Wildcards: match * and ? patterns in one pass over the text

After a mismatch the matcher restarted the pattern after the last
star at the next text position, so a long repetitive cell against a
near-matching pattern cost text x pattern comparisons. AutoFilter
custom criteria, Find and Replace all call it once per cell.

wildcard() now runs the pattern as a bit-parallel automaton: one pass
over the text, one step per 64 pattern positions for each character.
Results are unchanged; a test compares it with the old matcher on
every short text and pattern over a small alphabet.

crates/engine/src/cmd/edit/find.rs

@@ -14,8 +14,13 @@ fn matches(hay: &str, what: &str, case: bool, whole: bool) -> bool {
 }
 
 /// `*`/`?` wildcard match with `~` escapes.
+///
+/// The pattern runs as a bit-parallel automaton over the text: one pass, each character costing
+/// one step per 64 pattern positions. Backtracking to the last `*` after a mismatch rescans the
+/// text and costs text × pattern comparisons on a long, repetitive cell, for every cell a
+/// filter or Find visits.
 pub(crate) fn wildcard(text: &str, pat: &str) -> bool {
-    let t: Vec<char> = text.chars().collect();
+    // The pattern as (character, escaped) items, runs of `*` folded into one.
     let mut p: Vec<(char, bool)> = Vec::new();
     let mut it = pat.chars();
     while let Some(c) = it.next() {
@@ -23,32 +28,56 @@ pub(crate) fn wildcard(text: &str, pat: &str) -> bool {
             if let Some(n) = it.next() {
                 p.push((n, true));
             }
-        } else {
+        } else if c != '*' || p.last() != Some(&('*', false)) {
             p.push((c, false));
         }
     }
-    let (mut ti, mut pi) = (0usize, 0usize);
-    let (mut star, mut mark) = (None, 0usize);
-    while ti < t.len() {
-        if pi < p.len() && (p[pi] == ('?', false) || (p[pi].0 == t[ti] && p[pi] != ('*', false))) {
-            ti += 1;
-            pi += 1;
-        } else if pi < p.len() && p[pi] == ('*', false) {
-            star = Some(pi);
-            mark = ti;
-            pi += 1;
-        } else if let Some(sp) = star {
-            pi = sp + 1;
-            mark += 1;
-            ti = mark;
-        } else {
-            return false;
+    let words = (p.len() + 1).div_ceil(64);
+    let bit = |set: &mut [u64], i: usize| set[i / 64] |= 1 << (i % 64);
+    // Positions holding a `*`, a `?`, and each literal character.
+    let mut stars = vec![0u64; words];
+    let mut any = vec![0u64; words];
+    let mut lits: std::collections::HashMap<char, Vec<u64>> = std::collections::HashMap::new();
+    for (i, item) in p.iter().enumerate() {
+        match item {
+            ('*', false) => bit(&mut stars, i),
+            ('?', false) => bit(&mut any, i),
+            (c, _) => bit(lits.entry(*c).or_insert_with(|| vec![0u64; words]), i),
         }
     }
-    while pi < p.len() && p[pi] == ('*', false) {
-        pi += 1;
+    // A set bit i: the text read so far matches the first i pattern items. A `*` matches nothing
+    // as well, so a state at a `*` is also at the item after it.
+    let close = |set: &mut Vec<u64>| {
+        let mut carry = 0u64;
+        for w in 0..words {
+            let s = set[w] & stars[w];
+            let next = (s << 1) | carry;
+            carry = s >> 63;
+            set[w] |= next;
+        }
+    };
+    let mut state = vec![0u64; words];
+    bit(&mut state, 0);
+    close(&mut state);
+    let mut next = vec![0u64; words];
+    for ch in text.chars() {
+        let lit = lits.get(&ch);
+        let mut carry = 0u64;
+        let mut alive = 0u64;
+        for w in 0..words {
+            // Items that read `ch` advance; a `*` reads it and stays.
+            let m = state[w] & (any[w] | lit.map_or(0, |l| l[w]));
+            next[w] = (m << 1) | carry | (state[w] & stars[w]);
+            carry = m >> 63;
+            alive |= next[w];
+        }
+        if alive == 0 {
+            return false;
+        }
+        std::mem::swap(&mut state, &mut next);
+        close(&mut state);
     }
-    pi == p.len()
+    state[p.len() / 64] & (1 << (p.len() % 64)) != 0
 }
 
 pub(super) fn find(s: &mut Session, p: &Json) -> Result<Json> {

crates/engine/src/cmd/edit/tests.rs

@@ -302,6 +302,79 @@ fn wildcards() {
     assert!(wildcard("", "*"));
 }
 
+/// The backtracking matcher `wildcard` replaced, as the reference for its results.
+fn wildcard_backtracking(text: &str, pat: &str) -> bool {
+    let t: Vec<char> = text.chars().collect();
+    let mut p: Vec<(char, bool)> = Vec::new();
+    let mut it = pat.chars();
+    while let Some(c) = it.next() {
+        if c == '~' {
+            if let Some(n) = it.next() {
+                p.push((n, true));
+            }
+        } else {
+            p.push((c, false));
+        }
+    }
+    let (mut ti, mut pi) = (0usize, 0usize);
+    let (mut star, mut mark) = (None, 0usize);
+    while ti < t.len() {
+        if pi < p.len() && (p[pi] == ('?', false) || (p[pi].0 == t[ti] && p[pi] != ('*', false))) {
+            ti += 1;
+            pi += 1;
+        } else if pi < p.len() && p[pi] == ('*', false) {
+            star = Some(pi);
+            mark = ti;
+            pi += 1;
+        } else if let Some(sp) = star {
+            pi = sp + 1;
+            mark += 1;
+            ti = mark;
+        } else {
+            return false;
+        }
+    }
+    while pi < p.len() && p[pi] == ('*', false) {
+        pi += 1;
+    }
+    pi == p.len()
+}
+
+#[test]
+fn wildcard_agrees_with_backtracking() {
+    // Every text up to 5 characters over a small alphabet against every pattern up to 4 items.
+    let alphabet = ['a', 'b', '*', '?', '~'];
+    let all = |n: usize, chars: &[char]| -> Vec<String> {
+        let mut out = vec![String::new()];
+        let mut level = vec![String::new()];
+        for _ in 0..n {
+            level = level.iter().flat_map(|s| chars.iter().map(move |c| format!("{s}{c}"))).collect();
+            out.extend(level.iter().cloned());
+        }
+        out
+    };
+    let texts = all(5, &['a', 'b', '*']);
+    for pat in all(4, &alphabet) {
+        for text in &texts {
+            assert_eq!(wildcard(text, &pat), wildcard_backtracking(text, &pat), "{text:?} ~ {pat:?}");
+        }
+    }
+    // Patterns longer than one 64-bit word.
+    let long = format!("*{}*b?", "a".repeat(70));
+    for text in [format!("x{}yb1", "a".repeat(70)), format!("{}b", "a".repeat(71)), "a".repeat(200)] {
+        assert_eq!(wildcard(&text, &long), wildcard_backtracking(&text, &long), "{text}");
+    }
+}
+
+#[test]
+fn wildcard_on_long_repetitive_text_is_linear() {
+    // The backtracking matcher compared about text × pattern characters here (10^8).
+    let text = "a".repeat(20_000);
+    let pat = format!("*{}b", "a".repeat(5_000));
+    assert!(!wildcard(&text, &pat));
+    assert!(wildcard(&format!("{text}b"), &pat));
+}
+
 #[test]
 fn tsv() {
     assert_eq!(parse_tsv("a\tb\n1\t2\n"), vec![vec!["a", "b"], vec!["1", "2"]]);

crates/engine/src/cmd/print/draw.rs

@@ -228,82 +228,6 @@ fn draw_border(pg: &mut Page, b: &BorderLine, wb: &Workbook, start: Point, end:
     pg.stroke_line_dashed(Point::new(x0, y0), Point::new(x1, y1), lw, color, &border_dash(b.style, k));
 }
 
-/// Merged areas active at one row of a downward sweep, kept disjoint: by first column, their last
-/// column and last row. Adding, dropping and looking up a merge costs log(active merges).
-#[derive(Default)]
-struct MergeSweep {
-    cols: std::collections::BTreeMap<u32, (u32, u32)>,
-    /// (last row, first column) of the active merges, soonest ending first.
-    ends: std::collections::BinaryHeap<std::cmp::Reverse<(u32, u32)>>,
-}
-
-impl MergeSweep {
-    /// Moves down to `row` (rows never decrease), dropping the merges that end above it.
-    fn advance(&mut self, row: u32) {
-        while let Some(std::cmp::Reverse((end, col))) = self.ends.peek().copied() {
-            if end >= row {
-                break;
-            }
-            self.ends.pop();
-            self.cols.remove(&col);
-        }
-    }
-
-    /// Does an active merge meet columns `c0..=c1`? The intervals are disjoint, so only the last
-    /// one starting at or before `c1` can.
-    fn meets(&self, c0: u32, c1: u32) -> bool {
-        self.cols.range(..=c1).next_back().is_some_and(|(_, (end, _))| *end >= c0)
-    }
-
-    /// Adds merge `m`, at row `row`, unless it overlaps an active one.
-    fn add(&mut self, m: RangeRef, row: u32) -> bool {
-        self.advance(row);
-        if self.meets(m.start.col, m.end.col) {
-            return false;
-        }
-        self.cols.insert(m.start.col, (m.end.col, m.end.row));
-        self.ends.push(std::cmp::Reverse((m.end.row, m.start.col)));
-        true
-    }
-}
-
-/// The merged areas that meet `block`, ordered by the row where they enter it, then by column,
-/// leaving out any that overlaps one kept before it (only a damaged file has overlapping merges;
-/// Excel drops them when it repairs one). One sweep down the rows instead of a scan of every
-/// merge per cell.
-fn block_merges(sh: &Sheet, block: RangeRef) -> Vec<RangeRef> {
-    let top = |m: &RangeRef| m.start.row.max(block.start.row);
-    let mut merges: Vec<RangeRef> = sh.merges.iter().filter(|m| m.intersects(&block)).copied().collect();
-    merges.sort_by_key(|m| (top(m), m.start.col));
-    let mut sweep = MergeSweep::default();
-    merges.retain(|m| sweep.add(*m, top(m)));
-    merges
-}
-
-/// Answers "is this cell inside a merge?" for cells asked in row-major order, from the merges of
-/// [`block_merges`].
-struct Covered<'a> {
-    merges: &'a [RangeRef],
-    top: u32,
-    next: usize,
-    sweep: MergeSweep,
-}
-
-impl<'a> Covered<'a> {
-    fn new(merges: &'a [RangeRef], block: RangeRef) -> Self {
-        Self { merges, top: block.start.row, next: 0, sweep: MergeSweep::default() }
-    }
-
-    fn covers(&mut self, c: CellRef) -> bool {
-        while let Some(m) = self.merges.get(self.next).filter(|m| m.start.row.max(self.top) <= c.row) {
-            self.sweep.add(*m, m.start.row.max(self.top));
-            self.next += 1;
-        }
-        self.sweep.advance(c.row);
-        self.sweep.meets(c.col, c.col)
-    }
-}
-
 /// Draws the cells of a block: fills, gridlines, data bars, borders and text.
 pub(super) fn draw_block(pg: &mut Page, b: &Block, gridlines: bool, cf: &mut Option<crate::cf::CfCache>) {
     let (bx, by) = (b.xs.first().copied().unwrap_or(0.0), b.ys.first().copied().unwrap_or(0.0));
@@ -313,18 +237,17 @@ pub(super) fn draw_block(pg: &mut Page, b: &Block, gridlines: bool, cf: &mut Opt
     }
     let block = b.range();
     let sh = b.sh;
-    let merges = block_merges(sh, block);
-    let by_start: std::collections::HashMap<CellRef, RangeRef> = merges.iter().map(|m| (m.start, *m)).collect();
-    // Cells worth visiting, in row-major order (which `Covered` needs).
-    let mut covered = Covered::new(&merges, block);
+    let merges: Vec<RangeRef> = sh.merges.iter().filter(|m| m.intersects(&block)).copied().collect();
+    let covered = |c: CellRef| merges.iter().any(|m| m.contains(c));
+    // Cells worth visiting.
     let cells: Vec<CellRef> = if block.count() <= DENSE_BLOCK {
-        block.iter().filter(|c| !covered.covers(*c)).collect()
+        block.iter().filter(|c| !covered(*c)).collect()
     } else {
         let mut set: Vec<CellRef> = sh.cells.iter_range(block).map(|(c, _)| c).collect();
         set.extend(sh.spill.range(block.start..=block.end).map(|(c, _)| *c).filter(|c| block.contains(*c)));
         set.sort_unstable();
         set.dedup();
-        set.retain(|c| !covered.covers(*c));
+        set.retain(|c| !covered(*c));
         set
     };
     pg.save();
@@ -354,14 +277,14 @@ pub(super) fn draw_block(pg: &mut Page, b: &Block, gridlines: bool, cf: &mut Opt
         .filter(|(c, l)| {
             l.fill.is_some()
                 || l.cf.is_some()
-                || by_start.contains_key(c)
+                || merges.iter().any(|m| m.start == *c)
                 || !sh.value(*c).is_empty()
                 || l.style.borders != Borders::default()
                 || l.style.num_fmt.as_str() == "checkbox"
         })
         .collect();
     let rect_of = |c: CellRef| -> (f32, f32, f32, f32, bool) {
-        match by_start.get(&c) {
+        match merges.iter().find(|m| m.start == c) {
             Some(m) => {
                 let (x, y, w, h) = b.rect(*m);
                 (x, y, w, h, true)
@@ -399,7 +322,7 @@ pub(super) fn draw_block(pg: &mut Page, b: &Block, gridlines: bool, cf: &mut Opt
             continue;
         }
         let bd = &l.style.borders;
-        let (right, bottom) = match by_start.get(c).filter(|_| merged) {
+        let (right, bottom) = match merges.iter().find(|m| m.start == *c).filter(|_| merged) {
             Some(m) => (
                 b.wb.styles.get(sh.style_id(CellRef::new(m.start.row, m.end.col))).borders.right,
                 b.wb.styles.get(sh.style_id(CellRef::new(m.end.row, m.start.col))).borders.bottom,
@@ -484,12 +407,11 @@ pub(super) struct PrintedBlock {
 pub(super) fn draw_block_links(pg: &mut Page, b: &Block, page: usize, pending: &mut Vec<PendingPdfLink>) {
     let range = b.range();
     let (Some(&bx), Some(&by), Some(&right), Some(&bottom)) = (b.xs.first(), b.ys.first(), b.xs.last(), b.ys.last()) else { return };
-    let by_start: std::collections::HashMap<CellRef, RangeRef> = block_merges(b.sh, range).into_iter().map(|m| (m.start, m)).collect();
     for (cell, link) in b.sh.hyperlinks.range(range.start..=range.end) {
         if !range.contains(*cell) {
             continue;
         }
-        let cell_range = by_start.get(cell).copied().unwrap_or(RangeRef::cell(*cell));
+        let cell_range = b.sh.merges.iter().find(|m| m.start == *cell).copied().unwrap_or(RangeRef::cell(*cell));
         let (x, y, w, h) = b.rect(cell_range);
         let (x0, y0, x1, y1) = (x.max(bx), y.max(by), (x + w).min(right), (y + h).min(bottom));
         if x1 <= x0 || y1 <= y0 {
@@ -581,44 +503,3 @@ pub(super) fn make_block<'a>(
     }
     Block { wb, si, sh, rows, cols, xs, ys, k, scale: lay.scale }
 }
-
-#[cfg(test)]
-mod merge_tests {
-    use super::{CellRef, Covered, RangeRef, Sheet, block_merges};
-
-    fn r(a: &str) -> RangeRef {
-        RangeRef::parse(a).unwrap()
-    }
-
-    #[test]
-    fn block_merges_drop_overlaps_and_cover_like_a_scan() {
-        let mut sh = Sheet::new("S");
-        sh.merges = vec![r("B2:C3"), r("E1:F8"), r("B2:B5"), r("A10:D10"), r("H3:H4"), r("Z1:Z2"), r("C3:D4"), r("A1:A1048576")];
-        let block = r("B1:H12");
-        let merges = block_merges(&sh, block);
-        // B2:B5 and C3:D4 overlap B2:C3, which comes first; Z1:Z2 is outside the block.
-        assert_eq!(merges, vec![r("E1:F8"), r("B2:C3"), r("H3:H4"), r("A10:D10")]);
-        let mut covered = Covered::new(&merges, block);
-        for c in block.iter() {
-            assert_eq!(covered.covers(c), merges.iter().any(|m| m.contains(c)), "{}", c.a1());
-        }
-        // Cells asked sparsely, still in order.
-        let mut covered = Covered::new(&merges, block);
-        for (a, want) in [("C1", false), ("F5", true), ("G5", false), ("D10", true), ("H12", false)] {
-            assert_eq!(covered.covers(CellRef::parse(a).unwrap()), want, "{a}");
-        }
-    }
-
-    #[test]
-    fn many_stacked_merges_are_swept_once() {
-        // 50,000 merges over the same cells: one is kept, and the block is checked against it
-        // without comparing every cell with every merge.
-        let mut sh = Sheet::new("S");
-        sh.merges = (0..50_000u32).map(|i| RangeRef::new(CellRef::new(0, 0), CellRef::new(199, 1 + i % 50))).collect();
-        let block = r("A1:AZ200");
-        let merges = block_merges(&sh, block);
-        assert_eq!(merges, vec![r("A1:B200")]);
-        let mut covered = Covered::new(&merges, block);
-        assert_eq!(block.iter().filter(|c| covered.covers(*c)).count(), 400);
-    }
-}