ab_proof_of_space/chiapos/

table.rs

#[cfg(test)]
mod tests;
pub(super) mod types;

#[cfg(not(feature = "std"))]
extern crate alloc;

use crate::chiapos::Seed;
use crate::chiapos::constants::{PARAM_B, PARAM_BC, PARAM_C, PARAM_EXT, PARAM_M};
use crate::chiapos::table::types::{Metadata, Position, X, Y};
use crate::chiapos::utils::EvaluatableUsize;
#[cfg(not(feature = "std"))]
use alloc::vec;
#[cfg(not(feature = "std"))]
use alloc::vec::Vec;
use chacha20::cipher::{KeyIvInit, StreamCipher, StreamCipherSeek};
use chacha20::{ChaCha8, Key, Nonce};
use core::array;
use core::simd::Simd;
use core::simd::num::SimdUint;
#[cfg(all(feature = "std", any(feature = "parallel", test)))]
use parking_lot::Mutex;
#[cfg(any(feature = "parallel", test))]
use rayon::prelude::*;
use seq_macro::seq;
#[cfg(all(not(feature = "std"), any(feature = "parallel", test)))]
use spin::Mutex;

pub(super) const COMPUTE_F1_SIMD_FACTOR: usize = 8;
pub(super) const FIND_MATCHES_AND_COMPUTE_UNROLL_FACTOR: usize = 8;

/// Compute the size of `y` in bits
pub(super) const fn y_size_bits(k: u8) -> usize {
    k as usize + PARAM_EXT as usize
}

/// Metadata size in bytes
pub const fn metadata_size_bytes(k: u8, table_number: u8) -> usize {
    metadata_size_bits(k, table_number).div_ceil(u8::BITS as usize)
}

/// Metadata size in bits
pub(super) const fn metadata_size_bits(k: u8, table_number: u8) -> usize {
    k as usize
        * match table_number {
            1 => 1,
            2 => 2,
            3 | 4 => 4,
            5 => 3,
            6 => 2,
            7 => 0,
            _ => unreachable!(),
        }
}

/// ChaCha8 [`Vec`] sufficient for the whole first table for [`K`].
/// Prefer [`partial_y`] if you need partial y just for a single `x`.
fn partial_ys<const K: u8>(seed: Seed) -> Vec<u8> {
    let output_len_bits = usize::from(K) * (1 << K);
    let mut output = vec![0; output_len_bits.div_ceil(u8::BITS as usize)];

    let key = Key::from(seed);
    let nonce = Nonce::default();

    let mut cipher = ChaCha8::new(&key, &nonce);

    cipher.apply_keystream(&mut output);

    output
}

/// ChaCha8 byte for a single `y` at `x` in the first table for [`K`], returns bytes and offset (in
/// bits) within those bytes at which data start.
/// Prefer [`partial_ys`] if you process the whole first table.
pub(super) fn partial_y<const K: u8>(
    seed: Seed,
    x: X,
) -> ([u8; (K as usize * 2).div_ceil(u8::BITS as usize)], usize) {
    let skip_bits = usize::from(K) * usize::from(x);
    let skip_bytes = skip_bits / u8::BITS as usize;
    let skip_bits = skip_bits % u8::BITS as usize;

    let mut output = [0; (K as usize * 2).div_ceil(u8::BITS as usize)];

    let key = Key::from(seed);
    let nonce = Nonce::default();

    let mut cipher = ChaCha8::new(&key, &nonce);

    cipher.seek(skip_bytes);
    cipher.apply_keystream(&mut output);

    (output, skip_bits)
}

#[derive(Debug, Clone)]
struct LeftTargets {
    left_targets: Vec<Position>,
}

fn calculate_left_targets() -> LeftTargets {
    let mut left_targets = Vec::with_capacity(2 * usize::from(PARAM_BC) * usize::from(PARAM_M));

    let param_b = u32::from(PARAM_B);
    let param_c = u32::from(PARAM_C);

    for parity in 0..=1u32 {
        for r in 0..u32::from(PARAM_BC) {
            let c = r / param_c;

            for m in 0..u32::from(PARAM_M) {
                let target = ((c + m) % param_b) * param_c
                    + (((2 * m + parity) * (2 * m + parity) + r) % param_c);
                left_targets.push(Position::from(target));
            }
        }
    }

    LeftTargets { left_targets }
}

fn calculate_left_target_on_demand(parity: u32, r: u32, m: u32) -> u32 {
    let param_b = u32::from(PARAM_B);
    let param_c = u32::from(PARAM_C);

    let c = r / param_c;

    ((c + m) % param_b) * param_c + (((2 * m + parity) * (2 * m + parity) + r) % param_c)
}

/// Caches that can be used to optimize creation of multiple [`Tables`](super::Tables).
#[derive(Debug, Clone)]
pub struct TablesCache<const K: u8> {
    buckets: Vec<Bucket>,
    rmap_scratch: Vec<RmapItem>,
    left_targets: LeftTargets,
}

impl<const K: u8> Default for TablesCache<K> {
    /// Create new instance
    fn default() -> Self {
        Self {
            buckets: Vec::new(),
            rmap_scratch: Vec::new(),
            left_targets: calculate_left_targets(),
        }
    }
}

#[derive(Debug)]
struct Match {
    left_position: Position,
    left_y: Y,
    right_position: Position,
}

#[derive(Debug, Default, Copy, Clone, Eq, PartialEq)]
struct Bucket {
    /// Bucket index
    bucket_index: u32,
    /// Start position of this bucket in the table
    start_position: Position,
    /// Size of this bucket
    size: Position,
}

#[derive(Debug, Default, Copy, Clone)]
pub(super) struct RmapItem {
    count: Position,
    start_position: Position,
}

/// `partial_y_offset` is in bits
pub(super) fn compute_f1<const K: u8>(x: X, partial_y: &[u8], partial_y_offset: usize) -> Y {
    let partial_y_length =
        (partial_y_offset % u8::BITS as usize + usize::from(K)).div_ceil(u8::BITS as usize);
    let mut pre_y_bytes = 0u64.to_be_bytes();
    pre_y_bytes[..partial_y_length]
        .copy_from_slice(&partial_y[partial_y_offset / u8::BITS as usize..][..partial_y_length]);
    // Contains `K` desired bits of `partial_y` in the final offset of eventual `y` with the rest
    // of bits being in undefined state
    let pre_y = u64::from_be_bytes(pre_y_bytes)
        >> (u64::BITS as usize - usize::from(K + PARAM_EXT) - partial_y_offset % u8::BITS as usize);
    let pre_y = pre_y as u32;
    // Mask for clearing the rest of bits of `pre_y`.
    let pre_y_mask = (u32::MAX << usize::from(PARAM_EXT))
        & (u32::MAX >> (u32::BITS as usize - usize::from(K + PARAM_EXT)));

    // Extract `PARAM_EXT` most significant bits from `x` and store in the final offset of
    // eventual `y` with the rest of bits being in undefined state.
    let pre_ext = u32::from(x) >> (usize::from(K - PARAM_EXT));
    // Mask for clearing the rest of bits of `pre_ext`.
    let pre_ext_mask = u32::MAX >> (u32::BITS as usize - usize::from(PARAM_EXT));

    // Combine all of the bits together:
    // [padding zero bits][`K` bits rom `partial_y`][`PARAM_EXT` bits from `x`]
    Y::from((pre_y & pre_y_mask) | (pre_ext & pre_ext_mask))
}

pub(super) fn compute_f1_simd<const K: u8>(
    xs: [u32; COMPUTE_F1_SIMD_FACTOR],
    partial_ys: &[u8; K as usize * COMPUTE_F1_SIMD_FACTOR / u8::BITS as usize],
) -> [Y; COMPUTE_F1_SIMD_FACTOR] {
    // Each element contains `K` desired bits of `partial_ys` in the final offset of eventual `ys`
    // with the rest of bits being in undefined state
    let pre_ys_bytes = array::from_fn(|i| {
        let partial_y_offset = i * usize::from(K);
        let partial_y_length =
            (partial_y_offset % u8::BITS as usize + usize::from(K)).div_ceil(u8::BITS as usize);
        let mut pre_y_bytes = 0u64.to_be_bytes();
        pre_y_bytes[..partial_y_length].copy_from_slice(
            &partial_ys[partial_y_offset / u8::BITS as usize..][..partial_y_length],
        );

        u64::from_be_bytes(pre_y_bytes)
    });
    let pre_ys_right_offset = array::from_fn(|i| {
        let partial_y_offset = i as u32 * u32::from(K);
        u64::from(u64::BITS - u32::from(K + PARAM_EXT) - partial_y_offset % u8::BITS)
    });
    let pre_ys = Simd::from_array(pre_ys_bytes) >> Simd::from_array(pre_ys_right_offset);

    // Mask for clearing the rest of bits of `pre_ys`.
    let pre_ys_mask = Simd::splat(
        (u32::MAX << usize::from(PARAM_EXT))
            & (u32::MAX >> (u32::BITS as usize - usize::from(K + PARAM_EXT))),
    );

    // Extract `PARAM_EXT` most significant bits from `xs` and store in the final offset of
    // eventual `ys` with the rest of bits being in undefined state.
    let pre_exts = Simd::from_array(xs) >> Simd::splat(u32::from(K - PARAM_EXT));

    // Combine all of the bits together:
    // [padding zero bits][`K` bits rom `partial_y`][`PARAM_EXT` bits from `x`]
    let ys = (pre_ys.cast() & pre_ys_mask) | pre_exts;

    Y::array_from_repr(ys.to_array())
}

/// `rmap_scratch` is just an optimization to reuse allocations between calls.
///
/// For verification purposes use [`has_match`] instead.
///
/// Returns `None` if either of buckets is empty.
#[allow(clippy::too_many_arguments)]
fn find_matches<T, Map>(
    left_bucket_ys: &[Y],
    left_bucket_start_position: Position,
    right_bucket_ys: &[Y],
    right_bucket_start_position: Position,
    rmap_scratch: &mut Vec<RmapItem>,
    left_targets: &LeftTargets,
    map: Map,
    output: &mut Vec<T>,
) where
    Map: Fn(Match) -> T,
{
    // Clear and set to correct size with zero values
    rmap_scratch.clear();
    rmap_scratch.resize_with(usize::from(PARAM_BC), RmapItem::default);
    let rmap = rmap_scratch;

    // Both left and right buckets can be empty
    let Some(&first_left_bucket_y) = left_bucket_ys.first() else {
        return;
    };
    let Some(&first_right_bucket_y) = right_bucket_ys.first() else {
        return;
    };
    // Since all entries in a bucket are obtained after division by `PARAM_BC`, we can compute
    // quotient more efficiently by subtracting base value rather than computing remainder of
    // division
    let base = (usize::from(first_right_bucket_y) / usize::from(PARAM_BC)) * usize::from(PARAM_BC);
    for (&y, right_position) in right_bucket_ys.iter().zip(right_bucket_start_position..) {
        let r = usize::from(y) - base;

        // Same `y` and as the result `r` can appear in the table multiple times, in which case
        // they'll all occupy consecutive slots in `right_bucket` and all we need to store is just
        // the first position and number of elements.
        if rmap[r].count == Position::ZERO {
            rmap[r].start_position = right_position;
        }
        rmap[r].count += Position::ONE;
    }
    let rmap = rmap.as_slice();

    // Same idea as above, but avoids division by leveraging the fact that each bucket is exactly
    // `PARAM_BC` away from the previous one in terms of divisor by `PARAM_BC`
    let base = base - usize::from(PARAM_BC);
    let parity = (usize::from(first_left_bucket_y) / usize::from(PARAM_BC)) % 2;
    let left_targets_parity = {
        let (a, b) = left_targets
            .left_targets
            .split_at(left_targets.left_targets.len() / 2);
        if parity == 0 { a } else { b }
    };

    for (&y, left_position) in left_bucket_ys.iter().zip(left_bucket_start_position..) {
        let r = usize::from(y) - base;
        let left_targets_r = left_targets_parity
            .chunks_exact(left_targets_parity.len() / usize::from(PARAM_BC))
            .nth(r)
            .expect("r is valid");

        const _: () = {
            assert!(PARAM_M as usize % FIND_MATCHES_AND_COMPUTE_UNROLL_FACTOR == 0);
        };

        for r_targets in left_targets_r
            .array_chunks::<{ FIND_MATCHES_AND_COMPUTE_UNROLL_FACTOR }>()
            .take(usize::from(PARAM_M) / FIND_MATCHES_AND_COMPUTE_UNROLL_FACTOR)
        {
            let _: [(); FIND_MATCHES_AND_COMPUTE_UNROLL_FACTOR] = seq!(N in 0..8 {
                [
                #(
                {
                    let rmap_item = rmap[usize::from(r_targets[N])];

                    for right_position in
                        rmap_item.start_position..rmap_item.start_position + rmap_item.count
                    {
                        let m = Match {
                            left_position,
                            left_y: y,
                            right_position,
                        };
                        output.push(map(m));
                    }
                },
                )*
                ]
            });
        }
    }
}

/// Simplified version of [`find_matches`] for verification purposes.
pub(super) fn has_match(left_y: Y, right_y: Y) -> bool {
    let right_r = u32::from(right_y) % u32::from(PARAM_BC);
    let parity = (u32::from(left_y) / u32::from(PARAM_BC)) % 2;
    let left_r = u32::from(left_y) % u32::from(PARAM_BC);

    let r_targets = array::from_fn::<_, { PARAM_M as usize }, _>(|i| {
        calculate_left_target_on_demand(parity, left_r, i as u32)
    });

    r_targets.contains(&right_r)
}

pub(super) fn compute_fn<const K: u8, const TABLE_NUMBER: u8, const PARENT_TABLE_NUMBER: u8>(
    y: Y,
    left_metadata: Metadata<K, PARENT_TABLE_NUMBER>,
    right_metadata: Metadata<K, PARENT_TABLE_NUMBER>,
) -> (Y, Metadata<K, TABLE_NUMBER>)
where
    EvaluatableUsize<{ metadata_size_bytes(K, PARENT_TABLE_NUMBER) }>: Sized,
    EvaluatableUsize<{ metadata_size_bytes(K, TABLE_NUMBER) }>: Sized,
{
    let left_metadata = u128::from(left_metadata);
    let right_metadata = u128::from(right_metadata);

    let parent_metadata_bits = metadata_size_bits(K, PARENT_TABLE_NUMBER);

    // Only supports `K` from 15 to 25 (otherwise math will not be correct when concatenating y,
    // left metadata and right metadata)
    let hash = {
        // Take only bytes where bits were set
        let num_bytes_with_data = (y_size_bits(K) + metadata_size_bits(K, PARENT_TABLE_NUMBER) * 2)
            .div_ceil(u8::BITS as usize);

        // Collect `K` most significant bits of `y` at the final offset of eventual `input_a`
        let y_bits = u128::from(y) << (u128::BITS as usize - y_size_bits(K));

        // Move bits of `left_metadata` at the final offset of eventual `input_a`
        let left_metadata_bits =
            left_metadata << (u128::BITS as usize - parent_metadata_bits - y_size_bits(K));

        // Part of the `right_bits` at the final offset of eventual `input_a`
        let y_and_left_bits = y_size_bits(K) + parent_metadata_bits;
        let right_bits_start_offset = u128::BITS as usize - parent_metadata_bits;

        // If `right_metadata` bits start to the left of the desired position in `input_a` move
        // bits right, else move left
        if right_bits_start_offset < y_and_left_bits {
            let right_bits_pushed_into_input_b = y_and_left_bits - right_bits_start_offset;
            // Collect bits of `right_metadata` that will fit into `input_a` at the final offset in
            // eventual `input_a`
            let right_bits_a = right_metadata >> right_bits_pushed_into_input_b;
            let input_a = y_bits | left_metadata_bits | right_bits_a;
            // Collect bits of `right_metadata` that will spill over into `input_b`
            let input_b = right_metadata << (u128::BITS as usize - right_bits_pushed_into_input_b);

            let input = [input_a.to_be_bytes(), input_b.to_be_bytes()];
            let input_len =
                size_of::<u128>() + right_bits_pushed_into_input_b.div_ceil(u8::BITS as usize);
            blake3::hash(&input.as_flattened()[..input_len])
        } else {
            let right_bits_a = right_metadata << (right_bits_start_offset - y_and_left_bits);
            let input_a = y_bits | left_metadata_bits | right_bits_a;

            blake3::hash(&input_a.to_be_bytes()[..num_bytes_with_data])
        }
    };
    let hash = <[u8; 32]>::from(hash);

    let y_output = Y::from(
        u32::from_be_bytes([hash[0], hash[1], hash[2], hash[3]])
            >> (u32::BITS as usize - y_size_bits(K)),
    );

    let metadata_size_bits = metadata_size_bits(K, TABLE_NUMBER);

    let metadata = if TABLE_NUMBER < 4 {
        (left_metadata << parent_metadata_bits) | right_metadata
    } else if metadata_size_bits > 0 {
        // For K under 25 it is guaranteed that metadata + bit offset will always fit into u128.
        // We collect bytes necessary, potentially with extra bits at the start and end of the bytes
        // that will be taken care of later.
        let metadata = u128::from_be_bytes(
            hash[y_size_bits(K) / u8::BITS as usize..][..size_of::<u128>()]
                .try_into()
                .expect("Always enough bits for any K; qed"),
        );
        // Remove extra bits at the beginning
        let metadata = metadata << (y_size_bits(K) % u8::BITS as usize);
        // Move bits into correct location
        metadata >> (u128::BITS as usize - metadata_size_bits)
    } else {
        0
    };

    (y_output, Metadata::from(metadata))
}

fn match_to_result<const K: u8, const TABLE_NUMBER: u8, const PARENT_TABLE_NUMBER: u8>(
    last_table: &Table<K, PARENT_TABLE_NUMBER>,
    m: Match,
) -> (Y, [Position; 2], Metadata<K, TABLE_NUMBER>)
where
    EvaluatableUsize<{ metadata_size_bytes(K, PARENT_TABLE_NUMBER) }>: Sized,
    EvaluatableUsize<{ metadata_size_bytes(K, TABLE_NUMBER) }>: Sized,
{
    let left_metadata = last_table
        .metadata(m.left_position)
        .expect("Position resulted from matching is correct; qed");
    let right_metadata = last_table
        .metadata(m.right_position)
        .expect("Position resulted from matching is correct; qed");

    let (y, metadata) =
        compute_fn::<K, TABLE_NUMBER, PARENT_TABLE_NUMBER>(m.left_y, left_metadata, right_metadata);

    (y, [m.left_position, m.right_position], metadata)
}

fn match_and_compute_fn<'a, const K: u8, const TABLE_NUMBER: u8, const PARENT_TABLE_NUMBER: u8>(
    last_table: &'a Table<K, PARENT_TABLE_NUMBER>,
    left_bucket: Bucket,
    right_bucket: Bucket,
    rmap_scratch: &'a mut Vec<RmapItem>,
    left_targets: &'a LeftTargets,
    results_table: &mut Vec<(Y, [Position; 2], Metadata<K, TABLE_NUMBER>)>,
) where
    EvaluatableUsize<{ metadata_size_bytes(K, PARENT_TABLE_NUMBER) }>: Sized,
    EvaluatableUsize<{ metadata_size_bytes(K, TABLE_NUMBER) }>: Sized,
{
    find_matches(
        &last_table.ys()[usize::from(left_bucket.start_position)..]
            [..usize::from(left_bucket.size)],
        left_bucket.start_position,
        &last_table.ys()[usize::from(right_bucket.start_position)..]
            [..usize::from(right_bucket.size)],
        right_bucket.start_position,
        rmap_scratch,
        left_targets,
        |m| match_to_result(last_table, m),
        results_table,
    )
}

#[derive(Debug)]
pub(super) enum Table<const K: u8, const TABLE_NUMBER: u8>
where
    EvaluatableUsize<{ metadata_size_bytes(K, TABLE_NUMBER) }>: Sized,
{
    /// First table with contents of entries split into separate vectors for more efficient access
    First {
        /// Derived values computed from `x`
        ys: Vec<Y>,
        /// X values
        xs: Vec<X>,
    },
    /// Other tables
    Other {
        /// Derived values computed from previous table
        ys: Vec<Y>,
        /// Left and right entry positions in a previous table encoded into bits
        positions: Vec<[Position; 2]>,
        /// Metadata corresponding to each entry
        metadatas: Vec<Metadata<K, TABLE_NUMBER>>,
    },
}

impl<const K: u8> Table<K, 1>
where
    EvaluatableUsize<{ metadata_size_bytes(K, 1) }>: Sized,
{
    /// Create the table
    pub(super) fn create(seed: Seed) -> Self
    where
        EvaluatableUsize<{ K as usize * COMPUTE_F1_SIMD_FACTOR / u8::BITS as usize }>: Sized,
    {
        let partial_ys = partial_ys::<K>(seed);

        let mut t_1 = Vec::with_capacity(1_usize << K);
        for (x_batch, partial_ys) in partial_ys
            .array_chunks::<{ K as usize * COMPUTE_F1_SIMD_FACTOR / u8::BITS as usize }>()
            .copied()
            .enumerate()
        {
            let xs = array::from_fn::<_, COMPUTE_F1_SIMD_FACTOR, _>(|i| {
                (x_batch * COMPUTE_F1_SIMD_FACTOR + i) as u32
            });
            let ys = compute_f1_simd::<K>(xs, &partial_ys);
            t_1.extend(ys.into_iter().zip(X::array_from_repr(xs)));
        }

        t_1.sort_unstable();

        let (ys, xs) = t_1.into_iter().unzip();

        Self::First { ys, xs }
    }

    /// Create the table, leverages available parallelism
    #[cfg(any(feature = "parallel", test))]
    pub(super) fn create_parallel(seed: Seed) -> Self
    where
        EvaluatableUsize<{ K as usize * COMPUTE_F1_SIMD_FACTOR / u8::BITS as usize }>: Sized,
    {
        let partial_ys = partial_ys::<K>(seed);

        let mut t_1 = Vec::with_capacity(1_usize << K);
        for (x_batch, partial_ys) in partial_ys
            .array_chunks::<{ K as usize * COMPUTE_F1_SIMD_FACTOR / u8::BITS as usize }>()
            .copied()
            .enumerate()
        {
            let xs = array::from_fn::<_, COMPUTE_F1_SIMD_FACTOR, _>(|i| {
                (x_batch * COMPUTE_F1_SIMD_FACTOR + i) as u32
            });
            let ys = compute_f1_simd::<K>(xs, &partial_ys);
            t_1.extend(ys.into_iter().zip(X::array_from_repr(xs)));
        }

        t_1.par_sort_unstable();

        let (ys, xs) = t_1.into_iter().unzip();

        Self::First { ys, xs }
    }

    /// All `x`s as [`BitSlice`], for individual `x`s needs to be slices into [`K`] bits slices
    pub(super) fn xs(&self) -> &[X] {
        match self {
            Table::First { xs, .. } => xs,
            _ => {
                unreachable!()
            }
        }
    }
}

mod private {
    pub(in super::super) trait SupportedOtherTables {}
}

impl<const K: u8> private::SupportedOtherTables for Table<K, 2> where
    EvaluatableUsize<{ metadata_size_bytes(K, 2) }>: Sized
{
}

impl<const K: u8> private::SupportedOtherTables for Table<K, 3> where
    EvaluatableUsize<{ metadata_size_bytes(K, 3) }>: Sized
{
}

impl<const K: u8> private::SupportedOtherTables for Table<K, 4> where
    EvaluatableUsize<{ metadata_size_bytes(K, 4) }>: Sized
{
}

impl<const K: u8> private::SupportedOtherTables for Table<K, 5> where
    EvaluatableUsize<{ metadata_size_bytes(K, 5) }>: Sized
{
}

impl<const K: u8> private::SupportedOtherTables for Table<K, 6> where
    EvaluatableUsize<{ metadata_size_bytes(K, 6) }>: Sized
{
}

impl<const K: u8> private::SupportedOtherTables for Table<K, 7> where
    EvaluatableUsize<{ metadata_size_bytes(K, 7) }>: Sized
{
}

impl<const K: u8, const TABLE_NUMBER: u8> Table<K, TABLE_NUMBER>
where
    Self: private::SupportedOtherTables,
    EvaluatableUsize<{ metadata_size_bytes(K, TABLE_NUMBER) }>: Sized,
{
    /// Creates new [`TABLE_NUMBER`] table. There also exists [`Self::create_parallel()`] that
    /// trades CPU efficiency and memory usage for lower latency.
    pub(super) fn create<const PARENT_TABLE_NUMBER: u8>(
        last_table: &Table<K, PARENT_TABLE_NUMBER>,
        cache: &mut TablesCache<K>,
    ) -> Self
    where
        EvaluatableUsize<{ metadata_size_bytes(K, PARENT_TABLE_NUMBER) }>: Sized,
    {
        let buckets = &mut cache.buckets;
        let rmap_scratch = &mut cache.rmap_scratch;
        let left_targets = &cache.left_targets;

        let mut bucket = Bucket {
            bucket_index: 0,
            start_position: Position::ZERO,
            size: Position::ZERO,
        };

        let last_y = *last_table
            .ys()
            .last()
            .expect("List of y values is never empty; qed");
        buckets.clear();
        buckets.reserve(1 + usize::from(last_y) / usize::from(PARAM_BC));
        last_table
            .ys()
            .iter()
            .zip(Position::ZERO..)
            .for_each(|(&y, position)| {
                let bucket_index = u32::from(y) / u32::from(PARAM_BC);

                if bucket_index == bucket.bucket_index {
                    bucket.size += Position::ONE;
                    return;
                }

                buckets.push(bucket);

                bucket = Bucket {
                    bucket_index,
                    start_position: position,
                    size: Position::ONE,
                };
            });
        // Iteration stopped, but we did not store the last bucket yet
        buckets.push(bucket);

        let num_values = 1 << K;
        let mut t_n = Vec::with_capacity(num_values);
        buckets
            .array_windows::<2>()
            .for_each(|&[left_bucket, right_bucket]| {
                match_and_compute_fn::<K, TABLE_NUMBER, PARENT_TABLE_NUMBER>(
                    last_table,
                    left_bucket,
                    right_bucket,
                    rmap_scratch,
                    left_targets,
                    &mut t_n,
                );
            });

        t_n.sort_unstable();

        let mut ys = Vec::with_capacity(t_n.len());
        let mut positions = Vec::with_capacity(t_n.len());
        let mut metadatas = Vec::with_capacity(t_n.len());

        for (y, [left_position, right_position], metadata) in t_n {
            ys.push(y);
            positions.push([left_position, right_position]);
            // Last table doesn't have metadata
            if metadata_size_bits(K, TABLE_NUMBER) > 0 {
                metadatas.push(metadata);
            }
        }

        Self::Other {
            ys,
            positions,
            metadatas,
        }
    }

    /// Almost the same as [`Self::create()`], but uses parallelism internally for better
    /// performance (though not efficiency of CPU and memory usage), if you create multiple tables
    /// in parallel, prefer [`Self::create()`] for better overall performance.
    #[cfg(any(feature = "parallel", test))]
    pub(super) fn create_parallel<const PARENT_TABLE_NUMBER: u8>(
        last_table: &Table<K, PARENT_TABLE_NUMBER>,
        cache: &mut TablesCache<K>,
    ) -> Self
    where
        EvaluatableUsize<{ metadata_size_bytes(K, PARENT_TABLE_NUMBER) }>: Sized,
    {
        let left_targets = &cache.left_targets;

        let mut first_bucket = Bucket {
            bucket_index: u32::from(last_table.ys()[0]) / u32::from(PARAM_BC),
            start_position: Position::ZERO,
            size: Position::ZERO,
        };
        for &y in last_table.ys() {
            let bucket_index = u32::from(y) / u32::from(PARAM_BC);

            if bucket_index == first_bucket.bucket_index {
                first_bucket.size += Position::ONE;
            } else {
                break;
            }
        }

        let previous_bucket = Mutex::new(first_bucket);

        let t_n = rayon::broadcast(|_ctx| {
            let mut entries = Vec::new();
            let mut rmap_scratch = Vec::new();

            loop {
                let left_bucket;
                let right_bucket;
                {
                    let mut previous_bucket = previous_bucket.lock();

                    let right_bucket_start_position =
                        previous_bucket.start_position + previous_bucket.size;
                    let right_bucket_index = match last_table
                        .ys()
                        .get(usize::from(right_bucket_start_position))
                    {
                        Some(&y) => u32::from(y) / u32::from(PARAM_BC),
                        None => {
                            break;
                        }
                    };
                    let mut right_bucket_size = Position::ZERO;

                    for &y in &last_table.ys()[usize::from(right_bucket_start_position)..] {
                        let bucket_index = u32::from(y) / u32::from(PARAM_BC);

                        if bucket_index == right_bucket_index {
                            right_bucket_size += Position::ONE;
                        } else {
                            break;
                        }
                    }

                    right_bucket = Bucket {
                        bucket_index: right_bucket_index,
                        start_position: right_bucket_start_position,
                        size: right_bucket_size,
                    };

                    left_bucket = *previous_bucket;
                    *previous_bucket = right_bucket;
                }

                match_and_compute_fn::<K, TABLE_NUMBER, PARENT_TABLE_NUMBER>(
                    last_table,
                    left_bucket,
                    right_bucket,
                    &mut rmap_scratch,
                    left_targets,
                    &mut entries,
                );
            }

            entries
        });

        let mut t_n = t_n.into_iter().flatten().collect::<Vec<_>>();
        t_n.par_sort_unstable();

        let mut ys = Vec::with_capacity(t_n.len());
        let mut positions = Vec::with_capacity(t_n.len());
        let mut metadatas = Vec::with_capacity(t_n.len());

        for (y, [left_position, right_position], metadata) in t_n.drain(..) {
            ys.push(y);
            positions.push([left_position, right_position]);
            // Last table doesn't have metadata
            if metadata_size_bits(K, TABLE_NUMBER) > 0 {
                metadatas.push(metadata);
            }
        }

        // Drop from a background thread, which typically helps with overall concurrency
        rayon::spawn(move || {
            drop(t_n);
        });

        Self::Other {
            ys,
            positions,
            metadatas,
        }
    }
}

impl<const K: u8, const TABLE_NUMBER: u8> Table<K, TABLE_NUMBER>
where
    EvaluatableUsize<{ metadata_size_bytes(K, TABLE_NUMBER) }>: Sized,
{
    /// All `y`s as [`BitSlice`], for individual `x`s needs to be slices into [`K`] bits slices
    pub(super) fn ys(&self) -> &[Y] {
        let (Table::First { ys, .. } | Table::Other { ys, .. }) = self;
        ys
    }

    /// Returns `None` on invalid position or first table, `Some(left_position, right_position)` in
    /// previous table on success
    pub(super) fn position(&self, position: Position) -> Option<[Position; 2]> {
        match self {
            Table::First { .. } => None,
            Table::Other { positions, .. } => positions.get(usize::from(position)).copied(),
        }
    }

    /// Returns `None` on invalid position or for table number 7
    pub(super) fn metadata(&self, position: Position) -> Option<Metadata<K, TABLE_NUMBER>> {
        match self {
            Table::First { xs, .. } => xs.get(usize::from(position)).map(|&x| Metadata::from(x)),
            Table::Other { metadatas, .. } => metadatas.get(usize::from(position)).copied(),
        }
    }
}