Invent "multibitmapsets", and use them to speed up antijoin detection.

Implement a data structure that is a List of Bitmapsets, which is
essentially a 2-D boolean array except that the rows need not all
be the same width.  Operations such as union and intersection are
meaningful for these, just as they are for Bitmapsets.  Eventually
we might build many of the same operations that we have written for
Bitmapsets, but for the first use-case we just need a few.

That first use-case is for antijoin detection: reduce_outer_joins
needs to find the set of Vars that are certain to be non-null in a
successfully joined (not null-extended) left join row, and also
find the set of Vars subject to higher-level IS NULL constraints,
and intersect them.  We had been doing this by making Lists of
the Var nodes and then using list_intersect, which works but is
pretty inefficient compared to a bitmapset-like intersection.
Potentially it's O(N^2) if there are a lot of Vars involved,
which fortunately there generally aren't; still it's not great.
Moreover, that method requires the Vars of interest to be exactly
equal() in the join condition and the upper IS NULL condition,
which is problematic for my WIP patch that labels Vars according
to which outer joins have possibly nulled them.

Discussion: https://postgr.es/m/892228.1668437838@sss.pgh.pa.us
Discussion: https://postgr.es/m/CAMbWs4-mvPPCJ1W6iK6dD5HiNwoJdi6mZp=-7mE8N9Sh+cd0tQ@mail.gmail.com

src/backend/nodes/Makefile

@@ -21,6 +21,7 @@ OBJS = \
 	extensible.o \
 	list.o \
 	makefuncs.o \
+	multibitmapset.o \
 	nodeFuncs.o \
 	nodes.o \
 	outfuncs.o \

src/backend/nodes/README

@@ -58,6 +58,7 @@ FILES IN THIS DIRECTORY (src/backend/nodes/)
     Specialized manipulation functions:
 	bitmapset.c	- Bitmapset support
 	list.c		- generic list support
+	multibitmapset.c - List-of-Bitmapset support
 	params.c	- Param support
 	tidbitmap.c	- TIDBitmap support
 	value.c		- support for value nodes

src/backend/nodes/meson.build

@@ -3,6 +3,7 @@ backend_sources += files(
   'extensible.c',
   'list.c',
   'makefuncs.c',
+  'multibitmapset.c',
   'nodeFuncs.c',
   'nodes.c',
   'params.c',

src/backend/nodes/multibitmapset.c

@@ -0,0 +1,162 @@
+/*-------------------------------------------------------------------------
+ *
+ * multibitmapset.c
+ *	  Lists of Bitmapsets
+ *
+ * A multibitmapset is useful in situations where members of a set can
+ * be identified by two small integers; for example, varno and varattno
+ * of a group of Vars within a query.  The implementation is a List of
+ * Bitmapsets, so that the empty set can be represented by NIL.  (But,
+ * as with Bitmapsets, that's not the only allowed representation.)
+ * The zero-based index of a List element is the first identifying value,
+ * and the (also zero-based) index of a bit within that Bitmapset is
+ * the second identifying value.  There is no expectation that the
+ * Bitmapsets should all be the same size.
+ *
+ * The available operations on multibitmapsets are intended to parallel
+ * those on bitmapsets, for example union and intersection.  So far only
+ * a small fraction of that has been built out; we'll add more as needed.
+ *
+ *
+ * Copyright (c) 2022, PostgreSQL Global Development Group
+ *
+ * IDENTIFICATION
+ *	  src/backend/nodes/multibitmapset.c
+ *
+ *-------------------------------------------------------------------------
+ */
+#include "postgres.h"
+
+#include "nodes/multibitmapset.h"
+
+
+/*
+ * mbms_add_member
+ *		Add a new member to a multibitmapset.
+ *
+ * The new member is identified by "listidx", the zero-based index of the
+ * List element it should go into, and "bitidx", which specifies the bit
+ * number to be set therein.
+ *
+ * This is like bms_add_member, but for multibitmapsets.
+ */
+List *
+mbms_add_member(List *a, int listidx, int bitidx)
+{
+	Bitmapset  *bms;
+	ListCell   *lc;
+
+	if (listidx < 0 || bitidx < 0)
+		elog(ERROR, "negative multibitmapset member index not allowed");
+	/* Add empty elements as needed */
+	while (list_length(a) <= listidx)
+		a = lappend(a, NULL);
+	/* Update the target element */
+	lc = list_nth_cell(a, listidx);
+	bms = lfirst_node(Bitmapset, lc);
+	bms = bms_add_member(bms, bitidx);
+	lfirst(lc) = bms;
+	return a;
+}
+
+/*
+ * mbms_add_members
+ *		Add all members of set b to set a.
+ *
+ * This is a UNION operation, but the left input is modified in-place.
+ *
+ * This is like bms_add_members, but for multibitmapsets.
+ */
+List *
+mbms_add_members(List *a, const List *b)
+{
+	ListCell   *lca,
+			   *lcb;
+
+	/* Add empty elements to a, as needed */
+	while (list_length(a) < list_length(b))
+		a = lappend(a, NULL);
+	/* forboth will stop at the end of the shorter list, which is fine */
+	forboth(lca, a, lcb, b)
+	{
+		Bitmapset  *bmsa = lfirst_node(Bitmapset, lca);
+		const Bitmapset *bmsb = lfirst_node(Bitmapset, lcb);
+
+		bmsa = bms_add_members(bmsa, bmsb);
+		lfirst(lca) = bmsa;
+	}
+	return a;
+}
+
+/*
+ * mbms_int_members
+ *		Reduce set a to its intersection with set b.
+ *
+ * This is an INTERSECT operation, but the left input is modified in-place.
+ *
+ * This is like bms_int_members, but for multibitmapsets.
+ */
+List *
+mbms_int_members(List *a, const List *b)
+{
+	ListCell   *lca,
+			   *lcb;
+
+	/* Remove any elements of a that are no longer of use */
+	a = list_truncate(a, list_length(b));
+	/* forboth will stop at the end of the shorter list, which is fine */
+	forboth(lca, a, lcb, b)
+	{
+		Bitmapset  *bmsa = lfirst_node(Bitmapset, lca);
+		const Bitmapset *bmsb = lfirst_node(Bitmapset, lcb);
+
+		bmsa = bms_int_members(bmsa, bmsb);
+		lfirst(lca) = bmsa;
+	}
+	return a;
+}
+
+/*
+ * mbms_is_member
+ *		Is listidx/bitidx a member of A?
+ *
+ * This is like bms_is_member, but for multibitmapsets.
+ */
+bool
+mbms_is_member(int listidx, int bitidx, const List *a)
+{
+	const Bitmapset *bms;
+
+	/* XXX better to just return false for negative indexes? */
+	if (listidx < 0 || bitidx < 0)
+		elog(ERROR, "negative multibitmapset member index not allowed");
+	if (listidx >= list_length(a))
+		return false;
+	bms = list_nth_node(Bitmapset, a, listidx);
+	return bms_is_member(bitidx, bms);
+}
+
+/*
+ * mbms_overlap_sets
+ *		Identify the bitmapsets having common members in a and b.
+ *
+ * The result is a bitmapset of the list indexes of bitmapsets that overlap.
+ */
+Bitmapset *
+mbms_overlap_sets(const List *a, const List *b)
+{
+	Bitmapset  *result = NULL;
+	ListCell   *lca,
+			   *lcb;
+
+	/* forboth will stop at the end of the shorter list, which is fine */
+	forboth(lca, a, lcb, b)
+	{
+		const Bitmapset *bmsa = lfirst_node(Bitmapset, lca);
+		const Bitmapset *bmsb = lfirst_node(Bitmapset, lcb);
+
+		if (bms_overlap(bmsa, bmsb))
+			result = bms_add_member(result, foreach_current_index(lca));
+	}
+	return result;
+}

src/backend/optimizer/prep/prepjointree.c

@@ -28,6 +28,7 @@
 #include "catalog/pg_type.h"
 #include "funcapi.h"
 #include "nodes/makefuncs.h"
+#include "nodes/multibitmapset.h"
 #include "nodes/nodeFuncs.h"
 #include "optimizer/clauses.h"
 #include "optimizer/optimizer.h"
@@ -2769,7 +2770,7 @@ reduce_outer_joins_pass1(Node *jtnode)
  *	state: state data collected by phase 1 for this node
  *	root: toplevel planner state
  *	nonnullable_rels: set of base relids forced non-null by upper quals
- *	forced_null_vars: list of Vars forced null by upper quals
+ *	forced_null_vars: multibitmapset of Vars forced null by upper quals
  */
 static void
 reduce_outer_joins_pass2(Node *jtnode,
@@ -2799,8 +2800,8 @@ reduce_outer_joins_pass2(Node *jtnode,
 		pass_nonnullable_rels = bms_add_members(pass_nonnullable_rels,
 												nonnullable_rels);
 		pass_forced_null_vars = find_forced_null_vars(f->quals);
-		pass_forced_null_vars = list_concat(pass_forced_null_vars,
-											forced_null_vars);
+		pass_forced_null_vars = mbms_add_members(pass_forced_null_vars,
+												 forced_null_vars);
 		/* And recurse --- but only into interesting subtrees */
 		Assert(list_length(f->fromlist) == list_length(state->sub_states));
 		forboth(l, f->fromlist, s, state->sub_states)
@@ -2897,7 +2898,7 @@ reduce_outer_joins_pass2(Node *jtnode,
 		if (jointype == JOIN_LEFT)
 		{
 			List	   *nonnullable_vars;
-			List	   *overlap;
+			Bitmapset  *overlap;
 
 			/* Find Vars in j->quals that must be non-null in joined rows */
 			nonnullable_vars = find_nonnullable_vars(j->quals);
@@ -2907,11 +2908,8 @@ reduce_outer_joins_pass2(Node *jtnode,
 			 * forced_null_vars overlap: we need to know if the overlap
 			 * includes any RHS variables.
 			 */
-			overlap = list_intersection(nonnullable_vars,
-										forced_null_vars);
-			if (overlap != NIL &&
-				bms_overlap(pull_varnos(root, (Node *) overlap),
-							right_state->relids))
+			overlap = mbms_overlap_sets(nonnullable_vars, forced_null_vars);
+			if (bms_overlap(overlap, right_state->relids))
 				jointype = JOIN_ANTI;
 		}
 
@@ -2964,8 +2962,8 @@ reduce_outer_joins_pass2(Node *jtnode,
 					/* OK to merge upper and local constraints */
 					local_nonnullable_rels = bms_add_members(local_nonnullable_rels,
 															 nonnullable_rels);
-					local_forced_null_vars = list_concat(local_forced_null_vars,
-														 forced_null_vars);
+					local_forced_null_vars = mbms_add_members(local_forced_null_vars,
+															  forced_null_vars);
 				}
 			}
 			else

src/backend/optimizer/util/clauses.c

@@ -31,6 +31,7 @@
 #include "funcapi.h"
 #include "miscadmin.h"
 #include "nodes/makefuncs.h"
+#include "nodes/multibitmapset.h"
 #include "nodes/nodeFuncs.h"
 #include "nodes/subscripting.h"
 #include "nodes/supportnodes.h"
@@ -1566,7 +1567,7 @@ find_nonnullable_rels_walker(Node *node, bool top_level)
  * find_nonnullable_vars
  *		Determine which Vars are forced nonnullable by given clause.
  *
- * Returns a list of all level-zero Vars that are referenced in the clause in
+ * Returns the set of all level-zero Vars that are referenced in the clause in
  * such a way that the clause cannot possibly return TRUE if any of these Vars
  * is NULL.  (It is OK to err on the side of conservatism; hence the analysis
  * here is simplistic.)
@@ -1578,8 +1579,9 @@ find_nonnullable_rels_walker(Node *node, bool top_level)
  * the expression to have been AND/OR flattened and converted to implicit-AND
  * format.
  *
- * The result is a palloc'd List, but we have not copied the member Var nodes.
- * Also, we don't bother trying to eliminate duplicate entries.
+ * Attnos of the identified Vars are returned in a multibitmapset (a List of
+ * Bitmapsets).  List indexes correspond to relids (varnos), while the per-rel
+ * Bitmapsets hold varattnos offset by FirstLowInvalidHeapAttributeNumber.
  *
  * top_level is true while scanning top-level AND/OR structure; here, showing
  * the result is either FALSE or NULL is good enough.  top_level is false when
@@ -1608,7 +1610,9 @@ find_nonnullable_vars_walker(Node *node, bool top_level)
 		Var		   *var = (Var *) node;
 
 		if (var->varlevelsup == 0)
-			result = list_make1(var);
+			result = mbms_add_member(result,
+									 var->varno,
+									 var->varattno - FirstLowInvalidHeapAttributeNumber);
 	}
 	else if (IsA(node, List))
 	{
@@ -1623,9 +1627,9 @@ find_nonnullable_vars_walker(Node *node, bool top_level)
 		 */
 		foreach(l, (List *) node)
 		{
-			result = list_concat(result,
-								 find_nonnullable_vars_walker(lfirst(l),
-															  top_level));
+			result = mbms_add_members(result,
+									  find_nonnullable_vars_walker(lfirst(l),
+																   top_level));
 		}
 	}
 	else if (IsA(node, FuncExpr))
@@ -1657,7 +1661,12 @@ find_nonnullable_vars_walker(Node *node, bool top_level)
 		switch (expr->boolop)
 		{
 			case AND_EXPR:
-				/* At top level we can just recurse (to the List case) */
+
+				/*
+				 * At top level we can just recurse (to the List case), since
+				 * the result should be the union of what we can prove in each
+				 * arm.
+				 */
 				if (top_level)
 				{
 					result = find_nonnullable_vars_walker((Node *) expr->args,
@@ -1689,7 +1698,7 @@ find_nonnullable_vars_walker(Node *node, bool top_level)
 					if (result == NIL)	/* first subresult? */
 						result = subresult;
 					else
-						result = list_intersection(result, subresult);
+						result = mbms_int_members(result, subresult);
 
 					/*
 					 * If the intersection is empty, we can stop looking. This
@@ -1788,8 +1797,8 @@ find_nonnullable_vars_walker(Node *node, bool top_level)
  * side of conservatism; hence the analysis here is simplistic.  In fact,
  * we only detect simple "var IS NULL" tests at the top level.)
  *
- * The result is a palloc'd List, but we have not copied the member Var nodes.
- * Also, we don't bother trying to eliminate duplicate entries.
+ * As with find_nonnullable_vars, we return the varattnos of the identified
+ * Vars in a multibitmapset.
  */
 List *
 find_forced_null_vars(Node *node)
@@ -1804,7 +1813,9 @@ find_forced_null_vars(Node *node)
 	var = find_forced_null_var(node);
 	if (var)
 	{
-		result = list_make1(var);
+		result = mbms_add_member(result,
+								 var->varno,
+								 var->varattno - FirstLowInvalidHeapAttributeNumber);
 	}
 	/* Otherwise, handle AND-conditions */
 	else if (IsA(node, List))
@@ -1815,8 +1826,8 @@ find_forced_null_vars(Node *node)
 		 */
 		foreach(l, (List *) node)
 		{
-			result = list_concat(result,
-								 find_forced_null_vars(lfirst(l)));
+			result = mbms_add_members(result,
+									  find_forced_null_vars((Node *) lfirst(l)));
 		}
 	}
 	else if (IsA(node, BoolExpr))

src/include/nodes/multibitmapset.h

@@ -0,0 +1,39 @@
+/*-------------------------------------------------------------------------
+ *
+ * multibitmapset.h
+ *	  Lists of Bitmapsets
+ *
+ * A multibitmapset is useful in situations where members of a set can
+ * be identified by two small integers; for example, varno and varattno
+ * of a group of Vars within a query.  The implementation is a List of
+ * Bitmapsets, so that the empty set can be represented by NIL.  (But,
+ * as with Bitmapsets, that's not the only allowed representation.)
+ * The zero-based index of a List element is the first identifying value,
+ * and the (also zero-based) index of a bit within that Bitmapset is
+ * the second identifying value.  There is no expectation that the
+ * Bitmapsets should all be the same size.
+ *
+ * The available operations on multibitmapsets are intended to parallel
+ * those on bitmapsets, for example union and intersection.  So far only
+ * a small fraction of that has been built out; we'll add more as needed.
+ *
+ *
+ * Copyright (c) 2022, PostgreSQL Global Development Group
+ *
+ * src/include/nodes/multibitmapset.h
+ *
+ *-------------------------------------------------------------------------
+ */
+#ifndef MULTIBITMAPSET_H
+#define MULTIBITMAPSET_H
+
+#include "nodes/bitmapset.h"
+#include "nodes/pg_list.h"
+
+extern List *mbms_add_member(List *a, int listidx, int bitidx);
+extern List *mbms_add_members(List *a, const List *b);
+extern List *mbms_int_members(List *a, const List *b);
+extern bool mbms_is_member(int listidx, int bitidx, const List *a);
+extern Bitmapset *mbms_overlap_sets(const List *a, const List *b);
+
+#endif							/* MULTIBITMAPSET_H */