@@ -109,6 +109,25 @@ def num_in_numbits(num: int, numbits: bytes) -> bool:
     return bool(numbits[nbyte] & (1 << nbit))
 
 
+class NumbitsUnionAgg:
+    """SQLite aggregate function for computing union of numbits."""
+
+    def __init__(self) -> None:
+        self.result = 0
+        self.result_nbytes = 0
+
+    def step(self, value: bytes) -> None:
+        """Process one value in the aggregation."""
+        self.result |= int.from_bytes(value, "little")
+        self.result_nbytes = max(self.result_nbytes, len(value))
+
+    def finalize(self) -> bytes:
+        """Return the final aggregated result."""
+        if not self.result_nbytes:
+            return b""
+        return self.result.to_bytes(self.result_nbytes, "little")
+
+
 def register_sqlite_functions(connection: sqlite3.Connection) -> None:
     """
     Define numbits functions in a SQLite connection.
@@ -144,3 +163,4 @@ def register_sqlite_functions(connection: sqlite3.Connection) -> None:
     connection.create_function("numbits_any_intersection", 2, numbits_any_intersection)
     connection.create_function("num_in_numbits", 2, num_in_numbits)
     connection.create_function("numbits_to_nums", 1, lambda b: json.dumps(numbits_to_nums(b)))
+    connection.create_aggregate("numbits_union_agg", 1, NumbitsUnionAgg)  # type: ignore[arg-type]
@@ -28,7 +28,12 @@
 from coverage.debug import NoDebugging, auto_repr, file_summary
 from coverage.exceptions import CoverageException, DataError
 from coverage.misc import Hasher, file_be_gone, isolate_module
-from coverage.numbits import numbits_to_nums, numbits_union, nums_to_numbits
+from coverage.numbits import (
+    numbits_to_nums,
+    numbits_union,
+    nums_to_numbits,
+    register_sqlite_functions,
+)
 from coverage.sqlitedb import SqliteDb
 from coverage.types import AnyCallable, FilePath, TArc, TDebugCtl, TLineNo, TWarnFn
 from coverage.version import __version__
@@ -128,25 +133,6 @@ def _wrapped(self: CoverageData, *args: Any, **kwargs: Any) -> Any:
     return _wrapped
 
 
-class NumbitsUnionAgg:
-    """SQLite aggregate function for computing union of numbits."""
-
-    def __init__(self) -> None:
-        self.result = 0
-        self.result_nbytes = 0
-
-    def step(self, value: bytes) -> None:
-        """Process one value in the aggregation."""
-        self.result |= int.from_bytes(value, "little")
-        self.result_nbytes = max(self.result_nbytes, len(value))
-
-    def finalize(self) -> bytes:
-        """Return the final aggregated result."""
-        if not self.result_nbytes:
-            return b""
-        return self.result.to_bytes(self.result_nbytes, "little")
-
-
 class CoverageData:
     """Manages collected coverage data, including file storage.
 
@@ -750,13 +736,8 @@ def update(
             con.con.isolation_level = "IMMEDIATE"
 
             # Register functions for SQLite
-            con.con.create_function("numbits_union", 2, numbits_union)
+            register_sqlite_functions(con.con)
             con.con.create_function("map_path", 1, map_path)
-            con.con.create_aggregate(
-                "numbits_union_agg",
-                1,
-                NumbitsUnionAgg,  # type: ignore[arg-type]
-            )
 
             # Attach the other database
             con.execute_void("ATTACH DATABASE ? AS other_db", (other_data.data_filename(),))
 
@@ -20,7 +20,6 @@
     num_in_numbits,
     register_sqlite_functions,
 )
-from coverage.sqldata import NumbitsUnionAgg
 
 from tests.coveragetest import CoverageTest
 from tests.hypo import example, given, settings
@@ -113,11 +112,6 @@ def setUp(self) -> None:
         conn = sqlite3.connect(":memory:")
         register_sqlite_functions(conn)
         self.cursor = conn.cursor()
-        conn.create_aggregate(
-            "numbits_union_agg",
-            1,
-            NumbitsUnionAgg,  # type: ignore[arg-type]
-        )
         self.cursor.execute("create table data (id int, numbits blob)")
         self.cursor.executemany(
             "insert into data (id, numbits) values (?, ?)",