(entry, |candidate| candidate.node),
            )
        })
    }

    #[inline]
    fn build_budget(&self, take: usize) -> usize {
        take.saturating_mul(HNSW_BUILD_OVERSAMPLE)
            .max(HNSW_MIN_EF_BUILD)
            .min(self.node_levels.len())
    }

    /// Nearest node under an explicit beam, so tests can measure how assignment
    /// recall responds to the budget instead of asserting a constant.
    #[cfg(test)]
    pub(crate) fn search_best_with_ef(
        &self,
        query_distance: impl QueryDistance,
        ef: usize,
    ) -> Option<u32> {
        if self.node_levels.is_empty() {
            return None;
        }
        let ef_search = ef.clamp(1, self.node_levels.len());
        let mut entry = self.entry_point;
        for level in (1..=self.max_level as usize).rev() {
            entry = greedy_search_compact(self, entry, level, &query_distance);
        }
        HNSW_QUERY_SCRATCH.with(|scratch| {
            let mut scratch = scratch.borrow_mut();
            search_compact_layer_reusing(self, entry, ef_search, &query_distance, &mut scratch);
            Some(
                scratch
                    .best
                    .iter()
                    .min()
                    .map_or(entry, |candidate| candidate.node),
            )
        })
    }

    fn search_with_budget(
        &self,
        query_distance: impl QueryDistance,
        take: usize,
        ef_search: usize,
    ) -> Vec<u32> {
        let mut entry = self.entry_point;
        for level in (1..=self.max_level as usize).rev() {
            entry = greedy_search_compact(self, entry, level, &query_distance);
        }
        HNSW_QUERY_SCRATCH.with(|scratch| {
            let mut scratch = scratch.borrow_mut();
            search_compact_layer_reusing(self, entry, ef_search, &query_distance, &mut scratch);
            order_scratch_candidates(&mut scratch);
            scratch
                .ordered
                .iter()
                .take(take)
                .map(|candidate| candidate.node)
                .collect()
        })
    }

    pub fn validate(&self, expected_nodes: usize) -> bool {
        if self.m as usize != HNSW_M
            || self.ef_construction as usize != HNSW_EF_CONSTRUCTION
            || expected_nodes == 0
            || self.node_levels.len() != expected_nodes
            || self.node_offsets.len() != expected_nodes + 1
            || self.node_offsets.first() != Some(&0)
            || self.node_offsets.last().copied() != Some(self.level_offsets.len() as u32)
            || self.node_offsets.windows(2).any(|pair| pair[0] > pair[1])
            || self
                .node_offsets
                .iter()
                .any(|&offset| offset as usize > self.level_offsets.len())
            || self.entry_point as usize >= expected_nodes
            || self.node_levels[self.entry_point as usize] != self.max_level
            || self.node_levels.iter().copied().max() != Some(self.max_level)
            || self.level_offsets.last().copied() != Some(self.neighbors.len() as u32)
            || self.level_offsets.windows(2).any(|pair| pair[0] > pair[1])
            || self
                .neighbors
                .iter()
                .any(|&node| node as usize >= expected_nodes)
        {
            return false;
        }
        for node in 0..expected_nodes {
            let start = self.node_offsets[node] as usize;
            let end = self.node_offsets[node + 1] as usize;
            if end.saturating_sub(start) != self.node_levels[node] as usize + 2 {
                return false;
            }
            for level in 0..=self.node_levels[node] as usize {
                let adjacency = self.neighbors(node as u32, level);
                let max_connections = if level == 0 { HNSW_M * 2 } else { HNSW_M };
                if adjacency.len() > max_connections
                    || adjacency.contains(&(node as u32))
                    || adjacency.windows(2).any(|pair| pair[0] >= pair[1])
                {
                    return false;
                }
            }
        }
        true
    }

    pub fn size_bytes(&self) -> usize {
        self.node_levels.len()
            + self.node_offsets.len() * size_of::<u32>()
            + self.level_offsets.len() * size_of::<u32>()
            + self.neighbors.len() * size_of::<u32>()
            + 32
    }

    /// Visit the compact, immutable arrays touched by every HNSW route.
    /// Query scratch is thread-local and intentionally excluded.
    #[cfg(feature = "native")]
    pub(crate) fn visit_resident_regions(&self, visit: &mut dyn FnMut(&'static str, &[u8])) {
        visit("HNSW node levels", bytes_of_slice(&self.node_levels));
        visit("HNSW node offsets", bytes_of_slice(&self.node_offsets));
        visit("HNSW level offsets", bytes_of_slice(&self.level_offsets));
        visit("HNSW neighbors", bytes_of_slice(&self.neighbors));
    }
}

fn greedy_search_level(
    links: &[Vec<Vec<u32>>],
    mut current: u32,
    level: usize,
    query_distance: &impl QueryDistance,
) -> u32 {
    let mut current_distance = query_distance.distance(current);
    let mut scores = [0f32; NEIGHBOR_BLOCK];
    loop {
        let mut changed = false;
        for chunk in links[current as usize][level].chunks(NEIGHBOR_BLOCK) {
            let scored = &mut scores[..chunk.len()];
            query_distance.distances(chunk, scored);
            for (&candidate, &distance) in chunk.iter().zip(scored.iter()) {
                if distance < current_distance
                    || (distance == current_distance && candidate < current)
                {
                    current = candidate;
                    current_distance = distance;
                    changed = true;
                }
            }
        }
        if !changed {
            return current;
        }
    }
}

fn greedy_search_compact(
    graph: &HnswRoutingGraph,
    mut current: u32,
    level: usize,
    query_distance: &impl QueryDistance,
) -> u32 {
    let mut current_distance = query_distance.distance(current);
    let mut scores = [0f32; NEIGHBOR_BLOCK];
    loop {
        let mut changed = false;
        for chunk in graph.neighbors(current, level).chunks(NEIGHBOR_BLOCK) {
            let scored = &mut scores[..chunk.len()];
            query_distance.distances(chunk, scored);
            for (&candidate, &distance) in chunk.iter().zip(scored.iter()) {
                if distance < current_distance
                    || (distance == current_distance && candidate < current)
                {
                    current = candidate;
                    current_distance = distance;
                    changed = true;
                }
            }
        }
        if !changed {
            return current;
        }
    }
}

fn search_graph_layer(
    links: &[Vec<Vec<u32>>],
    entry: u32,
    level: usize,
    ef: usize,
    query_distance: &impl QueryDistance,
    visited: &mut VisitedNodes,
) -> Vec<GraphCandidate> {
    search_layer_impl(entry, ef, query_distance, visited, |node| {
        &links[node as usize][level]
    })
}

/// Expand the base layer into `scratch.best`, leaving `scratch.ordered` empty.
///
/// Callers that need a ranked list finish with [`order_scratch_candidates`];
/// single-candidate assignment skips that and scans the bounded heap instead.
fn search_compact_layer_reusing(
    graph: &HnswRoutingGraph,
    entry: u32,
    ef: usize,
    query_distance: &impl QueryDistance,
    scratch: &mut HnswQueryScratch,
) {
    scratch.visited.ensure_nodes(graph.node_levels.len());
    scratch.visited.reset();
    scratch.candidates.clear();
    scratch.best.clear();
    scratch.ordered.clear();
    scratch.visited.insert(entry);
    let first = GraphCandidate {
        node: entry,
        distance: query_distance.distance(entry),
    };
    scratch.candidates.push(Reverse(first));
    scratch.best.push(first);

    while let Some(Reverse(current)) = scratch.candidates.pop() {
        if scratch.best.len() >= ef
            && scratch
                .best
                .peek()
                .is_some_and(|worst| current.distance > worst.distance)
        {
            break;
        }
        // Score the whole unvisited frontier of this node in one call. The
        // accept test below still runs in adjacency order, so results are
        // identical to scoring node by node.
        scratch.pending.clear();
        for &neighbor in graph.neighbors(current.node, 0) {
            if scratch.visited.insert(neighbor) {
                scratch.pending.push(neighbor);
            }
        }
        if scratch.pending.is_empty() {
            continue;
        }
        scratch.pending_distances.clear();
        scratch.pending_distances.resize(scratch.pending.len(), 0.0);
        query_distance.distances(&scratch.pending, &mut scratch.pending_distances);

        for (&node, &distance) in scratch.pending.iter().zip(scratch.pending_distances.iter()) {
            let candidate = GraphCandidate { node, distance };
            if scratch.best.len() < ef
                || scratch.best.peek().is_some_and(|worst| candidate < *worst)
            {
                scratch.candidates.push(Reverse(candidate));
                scratch.best.push(candidate);
                if scratch.best.len() > ef {
                    scratch.best.pop();
                }
            }
        }
    }
}

fn order_scratch_candidates(scratch: &mut HnswQueryScratch) {
    scratch.ordered.extend(scratch.best.drain());
    scratch.ordered.sort_unstable();
}

fn search_layer_impl<'a>(
    entry: u32,
    ef: usize,
    query_distance: &impl QueryDistance,
    visited: &mut VisitedNodes,
    neighbors: impl Fn(u32) -> &'a [u32],
) -> Vec<GraphCandidate> {
    visited.reset();
    visited.insert(entry);
    let first = GraphCandidate {
        node: entry,
        distance: query_distance.distance(entry),
    };
    let mut candidates = BinaryHeap::new();
    let mut best = BinaryHeap::new();
    candidates.push(Reverse(first));
    best.push(first);
    let mut pending: Vec<u32> = Vec::new();
    let mut pending_distances: Vec<f32> = Vec::new();

    while let Some(Reverse(current)) = candidates.pop() {
        if best.len() >= ef
            && best
                .peek()
                .is_some_and(|worst| current.distance > worst.distance)
        {
            break;
        }
        pending.clear();
        for &neighbor in neighbors(current.node) {
            if visited.insert(neighbor) {
                pending.push(neighbor);
            }
        }
        if pending.is_empty() {
            continue;
        }
        pending_distances.clear();
        pending_distances.resize(pending.len(), 0.0);
        query_distance.distances(&pending, &mut pending_distances);

        for (&node, &distance) in pending.iter().zip(pending_distances.iter()) {
            let candidate = GraphCandidate { node, distance };
            if best.len() < ef || best.peek().is_some_and(|worst| candidate < *worst) {
                candidates.push(Reverse(candidate));
                best.push(candidate);
                if best.len() > ef {
                    best.pop();
                }
            }
        }
    }
    best.into_sorted_vec()
}

fn select_diverse_neighbors(
    query_node: u32,
    mut candidates: Vec<GraphCandidate>,
    limit: usize,
    distance: &impl PairDistance,
) -> Vec<u32> {
    candidates.sort_unstable();
    candidates.dedup_by_key(|candidate| candidate.node);
    let mut selected = Vec::with_capacity(limit);
    let mut deferred = Vec::new();
    for candidate in candidates {
        if candidate.node == query_node {
            continue;
        }
        if selected
            .iter()
            .all(|&neighbor| distance.distance(candidate.node, neighbor) > candidate.distance)
        {
            selected.push(candidate.node);
            if selected.len() == limit {
                return selected;
            }
        } else {
            deferred.push(candidate.node);
        }
    }
    for candidate in deferred {
        if selected.len() == limit {
            break;
        }
        selected.push(candidate);
    }
    selected
}

fn contiguous_leaf_run(children: &[u32]) -> bool {
    children
        .windows(2)
        .all(|pair| pair[1] == pair[0].saturating_add(1))
}

/// Compact parent-to-leaf adjacency shared by float and binary quantizers.
/// Offsets avoid one heap allocation per parent and serialize as two flat
/// arrays in the single index-level quantizer artifact.
#[derive(Debug, Clone, Default, PartialEq, Eq, Serialize, Deserialize)]
pub struct IvfRoutingTopology {
    child_offsets: Vec<u32>,
    leaf_ids: Vec<u32>,
}

impl IvfRoutingTopology {
    pub fn from_children(children: &[Vec<u32>]) -> Self {
        let mut child_offsets = Vec::with_capacity(children.len() + 1);
        let mut leaf_ids = Vec::new();
        child_offsets.push(0);
        for child_list in children {
            leaf_ids.extend_from_slice(child_list);
            child_offsets.push(leaf_ids.len() as u32);
        }
        Self {
            child_offsets,
            leaf_ids,
        }
    }

    pub fn parent_count(&self) -> usize {
        self.child_offsets.len().saturating_sub(1)
    }

    pub fn children(&self, parent: usize) -> &[u32] {
        let start = self.child_offsets[parent] as usize;
        let end = self.child_offsets[parent + 1] as usize;
        &self.leaf_ids[start..end]
    }

    /// Children of `parent` as a `(first_leaf, count)` run.
    ///
    /// Both trainers append each parent's leaves as one contiguous block, which
    /// lets a caller score a whole parent with a single batched pass over the
    /// centroid matrix instead of one kernel call per leaf. Returns `None` for
    /// an empty parent, and — defensively — for any non-contiguous list, so the
    /// scoring path stays correct even if the invariant is ever relaxed.
    pub fn children_run(&self, parent: usize) -> Option<(u32, usize)> {
        let children = self.children(parent);
        let first = *children.first()?;
        contiguous_leaf_run(children).then_some((first, children.len()))
    }

    pub fn validate(&self, num_leaves: usize) -> bool {
        if self.parent_count() == 0 {
            return self.child_offsets.is_empty() && self.leaf_ids.is_empty();
        }
        self.child_offsets.first() == Some(&0)
            && self.child_offsets.last().copied() == Some(self.leaf_ids.len() as u32)
            && self.child_offsets.windows(2).all(|pair| pair[0] <= pair[1])
            && self.leaf_ids.len() == num_leaves
            && self.leaf_ids.iter().all(|&leaf| leaf < num_leaves as u32)
            // Contiguity is a build invariant of both trainers; a topology
            // without it did not come from this codebase, so refuse it rather
            // than silently routing through a slower path.
            && (0..self.parent_count()).all(|parent| contiguous_leaf_run(self.children(parent)))
            && {
                let mut leaves = self.leaf_ids.clone();
                leaves.sort_unstable();
                leaves.iter().copied().eq(0..num_leaves as u32)
            }
    }

    #[cfg(feature = "native")]
    pub(crate) fn visit_resident_regions(&self, visit: &mut dyn FnMut(&'static str, &[u8])) {
        visit(
            "two-level child offsets",
            bytes_of_slice(&self.child_offsets),
        );
        visit("two-level leaf IDs", bytes_of_slice(&self.leaf_ids));
    }
}

/// View an initialized plain-data slice as bytes for residency operations.
/// The returned slice cannot outlive the source and is never mutated.
#[cfg(feature = "native")]
pub(crate) fn bytes_of_slice<T>(slice: &[T]) -> &[u8] {
    let byte_len = std::mem::size_of_val(slice);
    if byte_len == 0 {
        return &[];
    }
    // SAFETY: every byte in an initialized `T` allocation may be read as u8;
    // the lifetime remains tied to `slice`, and callers receive no mutation.
    unsafe { std::slice::from_raw_parts(slice.as_ptr().cast::<u8>(), byte_len) }
}

pub fn routing_parent_count(num_leaves: usize) -> usize {
    if num_leaves <= 1 {
        return num_leaves;
    }
    ((num_leaves as f64).sqrt().ceil() as usize)
        .clamp(2, 4_096)
        .min(num_leaves)
}

/// Allocate `total_clusters` child cells proportionally to populated parent
/// groups, or one per training point when fewer points are available.
pub fn allocate_child_clusters(group_sizes: &[usize], total_clusters: usize) -> Vec<usize> {
    let total_points: u128 = group_sizes.iter().map(|&size| size as u128).sum();
    let target = (total_clusters as u128).min(total_points) as usize;
    if target == 0 {
        return vec![0; group_sizes.len()];
    }

    let populated = group_sizes.iter().filter(|&&size| size > 0).count();
    let guarantee_populated = target >= populated;
    let mut allocated = vec![0usize; group_sizes.len()];
    let mut fixed = vec![false; group_sizes.len()];
    let mut fixed_cells = 0usize;

    if guarantee_populated {
        // Solve the lower-bounded proportional allocation
        //
        //     allocation_i = max(1, lambda * group_size_i)
        //
        // by successively fixing cells whose unconstrained quota is at most
        // one. This avoids letting the one-per-parent guarantee distort a
        // 90/10 population into an 80/20 child split.
        loop {
            let active_weight: u128 = group_sizes
                .iter()
                .enumerate()
                .filter(|(index, size)| **size > 0 && !fixed[*index])
                .map(|(_, &size)| size as u128)
                .sum();
            let active_target = target - fixed_cells;
            if active_weight == 0 || active_target == 0 {
                break;
            }
            let newly_fixed = group_sizes
                .iter()
                .enumerate()
                .filter_map(|(index, &size)| {
                    (size > 0
                        && !fixed[index]
                        && (size as u128) * (active_target as u128) <= active_weight)
                        .then_some(index)
                })
                .collect::<Vec<_>>();
            if newly_fixed.is_empty() {
                break;
            }
            for index in newly_fixed {
                fixed[index] = true;
                allocated[index] = 1;
                fixed_cells += 1;
            }
        }
    }

    let remaining = target - fixed_cells;
    if remaining == 0 {
        return allocated;
    }
    let active_weight: u128 = group_sizes
        .iter()
        .enumerate()
        .filter(|(index, size)| **size > 0 && !fixed[*index])
        .map(|(_, &size)| size as u128)
        .sum();
    debug_assert!(active_weight > 0);

    let mut remainders = Vec::with_capacity(group_sizes.len());
    for (index, &size) in group_sizes.iter().enumerate() {
        if size == 0 || fixed[index] {
            continue;
        }
        let numerator = (remaining as u128) * (size as u128);
        let whole = (numerator / active_weight) as usize;
        allocated[index] = whole;
        if whole < size {
            remainders.push((index, numerator % active_weight));
        }
    }

    let remainder_cells = target - allocated.iter().sum::<usize>();
    remainders.sort_unstable_by(|(left_index, left), (right_index, right)| {
        right.cmp(left).then_with(|| left_index.cmp(right_index))
    });
    debug_assert!(remainder_cells <= remainders.len());
    for (index, _) in remainders.into_iter().take(remainder_cells) {
        allocated[index] += 1;
    }
    debug_assert_eq!(allocated.iter().sum::<usize>(), target);
    debug_assert!(
        allocated
            .iter()
            .zip(group_sizes)
            .all(|(&cells, &size)| cells <= size)
    );
    allocated
}

/// A centroid selection computed once and reused by every segment.
#[derive(Debug, Clone, PartialEq, Eq)]
pub struct IvfProbePlan {
    pub quantizer_version: u64,
    /// Hash of the query, routing mode, and requested leaf count. This keeps a
    /// reused mutable query object from accidentally reusing an older route.
    pub request_fingerprint: u64,
    pub cluster_ids: Arc<[u32]>,
}

impl IvfProbePlan {
    pub fn new(quantizer_version: u64, request_fingerprint: u64, cluster_ids: Vec<u32>) -> Self {
        Self {
            quantizer_version,
            request_fingerprint,
            cluster_ids: cluster_ids.into(),
        }
    }
}

fn fingerprint_words(
    mode: IvfRoutingMode,
    nprobe: usize,
    words: impl IntoIterator<Item = u64>,
) -> u64 {
    // FNV-1a with an extra avalanche. This is a cache key, not a persisted
    // identity or an adversarial hash table key.
    let mut hash = 0xcbf2_9ce4_8422_2325u64;
    let mode_tag = match mode {
        IvfRoutingMode::Auto => 0u64,
        IvfRoutingMode::Flat => 1,
        IvfRoutingMode::TwoLevel => 2,
        IvfRoutingMode::Hnsw => 3,
    };
    for word in std::iter::once(mode_tag)
        .chain(std::iter::once(nprobe as u64))
        .chain(words)
    {
        hash ^= word;
        hash = hash.wrapping_mul(0x0000_0100_0000_01b3);
    }
    hash ^= hash >> 33;
    hash = hash.wrapping_mul(0xff51_afd7_ed55_8ccd);
    hash ^ (hash >> 33)
}

pub fn float_probe_fingerprint(query: &[f32], nprobe: usize, mode: IvfRoutingMode) -> u64 {
    fingerprint_words(
        mode,
        nprobe,
        query.iter().map(|value| value.to_bits() as u64),
    )
}

pub(crate) fn normalize_cosine_in_place(vector: &mut [f32]) {
    let norm = crate::structures::simd::dot_product_f32(vector, vector, vector.len()).sqrt();
    let inverse_norm = if norm.is_finite() && norm > 0.0 {
        1.0 / norm
    } else {
        0.0
    };
    vector.iter_mut().for_each(|value| *value *= inverse_norm);
}

pub(crate) fn normalized_cosine_query(query: &[f32]) -> Vec<f32> {
    let mut normalized = query.to_vec();
    normalize_cosine_in_place(&mut normalized);
    normalized
}

pub(crate) fn cosine_probe_fingerprint(query: &[f32], nprobe: usize, mode: IvfRoutingMode) -> u64 {
    let norm = crate::structures::simd::dot_product_f32(query, query, query.len()).sqrt();
    let inverse_norm = if norm.is_finite() && norm > 0.0 {
        1.0 / norm
    } else {
        0.0
    };
    fingerprint_words(
        mode,
        nprobe,
        query
            .iter()
            .map(|value| (value * inverse_norm).to_bits() as u64),
    )
}

pub fn binary_probe_fingerprint(query: &[u8], nprobe: usize, mode: IvfRoutingMode) -> u64 {
    fingerprint_words(mode, nprobe, query.iter().map(|&value| value as u64))
}

/// Resolve `Auto` for float centroids.
#[inline]
pub fn effective_routing_mode(mode: IvfRoutingMode, num_leaves: usize) -> IvfRoutingMode {
    resolve_auto_routing(mode, num_leaves, HNSW_AUTO_THRESHOLD)
}

/// Resolve `Auto` for packed binary centroids, whose flat pass stays cheap much
/// further up the leaf-count range.
///
/// Every binary site — training, validation, probing and assignment — must use
/// this, or a codebook trained without a graph would be asked to route through
/// one.
#[inline]
pub fn effective_binary_routing_mode(mode: IvfRoutingMode, num_leaves: usize) -> IvfRoutingMode {
    resolve_auto_routing(mode, num_leaves, BINARY_HNSW_AUTO_THRESHOLD)
}

#[inline]
fn resolve_auto_routing(
    mode: IvfRoutingMode,
    num_leaves: usize,
    auto_threshold: usize,
) -> IvfRoutingMode {
    match mode {
        IvfRoutingMode::Auto if num_leaves >= auto_threshold => IvfRoutingMode::Hnsw,
        IvfRoutingMode::Auto => IvfRoutingMode::Flat,
        explicit => explicit,
    }
}

/// Number of parent cells to put in the routing beam.
pub fn parent_probe_count(nprobe: usize, num_leaves: usize, num_parents: usize) -> usize {
    if num_parents == 0 || num_leaves == 0 {
        return 0;
    }
    let leaves_per_parent = num_leaves.div_ceil(num_parents).max(1);
    nprobe
        .saturating_mul(PARENT_BEAM_OVERSAMPLE)
        .div_ceil(leaves_per_parent)
        .clamp(1, num_parents)
}

/// Select the closest parent beam while guaranteeing enough child leaves to
/// satisfy the requested leaf budget. The usual oversubscribed beam remains
/// the fast path; only an uneven topology that underfills the budget pays for
/// ranking additional parents.
pub fn select_parent_beam<const HIGHER_IS_BETTER: bool>(
    scores: &[f32],
    topology: &IvfRoutingTopology,
    requested_leaves: usize,
) -> Vec<u32> {
    let parent_count = scores.len().min(topology.parent_count());
    let leaf_count = topology.leaf_ids.len();
    let requested_leaves = requested_leaves.min(leaf_count);
    if parent_count == 0 || requested_leaves == 0 {
        return Vec::new();
    }

    let initial_take =
        parent_probe_count(requested_leaves, leaf_count, parent_count).min(parent_count);
    let scores = &scores[..parent_count];
    let initial = select_best::<HIGHER_IS_BETTER>(scores, initial_take);
    let initial_coverage: usize = initial
        .iter()
        .map(|&parent| topology.children(parent as usize).len())
        .sum();
    if initial_coverage >= requested_leaves || initial_take == parent_count {
        return initial;
    }

    let mut ranked = select_best::<HIGHER_IS_BETTER>(scores, parent_count);
    let mut coverage = 0usize;
    let mut take = parent_count;
    for (index, &parent) in ranked.iter().enumerate() {
        coverage = coverage.saturating_add(topology.children(parent as usize).len());
        if index + 1 >= initial_take && coverage >= requested_leaves {
            take = index + 1;
            break;
        }
    }
    ranked.truncate(take);
    ranked
}

/// Select a construction-time parent beam without narrowing query routing.
///
/// The query beam remains the lower bound for leaf coverage, while offline
/// construction inspects at least four populated parents when available. Empty
/// parents are removed because they contribute no leaf candidates.
pub fn select_parent_beam_for_build<const HIGHER_IS_BETTER: bool>(
    scores: &[f32],
    topology: &IvfRoutingTopology,
    requested_leaves: usize,
) -> Vec<u32> {
    if requested_leaves == 0 {
        return Vec::new();
    }
    let parent_count = scores.len().min(topology.parent_count());
    if parent_count == 0 {
        return Vec::new();
    }

    let query_parents = select_parent_beam::<HIGHER_IS_BETTER>(scores, topology, requested_leaves);
    let query_populated = query_parents
        .iter()
        .filter(|&&parent| !topology.children(parent as usize).is_empty())
        .count();

    let scores = &scores[..parent_count];
    let mut ranked = select_best::<HIGHER_IS_BETTER>(scores, parent_count);
    ranked.retain(|&parent| !topology.children(parent as usize).is_empty());
    let take = query_populated
        .max(MIN_BUILD_PARENT_BEAM.min(ranked.len()))
        .min(ranked.len());
    ranked.truncate(take);
    ranked
}

/// Deterministically select the best score indexes without fully sorting the
/// input. `HIGHER_IS_BETTER` covers Hamming similarity; `false` covers L2.
pub fn select_best<const HIGHER_IS_BETTER: bool>(scores: &[f32], take: usize) -> Vec<u32> {
    let take = take.min(scores.len());
    if take == 0 {
        return Vec::new();
    }
    let mut order: Vec<u32> = (0..scores.len() as u32).collect();
    let compare = |left: &u32, right: &u32| {
        let left_score = scores[*left as usize];
        let right_score = scores[*right as usize];
        let score_order = if HIGHER_IS_BETTER {
            right_score.total_cmp(&left_score)
        } else {
            left_score.total_cmp(&right_score)
        };
        score_order.then_with(|| left.cmp(right))
    };
    if take < order.len() {
        order.select_nth_unstable_by(take, compare);
        order.truncate(take);
    }
    order.sort_unstable_by(compare);
    order
}

/// Select leaf IDs from a scored candidate set. Candidate IDs need not be
/// contiguous, which lets both metrics share the exact same two-level beam
/// implementation.
pub fn select_best_candidates<const HIGHER_IS_BETTER: bool>(
    candidates: &mut Vec<(u32, f32)>,
    take: usize,
) -> Vec<u32> {
    let take = take.min(candidates.len());
    if take == 0 {
        return Vec::new();
    }
    let compare = |left: &(u32, f32), right: &(u32, f32)| {
        let score_order = if HIGHER_IS_BETTER {
            right.1.total_cmp(&left.1)
        } else {
            left.1.total_cmp(&right.1)
        };
        score_order.then_with(|| left.0.cmp(&right.0))
    };
    if take < candidates.len() {
        candidates.select_nth_unstable_by(take, compare);
        candidates.truncate(take);
    }
    candidates.sort_unstable_by(compare);
    candidates
        .iter()
        .map(|(cluster_id, _)| *cluster_id)
        .collect()
}

#[cfg(test)]
mod tests {
    use super::*;

    /// For binary centroids, `Auto` must not pick the graph where an exact flat
    /// scan is both faster and more accurate; the switch point comes from the
    /// measured crossover documented on `BINARY_HNSW_AUTO_THRESHOLD`. The float
    /// threshold is separate because float leaves are ~10x wider per centroid.
    #[test]
    fn auto_routing_prefers_exact_flat_probing_below_the_measured_crossover() {
        for leaves in [1usize, 4_096, 16_384, BINARY_HNSW_AUTO_THRESHOLD - 1] {
            assert_eq!(
                effective_binary_routing_mode(IvfRoutingMode::Auto, leaves),
                IvfRoutingMode::Flat,
                "{leaves} binary leaves"
            );
        }
        for leaves in [BINARY_HNSW_AUTO_THRESHOLD, 114_309] {
            assert_eq!(
                effective_binary_routing_mode(IvfRoutingMode::Auto, leaves),
                IvfRoutingMode::Hnsw,
                "{leaves} binary leaves"
            );
        }
        // Float routing keeps its own, lower threshold.
        assert_eq!(
            effective_routing_mode(IvfRoutingMode::Auto, HNSW_AUTO_THRESHOLD),
            IvfRoutingMode::Hnsw
        );
        assert_eq!(
            effective_routing_mode(IvfRoutingMode::Auto, HNSW_AUTO_THRESHOLD - 1),
            IvfRoutingMode::Flat
        );
        // Explicit modes are honoured at any size, and large codebooks still
        // train hierarchically even when routing stays flat.
        for leaves in [64usize, 1_000_000] {
            assert_eq!(
                effective_binary_routing_mode(IvfRoutingMode::Hnsw, leaves),
                IvfRoutingMode::Hnsw
            );
            assert_eq!(
                effective_binary_routing_mode(IvfRoutingMode::TwoLevel, leaves),
                IvfRoutingMode::TwoLevel
            );
        }
        const {
            assert!(HIERARCHICAL_TRAINING_THRESHOLD <= BINARY_HNSW_AUTO_THRESHOLD);
        }
    }

    #[test]
    fn deterministic_selection_supports_both_metric_directions() {
        let scores = [0.5, 0.9, 0.1, 0.9];
        assert_eq!(select_best::<true>(&scores, 2), vec![1, 3]);
        assert_eq!(select_best::<false>(&scores, 2), vec![2, 0]);
    }

    #[test]
    fn two_level_beam_is_oversubscribed_but_bounded() {
        assert_eq!(parent_probe_count(32, 65_536, 256), 1);
        assert_eq!(parent_probe_count(256, 65_536, 256), 4);
        assert_eq!(parent_probe_count(65_536, 65_536, 256), 256);
    }

    #[test]
    fn two_level_beam_expands_until_skewed_parents_cover_leaf_budget() {
        let mut children: Vec<Vec<u32>> = (0..9).map(|leaf| vec![leaf]).collect();
        children.push((9..100).collect());
        let topology = IvfRoutingTopology::from_children(&children);

        // The average-size heuristic initially chooses two parents. The four
        // closest parents contain only one leaf each, so the beam must expand
        // to four to honor nprobe=4.
        let lower_is_better: Vec<f32> = (0..10).map(|score| score as f32).collect();
        assert_eq!(
            select_parent_beam::<false>(&lower_is_better, &topology, 4),
            vec![0, 1, 2, 3]
        );

        let higher_is_better: Vec<f32> = (0..10).rev().map(|score| score as f32).collect();
        assert_eq!(
            select_parent_beam::<true>(&higher_is_better, &topology, 4),
            vec![0, 1, 2, 3]
        );
    }

    #[test]
    fn build_parent_beam_uses_four_populated_parents_when_query_uses_one() {
        let children: Vec<Vec<u32>> = (0..4)
            .map(|parent| {
                let first = parent * 512;
                (first..first + 512).map(|leaf| leaf as u32).collect()
            })
            .collect();
        let topology = IvfRoutingTopology::from_children(&children);

        let lower_is_better = [0.0, 1.0, 2.0, 3.0];
        assert_eq!(
            select_parent_beam::<false>(&lower_is_better, &topology, 128),
            vec![0]
        );
        assert_eq!(
            select_parent_beam_for_build::<false>(&lower_is_better, &topology, 128),
            vec![0, 1, 2, 3]
        );

        let higher_is_better = [4.0, 3.0, 2.0, 1.0];
        assert_eq!(
            select_parent_beam::<true>(&higher_is_better, &topology, 128),
            vec![0]
        );
        assert_eq!(
            select_parent_beam_for_build::<true>(&higher_is_better, &topology, 128),
            vec![0, 1, 2, 3]
        );
    }

    #[test]
    fn build_parent_beam_uses_every_available_populated_parent() {
        let children = vec![vec![0], vec![], vec![1], vec![], vec![2]];
        let topology = IvfRoutingTopology::from_children(&children);
        let scores = [1.0, 0.0, 2.0, -1.0, 3.0];

        assert_eq!(
            select_parent_beam_for_build::<false>(&scores, &topology, 1),
            vec![0, 2, 4]
        );
    }

    #[test]
    fn child_allocation_uses_largest_remainders_instead_of_largest_parent() {
        assert_eq!(allocate_child_clusters(&[100, 90], 4), vec![2, 2]);
        assert_eq!(allocate_child_clusters(&[5, 5, 5], 5), vec![2, 2, 1]);
        assert_eq!(allocate_child_clusters(&[90, 10], 10), vec![9, 1]);
    }

    #[test]
    fn child_allocation_is_exact_capacity_bounded_and_deterministic() {
        assert_eq!(
            allocate_child_clusters(&[1, 100, 7, 0], 100),
            vec![1, 93, 6, 0]
        );
        assert_eq!(allocate_child_clusters(&[1, 2, 0], 10), vec![1, 2, 0]);
        assert_eq!(allocate_child_clusters(&[10, 9, 8], 2), vec![1, 1, 0]);

        for target in 0..=140 {
            let sizes = [100, 30, 0, 7];
            let allocation = allocate_child_clusters(&sizes, target);
            assert_eq!(
                allocation.iter().sum::<usize>(),
                target.min(sizes.iter().sum())
            );
            assert!(
                allocation
                    .iter()
                    .zip(sizes)
                    .all(|(&cells, size)| cells <= size)
            );
            if target >= sizes.iter().filter(|&&size| size > 0).count() {
                assert!(
                    allocation
                        .iter()
                        .zip(sizes)
                        .all(|(&cells, size)| size == 0 || cells > 0)
                );
            }
        }
    }

    #[test]
    fn compact_hnsw_routes_without_copying_points() {
        let points: Vec<[f32; 2]> = (0..512)
            .map(|index| {
                let angle = index as f32 * std::f32::consts::TAU / 512.0;
                [angle.cos(), angle.sin()]
            })
            .collect();
        let distance = |left: u32, right: u32| {
            let [lx, ly] = points[left as usize];
            let [rx, ry] = points[right as usize];
            (lx - rx).powi(2) + (ly - ry).powi(2)
        };
        let graph = HnswRoutingGraph::build(points.len(), distance, 42);
        assert!(graph.validate(points.len()));
        assert!(graph.size_bytes() < points.len() * 512);

        let query = [0.37f32, -0.91];
        let query_distance_calls = std::cell::Cell::new(0usize);
        let routed = graph.search(
            |node| {
                query_distance_calls.set(query_distance_calls.get() + 1);
                let [x, y] = points[node as usize];
                (x - query[0]).powi(2) + (y - query[1]).powi(2)
            },
            10,
        );
        let mut exact: Vec<u32> = (0..points.len() as u32).collect();
        exact.sort_unstable_by(|&left, &right| {
            let score = |node: u32| {
                let [x, y] = points[node as usize];
                (x - query[0]).powi(2) + (y - query[1]).powi(2)
            };
            score(left)
                .total_cmp(&score(right))
                .then_with(|| left.cmp(&right))
        });
        assert_eq!(routed, exact[..10]);

        let build_distance_calls = std::cell::Cell::new(0usize);
        let build_routed = graph.search_for_build(
            |node| {
                build_distance_calls.set(build_distance_calls.get() + 1);
                let [x, y] = points[node as usize];
                (x - query[0]).powi(2) + (y - query[1]).powi(2)
            },
            10,
        );
        assert_eq!(build_routed, exact[..10]);
        // Both budgets share the same floor, so a small take costs the same
        // either way; construction only widens once its oversample exceeds the
        // floor. The floor is what per-vector assignment pays, and it is set
        // from measured recall (see
        // `index::binary_ivf::tests::hnsw_build_beam_recall_saturates_before_the_floor`).
        assert_eq!(build_distance_calls.get(), query_distance_calls.get());

        let wide_query_calls = std::cell::Cell::new(0usize);
        graph.search(
            |node| {
                wide_query_calls.set(wide_query_calls.get() + 1);
                let [x, y] = points[node as usize];
                (x - query[0]).powi(2) + (y - query[1]).powi(2)
            },
            64,
        );
        let wide_build_calls = std::cell::Cell::new(0usize);
        graph.search_for_build(
            |node| {
                wide_build_calls.set(wide_build_calls.get() + 1);
                let [x, y] = points[node as usize];
                (x - query[0]).powi(2) + (y - query[1]).powi(2)
            },
            64,
        );
        assert!(
            wide_build_calls.get() > wide_query_calls.get(),
            "multi-candidate construction should spend its wider search budget"
        );

        // Single-candidate assignment returns the same leaf the ranked search
        // would have put first, without allocating a result list.
        let assigned = graph.search_best_for_build(|node| {
            let [x, y] = points[node as usize];
            (x - query[0]).powi(2) + (y - query[1]).powi(2)
        });
        assert_eq!(assigned, Some(exact[0]));

        let bytes = bincode::serde::encode_to_vec(&graph, bincode::config::standard()).unwrap();
        let (decoded, consumed): (HnswRoutingGraph, usize) =
            bincode::serde::decode_from_slice(&bytes, bincode::config::standard()).unwrap();
        assert_eq!(consumed, bytes.len());
        assert!(decoded.validate(points.len()));

        let mut corrupted = decoded;
        corrupted.node_offsets[1] = u32::MAX;
        assert!(!corrupted.validate(points.len()));
    }
}