structured_zstd/dictionary/

legacy.rs

//! The reference's original dictionary trainer (`zdict.c`,
//! `ZDICT_trainFromBuffer_legacy`), which `zstd --train-legacy` runs.
//!
//! It walks the suffix array of the whole corpus and, for every position not
//! yet covered, measures how many other positions share a prefix of at least
//! [`MIN_MATCH_LENGTH`] bytes with it. A prefix repeated often enough becomes a
//! candidate segment, scored by the bytes it would save; overlapping candidates
//! merge, and the best of them, up to the requested size, are the dictionary.
//! Selectivity sets how often "often enough" is: a candidate needs at least
//! `samples >> selectivity` repetitions, and never fewer than [`MIN_RATIO`].

use alloc::vec;
use alloc::vec::Vec;

use super::suffix_array::suffix_array;
use crate::encoding::fastpath::{
    FastpathKernel, dispatch_common_prefix_len_ptr_with_kernel, select_kernel,
};

/// Fewest repetitions that make a prefix a candidate (`MINRATIO`).
const MIN_RATIO: u32 = 4;
/// Shortest prefix counted as a repetition (`MINMATCHLENGTH`).
const MIN_MATCH_LENGTH: usize = 7;
/// Longest repetition length told apart when scoring (`LLIMIT`).
const LENGTH_LIMIT: usize = 64;
/// Smallest candidate table (`DICTLISTSIZE_DEFAULT`).
const DICT_LIST_SIZE_DEFAULT: usize = 10_000;
/// Bytes of noise after the corpus, so a comparison running off its end stops
/// on a mismatch (`NOISELENGTH`).
const NOISE_LENGTH: usize = 32;
/// Most corpus the trainer reads; whole samples beyond it are dropped
/// (`ZDICT_MAX_SAMPLES_SIZE`).
const MAX_SAMPLES_SIZE: usize = 2000 << 20;
/// Smallest dictionary content the trainer returns (`ZDICT_CONTENTSIZE_MIN`).
const CONTENT_SIZE_MIN: usize = 128;
/// Smallest corpus worth training on (`ZDICT_MIN_SAMPLES_SIZE`).
pub(crate) const MIN_SAMPLES_SIZE: usize = CONTENT_SIZE_MIN * MIN_RATIO as usize;
/// Selectivity the reference uses when none is given (`g_selectivity_default`).
pub const DEFAULT_SELECTIVITY: u32 = 9;

/// Smallest dictionary the trainer is asked for (`ZDICT_DICTSIZE_MIN`).
pub(crate) const DICT_SIZE_MIN: usize = super::MIN_TRAINED_DICT_SIZE;

/// What was too small for the legacy trainer to produce a dictionary.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub(crate) enum TooSmall {
    /// The requested size is below [`DICT_SIZE_MIN`].
    Dictionary,
    /// The corpus is smaller than [`MIN_SAMPLES_SIZE`].
    Corpus,
    /// The corpus repeats too little to fill [`CONTENT_SIZE_MIN`] bytes.
    Content,
}

/// A candidate segment (`dictItem`). In the table, entry 0 is a header whose
/// `pos` counts the entries in use, the header included, and whose `savings`
/// is the largest value, so the sorted insert stops on it.
#[derive(Debug, Clone, Copy, Default)]
struct DictItem {
    pos: u32,
    length: u32,
    savings: u32,
}

/// The reference's noise band (`ZDICT_fillNoise`), the same bytes on every run.
fn noise_band() -> [u8; NOISE_LENGTH] {
    let mut band = [0u8; NOISE_LENGTH];
    let mut acc: u32 = 2_654_435_761;
    for byte in &mut band {
        acc = acc.wrapping_mul(2_246_822_519);
        *byte = (acc >> 21) as u8;
    }
    band
}

/// The corpus followed by its noise band, read through bounds-checked
/// accessors that treat anything past the band as a mismatch.
///
/// The samples are borrowed and the band kept apart, and the accessors join
/// the two. The reference copies the whole corpus into a buffer one band
/// longer (`ZDICT_trainFromBuffer_legacy`), a second copy of the samples while
/// the caller still holds them for the finalizer.
struct Corpus<'a> {
    samples: &'a [u8],
    noise: [u8; NOISE_LENGTH],
    /// The compare kernel for this CPU, resolved once for the whole run.
    kernel: FastpathKernel,
}

impl<'a> Corpus<'a> {
    fn new(samples: &'a [u8]) -> Self {
        Self {
            samples,
            noise: noise_band(),
            kernel: select_kernel(),
        }
    }

    /// Length of the samples and the band together.
    #[inline]
    fn len(&self) -> usize {
        self.samples.len() + NOISE_LENGTH
    }

    #[inline]
    fn byte(&self, at: usize) -> Option<u8> {
        match self.samples.get(at) {
            Some(&byte) => Some(byte),
            None => self.noise.get(at - self.samples.len()).copied(),
        }
    }

    /// `N` bytes from `at`, or `None` past the band.
    #[inline(always)]
    fn read<const N: usize>(&self, at: usize) -> Option<[u8; N]> {
        if let Some(bytes) = self.samples.get(at..at + N) {
            return Some(bytes.try_into().expect("N bytes"));
        }
        self.read_across(at)
    }

    /// [`Self::read`] for a read that reaches the band, which only the last
    /// few positions of the corpus make.
    #[cold]
    #[inline(never)]
    fn read_across<const N: usize>(&self, at: usize) -> Option<[u8; N]> {
        let mut out = [0u8; N];
        for (i, slot) in out.iter_mut().enumerate() {
            *slot = self.byte(at + i)?;
        }
        Some(out)
    }

    #[inline]
    fn read16(&self, at: usize) -> Option<u16> {
        self.read::<2>(at).map(u16::from_le_bytes)
    }

    #[inline]
    fn read64(&self, at: usize) -> Option<u64> {
        self.read::<8>(at).map(u64::from_le_bytes)
    }

    /// Bytes `a` and `b` have in common (`ZDICT_count`): through the CPU's
    /// vector compare while both runs lie in the samples, where the corpus'
    /// long repeats make the comparison most of the analysis, then a byte at
    /// a time across into the band.
    #[inline]
    fn common(&self, a: usize, b: usize) -> usize {
        let samples = self.samples;
        // Every position compared is a suffix, below the samples' length, or
        // the noise slot, at it; one at the slot compares nothing in the
        // samples and goes straight to the band.
        debug_assert!(a.max(b) <= samples.len());
        let in_samples = samples.len() - a.max(b);
        let base = samples.as_ptr();
        // SAFETY: `a, b <= max(a, b)` and `in_samples == samples.len() -
        // max(a, b)`, so both runs of `in_samples` bytes lie in the samples.
        let n = unsafe {
            dispatch_common_prefix_len_ptr_with_kernel(
                self.kernel,
                base.add(a),
                base.add(b),
                in_samples,
            )
        };
        if n < in_samples {
            return n;
        }
        self.common_tail(a, b, n)
    }

    /// The bytes of [`Self::common`] from `n` on, where the shorter run has
    /// reached the end of the samples: on into the band.
    #[cold]
    #[inline(never)]
    fn common_tail(&self, a: usize, b: usize, mut n: usize) -> usize {
        let Some(limit) = self.len().checked_sub(a.max(b)) else {
            return 0;
        };
        while n < limit && self.byte(a + n) == self.byte(b + n) {
            n += 1;
        }
        n
    }

    /// Copy the `out.len()` bytes from `from` into `out`.
    fn copy_to(&self, from: usize, out: &mut [u8]) {
        if let Some(bytes) = self.samples.get(from..from + out.len()) {
            out.copy_from_slice(bytes);
            return;
        }
        for (i, slot) in out.iter_mut().enumerate() {
            *slot = self
                .byte(from + i)
                .expect("a segment lies inside the corpus");
        }
    }
}

/// How many text positions ahead the analysis warms the suffix-array line
/// around a position's rank.
const FAR_AHEAD: usize = 16;

/// How many text positions ahead the analysis warms the text of a position's
/// two neighbours in suffix order.
const NEAR_AHEAD: usize = 8;

/// The suffix array with one extra slot on each side, both pointing into the
/// noise band, as the reference lays it out (`suffix0[0]` and
/// `suffix[bufferSize]`): a walk off either end compares against noise and
/// stops there.
struct Suffixes {
    sa: Vec<u32>,
    noise: usize,
}

impl Suffixes {
    fn new(sa: Vec<u32>, len: usize) -> Self {
        Self { sa, noise: len }
    }

    /// Ranks in the array; rank `ranks()` is the upper noise slot.
    #[inline]
    fn ranks(&self) -> i64 {
        self.sa.len() as i64
    }

    /// `suffix[at]`, where ranks `-1` and `len` are the noise band (the walks
    /// stop at those two slots). A negative rank wraps past every real one,
    /// so a single compare tells the two apart.
    #[inline]
    fn at(&self, at: i64) -> usize {
        match self.sa.get(at as u64 as usize) {
            Some(&pos) => pos as usize,
            None => self.noise,
        }
    }

    /// Warm what the analysis of text position `cursor` will read, ahead of
    /// reaching it: its rank is random, so the array around that rank and the
    /// text of the two neighbours there miss the cache every time. The array
    /// line is warmed for the position [`FAR_AHEAD`] on, the neighbours' text
    /// for the one [`NEAR_AHEAD`] on, whose array line that earlier hint has
    /// brought in. A hint only; ranks at either end read a clamped slot.
    #[inline(always)]
    fn prefetch_for(&self, rank: &[u32], samples: &[u8], cursor: usize) {
        use crate::decoding::prefetch::prefetch_l1_at;
        let len = self.sa.len();
        if let Some(&far) = rank.get(cursor + FAR_AHEAD) {
            prefetch_l1_at(self.sa.as_ptr().wrapping_add(far as usize).cast());
        }
        if let Some(&near) = rank.get(cursor + NEAR_AHEAD) {
            let near = near as usize;
            // Rank 0 wraps past the end and clamps with the top rank.
            let below = near.wrapping_sub(1).min(len - 1);
            let above = (near + 1).min(len - 1);
            // SAFETY: both are clamped below `len == self.sa.len()`.
            let (below, above) = unsafe {
                (
                    *self.sa.get_unchecked(below) as usize,
                    *self.sa.get_unchecked(above) as usize,
                )
            };
            prefetch_l1_at(samples.as_ptr().wrapping_add(below));
            prefetch_l1_at(samples.as_ptr().wrapping_add(above));
        }
    }
}

/// Train dictionary content from `samples`, the concatenation of samples whose
/// lengths are `sample_sizes`, keeping at most `dict_size` bytes.
///
/// The segments are laid out best last, so the most valuable content sits
/// nearest the data and is reached with the smallest offsets. `selectivity` of
/// zero is [`DEFAULT_SELECTIVITY`].
pub(crate) fn train_legacy_raw(
    samples: &[u8],
    sample_sizes: &[usize],
    dict_size: usize,
    selectivity: u32,
) -> Result<Vec<u8>, TooSmall> {
    let total: usize = sample_sizes.iter().sum();
    debug_assert_eq!(total, samples.len(), "the sizes describe the corpus");
    // The corpus first, as upstream checks it before anything else
    // (zdict.c, `ZDICT_trainFromBuffer_legacy`).
    if total < MIN_SAMPLES_SIZE {
        return Err(TooSmall::Corpus);
    }
    if dict_size < DICT_SIZE_MIN {
        return Err(TooSmall::Dictionary);
    }
    let selectivity = if selectivity == 0 {
        DEFAULT_SELECTIVITY
    } else {
        selectivity
    };
    let nb_samples = sample_sizes.len();
    let min_rep = if selectivity > 30 {
        MIN_RATIO
    } else {
        // A repetition count past u32 is more than a u32-indexed corpus has
        // positions, so nothing could qualify.
        u32::try_from(nb_samples >> selectivity).map_err(|_| TooSmall::Content)?
    };
    let list_size = DICT_LIST_SIZE_DEFAULT.max(nb_samples).max(dict_size / 16);
    let mut list = vec![DictItem::default(); list_size];
    list[0] = DictItem {
        pos: 1,
        length: 0,
        savings: u32::MAX,
    };

    // Whole samples past the size limit are left out, last first.
    let mut used = total;
    let mut kept = nb_samples;
    while used > MAX_SAMPLES_SIZE {
        kept -= 1;
        used -= sample_sizes[kept];
    }
    let corpus = Corpus::new(&samples[..used]);
    find_segments(&mut list, &corpus, used, min_rep);

    let segments = list[0].pos as usize;
    let content_size: usize = list[1..segments].iter().map(|d| d.length as usize).sum();
    if content_size < CONTENT_SIZE_MIN {
        return Err(TooSmall::Content);
    }
    // Keep the best segments that fit, in rank order.
    let mut fit = 1;
    let mut size = 0usize;
    while fit < segments {
        let next = size + list[fit].length as usize;
        if next > dict_size {
            break;
        }
        size = next;
        fit += 1;
    }
    // Filled from the back, as the reference fills its buffer: rank 1 last.
    let mut content = vec![0u8; size];
    let mut end = size;
    for item in &list[1..fit] {
        let length = item.length as usize;
        let start = end - length;
        let from = item.pos as usize;
        corpus.copy_to(from, &mut content[start..end]);
        end = start;
    }
    debug_assert_eq!(end, 0, "the kept segments fill the content exactly");
    Ok(content)
}

/// `ZDICT_trainBuffer_legacy`: walk every uncovered position of the corpus in
/// text order and insert the segment its suffix neighbourhood yields.
fn find_segments(list: &mut [DictItem], corpus: &Corpus<'_>, len: usize, min_rep: u32) {
    let min_ratio = min_rep.max(MIN_RATIO);
    debug_assert_eq!(corpus.samples.len(), len);
    let sa = suffix_array(corpus.samples);
    let mut rank = vec![0u32; len];
    for (at, &pos) in sa.iter().enumerate() {
        rank[pos as usize] = at as u32;
    }
    let suffixes = Suffixes::new(sa, len);
    // Slack past the corpus, as the reference allocates it: a covered run may
    // be marked into the noise band.
    let mut done = vec![false; len + 16];
    let max_size = list.len() as u32;

    let mut cursor = 0usize;
    while cursor < len {
        suffixes.prefetch_for(&rank, corpus.samples, cursor);
        if done[cursor] {
            cursor += 1;
            continue;
        }
        let solution = analyze_position(
            &mut done,
            &suffixes,
            i64::from(rank[cursor]),
            corpus,
            min_ratio,
        );
        if solution.length == 0 {
            cursor += 1;
            continue;
        }
        insert_item(list, max_size, solution, corpus);
        cursor += solution.length as usize;
    }
}

/// Mark `at` covered, if it lies inside the marks.
#[inline]
fn mark(done: &mut [bool], at: usize) {
    if let Some(slot) = done.get_mut(at) {
        *slot = true;
    }
}

/// Mark `len` positions from `at` covered, as far as the marks reach. Both
/// are bounded by the corpus length, so the sum cannot overflow.
#[inline]
fn mark_run(done: &mut [bool], at: usize, len: usize) {
    let end = (at + len).min(done.len());
    if at < end {
        done[at..end].fill(true);
    }
}

/// `ZDICT_analyzePos`: the segment the suffix of rank `start` leads to, or an
/// empty one. Every position the analysis settles is marked in `done`.
fn analyze_position(
    done: &mut [bool],
    suffixes: &Suffixes,
    mut start: i64,
    corpus: &Corpus<'_>,
    min_ratio: u32,
) -> DictItem {
    let mut pos = suffixes.at(start);
    let mut end = start;
    let empty = DictItem::default();
    mark(done, pos);

    // A run of one repeated pair is skipped whole: it compresses without a
    // dictionary.
    let repeats = |a: usize, b: usize| matches!((corpus.read16(a), corpus.read16(b)), (Some(x), Some(y)) if x == y);
    if repeats(pos, pos + 2) || repeats(pos + 1, pos + 3) || repeats(pos + 2, pos + 4) {
        let pattern = corpus.read16(pos + 4);
        let mut pattern_end = 6usize;
        while pattern.is_some() && corpus.read16(pos + pattern_end) == pattern {
            pattern_end += 2;
        }
        if corpus.byte(pos + pattern_end).is_some()
            && corpus.byte(pos + pattern_end) == corpus.byte(pos + pattern_end - 1)
        {
            pattern_end += 1;
        }
        mark_run(done, pos + 1, pattern_end - 1);
        return empty;
    }

    // The neighbours sharing at least the minimum length, forward then back.
    // Each walk stops at its noise slot as well as on a short match: every
    // rank past the array reads the same band, so a corpus that repeats the
    // band would otherwise walk forever. The reference reads past its two
    // slots there, so it has no result to keep; on every other corpus the
    // slot holds noise that ends the walk anyway.
    loop {
        end += 1;
        if end >= suffixes.ranks() || corpus.common(pos, suffixes.at(end)) < MIN_MATCH_LENGTH {
            break;
        }
    }
    while start > 0 && corpus.common(pos, suffixes.at(start - 1)) >= MIN_MATCH_LENGTH {
        start -= 1;
    }

    if ((end - start) as u32) < min_ratio {
        for id in start..end {
            mark(done, suffixes.at(id));
        }
        return empty;
    }

    // Lengthen the shared prefix one byte at a time while the most common
    // continuation still repeats often enough.
    let mut refined_start = start;
    let mut refined_end = end;
    let mut mml = MIN_MATCH_LENGTH;
    loop {
        let mut current_char = 0u8;
        let mut current_count = 0u32;
        let mut current_id = refined_start;
        let mut selected_count = 0u32;
        let mut selected_id = current_id;
        for id in refined_start..refined_end {
            let c = corpus.byte(suffixes.at(id) + mml).unwrap_or(0);
            if c != current_char {
                if current_count > selected_count {
                    selected_count = current_count;
                    selected_id = current_id;
                }
                current_id = id;
                current_char = c;
                current_count = 0;
            }
            current_count += 1;
        }
        if current_count > selected_count {
            selected_count = current_count;
            selected_id = current_id;
        }
        if selected_count < min_ratio {
            break;
        }
        refined_start = selected_id;
        refined_end = refined_start + i64::from(selected_count);
        mml += 1;
    }

    // Measure the refined segment's neighbourhood.
    start = refined_start;
    pos = suffixes.at(refined_start);
    end = start;
    let mut lengths = [0u32; LENGTH_LIMIT];
    loop {
        end += 1;
        let length = corpus.common(pos, suffixes.at(end)).min(LENGTH_LIMIT - 1);
        lengths[length] += 1;
        // The upper noise slot is counted, as the reference counts it, and
        // ends the walk (see the first walk above).
        if length < MIN_MATCH_LENGTH || end >= suffixes.ranks() {
            break;
        }
    }
    {
        let mut length = MIN_MATCH_LENGTH;
        while length >= MIN_MATCH_LENGTH && start > 0 {
            length = corpus
                .common(pos, suffixes.at(start - 1))
                .min(LENGTH_LIMIT - 1);
            lengths[length] += 1;
            if length >= MIN_MATCH_LENGTH {
                start -= 1;
            }
        }
    }

    // The longest length still shared by enough neighbours.
    let mut cumulative = [0u32; LENGTH_LIMIT];
    cumulative[LENGTH_LIMIT - 1] = lengths[LENGTH_LIMIT - 1];
    for i in (0..LENGTH_LIMIT - 1).rev() {
        cumulative[i] = cumulative[i + 1] + lengths[i];
    }
    let mut max_length = LENGTH_LIMIT - 1;
    while max_length >= MIN_MATCH_LENGTH && cumulative[max_length] < min_ratio {
        max_length -= 1;
    }
    // Do not end inside a run of the last byte.
    {
        let last = corpus.byte(pos + max_length - 1);
        let mut l = max_length;
        while l >= 2 && corpus.byte(pos + l - 2) == last {
            l -= 1;
        }
        max_length = l;
    }
    if max_length < MIN_MATCH_LENGTH {
        return empty;
    }

    let mut savings = [0u32; LENGTH_LIMIT];
    for i in MIN_MATCH_LENGTH..=max_length {
        savings[i] = savings[i - 1].wrapping_add(lengths[i].wrapping_mul((i - 3) as u32));
    }
    let solution = DictItem {
        pos: pos as u32,
        length: max_length as u32,
        savings: savings[max_length],
    };

    for id in start..end {
        let tested = suffixes.at(id);
        let length = if tested == pos {
            max_length
        } else {
            corpus.common(pos, tested).min(max_length)
        };
        mark_run(done, tested, length);
    }
    solution
}

/// Whether the `length` bytes at `a` equal those at `b` (`isIncluded`); both
/// runs must lie inside the corpus. Compares `length` bytes and no more, where
/// `common` would run on to the end of the shared prefix.
fn is_included(corpus: &Corpus<'_>, a: usize, b: usize, length: usize) -> bool {
    let samples = corpus.samples;
    if let (Some(x), Some(y)) = (samples.get(a..a + length), samples.get(b..b + length)) {
        return x == y;
    }
    a.max(b) + length <= corpus.len()
        && (0..length).all(|i| corpus.byte(a + i) == corpus.byte(b + i))
}

/// Move entry `at` towards the front while its savings beat its predecessor's.
fn promote(list: &mut [DictItem], mut at: usize) -> usize {
    let item = list[at];
    while at > 1 && list[at - 1].savings < item.savings {
        list[at] = list[at - 1];
        at -= 1;
    }
    list[at] = item;
    at
}

/// `ZDICT_tryMerge`: fold `elt` into an entry it overlaps, skipping entry
/// `skip`. Returns the merged entry's index, or 0 when nothing merged.
fn try_merge(list: &mut [DictItem], elt: DictItem, skip: usize, corpus: &Corpus<'_>) -> usize {
    let size = list[0].pos as usize;
    let elt_end = elt.pos + elt.length;

    // An existing entry starts inside `elt`: extend it backwards. The scans
    // walk the table as a slice, and the rare skipped entry is tested last.
    let mut hit = 0;
    for (u, item) in list[..size].iter().enumerate().skip(1) {
        if item.pos > elt.pos && item.pos <= elt_end && u != skip {
            hit = u;
            break;
        }
    }
    if hit != 0 {
        let item = &mut list[hit];
        let added = item.pos - elt.pos;
        item.length += added;
        item.pos = elt.pos;
        item.savings = item
            .savings
            .wrapping_add(elt.savings.wrapping_mul(added) / elt.length);
        item.savings = item.savings.wrapping_add(elt.length / 8);
        return promote(list, hit);
    }

    // `elt` starts inside an existing entry, or right after a copy of it. The
    // eight bytes after `elt`'s start are the same for every entry, so they
    // are read once rather than per entry as the reference reads them.
    let elt_head = corpus.read64(elt.pos as usize + 1);
    for u in 1..size {
        let item = list[u];
        if u == skip {
            continue;
        }
        if item.pos + item.length >= elt.pos && item.pos < elt.pos {
            let added = elt_end as i64 - i64::from(item.pos + item.length);
            let item = &mut list[u];
            item.savings = item.savings.wrapping_add(elt.length / 8);
            if added > 0 {
                item.length += added as u32;
                item.savings = item
                    .savings
                    .wrapping_add(elt.savings.wrapping_mul(added as u32) / elt.length);
            }
            return promote(list, u);
        }
        if elt_head.is_some()
            && corpus.read64(item.pos as usize) == elt_head
            && is_included(
                corpus,
                item.pos as usize,
                elt.pos as usize + 1,
                item.length as usize,
            )
        {
            // The reference takes this product at pointer width, where it does
            // not wrap, unlike the two above.
            let added = (i64::from(elt.length) - i64::from(item.length)).max(1) as u64;
            let item = &mut list[u];
            item.pos = elt.pos;
            item.savings = item
                .savings
                .wrapping_add((u64::from(elt.savings) * added / u64::from(elt.length)) as u32);
            item.length = elt.length.min(item.length + 1);
            return u;
        }
    }
    0
}

/// `ZDICT_removeDictItem`.
fn remove_item(list: &mut [DictItem], id: usize) {
    if id == 0 {
        return;
    }
    let max = list[0].pos as usize;
    for u in id..max - 1 {
        list[u] = list[u + 1];
    }
    list[0].pos -= 1;
}

/// `ZDICT_insertDictItem`: merge `elt` into the table if it overlaps an entry,
/// and keep merging while the merged entry overlaps another; otherwise insert
/// it in savings order, dropping the last entry when the table is full.
fn insert_item(list: &mut [DictItem], max_size: u32, elt: DictItem, corpus: &Corpus<'_>) {
    let mut merge_id = try_merge(list, elt, 0, corpus);
    if merge_id != 0 {
        loop {
            let merged = try_merge(list, list[merge_id], merge_id, corpus);
            if merged == 0 {
                return;
            }
            remove_item(list, merge_id);
            merge_id = merged;
        }
    }
    let next = list[0].pos.min(max_size - 1) as usize;
    let mut current = next - 1;
    while list[current].savings < elt.savings {
        list[current + 1] = list[current];
        current -= 1;
    }
    list[current + 1] = elt;
    list[0].pos = next as u32 + 1;
}

#[cfg(test)]
mod tests;