ブリットソートで配列を並び替える
ブリットソートを使用する
ブリットソート (blitsort) は、固定長の小さなスワップ領域と配列回転を使い、安定かつほぼインプレースに整列するハイブリッド比較ソートである。
整列度が低い区間では回転クイックソート、整列度が高い区間では回転マージソートを使い分ける。
回転クイックではピボットで安定分割して再帰する。区間がスワップ以下なら二重書き込みで分け、それより長い区間は半分に再帰したあと中央帯を回転でつなぐ。回転マージでは、隣接する整列済みランの左中央を取り、右ランでそれ未満の個数を二分探索してから回転し、スワップに収まるまで小さくして安定マージする。
本記事では高速な三区間回転や単境界の二分探索、分岐の少ない分割の代わりに、分かりやすい回転・通常の二分探索・二重書き込み分割を用いて簡略化している。小区間の仕上げは挿入ソート、回転マージを打ち切ったあとは通常の安定マージで代用する。
- 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。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。
- 回転クイックソート: 9 点の準中央値をピボットにし、スワップ長以下なら安定な二重書き込み分割、それより長い区間は半分ずつ分割してから中央帯を回転して
<= ピボットを前方へ集める。 - 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。 - 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。最悪計算量を \(O(n \log n)\) に抑えるためのガードである。
- 回転マージ: 左ランの中央要素を取り、右ランでそれ未満の個数を二分探索し、中央ブロックを回転してから左右を再帰する。どちらかがスワップに収まったら通常の安定マージで打ち切る。
- 小区間: 要素数が閾値未満なら挿入ソートで仕上げる。スワップは既定で 512 要素(配列がそれより短ければ配列長)に固定する。
procedure blit_rotate(A, left, swap)
// 先頭 left 個を末尾へ移す。短い側が swap に収まるなら block move、
// そうでなければ 3 回の reverse(三区間回転の説明用代用)
procedure blit_stable_partition(A, swap, pivot)
if length(A) > length(swap) then
h := length(A) / 2
l := blit_stable_partition(A[0 .. h), swap, pivot)
r := blit_stable_partition(A[h .. end), swap, pivot)
blit_rotate(A[l .. h+r), h - l, swap)
return l + r
// さもなくば swap へ退避して <= pivot を前方へ安定に書き戻す
procedure blit_rotate_merge_block(A, left_len, right_len, swap)
if A[left_len-1] <= A[left_len] then return
if left_len <= length(swap) or right_len <= length(swap) then
stable_merge via swap; return
rblock := left_len / 2; lblock := left_len - rblock
left := lower_bound(A[left_len ..), A[lblock])
blit_rotate(A[lblock .. lblock+rblock+left), rblock, swap)
blit_rotate_merge_block(A[0 .. lblock+left), lblock, left, swap)
blit_rotate_merge_block(A[lblock+left ..), rblock, right_len-left, swap)
procedure blitsort(A)
if A is sorted then return
if A is reverse-sorted then reverse(A); return
swap := buffer of min(512, length(A))
for each quarter Q of A
if ordered_pairs(Q) > half then blit_rotate_mergesort(Q, swap)
if A is sorted then return
blit_partition_sort(A, swap)
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。補助メモリは固定長スワップ(既定 512 要素)に加え、再帰の深さ分の \(O(\log n)\) のスタックを使う。
以下のデモでは視認性のため挿入閾値を 4、スワップを 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。ブリットソートは同じ安定分割の発想を、固定スワップ+回転の組立に落とし込み、補助メモリを定数寄りに抑える。
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する。ブリットソートは安定性を保ったまま回転で区間を寄せる点が対照的である。
クワッドソートはボトムアップのクワッドマージが本体である。ブリットソートは整列度が高いときだけ回転マージへ寄せ、ランダム寄りでは回転クイックを主とする。
ウィキソートやグレイルソートも小さなバッファで安定なインプレース寄りマージを目指すが、ブロックマージと内部バッファの設計が中心である。ブリットソートはクイック型の分割と回転マージのハイブリッドである。
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 | 0.000007 | 0.000046 | 2 | 2 |
| 512 | 0.000015 | 0.000084 | 4 | 4 |
| 1024 | 0.000032 | 0.000094 | 4 | 4 |
| 2048 | 0.000066 | 0.000399 | 4 | 4 |
| 4096 | 0.000140 | 0.000226 | 4 | 4 |
| 8192 | 0.000304 | 0.000481 | 4 | 4 |
| 16384 | 0.000669 | 0.001586 | 4 | 4 |
| 32768 | 0.001434 | 0.002856 | 4 | 4 |
| 65536 | 0.003136 | 0.004310 | 4 | 4 |
| 131072 | 0.006816 | 0.009194 | 4 | 4 |
| 262144 | 0.014779 | 0.022818 | 4 | 4 |
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 blitsort (rotate merge / rotate quick).
/// Production uses trinity rotations, monobound binary search, quadsort blocks,
/// and branchless partitioning; here those are replaced with clearer routines
/// and a fixed swap of `BLIT_SWAP` elements (default 512, as in the reference).
let BLIT_SWAP = 512
let BLIT_OUT = 24
func blit_reverse_range(_ a: UnsafeMutableBufferPointer<Int>) {
var lo = 0
var hi = a.count
while lo + 1 < hi {
hi -= 1
a.swapAt(lo, hi)
lo += 1
}
}
func blit_is_sorted(_ a: UnsafeMutableBufferPointer<Int>) -> Bool {
if a.count < 2 {
return true
}
for i in 1..<a.count {
if a[i - 1] > a[i] {
return false
}
}
return true
}
func blit_is_reverse_sorted(_ a: UnsafeMutableBufferPointer<Int>) -> Bool {
if a.count < 2 {
return true
}
for i in 1..<a.count {
if a[i - 1] < a[i] {
return false
}
}
return true
}
func blit_reverse(_ a: UnsafeMutableBufferPointer<Int>) {
blit_reverse_range(a)
}
func blit_ordered_pairs(_ a: UnsafeMutableBufferPointer<Int>) -> Int {
if a.count < 2 {
return 0
}
var count = 0
for i in 1..<a.count {
if a[i - 1] <= a[i] {
count += 1
}
}
return count
}
func blit_median3_idx(_ a: UnsafeMutableBufferPointer<Int>, _ i: Int, _ j: Int, _ k: Int) -> Int {
let x = a[i]
let y = a[j]
let z = 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
}
}
func blit_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 = blit_median3_idx(a, i0, i1, i2)
let m1 = blit_median3_idx(a, i3, i4, i5)
let m2 = blit_median3_idx(a, i6, i7, i8)
return a[blit_median3_idx(a, m0, m1, m2)]
}
/// Rotate `a` so the prefix of length `left` moves after the suffix.
/// Prefer a swap-assisted block move; otherwise fall back to three reverses
/// (educational stand-in for trinity / bridge rotations).
func blit_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]
}
let moved = Array(a[left..<n])
for i in 0..<moved.count {
a[i] = moved[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]
}
let moved = Array(a[0..<left])
for i in 0..<moved.count {
a[right + i] = moved[i]
}
for i in 0..<right {
a[i] = swap[i]
}
return
}
blit_reverse_range(UnsafeMutableBufferPointer(rebasing: a[0..<left]))
blit_reverse_range(UnsafeMutableBufferPointer(rebasing: a[left..<n]))
blit_reverse_range(a)
}
/// Lower bound: first index `i` in `hay` with `hay[i] >= needle`.
func blit_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
}
func blit_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
}
}
/// Merge two adjacent sorted runs `[0..left_len)` and `[left_len..left_len+right_len)`
/// by rotating around the left run's center until the pieces fit in `swap`.
func blit_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 {
blit_merge_with_swap(a, left_len, swap)
return
}
if left_len <= swap_cap {
blit_merge_with_swap(a, left_len, swap)
return
}
if right_len <= swap_cap {
// Partial backward merge: right run fits in swap.
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 = blit_lower_bound(UnsafeMutableBufferPointer(rebasing: a[left_len..<total]), center)
let right = right_len - left
// Layout: [ lblock | rblock | left | right ]
if left > 0 {
blit_rotate(
UnsafeMutableBufferPointer(rebasing: a[lblock..<(lblock + rblock + left)]),
rblock,
swap
)
// Now: [ lblock | left | rblock | right ]
blit_rotate_merge_block(a, lblock, left, swap)
blit_rotate_merge_block(
UnsafeMutableBufferPointer(rebasing: a[(lblock + left)..<total]),
rblock,
right,
swap
)
} else if right > 0 {
blit_rotate_merge_block(
UnsafeMutableBufferPointer(rebasing: a[lblock..<total]),
rblock,
right,
swap
)
}
}
func blit_rotate_mergesort(_ a: UnsafeMutableBufferPointer<Int>, _ swap: UnsafeMutableBufferPointer<Int>) {
let n = a.count
if n <= 1 {
return
}
let block0 = max(min(BLIT_OUT, 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
blit_rotate_merge_block(
UnsafeMutableBufferPointer(rebasing: a[start..<end]),
left_len,
right_len,
swap
)
start = end
}
if block > Int.max / 2 {
break
}
block *= 2
if block == 0 {
break
}
}
}
/// Stable partition: keys `<= pivot` stay toward the front.
/// When the range exceeds the swap, recurse on halves and rotate the middle
/// so left parts gather contiguously (rotate quicksort's assembly step).
func blit_stable_partition(
_ a: UnsafeMutableBufferPointer<Int>,
_ swap: UnsafeMutableBufferPointer<Int>,
_ pivot: Int
) -> Int {
let n = a.count
let swap_cap = swap.count
if n == 0 {
return 0
}
if n > swap_cap {
let h = n / 2
let l = blit_stable_partition(UnsafeMutableBufferPointer(rebasing: a[0..<h]), swap, pivot)
let r = blit_stable_partition(UnsafeMutableBufferPointer(rebasing: a[h..<n]), swap, pivot)
// Middle band `a[l..h]` holds the right half of the left partition
// (`> pivot`); length `h - l`. Right partition contributed `r` left keys
// at `a[h..h+r]`. Rotate that band of length `(h - l) + r` by `h - l`.
blit_rotate(UnsafeMutableBufferPointer(rebasing: a[l..<(h + r)]), h - l, swap)
return l + r
}
for i in 0..<n {
swap[i] = a[i]
}
var left = 0
for i in 0..<n {
if swap[i] <= pivot {
left += 1
}
}
var l = 0
var r = left
for i in 0..<n {
let x = swap[i]
if x <= pivot {
a[l] = x
l += 1
} else {
a[r] = x
r += 1
}
}
return left
}
/// Like `blit_stable_partition`, but left keys are strictly less than `pivot`.
/// Used for the equal-key second sweep so ranges larger than the fixed swap
/// still stay within that buffer via half-recursion and rotate.
func blit_strict_partition(
_ a: UnsafeMutableBufferPointer<Int>,
_ swap: UnsafeMutableBufferPointer<Int>,
_ pivot: Int
) -> Int {
let n = a.count
let swap_cap = swap.count
if n == 0 {
return 0
}
if n > swap_cap {
let h = n / 2
let l = blit_strict_partition(UnsafeMutableBufferPointer(rebasing: a[0..<h]), swap, pivot)
let r = blit_strict_partition(UnsafeMutableBufferPointer(rebasing: a[h..<n]), swap, pivot)
blit_rotate(UnsafeMutableBufferPointer(rebasing: a[l..<(h + r)]), h - l, swap)
return l + r
}
for i in 0..<n {
swap[i] = a[i]
}
var left = 0
for i in 0..<n {
if swap[i] < pivot {
left += 1
}
}
var l = 0
var r = left
for i in 0..<n {
let x = swap[i]
if x < pivot {
a[l] = x
l += 1
} else {
a[r] = x
r += 1
}
}
return left
}
func blit_partition_sort(_ a: UnsafeMutableBufferPointer<Int>, _ swap: UnsafeMutableBufferPointer<Int>) {
let n = a.count
if n <= 1 {
return
}
if n <= BLIT_OUT {
insertion_sort(a)
return
}
let pivot = blit_quasimedian9(a)
let left = blit_stable_partition(a, swap, pivot)
let right = n - left
if right == 0 {
// Second sweep: gather keys strictly less than pivot. When `n` exceeds
// the fixed swap, recurse + rotate instead of copying the whole range.
let lt = blit_strict_partition(a, swap, pivot)
if lt > 1 {
blit_partition_sort(UnsafeMutableBufferPointer(rebasing: a[0..<lt]), swap)
}
return
}
let unbalanced = (left > 0 && left < n / 16) || (right > 0 && right < n / 16)
if unbalanced {
if left > 1 {
blit_rotate_mergesort(UnsafeMutableBufferPointer(rebasing: a[0..<left]), swap)
}
if right > 1 {
blit_rotate_mergesort(UnsafeMutableBufferPointer(rebasing: a[left..<n]), swap)
}
return
}
if left > 1 {
blit_partition_sort(UnsafeMutableBufferPointer(rebasing: a[0..<left]), swap)
}
if right > 1 {
blit_partition_sort(UnsafeMutableBufferPointer(rebasing: a[left..<n]), swap)
}
}
func blit_analyze(_ a: UnsafeMutableBufferPointer<Int>, _ swap: UnsafeMutableBufferPointer<Int>) -> Bool {
let n = a.count
if n <= 1 {
return true
}
if blit_is_sorted(a) {
return true
}
if blit_is_reverse_sorted(a) {
blit_reverse(a)
return true
}
// Four-segment presortedness (flux / blit analyzer stand-in): finish
// mostly-ordered quarters with rotate mergesort, then fall through to
// rotate quicksort for remaining disorder.
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 blit_ordered_pairs(UnsafeMutableBufferPointer(rebasing: a[lo..<hi])) * 2 > pairs {
blit_rotate_mergesort(UnsafeMutableBufferPointer(rebasing: a[lo..<hi]), swap)
}
}
if blit_is_sorted(a) {
return true
}
}
return false
}
func blit_sort(_ a: inout [Int]) {
a.withUnsafeMutableBufferPointer { blit_sort($0) }
}
func blit_sort(_ a: UnsafeMutableBufferPointer<Int>) {
let n = a.count
if n <= 1 {
return
}
if n <= BLIT_OUT {
insertion_sort(a)
return
}
let swap_len = min(BLIT_SWAP, n)
var swap = Array(repeating: 0, count: swap_len)
let done = swap.withUnsafeMutableBufferPointer { swapBuf -> Bool in
blit_analyze(a, swapBuf)
}
if done {
return
}
swap.withUnsafeMutableBufferPointer { swapBuf in
blit_partition_sort(a, swapBuf)
}
}
func benchmark_sort(_ array: inout [Int]) {
blit_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)
}