diff --git a/Cargo.lock b/Cargo.lock
index 79b7d92425a7..6f7bedf7d123 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -3965,6 +3965,7 @@ dependencies = [
  "arrayvec",
  "rustc_macros",
  "rustc_serialize",
+ "smallvec",
 ]
 
 [[package]]
diff --git a/compiler/rustc_index/Cargo.toml b/compiler/rustc_index/Cargo.toml
index b984a1321e0a..89419bfce6f5 100644
--- a/compiler/rustc_index/Cargo.toml
+++ b/compiler/rustc_index/Cargo.toml
@@ -10,3 +10,4 @@ doctest = false
 arrayvec = { version = "0.7", default-features = false }
 rustc_serialize = { path = "../rustc_serialize" }
 rustc_macros = { path = "../rustc_macros" }
+smallvec = "1"
diff --git a/compiler/rustc_index/src/interval.rs b/compiler/rustc_index/src/interval.rs
new file mode 100644
index 000000000000..6da95053b116
--- /dev/null
+++ b/compiler/rustc_index/src/interval.rs
@@ -0,0 +1,269 @@
+use std::iter::Step;
+use std::marker::PhantomData;
+use std::ops::Bound;
+use std::ops::RangeBounds;
+
+use crate::vec::Idx;
+use crate::vec::IndexVec;
+use smallvec::SmallVec;
+
+#[cfg(test)]
+mod tests;
+
+/// Stores a set of intervals on the indices.
+#[derive(Debug, Clone)]
+pub struct IntervalSet<I> {
+    // Start, end
+    map: SmallVec<[(u32, u32); 4]>,
+    domain: usize,
+    _data: PhantomData<I>,
+}
+
+#[inline]
+fn inclusive_start<T: Idx>(range: impl RangeBounds<T>) -> u32 {
+    match range.start_bound() {
+        Bound::Included(start) => start.index() as u32,
+        Bound::Excluded(start) => start.index() as u32 + 1,
+        Bound::Unbounded => 0,
+    }
+}
+
+#[inline]
+fn inclusive_end<T: Idx>(domain: usize, range: impl RangeBounds<T>) -> Option<u32> {
+    let end = match range.end_bound() {
+        Bound::Included(end) => end.index() as u32,
+        Bound::Excluded(end) => end.index().checked_sub(1)? as u32,
+        Bound::Unbounded => domain.checked_sub(1)? as u32,
+    };
+    Some(end)
+}
+
+impl<I: Idx> IntervalSet<I> {
+    pub fn new(domain: usize) -> IntervalSet<I> {
+        IntervalSet { map: SmallVec::new(), domain, _data: PhantomData }
+    }
+
+    pub fn clear(&mut self) {
+        self.map.clear();
+    }
+
+    pub fn iter(&self) -> impl Iterator<Item = I> + '_
+    where
+        I: Step,
+    {
+        self.iter_intervals().flatten()
+    }
+
+    /// Iterates through intervals stored in the set, in order.
+    pub fn iter_intervals(&self) -> impl Iterator<Item = std::ops::Range<I>> + '_
+    where
+        I: Step,
+    {
+        self.map.iter().map(|&(start, end)| I::new(start as usize)..I::new(end as usize + 1))
+    }
+
+    /// Returns true if we increased the number of elements present.
+    pub fn insert(&mut self, point: I) -> bool {
+        self.insert_range(point..=point)
+    }
+
+    /// Returns true if we increased the number of elements present.
+    pub fn insert_range(&mut self, range: impl RangeBounds<I> + Clone) -> bool {
+        let start = inclusive_start(range.clone());
+        let Some(mut end) = inclusive_end(self.domain, range) else {
+            // empty range
+            return false;
+        };
+        if start > end {
+            return false;
+        }
+
+        loop {
+            // This condition looks a bit weird, but actually makes sense.
+            //
+            // if r.0 == end + 1, then we're actually adjacent, so we want to
+            // continue to the next range. We're looking here for the first
+            // range which starts *non-adjacently* to our end.
+            let next = self.map.partition_point(|r| r.0 <= end + 1);
+            if let Some(last) = next.checked_sub(1) {
+                let (prev_start, prev_end) = &mut self.map[last];
+                if *prev_end + 1 >= start {
+                    // If the start for the inserted range is adjacent to the
+                    // end of the previous, we can extend the previous range.
+                    if start < *prev_start {
+                        // Our range starts before the one we found. We'll need
+                        // to *remove* it, and then try again.
+                        //
+                        // FIXME: This is not so efficient; we may need to
+                        // recurse a bunch of times here. Instead, it's probably
+                        // better to do something like drain_filter(...) on the
+                        // map to be able to delete or modify all the ranges in
+                        // start..=end and then potentially re-insert a new
+                        // range.
+                        end = std::cmp::max(end, *prev_end);
+                        self.map.remove(last);
+                    } else {
+                        // We overlap with the previous range, increase it to
+                        // include us.
+                        //
+                        // Make sure we're actually going to *increase* it though --
+                        // it may be that end is just inside the previously existing
+                        // set.
+                        return if end > *prev_end {
+                            *prev_end = end;
+                            true
+                        } else {
+                            false
+                        };
+                    }
+                } else {
+                    // Otherwise, we don't overlap, so just insert
+                    self.map.insert(last + 1, (start, end));
+                    return true;
+                }
+            } else {
+                if self.map.is_empty() {
+                    // Quite common in practice, and expensive to call memcpy
+                    // with length zero.
+                    self.map.push((start, end));
+                } else {
+                    self.map.insert(next, (start, end));
+                }
+                return true;
+            }
+        }
+    }
+
+    pub fn contains(&self, needle: I) -> bool {
+        let needle = needle.index() as u32;
+        let last = match self.map.partition_point(|r| r.0 <= needle).checked_sub(1) {
+            Some(idx) => idx,
+            None => {
+                // All ranges in the map start after the new range's end
+                return false;
+            }
+        };
+        let (_, prev_end) = &self.map[last];
+        needle <= *prev_end
+    }
+
+    pub fn superset(&self, other: &IntervalSet<I>) -> bool
+    where
+        I: Step,
+    {
+        // FIXME: Performance here is probably not great. We will be doing a lot
+        // of pointless tree traversals.
+        other.iter().all(|elem| self.contains(elem))
+    }
+
+    pub fn is_empty(&self) -> bool {
+        self.map.is_empty()
+    }
+
+    /// Returns the maximum (last) element present in the set from `range`.
+    pub fn last_set_in(&self, range: impl RangeBounds<I> + Clone) -> Option<I> {
+        let start = inclusive_start(range.clone());
+        let Some(end) = inclusive_end(self.domain, range) else {
+            // empty range
+            return None;
+        };
+        if start > end {
+            return None;
+        }
+        let last = match self.map.partition_point(|r| r.0 <= end).checked_sub(1) {
+            Some(idx) => idx,
+            None => {
+                // All ranges in the map start after the new range's end
+                return None;
+            }
+        };
+        let (_, prev_end) = &self.map[last];
+        if start <= *prev_end { Some(I::new(std::cmp::min(*prev_end, end) as usize)) } else { None }
+    }
+
+    pub fn insert_all(&mut self) {
+        self.clear();
+        self.map.push((0, self.domain.try_into().unwrap()));
+    }
+
+    pub fn union(&mut self, other: &IntervalSet<I>) -> bool
+    where
+        I: Step,
+    {
+        assert_eq!(self.domain, other.domain);
+        let mut did_insert = false;
+        for range in other.iter_intervals() {
+            did_insert |= self.insert_range(range);
+        }
+        did_insert
+    }
+}
+
+/// This data structure optimizes for cases where the stored bits in each row
+/// are expected to be highly contiguous (long ranges of 1s or 0s), in contrast
+/// to BitMatrix and SparseBitMatrix which are optimized for
+/// "random"/non-contiguous bits and cheap(er) point queries at the expense of
+/// memory usage.
+#[derive(Clone)]
+pub struct SparseIntervalMatrix<R, C>
+where
+    R: Idx,
+    C: Idx,
+{
+    rows: IndexVec<R, IntervalSet<C>>,
+    column_size: usize,
+}
+
+impl<R: Idx, C: Step + Idx> SparseIntervalMatrix<R, C> {
+    pub fn new(column_size: usize) -> SparseIntervalMatrix<R, C> {
+        SparseIntervalMatrix { rows: IndexVec::new(), column_size }
+    }
+
+    pub fn rows(&self) -> impl Iterator<Item = R> {
+        self.rows.indices()
+    }
+
+    pub fn row(&self, row: R) -> Option<&IntervalSet<C>> {
+        self.rows.get(row)
+    }
+
+    fn ensure_row(&mut self, row: R) -> &mut IntervalSet<C> {
+        self.rows.ensure_contains_elem(row, || IntervalSet::new(self.column_size));
+        &mut self.rows[row]
+    }
+
+    pub fn union_row(&mut self, row: R, from: &IntervalSet<C>) -> bool
+    where
+        C: Step,
+    {
+        self.ensure_row(row).union(from)
+    }
+
+    pub fn union_rows(&mut self, read: R, write: R) -> bool
+    where
+        C: Step,
+    {
+        if read == write || self.rows.get(read).is_none() {
+            return false;
+        }
+        self.ensure_row(write);
+        let (read_row, write_row) = self.rows.pick2_mut(read, write);
+        write_row.union(read_row)
+    }
+
+    pub fn insert_all_into_row(&mut self, row: R) {
+        self.ensure_row(row).insert_all();
+    }
+
+    pub fn insert_range(&mut self, row: R, range: impl RangeBounds<C> + Clone) {
+        self.ensure_row(row).insert_range(range);
+    }
+
+    pub fn insert(&mut self, row: R, point: C) -> bool {
+        self.ensure_row(row).insert(point)
+    }
+
+    pub fn contains(&self, row: R, point: C) -> bool {
+        self.row(row).map_or(false, |r| r.contains(point))
+    }
+}
diff --git a/compiler/rustc_index/src/interval/tests.rs b/compiler/rustc_index/src/interval/tests.rs
new file mode 100644
index 000000000000..d90b449f3260
--- /dev/null
+++ b/compiler/rustc_index/src/interval/tests.rs
@@ -0,0 +1,199 @@
+use super::*;
+
+#[test]
+fn insert_collapses() {
+    let mut set = IntervalSet::<u32>::new(3000);
+    set.insert_range(9831..=9837);
+    set.insert_range(43..=9830);
+    assert_eq!(set.iter_intervals().collect::<Vec<_>>(), [43..9838]);
+}
+
+#[test]
+fn contains() {
+    let mut set = IntervalSet::new(300);
+    set.insert(0u32);
+    assert!(set.contains(0));
+    set.insert_range(0..10);
+    assert!(set.contains(9));
+    assert!(!set.contains(10));
+    set.insert_range(10..11);
+    assert!(set.contains(10));
+}
+
+#[test]
+fn insert() {
+    for i in 0..30usize {
+        let mut set = IntervalSet::new(300);
+        for j in i..30usize {
+            set.insert(j);
+            for k in i..j {
+                assert!(set.contains(k));
+            }
+        }
+    }
+
+    let mut set = IntervalSet::new(300);
+    set.insert_range(0..1u32);
+    assert!(set.contains(0), "{:?}", set.map);
+    assert!(!set.contains(1));
+    set.insert_range(1..1);
+    assert!(set.contains(0));
+    assert!(!set.contains(1));
+
+    let mut set = IntervalSet::new(300);
+    set.insert_range(4..5u32);
+    set.insert_range(5..10);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [4, 5, 6, 7, 8, 9]);
+    set.insert_range(3..7);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [3, 4, 5, 6, 7, 8, 9]);
+
+    let mut set = IntervalSet::new(300);
+    set.insert_range(0..10u32);
+    set.insert_range(3..5);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
+
+    let mut set = IntervalSet::new(300);
+    set.insert_range(0..10u32);
+    set.insert_range(0..3);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
+
+    let mut set = IntervalSet::new(300);
+    set.insert_range(0..10u32);
+    set.insert_range(0..10);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
+
+    let mut set = IntervalSet::new(300);
+    set.insert_range(0..10u32);
+    set.insert_range(5..10);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
+
+    let mut set = IntervalSet::new(300);
+    set.insert_range(0..10u32);
+    set.insert_range(5..13);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]);
+}
+
+#[test]
+fn insert_range() {
+    #[track_caller]
+    fn check<R>(range: R)
+    where
+        R: RangeBounds<usize> + Clone + IntoIterator<Item = usize> + std::fmt::Debug,
+    {
+        let mut set = IntervalSet::new(300);
+        set.insert_range(range.clone());
+        for i in set.iter() {
+            assert!(range.contains(&i));
+        }
+        for i in range.clone() {
+            assert!(set.contains(i), "A: {} in {:?}, inserted {:?}", i, set, range);
+        }
+        set.insert_range(range.clone());
+        for i in set.iter() {
+            assert!(range.contains(&i), "{} in {:?}", i, set);
+        }
+        for i in range.clone() {
+            assert!(set.contains(i), "B: {} in {:?}, inserted {:?}", i, set, range);
+        }
+    }
+    check(10..10);
+    check(10..100);
+    check(10..30);
+    check(0..5);
+    check(0..250);
+    check(200..250);
+
+    check(10..=10);
+    check(10..=100);
+    check(10..=30);
+    check(0..=5);
+    check(0..=250);
+    check(200..=250);
+
+    for i in 0..30 {
+        for j in i..30 {
+            check(i..j);
+            check(i..=j);
+        }
+    }
+}
+
+#[test]
+fn insert_range_dual() {
+    let mut set = IntervalSet::<u32>::new(300);
+    set.insert_range(0..3);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2]);
+    set.insert_range(5..7);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2, 5, 6]);
+    set.insert_range(3..4);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2, 3, 5, 6]);
+    set.insert_range(3..5);
+    assert_eq!(set.iter().collect::<Vec<_>>(), [0, 1, 2, 3, 4, 5, 6]);
+}
+
+#[test]
+fn last_set_before_adjacent() {
+    let mut set = IntervalSet::<u32>::new(300);
+    set.insert_range(0..3);
+    set.insert_range(3..5);
+    assert_eq!(set.last_set_in(0..3), Some(2));
+    assert_eq!(set.last_set_in(0..5), Some(4));
+    assert_eq!(set.last_set_in(3..5), Some(4));
+    set.insert_range(2..5);
+    assert_eq!(set.last_set_in(0..3), Some(2));
+    assert_eq!(set.last_set_in(0..5), Some(4));
+    assert_eq!(set.last_set_in(3..5), Some(4));
+}
+
+#[test]
+fn last_set_in() {
+    fn easy(set: &IntervalSet<usize>, needle: impl RangeBounds<usize>) -> Option<usize> {
+        let mut last_leq = None;
+        for e in set.iter() {
+            if needle.contains(&e) {
+                last_leq = Some(e);
+            }
+        }
+        last_leq
+    }
+
+    #[track_caller]
+    fn cmp(set: &IntervalSet<usize>, needle: impl RangeBounds<usize> + Clone + std::fmt::Debug) {
+        assert_eq!(
+            set.last_set_in(needle.clone()),
+            easy(set, needle.clone()),
+            "{:?} in {:?}",
+            needle,
+            set
+        );
+    }
+    let mut set = IntervalSet::new(300);
+    cmp(&set, 50..=50);
+    set.insert(64);
+    cmp(&set, 64..=64);
+    set.insert(64 - 1);
+    cmp(&set, 0..=64 - 1);
+    cmp(&set, 0..=5);
+    cmp(&set, 10..100);
+    set.insert(100);
+    cmp(&set, 100..110);
+    cmp(&set, 99..100);
+    cmp(&set, 99..=100);
+
+    for i in 0..=30 {
+        for j in i..=30 {
+            for k in 0..30 {
+                let mut set = IntervalSet::new(100);
+                cmp(&set, ..j);
+                cmp(&set, i..);
+                cmp(&set, i..j);
+                cmp(&set, i..=j);
+                set.insert(k);
+                cmp(&set, ..j);
+                cmp(&set, i..);
+                cmp(&set, i..j);
+                cmp(&set, i..=j);
+            }
+        }
+    }
+}
diff --git a/compiler/rustc_index/src/lib.rs b/compiler/rustc_index/src/lib.rs
index a9efd6bb8bc8..359b1859c688 100644
--- a/compiler/rustc_index/src/lib.rs
+++ b/compiler/rustc_index/src/lib.rs
@@ -7,6 +7,7 @@
 #![feature(let_else)]
 
 pub mod bit_set;
+pub mod interval;
 pub mod vec;
 
 // FIXME(#56935): Work around ICEs during cross-compilation.