クラムソートを使用する

クラムソート (crumsort) はフラックスソートと同じく、ピボットで分割して再帰するトップダウン方式のハイブリッド比較ソートである。違いは分割が不安定かつインプレースな点で、補助配列への二重書き込みの代わりにフルクラム(支点)分割を使う。

整列度が高い区間や小区間・不均衡時はクワッドソート(マージソート系)へ切り替える。本番実装は分岐の少ない比較や固定長の小さなスワップ領域(既定で数百要素)を用いるが、本記事の実装は説明用に簡略化している。小区間は挿入ソート、フォールバックは固定スワップと回転ベースのマージで代用し、ピボットは9点の準中央値のみとする。

  1. アナライザ: 全体が昇順なら何もしない。降順(同値を含む非増加)なら反転して終了する(比較・移動とも \(O(n)\))。配列を 4 分割し、各区間の隣接昇順ペアが半数超ならその区間を回転マージソートで仕上げる(本番ではクワッドソート)。
  2. ピボット選択: 区間をほぼ等間隔に 9 点取り、3 組の三点中央値の中央値(準中央値)をピボットにする。
  3. フルクラム分割: ピボット値を 1 要素ぶんの退避スロットに置き、先頭側(head)と末尾側(tail)から走査する。<= ピボット は前方へ、> ピボット は後方へ 2 代入で書き分ける(通常の 3 代入スワップより軽い)。同値の相対順序は保たない。
  4. 等値の第二走査: 右側が空(すべて <= ピボット)なら、< ピボット だけを前方へ寄せて等値帯を再帰から外す。重複の多い入力向けの対策である。
  5. 不均衡フォールバック: 左右の長さ比が 1:16 を超えて偏ったら、両側を回転マージソートする(本番ではクワッドソート)。最悪計算量を \(O(n \log n)\) に抑えるためのガードである。
  6. 小区間: 要素数が閾値未満なら挿入ソートで仕上げる(本番の閾値付近ではクワッドソートの小区間ルーチン)。
procedure crum_fulcrum_partition(A, pivot)
  // A[0] にピボットを置き、値はローカルへ退避(1 要素の swap 領域)
  move pivot into A[0]; pivot_val := A[0]
  head := 0; tail := length(A) - 1
  loop
    while head < tail and A[tail] > pivot_val
      tail := tail - 1
    if head >= tail then
      A[head] := pivot_val; return head
    A[head] := A[tail]; head := head + 1
    while head < tail and A[head] <= pivot_val
      head := head + 1
    if head >= tail then
      A[head] := pivot_val; return head
    A[tail] := A[head]; tail := tail - 1

procedure crum_sort_range(A)
  if length(A) < INSERTION_THRESHOLD then
    insertion_sort(A); return
  pivot := quasimedian_of_9(A)
  mid := crum_fulcrum_partition(A, pivot)
  left := mid; right := length(A) - mid - 1
  if right = 0 then
    gather keys < pivot to front
    crum_sort_range(A[0 .. lt))
    return
  if left < length(A)/16 or right < length(A)/16 then
    rotate_mergesort(A[0 .. left)); rotate_mergesort(A[mid+1 .. end)); return
  crum_sort_range(A[0 .. left))
  crum_sort_range(A[mid+1 .. end))

procedure crumsort(A)
  if A is sorted then return
  if A is reverse-sorted then reverse(A); return
  for each quarter Q of A
    if ordered_pairs(Q) > half then rotate_mergesort(Q)
  if A is sorted then return
  crum_sort_range(A)

最良は整列済み検出により \(O(n)\)、平均・最悪は \(O(n \log n)\) である。分割そのものはインプレースで、補助メモリは固定長スワップ(既定 512 要素)に加え再帰深さ分の \(O(\log n)\) のスタックに抑えられ、不安定である。

以下のデモでは視認性のため挿入閾値を 4、不均衡判定を 1/4 に緩めている。

類似アルゴリズムとの相違点

フラックスソートは安定な二重書き込み分割と最大 \(O(n)\) の補助配列を使う。クラムソートはフルクラム分割で不安定・インプレース寄りにし、ランダム入力では大規模でフラックスソートを追い抜きやすい一方、既存の並びパターンを崩しやすい。

クワッドソートは分割を行わず、ボトムアップのクワッドマージだけで完結する。クラムソートはランダム寄りの入力ではフルクラム分割を主とし、整列度が高い区間・小区間・不均衡時だけクワッドソート系へ寄せる。

ホーア分割型クイックソートも両端から詰めるインプレース分割だが、フルクラムはピボットを 1 要素の退避スロットに置き、3 代入のスワップを 2 代入の書き分けに置き換える。

パターン撃退型クイックソートも悪パターン対策のハイブリッドで不安定・低補助メモリである。クラムソートは先頭アナライザと不均衡時のマージ切替、等値の第二走査を組み合わせる点が近い。

時間計算量および空間計算量を計測する

Size Average time (s) Maximum time (s) Average memory (KiB) Maximum memory (KiB)
256 0.000008 0.000062 0 0
512 0.000016 0.000232 0 0
1024 0.000033 0.000167 0 0
2048 0.000073 0.000134 0 0
4096 0.000167 0.000286 0 0
8192 0.000367 0.001124 0 0
16384 0.000726 0.001117 0 0
32768 0.001562 0.002360 0 0
65536 0.003485 0.006603 0 0
131072 0.007742 0.021650 0 0
262144 0.016572 0.050982 0 0
計測に使用したコードを表示する

#!/usr/bin/env swift
import Foundation

// This standalone Swift driver creates the same temporary Docker build
// context as the former shell wrapper.  The benchmark program itself remains
// embedded below so readers can copy one complete, reproducible file.
struct BenchmarkError: Error, CustomStringConvertible {
    let message: String

    var description: String { message }

    init(_ message: String) {
        self.message = message
    }
}

func runCommand(_ executable: String, _ arguments: [String]) throws {
    let process = Process()
    process.executableURL = URL(fileURLWithPath: "/usr/bin/env")
    process.arguments = [executable] + arguments
    process.standardInput = FileHandle.standardInput
    process.standardOutput = FileHandle.standardOutput
    process.standardError = FileHandle.standardError

    do {
        try process.run()
    } catch {
        throw BenchmarkError("Could not start \(executable): \(error)")
    }
    process.waitUntilExit()
    guard process.terminationStatus == 0 else {
        throw BenchmarkError(
            "Command failed (\(process.terminationStatus)): " +
            "\(executable) \(arguments.joined(separator: " "))"
        )
    }
}

do {
    // The UUID avoids collisions when two benchmark copies are run at once.
    let workdir = FileManager.default.temporaryDirectory
        .appendingPathComponent("swift-sort-benchmark-\(UUID().uuidString)")
    try FileManager.default.createDirectory(at: workdir, withIntermediateDirectories: true)
    defer { try? FileManager.default.removeItem(at: workdir) }

    // A raw Swift string is used so the nested main.swift keeps its own
    // interpolation expressions such as \(seed) until Docker compiles it.
    let dockerfile = #"""
FROM swift:6.0

WORKDIR /app

RUN cat > alloc_track.c <<'ALLOC'
#define _GNU_SOURCE
#include <dlfcn.h>
#include <malloc.h>
#include <stdatomic.h>
#include <stddef.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>

static atomic_size_t live_bytes = 0;
static atomic_size_t peak_bytes = 0;

static void *(*real_malloc)(size_t) = NULL;
static void *(*real_calloc)(size_t, size_t) = NULL;
static void *(*real_realloc)(void *, size_t) = NULL;
static void (*real_free)(void *) = NULL;

static void init_reals(void) {
    if (real_malloc) {
        return;
    }
    real_malloc = (void *(*)(size_t))dlsym(RTLD_NEXT, "malloc");
    real_calloc = (void *(*)(size_t, size_t))dlsym(RTLD_NEXT, "calloc");
    real_realloc = (void *(*)(void *, size_t))dlsym(RTLD_NEXT, "realloc");
    real_free = (void (*)(void *))dlsym(RTLD_NEXT, "free");
}

static void record_alloc(size_t size) {
    size_t live = atomic_fetch_add(&live_bytes, size) + size;
    size_t peak = atomic_load(&peak_bytes);
    while (live > peak) {
        if (atomic_compare_exchange_weak(&peak_bytes, &peak, live)) {
            break;
        }
    }
}

void alloc_track_reset_peak(void) {
    atomic_store(&peak_bytes, atomic_load(&live_bytes));
}

size_t alloc_track_live(void) { return atomic_load(&live_bytes); }
size_t alloc_track_peak(void) { return atomic_load(&peak_bytes); }

void *malloc(size_t size) {
    init_reals();
    void *p = real_malloc(size);
    if (p) {
        record_alloc(malloc_usable_size(p));
    }
    return p;
}

void *calloc(size_t nmemb, size_t size) {
    init_reals();
    void *p = real_calloc(nmemb, size);
    if (p) {
        record_alloc(malloc_usable_size(p));
    }
    return p;
}

void *realloc(void *ptr, size_t size) {
    init_reals();
    size_t old_size = 0;
    if (ptr) {
        old_size = malloc_usable_size(ptr);
    }
    void *p = real_realloc(ptr, size);
    if (p) {
        atomic_fetch_sub(&live_bytes, old_size);
        record_alloc(malloc_usable_size(p));
    } else if (size == 0) {
        atomic_fetch_sub(&live_bytes, old_size);
    }
    return p;
}

void free(void *ptr) {
    init_reals();
    if (ptr) {
        atomic_fetch_sub(&live_bytes, malloc_usable_size(ptr));
        real_free(ptr);
    }
}

ALLOC

RUN cat > main.swift <<'SWIFT'
import Foundation
#if canImport(Glibc)
import Glibc
#elseif canImport(Darwin)
import Darwin
#endif

@_silgen_name("alloc_track_live") func alloc_track_live() -> Int
@_silgen_name("alloc_track_peak") func alloc_track_peak() -> Int
@_silgen_name("alloc_track_reset_peak") func alloc_track_reset_peak()

extension UnsafeMutableBufferPointer where Element == Int {
    func swapAt(_ i: Int, _ j: Int) {
        let t = self[i]; self[i] = self[j]; self[j] = t
    }
}

let MIN_POWER: Int = 8
let MAX_POWER: Int = 18
let RUNS: Int = 8192
func insertion_sort(_ a: inout [Int]) {
    a.withUnsafeMutableBufferPointer { insertion_sort($0) }
}

func insertion_sort(_ a: UnsafeMutableBufferPointer<Int>) {
    if a.count < 2 {
        return
    }
    for i in 1..<a.count {
        var j = i
        while j > 0 && a[j - 1] > a[j] {
            a.swapAt(j - 1, j)
            j -= 1
        }
    }
}



/// Educational stand-in for scandum's crumsort (fulcrum partition + rotate merge).

private let CRUM_SWAP = 512
private let CRUM_INSERTION_THRESHOLD = 24

private func crum_is_sorted(_ a: UnsafeMutableBufferPointer<Int>) -> Bool {
    if a.count < 2 { return true }
    for i in 0..<(a.count - 1) {
        if a[i] > a[i + 1] { return false }
    }
    return true
}

private func crum_is_reverse_sorted(_ a: UnsafeMutableBufferPointer<Int>) -> Bool {
    if a.count < 2 { return true }
    for i in 0..<(a.count - 1) {
        if a[i] < a[i + 1] { return false }
    }
    return true
}

private func crum_reverse(_ a: UnsafeMutableBufferPointer<Int>) {
    var lo = 0
    var hi = a.count
    while lo + 1 < hi {
        hi -= 1
        a.swapAt(lo, hi)
        lo += 1
    }
}

private func crum_ordered_pairs(_ a: UnsafeMutableBufferPointer<Int>) -> Int {
    if a.count < 2 { return 0 }
    var c = 0
    for i in 0..<(a.count - 1) {
        if a[i] <= a[i + 1] { c += 1 }
    }
    return c
}

private func crum_median3_idx(
    _ a: UnsafeMutableBufferPointer<Int>,
    _ i: Int,
    _ j: Int,
    _ k: Int
) -> Int {
    let (x, y, z) = (a[i], a[j], a[k])
    if x < y {
        if y < z {
            return j
        } else if x < z {
            return k
        } else {
            return i
        }
    } else if x < z {
        return i
    } else if y < z {
        return k
    } else {
        return j
    }
}

private func crum_quasimedian9(_ a: UnsafeMutableBufferPointer<Int>) -> Int {
    let n = a.count
    if n < 9 {
        return a[n / 2]
    }
    let step = n / 8
    let i0 = 0
    let i1 = step
    let i2 = step * 2
    let i3 = step * 3
    let i4 = step * 4
    let i5 = step * 5
    let i6 = step * 6
    let i7 = step * 7
    let i8 = n - 1
    let m0 = crum_median3_idx(a, i0, i1, i2)
    let m1 = crum_median3_idx(a, i3, i4, i5)
    let m2 = crum_median3_idx(a, i6, i7, i8)
    return a[crum_median3_idx(a, m0, m1, m2)]
}

private func crum_rotate(
    _ a: UnsafeMutableBufferPointer<Int>,
    _ left: Int,
    _ swap: UnsafeMutableBufferPointer<Int>
) {
    let n = a.count
    if left == 0 || left == n {
        return
    }
    let right = n - left
    let swap_cap = swap.count

    if left <= right {
        if left <= swap_cap {
            for i in 0..<left {
                swap[i] = a[i]
            }
            for i in 0..<right {
                a[i] = a[left + i]
            }
            for i in 0..<left {
                a[right + i] = swap[i]
            }
            return
        }
    } else if right <= swap_cap {
        for i in 0..<right {
            swap[i] = a[left + i]
        }
        for i in stride(from: left - 1, through: 0, by: -1) {
            a[i + right] = a[i]
        }
        for i in 0..<right {
            a[i] = swap[i]
        }
        return
    }

    // three reverses
    var lo = 0
    var hi = left
    while lo + 1 < hi {
        hi -= 1
        a.swapAt(lo, hi)
        lo += 1
    }
    lo = left
    hi = n
    while lo + 1 < hi {
        hi -= 1
        a.swapAt(lo, hi)
        lo += 1
    }
    lo = 0
    hi = n
    while lo + 1 < hi {
        hi -= 1
        a.swapAt(lo, hi)
        lo += 1
    }
}

private func crum_lower_bound(_ hay: UnsafeMutableBufferPointer<Int>, _ needle: Int) -> Int {
    var lo = 0
    var hi = hay.count
    while lo < hi {
        let mid = lo + (hi - lo) / 2
        if hay[mid] < needle {
            lo = mid + 1
        } else {
            hi = mid
        }
    }
    return lo
}

private func crum_merge_with_swap(
    _ a: UnsafeMutableBufferPointer<Int>,
    _ mid: Int,
    _ swap: UnsafeMutableBufferPointer<Int>
) {
    let n = a.count
    for i in 0..<mid {
        swap[i] = a[i]
    }
    var i = 0
    var j = mid
    var k = 0
    while i < mid && j < n {
        if swap[i] <= a[j] {
            a[k] = swap[i]
            i += 1
        } else {
            a[k] = a[j]
            j += 1
        }
        k += 1
    }
    while i < mid {
        a[k] = swap[i]
        i += 1
        k += 1
    }
}

private func crum_rotate_merge_block(
    _ a: UnsafeMutableBufferPointer<Int>,
    _ left_len: Int,
    _ right_len: Int,
    _ swap: UnsafeMutableBufferPointer<Int>
) {
    if left_len == 0 || right_len == 0 {
        return
    }
    if a[left_len - 1] <= a[left_len] {
        return
    }

    let total = left_len + right_len
    let swap_cap = swap.count
    if total <= swap_cap {
        crum_merge_with_swap(a, left_len, swap)
        return
    }
    if left_len <= swap_cap {
        crum_merge_with_swap(a, left_len, swap)
        return
    }
    if right_len <= swap_cap {
        for i in 0..<right_len {
            swap[i] = a[left_len + i]
        }
        var i = left_len
        var j = right_len
        var k = total
        while i > 0 && j > 0 {
            if a[i - 1] > swap[j - 1] {
                k -= 1
                i -= 1
                a[k] = a[i]
            } else {
                k -= 1
                j -= 1
                a[k] = swap[j]
            }
        }
        while j > 0 {
            k -= 1
            j -= 1
            a[k] = swap[j]
        }
        return
    }

    let rblock = left_len / 2
    let lblock = left_len - rblock
    let center = a[lblock]
    let left = crum_lower_bound(
        UnsafeMutableBufferPointer(rebasing: a[left_len..<total]),
        center
    )
    let right = right_len - left

    if left > 0 {
        crum_rotate(
            UnsafeMutableBufferPointer(rebasing: a[lblock..<(lblock + rblock + left)]),
            rblock,
            swap
        )
        crum_rotate_merge_block(a, lblock, left, swap)
        crum_rotate_merge_block(
            UnsafeMutableBufferPointer(rebasing: a[(lblock + left)..<total]),
            rblock,
            right,
            swap
        )
    } else if right > 0 {
        crum_rotate_merge_block(
            UnsafeMutableBufferPointer(rebasing: a[lblock..<total]),
            rblock,
            right,
            swap
        )
    }
}

private func crum_rotate_mergesort(
    _ a: UnsafeMutableBufferPointer<Int>,
    _ swap: UnsafeMutableBufferPointer<Int>
) {
    let n = a.count
    if n <= 1 {
        return
    }
    let block0 = max(min(CRUM_INSERTION_THRESHOLD, swap.count), 1)
    var i = 0
    while i < n {
        let end = min(i + block0, n)
        insertion_sort(UnsafeMutableBufferPointer(rebasing: a[i..<end]))
        i = end
    }
    var block = block0
    while block < n {
        var start = 0
        while start < n {
            let mid = start + block
            if mid >= n {
                break
            }
            let end = min(mid + block, n)
            let left_len = mid - start
            let right_len = end - mid
            crum_rotate_merge_block(
                UnsafeMutableBufferPointer(rebasing: a[start..<end]),
                left_len,
                right_len,
                swap
            )
            start = end
        }
        let next = block &* 2
        if next == 0 || next / 2 != block {
            break
        }
        block = next
    }
}

private func crum_fulcrum_partition(_ a: UnsafeMutableBufferPointer<Int>, _ pivot: Int) -> Int {
    let n = a.count

    var pivot_idx = 0
    for i in 0..<n {
        if a[i] == pivot {
            pivot_idx = i
            break
        }
    }
    a.swapAt(0, pivot_idx)

    let pivot_val = a[0]
    var head = 0
    var tail = n - 1

    while true {
        while head < tail && a[tail] > pivot_val {
            tail -= 1
        }
        if head >= tail {
            a[head] = pivot_val
            return head
        }
        a[head] = a[tail]
        head += 1

        while head < tail && a[head] <= pivot_val {
            head += 1
        }
        if head >= tail {
            a[head] = pivot_val
            return head
        }
        a[tail] = a[head]
        tail -= 1
    }
}

private func crum_partition_sort(
    _ a: UnsafeMutableBufferPointer<Int>,
    _ swap: UnsafeMutableBufferPointer<Int>
) {
    let n = a.count
    if n <= 1 {
        return
    }
    if n < CRUM_INSERTION_THRESHOLD {
        insertion_sort(a)
        return
    }

    let pivot = crum_quasimedian9(a)
    let mid = crum_fulcrum_partition(a, pivot)
    let left_len = mid
    let right_len = n - mid - 1

    if right_len == 0 {
        var lt = 0
        for i in 0..<n {
            if a[i] < pivot {
                a.swapAt(lt, i)
                lt += 1
            }
        }
        if lt > 1 {
            crum_partition_sort(UnsafeMutableBufferPointer(rebasing: a[0..<lt]), swap)
        }
        return
    }

    let unbalanced = (left_len > 0 && left_len < n / 16)
        || (right_len > 0 && right_len < n / 16)

    if unbalanced {
        if left_len > 1 {
            crum_rotate_mergesort(UnsafeMutableBufferPointer(rebasing: a[0..<left_len]), swap)
        }
        if right_len > 1 {
            crum_rotate_mergesort(UnsafeMutableBufferPointer(rebasing: a[(mid + 1)..<n]), swap)
        }
        return
    }

    if left_len > 1 {
        crum_partition_sort(UnsafeMutableBufferPointer(rebasing: a[0..<left_len]), swap)
    }
    if right_len > 1 {
        crum_partition_sort(UnsafeMutableBufferPointer(rebasing: a[(mid + 1)..<n]), swap)
    }
}

private func crum_analyze(
    _ a: UnsafeMutableBufferPointer<Int>,
    _ swap: UnsafeMutableBufferPointer<Int>
) -> Bool {
    let n = a.count
    if n <= 1 {
        return true
    }
    if crum_is_sorted(a) {
        return true
    }
    if crum_is_reverse_sorted(a) {
        crum_reverse(a)
        return true
    }

    let q = n / 4
    if q >= 2 {
        let bounds = [0, q, q * 2, q * 3, n]
        for s in 0..<4 {
            let lo = bounds[s]
            let hi = bounds[s + 1]
            if hi - lo < 2 {
                continue
            }
            let pairs = hi - lo - 1
            if crum_ordered_pairs(UnsafeMutableBufferPointer(rebasing: a[lo..<hi])) * 2 > pairs {
                crum_rotate_mergesort(UnsafeMutableBufferPointer(rebasing: a[lo..<hi]), swap)
            }
        }
        if crum_is_sorted(a) {
            return true
        }
    }
    return false
}

func crum_sort(_ a: inout [Int]) {
    a.withUnsafeMutableBufferPointer { crum_sort($0) }
}

func crum_sort(_ a: UnsafeMutableBufferPointer<Int>) {
    let n = a.count
    if n <= 1 {
        return
    }
    var swapStorage = [Int](repeating: 0, count: CRUM_SWAP)
    swapStorage.withUnsafeMutableBufferPointer { swap in
        if crum_analyze(a, swap) {
            return
        }
        crum_partition_sort(a, swap)
    }
}


func benchmark_sort(_ array: inout [Int]) {

    crum_sort(&array)

}

func is_non_decreasing(_ a: [Int]) -> Bool {
    guard a.count >= 2 else { return true }
    for i in 1..<a.count {
        if a[i - 1] > a[i] { return false }
    }
    return true
}

func same_multiset(_ a: [Int], _ b: [Int]) -> Bool {
    if a.count != b.count {
        return false
    }

    var left = a
    var right = b
    left.sort()
    right.sort()
    return left == right
}

func check_correctness_case(_ label: String, _ input: [Int]) {
    var input = input
    let original = input

    benchmark_sort(&input)

    if !is_non_decreasing(input) {
        fatalError("correctness case \(label): output is not sorted")
    }

    if !same_multiset(input, original) {
        fatalError("correctness case \(label): elements were lost or added")
    }
}

// Skip cases larger than the algorithm's measured size cap (MAX_POWER). That
// cap exists because larger inputs are impractically slow; forcing them here
// would stall the published measurement script before any table rows print.
func check_correctness_case_within_limit(_ label: String, _ input: [Int]) {
    if input.count > (1 << MAX_POWER) {
        return
    }
    check_correctness_case(label, input)
}

func few_unique_values(_ size: Int, _ unique: Int, _ seed: UInt64) -> [Int] {
    var state = seed
    var result = [Int]()
    result.reserveCapacity(size)
    for _ in 0..<size {
        state ^= state << 13
        state ^= state >> 7
        state ^= state << 17
        result.append(Int(state % UInt64(unique)) + 1)
    }
    return result
}

func run_correctness_checks() {
    check_correctness_case("empty", [])
    check_correctness_case("single", [42])
    check_correctness_case("duplicates", [3, 1, 3, 2, 1, 2])
    check_correctness_case("sorted", [1, 2, 3, 4, 5])
    check_correctness_case("reverse", [5, 4, 3, 2, 1])
    check_correctness_case("all_equal", [7, 7, 7, 7])
    check_correctness_case("skewed_range", [1_000_000, 2, 1_000_001, 1, 999_999])
    // Static-buffer Grail skips the in-buffer build when key collection is sparse
    // (ideal_buffer = false). Exercising that path catches regressions in buffer gating.
    check_correctness_case(
        "few_keys_len16",
        [2, 2, 2, 2, 2, 2, 2, 2, 4, 3, 1, 2, 3, 4, 1, 4]
    )
    // Seed 0 is a fixed point of the xorshift below, so it would degenerate into
    // yet another all-equal case instead of a 4-value mix. Start at 1.
    for seed in 1...32 {
        check_correctness_case(
            "few_keys_len32_seed_\(seed)",
            few_unique_values(32, 4, UInt64(seed))
        )
    }
    // Small-input cutoffs (insertion sort below 32 elements, etc.) hide duplicate-key
    // bugs in the recursive path, so repeat the duplicate cases at the smallest
    // benchmark size, which every algorithm must handle within reasonable time.
    check_correctness_case("all_equal_len256", [Int](repeating: 7, count: 256))
    for seed in 1...4 {
        check_correctness_case(
            "few_keys_len256_seed_\(seed)",
            few_unique_values(256, 4, UInt64(seed))
        )
    }
    // Blit's equal-key second sweep used to copy the whole range into a fixed
    // 512-element swap; lengths above that must still sort without panicking.
    // Respect MAX_POWER so algorithms with a low measured-size cap (slow,
    // sleep) do not hang here for minutes or months.
    check_correctness_case_within_limit("all_equal_len600", [Int](repeating: 7, count: 600))
    for seed in 1...4 {
        check_correctness_case_within_limit(
            "few_keys_len2048_seed_\(seed)",
            few_unique_values(2048, 4, UInt64(seed))
        )
    }
}


func shuffled(_ size: Int, seed: UInt64) -> [Int] {
    guard size > 0 else { return [] }

    var v = Array(1...size)
    var state = seed

    if size > 1 {
        for i in stride(from: size - 1, through: 1, by: -1) {
            state ^= state << 13
            state ^= state >> 7
            state ^= state << 17

            let j = Int(state % UInt64(i + 1))
            v.swapAt(i, j)
        }
    }

    return v
}

func micros(_ d: Duration) -> UInt64 {
    let c = d.components
    let fromSeconds = UInt64(c.seconds) * 1_000_000
    let fromAttos = UInt64(max(0, c.attoseconds / 1_000_000_000_000))
    return fromSeconds + fromAttos
}

func padLeft(_ value: String, _ width: Int) -> String {
    if value.count >= width {
        return value
    }
    return String(repeating: " ", count: width - value.count) + value
}

func formatSeconds(_ micros: UInt64) -> String {
    let whole = micros / 1_000_000
    let frac = micros % 1_000_000
    let fracStr = padLeft(String(frac), 6).replacingOccurrences(of: " ", with: "0")
    return "\(whole).\(fracStr)"
}

func input_array(_ size: Int, seed: UInt64) -> [Int] {
    shuffled(size, seed: seed)
}

/// Peak heap growth during `benchmark_sort`, in bytes (explicit buffers such as swap).
/// Kept in bytes so the parent can average before rounding; converting to KiB here
/// would truncate sub-KiB buffers to 0 in every run and hide them from the average.
func run_once(size: Int, seed: Int) -> (UInt64, Int) {
    var array = input_array(size, seed: UInt64(seed))

    let baseBytes = alloc_track_live()
    alloc_track_reset_peak()

    let start = ContinuousClock.now

    benchmark_sort(&array)

    let elapsed = ContinuousClock.now - start
    let peakBytes = alloc_track_peak()
    let auxBytes = max(0, peakBytes - baseBytes)

    let expected: [Int] = size > 0 ? Array(1...size) : []
    if array != expected {
        fatalError("sort failed with seed \(seed) for size \(size)")
    }

    return (micros(elapsed), auxBytes)
}

func run_child(_ args: [String]) {
    let size = Int(args[2])!
    let seed = Int(args[3])!
    let (elapsedUs, mem) = run_once(size: size, seed: seed)
    print("\(elapsedUs) \(mem)")
}

let args = CommandLine.arguments
if args.count > 1 && args[1] == "--run-once" {
    run_child(args)
} else {
    run_correctness_checks()

    let tableHeader =
        "| \(padLeft("Size", 10)) | " +
        "\(padLeft("Average time (s)", 16)) | " +
        "\(padLeft("Maximum time (s)", 16)) | " +
        "\(padLeft("Average memory (KiB)", 20)) | " +
        "\(padLeft("Maximum memory (KiB)", 20)) |"
    print(tableHeader)
    print("|-----------:|-----------------:|-----------------:|---------------------:|---------------------:|")

    for power in MIN_POWER...MAX_POWER {
        let size = 1 << power

        var totalTime: UInt64 = 0
        var maxTime: UInt64 = 0

        var totalMem = 0
        var maxMem = 0

        for seed in 1...RUNS {
            let process = Process()
            process.executableURL = URL(fileURLWithPath: args[0])
            process.arguments = ["--run-once", "\(size)", "\(seed)"]
            let stdout = Pipe()
            let stderr = Pipe()
            process.standardOutput = stdout
            process.standardError = stderr

            do {
                try process.run()
            } catch {
                fatalError("failed to run benchmark child process: \(error)")
            }
            process.waitUntilExit()

            if process.terminationStatus != 0 {
                let err = String(data: stderr.fileHandleForReading.readDataToEndOfFile(), encoding: .utf8) ?? ""
                fatalError("benchmark child process failed: \(err)")
            }

            let data = stdout.fileHandleForReading.readDataToEndOfFile()
            let stdoutText = String(data: data, encoding: .utf8) ?? ""
            let fields = stdoutText.split(whereSeparator: \.isWhitespace)
            guard fields.count >= 2,
                  let elapsedUs = UInt64(fields[0]),
                  let auxMem = Int(fields[1]) else {
                fatalError("invalid child process output: \(stdoutText)")
            }

            totalTime += elapsedUs
            if elapsedUs > maxTime {
                maxTime = elapsedUs
            }

            totalMem += auxMem
            if auxMem > maxMem {
                maxMem = auxMem
            }
        }

        let avgTime = totalTime / UInt64(RUNS)
        // Memory is summed in bytes and converted to KiB once, after averaging.
        let avgMemKb = totalMem / RUNS / 1024
        let maxMemKb = maxMem / 1024

        let tableRow =
            "| \(padLeft(String(size), 10)) | " +
            "\(padLeft(formatSeconds(avgTime), 16)) | " +
            "\(padLeft(formatSeconds(maxTime), 16)) | " +
            "\(padLeft(String(avgMemKb), 20)) | " +
            "\(padLeft(String(maxMemKb), 20)) |"
        print(tableRow)
    }
}
SWIFT

RUN clang -O2 -fPIC -shared alloc_track.c -o liballoc_track.so -ldl

RUN swiftc -Ounchecked -whole-module-optimization \
    main.swift \
    -o swift-benchmark \
    -L. -lalloc_track \
    -Xlinker -rpath -Xlinker /app

ENV LD_PRELOAD=/app/liballoc_track.so
CMD ["./swift-benchmark"]
"""#
    try dockerfile.write(
        to: workdir.appendingPathComponent("Dockerfile"),
        atomically: true,
        encoding: .utf8
    )

    // Keeping build and run as separate child processes preserves Docker's
    // normal output and the original image tag used by the benchmark skill.
    try runCommand("docker", ["build", "-t", "swift-benchmark", workdir.path])
    try runCommand("docker", ["run", "--rm", "--init", "swift-benchmark"])
} catch {
    fputs("\(error)\n", stderr)
    exit(1)
}