joemarshall commented on code in PR #41125:
URL: https://github.com/apache/arrow/pull/41125#discussion_r1617953414


##########
cpp/src/arrow/acero/asof_join_node.cc:
##########
@@ -1425,31 +1431,86 @@ class AsofJoinNode : public ExecNode {
     // The reason for this is that there are cases at the end of a table where 
we don't
     // know whether the RHS of the join is up-to-date until we know that the 
table is
     // finished.
-    process_.Push(true);
+    PushProcess(true);
+
     return Status::OK();
   }
+  void PushProcess(bool value) {
+#ifdef ARROW_ENABLE_THREADING
+    process_.Push(value);
+#else
+    if (value) {
+      ProcessNonThreaded();
+    }
+#endif
+  }
 
-  Status StartProducing() override {
 #ifndef ARROW_ENABLE_THREADING
-    return Status::NotImplemented("ASOF join requires threading enabled");
+  bool ProcessNonThreaded() {
+    while (!process_task_.is_finished()) {

Review Comment:
   yep.



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