diff --git a/compiler/rustc_index/src/bit_set.rs b/compiler/rustc_index/src/bit_set.rs
index 059755a743b..f2eaef1e149 100644
--- a/compiler/rustc_index/src/bit_set.rs
+++ b/compiler/rustc_index/src/bit_set.rs
@@ -681,6 +681,48 @@ fn intersect(&mut self, _other: &HybridBitSet<T>) -> bool {
     }
 }
 
+impl<T: Idx> BitRelations<ChunkedBitSet<T>> for BitSet<T> {
+    fn union(&mut self, other: &ChunkedBitSet<T>) -> bool {
+        sequential_update(|elem| self.insert(elem), other.iter())
+    }
+
+    fn subtract(&mut self, _other: &ChunkedBitSet<T>) -> bool {
+        unimplemented!("implement if/when necessary");
+    }
+
+    fn intersect(&mut self, other: &ChunkedBitSet<T>) -> bool {
+        assert_eq!(self.domain_size(), other.domain_size);
+        let mut changed = false;
+        for (i, chunk) in other.chunks.iter().enumerate() {
+            let mut words = &mut self.words[i * CHUNK_WORDS..];
+            if words.len() > CHUNK_WORDS {
+                words = &mut words[..CHUNK_WORDS];
+            }
+            match chunk {
+                Chunk::Zeros(..) => {
+                    for word in words {
+                        if *word != 0 {
+                            changed = true;
+                            *word = 0;
+                        }
+                    }
+                }
+                Chunk::Ones(..) => (),
+                Chunk::Mixed(_, _, data) => {
+                    for (i, word) in words.iter_mut().enumerate() {
+                        let new_val = *word & data[i];
+                        if new_val != *word {
+                            changed = true;
+                            *word = new_val;
+                        }
+                    }
+                }
+            }
+        }
+        changed
+    }
+}
+
 impl<T> Clone for ChunkedBitSet<T> {
     fn clone(&self) -> Self {
         ChunkedBitSet {
@@ -743,6 +785,41 @@ fn next(&mut self) -> Option<T> {
         }
         None
     }
+
+    fn fold<B, F>(mut self, mut init: B, mut f: F) -> B
+    where
+        F: FnMut(B, Self::Item) -> B,
+    {
+        // If `next` has already been called, we may not be at the start of a chunk, so we first
+        // advance the iterator to the start of the next chunk, before proceeding in chunk sized
+        // steps.
+        while self.index % CHUNK_BITS != 0 {
+            let Some(item) = self.next() else {
+                return init
+            };
+            init = f(init, item);
+        }
+        let start_chunk = self.index / CHUNK_BITS;
+        let chunks = &self.bitset.chunks[start_chunk..];
+        for (i, chunk) in chunks.iter().enumerate() {
+            let base = (start_chunk + i) * CHUNK_BITS;
+            match chunk {
+                Chunk::Zeros(_) => (),
+                Chunk::Ones(limit) => {
+                    for j in 0..(*limit as usize) {
+                        init = f(init, T::new(base + j));
+                    }
+                }
+                Chunk::Mixed(_, _, words) => {
+                    init = BitIter::new(&**words).fold(init, |val, mut item: T| {
+                        item.increment_by(base);
+                        f(val, item)
+                    });
+                }
+            }
+        }
+        init
+    }
 }
 
 impl Chunk {
@@ -799,11 +876,7 @@ fn sequential_update<T: Idx>(
     mut self_update: impl FnMut(T) -> bool,
     it: impl Iterator<Item = T>,
 ) -> bool {
-    let mut changed = false;
-    for elem in it {
-        changed |= self_update(elem);
-    }
-    changed
+    it.fold(false, |changed, elem| self_update(elem) | changed)
 }
 
 // Optimization of intersection for SparseBitSet that's generic
diff --git a/compiler/rustc_index/src/bit_set/tests.rs b/compiler/rustc_index/src/bit_set/tests.rs
index cfc891e97a3..a58133e4aed 100644
--- a/compiler/rustc_index/src/bit_set/tests.rs
+++ b/compiler/rustc_index/src/bit_set/tests.rs
@@ -342,38 +342,82 @@ fn chunked_bitset() {
     b10000b.assert_valid();
 }
 
+fn with_elements_chunked(elements: &[usize], domain_size: usize) -> ChunkedBitSet<usize> {
+    let mut s = ChunkedBitSet::new_empty(domain_size);
+    for &e in elements {
+        assert!(s.insert(e));
+    }
+    s
+}
+
+fn with_elements_standard(elements: &[usize], domain_size: usize) -> BitSet<usize> {
+    let mut s = BitSet::new_empty(domain_size);
+    for &e in elements {
+        assert!(s.insert(e));
+    }
+    s
+}
+
+#[test]
+fn chunked_bitset_into_bitset_operations() {
+    let a = vec![1, 5, 7, 11, 15, 2000, 3000];
+    let b = vec![3, 4, 11, 3000, 4000];
+    let aub = vec![1, 3, 4, 5, 7, 11, 15, 2000, 3000, 4000];
+    let aib = vec![11, 3000];
+
+    let b = with_elements_chunked(&b, 9876);
+
+    let mut union = with_elements_standard(&a, 9876);
+    assert!(union.union(&b));
+    assert!(!union.union(&b));
+    assert!(union.iter().eq(aub.iter().copied()));
+
+    let mut intersection = with_elements_standard(&a, 9876);
+    assert!(intersection.intersect(&b));
+    assert!(!intersection.intersect(&b));
+    assert!(intersection.iter().eq(aib.iter().copied()));
+}
+
 #[test]
 fn chunked_bitset_iter() {
-    fn with_elements(elements: &[usize], domain_size: usize) -> ChunkedBitSet<usize> {
-        let mut s = ChunkedBitSet::new_empty(domain_size);
-        for &e in elements {
-            s.insert(e);
+    fn check_iter(bit: &ChunkedBitSet<usize>, vec: &Vec<usize>) {
+        // Test collecting via both `.next()` and `.fold()` calls, to make sure both are correct
+        let mut collect_next = Vec::new();
+        let mut bit_iter = bit.iter();
+        while let Some(item) = bit_iter.next() {
+            collect_next.push(item);
         }
-        s
+        assert_eq!(vec, &collect_next);
+
+        let collect_fold = bit.iter().fold(Vec::new(), |mut v, item| {
+            v.push(item);
+            v
+        });
+        assert_eq!(vec, &collect_fold);
     }
 
     // Empty
     let vec: Vec<usize> = Vec::new();
-    let bit = with_elements(&vec, 9000);
-    assert_eq!(vec, bit.iter().collect::<Vec<_>>());
+    let bit = with_elements_chunked(&vec, 9000);
+    check_iter(&bit, &vec);
 
     // Filled
     let n = 10000;
     let vec: Vec<usize> = (0..n).collect();
-    let bit = with_elements(&vec, n);
-    assert_eq!(vec, bit.iter().collect::<Vec<_>>());
+    let bit = with_elements_chunked(&vec, n);
+    check_iter(&bit, &vec);
 
     // Filled with trailing zeros
     let n = 10000;
     let vec: Vec<usize> = (0..n).collect();
-    let bit = with_elements(&vec, 2 * n);
-    assert_eq!(vec, bit.iter().collect::<Vec<_>>());
+    let bit = with_elements_chunked(&vec, 2 * n);
+    check_iter(&bit, &vec);
 
     // Mixed
     let n = 12345;
     let vec: Vec<usize> = vec![0, 1, 2, 2010, 2047, 2099, 6000, 6002, 6004];
-    let bit = with_elements(&vec, n);
-    assert_eq!(vec, bit.iter().collect::<Vec<_>>());
+    let bit = with_elements_chunked(&vec, n);
+    check_iter(&bit, &vec);
 }
 
 #[test]
diff --git a/compiler/rustc_mir_dataflow/src/impls/liveness.rs b/compiler/rustc_mir_dataflow/src/impls/liveness.rs
index 7076fbe1bdb..51c59e42101 100644
--- a/compiler/rustc_mir_dataflow/src/impls/liveness.rs
+++ b/compiler/rustc_mir_dataflow/src/impls/liveness.rs
@@ -30,14 +30,14 @@ fn transfer_function<'a, T>(&self, trans: &'a mut T) -> TransferFunction<'a, T>
 }
 
 impl<'tcx> AnalysisDomain<'tcx> for MaybeLiveLocals {
-    type Domain = BitSet<Local>;
+    type Domain = ChunkedBitSet<Local>;
     type Direction = Backward;
 
     const NAME: &'static str = "liveness";
 
     fn bottom_value(&self, body: &mir::Body<'tcx>) -> Self::Domain {
         // bottom = not live
-        BitSet::new_empty(body.local_decls.len())
+        ChunkedBitSet::new_empty(body.local_decls.len())
     }
 
     fn initialize_start_block(&self, _: &mir::Body<'tcx>, _: &mut Self::Domain) {
diff --git a/compiler/rustc_mir_dataflow/src/rustc_peek.rs b/compiler/rustc_mir_dataflow/src/rustc_peek.rs
index 2f884887ad9..e1df482786f 100644
--- a/compiler/rustc_mir_dataflow/src/rustc_peek.rs
+++ b/compiler/rustc_mir_dataflow/src/rustc_peek.rs
@@ -1,7 +1,7 @@
 use rustc_span::symbol::sym;
 use rustc_span::Span;
 
-use rustc_index::bit_set::BitSet;
+use rustc_index::bit_set::ChunkedBitSet;
 use rustc_middle::mir::MirPass;
 use rustc_middle::mir::{self, Body, Local, Location};
 use rustc_middle::ty::{self, Ty, TyCtxt};
@@ -271,7 +271,7 @@ fn peek_at(
         &self,
         tcx: TyCtxt<'tcx>,
         place: mir::Place<'tcx>,
-        flow_state: &BitSet<Local>,
+        flow_state: &ChunkedBitSet<Local>,
         call: PeekCall,
     ) {
         info!(?place, "peek_at");
diff --git a/compiler/rustc_mir_transform/src/generator.rs b/compiler/rustc_mir_transform/src/generator.rs
index 9eb77f60213..9b7354da841 100644
--- a/compiler/rustc_mir_transform/src/generator.rs
+++ b/compiler/rustc_mir_transform/src/generator.rs
@@ -495,7 +495,8 @@ fn locals_live_across_suspend_points<'tcx>(
             let loc = Location { block, statement_index: data.statements.len() };
 
             liveness.seek_to_block_end(block);
-            let mut live_locals = liveness.get().clone();
+            let mut live_locals: BitSet<_> = BitSet::new_empty(body.local_decls.len());
+            live_locals.union(liveness.get());
 
             if !movable {
                 // The `liveness` variable contains the liveness of MIR locals ignoring borrows.