ブロッククイックソートで配列を並び替える

set -euo pipefail

WORKDIR="$(mktemp -d)"
trap 'rm -rf "$WORKDIR"' EXIT

cat > "$WORKDIR/Dockerfile" <<'EOF'
FROM rust:1.95.0

WORKDIR /app

RUN mkdir -p src

RUN cat > Cargo.toml <<'CARGO'
[package]
name = "rust-benchmark"
version = "0.1.0"
edition = "2021"

[profile.release]
lto = true
codegen-units = 1
panic = "abort"
CARGO

RUN cat > src/main.rs <<'RUST'
use std::{
    alloc::{GlobalAlloc, Layout, System},
    env,
    process::Command,
    sync::atomic::{AtomicUsize, Ordering as AtomicOrdering},
    time::{Duration, Instant},
};

/// Counts live heap bytes and the high-water mark so auxiliary sort buffers
/// (swap Vecs, etc.) are measured as explicit heap growth during the sort.
struct TrackingAllocator;

static LIVE_BYTES: AtomicUsize = AtomicUsize::new(0);
static PEAK_BYTES: AtomicUsize = AtomicUsize::new(0);

fn record_alloc(size: usize) {
    let live = LIVE_BYTES.fetch_add(size, AtomicOrdering::Relaxed) + size;
    PEAK_BYTES.fetch_max(live, AtomicOrdering::Relaxed);
}

unsafe impl GlobalAlloc for TrackingAllocator {
    unsafe fn alloc(&self, layout: Layout) -> *mut u8 {
        let ptr = System.alloc(layout);
        if !ptr.is_null() {
            record_alloc(layout.size());
        }
        ptr
    }

    unsafe fn dealloc(&self, ptr: *mut u8, layout: Layout) {
        LIVE_BYTES.fetch_sub(layout.size(), AtomicOrdering::Relaxed);
        System.dealloc(ptr, layout);
    }

    unsafe fn alloc_zeroed(&self, layout: Layout) -> *mut u8 {
        let ptr = System.alloc_zeroed(layout);
        if !ptr.is_null() {
            record_alloc(layout.size());
        }
        ptr
    }

    unsafe fn realloc(&self, ptr: *mut u8, layout: Layout, new_size: usize) -> *mut u8 {
        let new_ptr = System.realloc(ptr, layout, new_size);
        if !new_ptr.is_null() {
            LIVE_BYTES.fetch_sub(layout.size(), AtomicOrdering::Relaxed);
            record_alloc(new_size);
        }
        new_ptr
    }
}

#[global_allocator]
static GLOBAL: TrackingAllocator = TrackingAllocator;
const MIN_POWER: u32 = 8;
const MAX_POWER: u32 = 18;
const RUNS: usize = 8192;
fn insertion_sort(a: &mut [usize]) {
    for i in 1..a.len() {
        let mut j = i;
        while j > 0 && a[j - 1] > a[j] {
            a.swap(j - 1, j);
            j -= 1;
        }
    }
}



const BLOCK_SIZE: usize = 128;
const INSERTION_THRESHOLD: usize = 16;

/// Branch-light Hoare-style partition used by BlockQuicksort (Edelkamp & Weiß).
/// Returns the final index of the pivot.
fn quick_block_partition(a: &mut [usize], mut begin: usize, end: usize) -> usize {
    // end is exclusive; pivot starts at midpoint of [begin, end).
    let mid = begin + (end - begin) / 2;
    a.swap(mid, end - 1);
    let pivot = a[end - 1];
    let mut last = end - 2;

    let mut index_l = [0usize; BLOCK_SIZE];
    let mut index_r = [0usize; BLOCK_SIZE];
    let mut num_left = 0usize;
    let mut num_right = 0usize;
    let mut start_left = 0usize;
    let mut start_right = 0usize;

    while begin <= last && last - begin + 1 > 2 * BLOCK_SIZE {
        if num_left == 0 {
            start_left = 0;
            for j in 0..BLOCK_SIZE {
                index_l[num_left] = j;
                // left buffer: elements >= pivot (need to move right)
                num_left += usize::from(!(a[begin + j] < pivot));
            }
        }
        if num_right == 0 {
            start_right = 0;
            for j in 0..BLOCK_SIZE {
                index_r[num_right] = j;
                // right buffer: elements <= pivot (need to move left)
                num_right += usize::from(!(pivot < a[last - j]));
            }
        }

        let num = num_left.min(num_right);
        for j in 0..num {
            let li = begin + index_l[start_left + j];
            let ri = last - index_r[start_right + j];
            a.swap(li, ri);
        }
        num_left -= num;
        num_right -= num;
        start_left += num;
        start_right += num;
        if num_left == 0 {
            begin += BLOCK_SIZE;
        }
        if num_right == 0 {
            last -= BLOCK_SIZE;
        }
    }

    // Final (partial) scan of the remaining ≤ 2B elements.
    let (shift_l, shift_r) = if num_right == 0 && num_left == 0 {
        debug_assert!(begin <= last);
        let len = last - begin + 1;
        let shift_l = len / 2;
        let shift_r = len - shift_l;
        start_left = 0;
        start_right = 0;
        for j in 0..shift_l {
            index_l[num_left] = j;
            num_left += usize::from(!(a[begin + j] < pivot));
            index_r[num_right] = j;
            num_right += usize::from(!(pivot < a[last - j]));
        }
        if shift_l < shift_r {
            index_r[num_right] = shift_r - 1;
            num_right += usize::from(!(pivot < a[last - (shift_r - 1)]));
        }
        (shift_l, shift_r)
    } else if num_right != 0 {
        let shift_l = last - begin + 1 - BLOCK_SIZE;
        start_left = 0;
        for j in 0..shift_l {
            index_l[num_left] = j;
            num_left += usize::from(!(a[begin + j] < pivot));
        }
        (shift_l, BLOCK_SIZE)
    } else {
        let shift_r = last - begin + 1 - BLOCK_SIZE;
        start_right = 0;
        for j in 0..shift_r {
            index_r[num_right] = j;
            num_right += usize::from(!(pivot < a[last - j]));
        }
        (BLOCK_SIZE, shift_r)
    };

    let num = num_left.min(num_right);
    for j in 0..num {
        let li = begin + index_l[start_left + j];
        let ri = last - index_r[start_right + j];
        a.swap(li, ri);
    }
    num_left -= num;
    num_right -= num;
    start_left += num;
    start_right += num;
    if num_left == 0 {
        begin += shift_l;
    }
    if num_right == 0 {
        last = last.wrapping_sub(shift_r);
    }

    // Drain leftovers still recorded in one buffer.
    // `upper` is signed because the reference finish may leave it at -1.
    if num_left != 0 {
        let mut lower_i = (start_left + num_left - 1) as isize;
        let mut upper = last as isize - begin as isize;
        while lower_i >= start_left as isize && index_l[lower_i as usize] as isize == upper {
            upper -= 1;
            lower_i -= 1;
        }
        while lower_i >= start_left as isize {
            a.swap(
                (begin as isize + upper) as usize,
                begin + index_l[lower_i as usize],
            );
            upper -= 1;
            lower_i -= 1;
        }
        let pivot_pos = (begin as isize + upper + 1) as usize;
        a.swap(end - 1, pivot_pos);
        pivot_pos
    } else if num_right != 0 {
        let mut lower_i = (start_right + num_right - 1) as isize;
        let mut upper = last as isize - begin as isize;
        while lower_i >= start_right as isize && index_r[lower_i as usize] as isize == upper {
            upper -= 1;
            lower_i -= 1;
        }
        while lower_i >= start_right as isize {
            a.swap(
                (last as isize - upper) as usize,
                (last as isize - index_r[lower_i as usize] as isize) as usize,
            );
            upper -= 1;
            lower_i -= 1;
        }
        let pivot_pos = (last as isize - upper) as usize;
        a.swap(end - 1, pivot_pos);
        pivot_pos
    } else {
        a.swap(end - 1, begin);
        begin
    }
}

fn quick_block_sort_range(a: &mut [usize], lo: usize, hi: usize) {
    if hi <= lo {
        return;
    }
    if hi - lo < INSERTION_THRESHOLD {
        insertion_sort(&mut a[lo..=hi]);
        return;
    }
    let pivot_pos = quick_block_partition(a, lo, hi + 1);
    if pivot_pos > lo {
        quick_block_sort_range(a, lo, pivot_pos - 1);
    }
    if pivot_pos < hi {
        quick_block_sort_range(a, pivot_pos + 1, hi);
    }
}

fn quick_block_sort(a: &mut [usize]) {
    if let Some(hi) = a.len().checked_sub(1) {
        quick_block_sort_range(a, 0, hi);
    }
}


fn benchmark_sort(array: &mut [usize]) {

    quick_block_sort(array);

}

fn is_non_decreasing(a: &[usize]) -> bool {
    a.windows(2).all(|w| w[0] <= w[1])
}

fn same_multiset(a: &[usize], b: &[usize]) -> bool {
    if a.len() != b.len() {
        return false;
    }

    let mut left = a.to_vec();
    let mut right = b.to_vec();
    left.sort_unstable();
    right.sort_unstable();
    left == right
}

fn check_correctness_case(label: &str, mut input: Vec<usize>) {
    let original = input.clone();

    benchmark_sort(&mut input);

    if !is_non_decreasing(&input) {
        panic!("correctness case {}: output is not sorted", label);
    }

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

// 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.
fn check_correctness_case_within_limit(label: &str, input: Vec<usize>) {
    if input.len() > (1usize << MAX_POWER) {
        return;
    }
    check_correctness_case(label, input);
}

fn few_unique_values(size: usize, unique: usize, seed: u64) -> Vec<usize> {
    let mut state = seed;

    (0..size)
        .map(|_| {
            state ^= state << 13;
            state ^= state >> 7;
            state ^= state << 17;
            (state as usize % unique) + 1
        })
        .collect()
}

fn run_correctness_checks() {
    check_correctness_case("empty", vec![]);
    check_correctness_case("single", vec![42]);
    check_correctness_case("duplicates", vec![3, 1, 3, 2, 1, 2]);
    check_correctness_case("sorted", vec![1, 2, 3, 4, 5]);
    check_correctness_case("reverse", vec![5, 4, 3, 2, 1]);
    check_correctness_case("all_equal", vec![7, 7, 7, 7]);
    check_correctness_case("skewed_range", vec![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",
        vec![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(
            &format!("few_keys_len32_seed_{seed}"),
            few_unique_values(32, 4, 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", vec![7; 256]);
    for seed in 1..=4 {
        check_correctness_case(
            &format!("few_keys_len256_seed_{seed}"),
            few_unique_values(256, 4, 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", vec![7; 600]);
    for seed in 1..=4 {
        check_correctness_case_within_limit(
            &format!("few_keys_len2048_seed_{seed}"),
            few_unique_values(2048, 4, seed),
        );
    }
}


fn shuffled(size: usize, seed: u64) -> Vec<usize> {
    let mut v: Vec<usize> = (1..=size).collect();

    let mut state = seed;

    for i in (1..size).rev() {
        state ^= state << 13;
        state ^= state >> 7;
        state ^= state << 17;

        let j = (state as usize) % (i + 1);

        v.swap(i, j);
    }

    v
}

fn micros(d: Duration) -> u128 {
    d.as_micros()
}

fn input_array(size: usize, seed: u64) -> Vec<usize> {
    shuffled(size, 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.
fn run_once(size: usize, seed: usize) -> (u128, usize) {
    let mut array = input_array(size, seed as u64);

    let base_bytes = LIVE_BYTES.load(AtomicOrdering::Relaxed);
    PEAK_BYTES.store(base_bytes, AtomicOrdering::Relaxed);

    let start = Instant::now();

    benchmark_sort(&mut array);

    let elapsed = start.elapsed();
    let peak_bytes = PEAK_BYTES.load(AtomicOrdering::Relaxed);
    let aux_bytes = peak_bytes.saturating_sub(base_bytes);

    let expected: Vec<usize> = (1..=size).collect();
    if array != expected {
        panic!(
            "sort failed with seed {} for size {}",
            seed,
            size
        );
    }

    (micros(elapsed), aux_bytes)
}

fn run_child(args: &[String]) {
    let size = args[2].parse::<usize>().expect("invalid size");
    let seed = args[3].parse::<usize>().expect("invalid seed");
    let (elapsed_us, mem) = run_once(size, seed);
    println!("{} {}", elapsed_us, mem);
}

fn main() {
    let args: Vec<String> = env::args().collect();
    if args.get(1).is_some_and(|arg| arg == "--run-once") {
        run_child(&args);
        return;
    }

    run_correctness_checks();

    println!(
        "| {:>10} | {:>16} | {:>16} | {:>20} | {:>20} |",
        "Size",
        "Average time (s)",
        "Maximum time (s)",
        "Average memory (KiB)",
        "Maximum memory (KiB)"
    );

    println!(
        "|{:-<11}:|{:-<17}:|{:-<17}:|{:-<21}:|{:-<21}:|",
        "",
        "",
        "",
        "",
        ""
    );

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

        let mut total_time: u128 = 0;
        let mut max_time: u128 = 0;

        let mut total_mem: usize = 0;
        let mut max_mem: usize = 0;

        for seed in 1..=RUNS {
            let output = Command::new(env::current_exe().expect("failed to find current executable"))
                .arg("--run-once")
                .arg(size.to_string())
                .arg(seed.to_string())
                .output()
                .expect("failed to run benchmark child process");

            if !output.status.success() {
                panic!(
                    "benchmark child process failed: {}",
                    String::from_utf8_lossy(&output.stderr)
                );
            }

            let stdout = String::from_utf8(output.stdout)
                .expect("child process returned non-UTF-8 output");
            let mut fields = stdout.split_whitespace();
            let elapsed_us = fields
                .next()
                .expect("missing elapsed time")
                .parse::<u128>()
                .expect("invalid elapsed time");
            let aux_mem = fields
                .next()
                .expect("missing memory usage")
                .parse::<usize>()
                .expect("invalid memory usage");

            total_time += elapsed_us;

            if elapsed_us > max_time {
                max_time = elapsed_us;
            }

            total_mem += aux_mem;

            if aux_mem > max_mem {
                max_mem = aux_mem;
            }
        }

        let avg_time = total_time / RUNS as u128;
        // Memory is summed in bytes and converted to KiB once, after averaging.
        let avg_mem_kb = total_mem / RUNS / 1024;
        let max_mem_kb = max_mem / 1024;

        println!(
            "| {:>10} | {:>16} | {:>16} | {:>20} | {:>20} |",
            size,
            format!("{}.{:06}", avg_time / 1_000_000, avg_time % 1_000_000),
            format!("{}.{:06}", max_time / 1_000_000, max_time % 1_000_000),
            avg_mem_kb,
            max_mem_kb
        );
    }
}
RUST

RUN cargo build --release

CMD ["./target/release/rust-benchmark"]
EOF

docker build -t rust-benchmark "$WORKDIR"
docker run --rm --init rust-benchmark