二項ヒープソートで配列を並び替える

#!/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


final class BinomialNode {
    var key: Int
    var degree: UInt32
    var child: BinomialNode?
    var sibling: BinomialNode?

    init(key: Int, degree: UInt32 = 0, child: BinomialNode? = nil, sibling: BinomialNode? = nil) {
        self.key = key
        self.degree = degree
        self.child = child
        self.sibling = sibling
    }
}

func link(_ child: BinomialNode, _ parent: BinomialNode) -> BinomialNode {
    child.sibling = parent.child
    parent.child = child
    parent.degree += 1
    return parent
}

func roots_to_vec(_ head: BinomialNode?) -> [BinomialNode] {
    var head = head
    var roots = [BinomialNode]()
    while let node = head {
        head = node.sibling
        node.sibling = nil
        roots.append(node)
    }
    return roots
}

func vec_to_roots(_ roots: [BinomialNode]) -> BinomialNode? {
    var head: BinomialNode? = nil
    var tail: BinomialNode? = nil
    for node in roots {
        node.sibling = nil
        if head == nil {
            head = node
            tail = node
        } else {
            tail!.sibling = node
            tail = node
        }
    }
    return head
}

func merge_root_lists(_ a: BinomialNode?, _ b: BinomialNode?) -> BinomialNode? {
    var a = a
    var b = b
    var merged = [BinomialNode]()
    while let aNode = a, let bNode = b {
        if aNode.degree <= bNode.degree {
            a = aNode.sibling
            aNode.sibling = nil
            merged.append(aNode)
        } else {
            b = bNode.sibling
            bNode.sibling = nil
            merged.append(bNode)
        }
    }
    while let node = a {
        a = node.sibling
        node.sibling = nil
        merged.append(node)
    }
    while let node = b {
        b = node.sibling
        node.sibling = nil
        merged.append(node)
    }
    return vec_to_roots(merged)
}

func consolidate(_ head: BinomialNode?) -> BinomialNode? {
    var roots = roots_to_vec(head)
    var i = 0
    while i + 1 < roots.count {
        if roots[i].degree != roots[i + 1].degree {
            i += 1
            continue
        }
        // Three equal degrees: leave the first and merge the latter two (CLRS).
        if i + 2 < roots.count && roots[i + 2].degree == roots[i].degree {
            i += 1
            continue
        }
        let a = roots.remove(at: i)
        let b = roots.remove(at: i)
        let linked: BinomialNode
        if a.key <= b.key {
            linked = link(b, a)
        } else {
            linked = link(a, b)
        }
        roots.insert(linked, at: i)
    }
    return vec_to_roots(roots)
}

func union(_ h1: BinomialNode?, _ h2: BinomialNode?) -> BinomialNode? {
    consolidate(merge_root_lists(h1, h2))
}

func insert_key(_ heap: BinomialNode?, _ key: Int) -> BinomialNode? {
    let node = BinomialNode(key: key)
    return union(heap, node)
}

func reverse_children(_ child: BinomialNode?) -> BinomialNode? {
    var child = child
    var rev: BinomialNode? = nil
    while let node = child {
        child = node.sibling
        node.sibling = rev
        rev = node
    }
    return rev
}

func extract_min(_ heap: BinomialNode?) -> (Int?, BinomialNode?) {
    guard let head = heap else {
        return (nil, nil)
    }

    var roots = roots_to_vec(head)
    var min_i = 0
    for i in 1..<roots.count {
        if roots[i].key < roots[min_i].key {
            min_i = i
        }
    }

    let min_node = roots.remove(at: min_i)
    let key = min_node.key
    let children = reverse_children(min_node.child)
    min_node.child = nil
    return (key, union(vec_to_roots(roots), children))
}

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

func binomial_heap_sort(_ a: UnsafeMutableBufferPointer<Int>) {
    var heap: BinomialNode? = nil
    for i in 0..<a.count {
        heap = insert_key(heap, a[i])
    }
    for i in 0..<a.count {
        let (key, next) = extract_min(heap)
        heap = next
        guard let key else {
            fatalError("binomial heap exhausted early")
        }
        a[i] = key
    }
}


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

    binomial_heap_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)
}