フランチェスキーニ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::{
    env,
    process::Command,
    time::{Duration, Instant},
};
const MIN_POWER: u32 = 8;
const MAX_POWER: u32 = 18;
const RUNS: usize = 8192;


// Pedagogical Franceschini–Geffert skeleton:
// peel ~n/4 elements by rank, sort that prefix with the remaining suffix as a
// swap buffer via a high-arity heap (constant-ish height → few moves per element),
// then recurse on the unsorted suffix. The published algorithm adds sample /
// segment / bit-encoding machinery for full O(n)-move asymptotics; this port
// keeps the outer structure and the d-ary heap idea for measurement.

fn franceschini_branch_factor(len: usize) -> usize {
    if len <= 2 {
        return 2;
    }
    // Aim for heap height around 4: d ≈ n^(1/4).
    let mut d = 2usize;
    while d * d * d * d < len {
        d += 1;
        if d > 64 {
            break;
        }
    }
    d.max(2)
}

fn franceschini_child(parent: usize, which: usize, d: usize) -> usize {
    parent * d + 1 + which
}

fn franceschini_sift_down(a: &mut [usize], mut root: usize, end: usize, d: usize) {
    loop {
        let first = franceschini_child(root, 0, d);
        if first > end {
            break;
        }
        let mut best = first;
        let last = (first + d - 1).min(end);
        for child in first + 1..=last {
            if a[child] > a[best] {
                best = child;
            }
        }
        if a[root] >= a[best] {
            break;
        }
        a.swap(root, best);
        root = best;
    }
}

fn franceschini_dary_heap_sort(a: &mut [usize]) {
    let n = a.len();
    if n <= 1 {
        return;
    }
    let d = franceschini_branch_factor(n);
    let last_parent = (n - 2) / d;
    for start in (0..=last_parent).rev() {
        franceschini_sift_down(a, start, n - 1, d);
    }
    for end in (1..n).rev() {
        a.swap(0, end);
        if end > 1 {
            franceschini_sift_down(a, 0, end - 1, d);
        }
    }
}

fn franceschini_insertion_sort(a: &mut [usize]) {
    for i in 1..a.len() {
        let key = a[i];
        let mut j = i;
        while j > 0 && a[j - 1] > key {
            a[j] = a[j - 1];
            j -= 1;
        }
        a[j] = key;
    }
}

fn franceschini_partition_at(a: &mut [usize], left: usize, right: usize, pivot_index: usize) -> usize {
    a.swap(pivot_index, right);
    let pivot = a[right];
    let mut store = left;
    for i in left..right {
        if a[i] < pivot {
            a.swap(store, i);
            store += 1;
        }
    }
    a.swap(store, right);
    store
}

fn franceschini_quickselect(a: &mut [usize], mut left: usize, mut right: usize, k: usize) {
    while left < right {
        let mid = left + (right - left) / 2;
        // Median-of-three pivot index.
        if a[right] < a[left] {
            a.swap(left, right);
        }
        if a[mid] < a[left] {
            a.swap(left, mid);
        }
        if a[right] < a[mid] {
            a.swap(mid, right);
        }
        let pivot_index = franceschini_partition_at(a, left, right, mid);
        if k == pivot_index {
            return;
        } else if k < pivot_index {
            if pivot_index == 0 {
                return;
            }
            right = pivot_index - 1;
        } else {
            left = pivot_index + 1;
        }
    }
}

fn franceschini_sort_with_buffer(active: &mut [usize], buffer: &mut [usize]) {
    let m = active.len();
    if m == 0 {
        return;
    }
    debug_assert!(buffer.len() >= m);
    for i in 0..m {
        std::mem::swap(&mut active[i], &mut buffer[i]);
    }
    if m <= 32 {
        franceschini_insertion_sort(&mut buffer[..m]);
    } else {
        franceschini_dary_heap_sort(&mut buffer[..m]);
    }
    for i in 0..m {
        std::mem::swap(&mut active[i], &mut buffer[i]);
    }
}

fn franceschini_rec(a: &mut [usize]) {
    let n = a.len();
    if n <= 1 {
        return;
    }
    if n <= 64 {
        if n <= 32 {
            franceschini_insertion_sort(a);
        } else {
            franceschini_dary_heap_sort(a);
        }
        return;
    }

    let rank = n / 4;
    franceschini_quickselect(a, 0, n - 1, rank);
    let pivot = a[rank];

    let mut split = 0usize;
    for i in 0..n {
        if a[i] < pivot {
            a.swap(split, i);
            split += 1;
        }
    }

    // Need a non-empty active prefix and a buffer at least as large.
    if split == 0 || split > n - split {
        franceschini_dary_heap_sort(a);
        return;
    }

    {
        let (left, right) = a.split_at_mut(split);
        franceschini_sort_with_buffer(left, right);
    }

    franceschini_rec(&mut a[split..]);
}

fn franceschini_sort(a: &mut [usize]) {
    franceschini_rec(a);
}


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

    franceschini_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);
    }
}

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],
    );
    for seed in 0..32 {
        check_correctness_case(
            &format!("few_keys_len32_seed_{seed}"),
            few_unique_values(32, 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 memory_usage_kb() -> usize {
    // VmHWM (peak RSS, KiB). Reported memory subtracts a per-size baseline that only
    // holds the input array, so the table reflects auxiliary space during sorting.
    let contents = std::fs::read_to_string("/proc/self/status")
        .unwrap_or_default();

    for line in contents.lines() {
        if let Some(rest) = line.strip_prefix("VmHWM:") {
            let kb = rest
                .split_whitespace()
                .next()
                .unwrap_or("0")
                .parse::<usize>()
                .unwrap_or(0);

            return kb;
        }
    }

    0
}

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

fn input_array(size: usize, seed: u64) -> Vec<usize> {
    shuffled(size, seed)
}

fn run_baseline(size: usize) -> usize {
    let _hold = input_array(size, 1);
    memory_usage_kb()
}

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

    let start = Instant::now();

    benchmark_sort(&mut array);

    let elapsed = start.elapsed();
    let mem = memory_usage_kb();

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

    (micros(elapsed), mem)
}

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

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 == "--baseline-once") {
        run_baseline_child(&args);
        return;
    }
    if args.get(1).is_some_and(|arg| arg == "--run-once") {
        run_child(&args);
        return;
    }

    run_correctness_checks();

    println!(
        "| {:>10} | {:>15} | {:>15} | {:>15} | {:>15} |",
        "Size",
        "Average time",
        "Maximum time",
        "Average memory",
        "Maximum memory"
    );

    println!(
        "|{:-<11}:|{:-<16}:|{:-<16}:|{:-<16}:|{:-<16}:|",
        "",
        "",
        "",
        "",
        ""
    );

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

        let baseline_output = Command::new(env::current_exe().expect("failed to find current executable"))
            .arg("--baseline-once")
            .arg(size.to_string())
            .output()
            .expect("failed to run benchmark baseline process");

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

        let baseline_stdout = String::from_utf8(baseline_output.stdout)
            .expect("baseline process returned non-UTF-8 output");
        let baseline_mem = baseline_stdout
            .split_whitespace()
            .next()
            .expect("missing baseline memory usage")
            .parse::<usize>()
            .expect("invalid baseline memory usage");

        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 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;
            }

            let aux_mem = mem.saturating_sub(baseline_mem);

            total_mem += aux_mem;

            if aux_mem > max_mem {
                max_mem = aux_mem;
            }
        }

        let avg_time = total_time / RUNS as u128;
        let avg_mem = total_mem / RUNS;

        println!(
            "| {:>10} | {:>15} | {:>15} | {:>15} | {:>15} |",
            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,
            max_mem
        );
    }
}
RUST

RUN cargo build --release

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

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