Added search parameters to EXPLAIN [skip ci]

This reverts commit 7043cce893.

.github/workflows/build.yml

@@ -8,8 +8,8 @@ jobs:
       fail-fast: false
       matrix:
         include:
-          # - postgres: 18
-          #   os: ubuntu-24.04
+          - postgres: 18
+            os: ubuntu-24.04
           - postgres: 17
             os: ubuntu-24.04
           - postgres: 16
@@ -49,7 +49,7 @@ jobs:
           - postgres: 16
             os: macos-14
           - postgres: 14
-            os: macos-12
+            os: macos-13
     steps:
       - uses: actions/checkout@v4
       - uses: ankane/setup-postgres@v1

CHANGELOG.md

@@ -1,6 +1,6 @@
 ## 0.8.0 (unreleased)
 
-- Added support for inline filtering with IVFFlat
+- Added support for iterative index scans
 - Added casts for arrays to `sparsevec`
 - Improved cost estimation
 - Improved performance of HNSW inserts and on-disk index builds

README.md

@@ -439,12 +439,6 @@ Create an index on one [or more](https://www.postgresql.org/docs/current/indexes
 CREATE INDEX ON items (category_id);
 ```
 
-Or a composite IVFFlat index for approximate search (added in 0.8.0)
-
-```sql
-CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops, category_id) WITH (lists = 100);
-```
-
 Or a [partial index](https://www.postgresql.org/docs/current/indexes-partial.html) on the vector column for approximate search
 
 ```sql
@@ -457,6 +451,89 @@ Use [partitioning](https://www.postgresql.org/docs/current/ddl-partitioning.html
 CREATE TABLE items (embedding vector(3), category_id int) PARTITION BY LIST(category_id);
 ```
 
+## Iterative Index Scans
+
+*Unreleased*
+
+With approximate indexes, queries with filtering can return less results (due to post-filtering). Starting with 0.8.0, you can enable iterative index scans. If too few results from the initial scan match the filters, the scan will resume until enough results are found (or it reaches `hnsw.max_scan_tuples` or `ivfflat.max_probes`). This can significantly improve recall.
+
+There are two modes for iterative scans: strict and relaxed.
+
+Strict ensures results are in the exact order by distance
+
+```sql
+SET hnsw.iterative_scan = strict_order;
+```
+
+Relaxed allows results to be slightly out of order by distance, but provides better recall
+
+```sql
+SET hnsw.iterative_scan = relaxed_order;
+# or
+SET ivfflat.iterative_scan = relaxed_order;
+```
+
+With relaxed ordering, you can use a [materialized CTE](https://www.postgresql.org/docs/current/queries-with.html#QUERIES-WITH-CTE-MATERIALIZATION) to get strict ordering
+
+```sql
+WITH relaxed_results AS MATERIALIZED (
+    SELECT id, embedding <-> '[1,2,3]' AS distance FROM items WHERE category_id = 123 ORDER BY distance LIMIT 5
+) SELECT * FROM relaxed_results ORDER BY distance;
+```
+
+For queries that filter by distance, use a materialized CTE and place the distance filter outside of it for best performance (due to the [current behavior](https://www.postgresql.org/message-id/flat/CAOdR5yGUoMQ6j7M5hNUXrySzaqZVGf_Ne%2B8fwZMRKTFxU1nbJg%40mail.gmail.com) of the Postgres executor)
+
+```sql
+WITH nearest_results AS MATERIALIZED (
+    SELECT id, embedding <-> '[1,2,3]' AS distance FROM items ORDER BY distance LIMIT 5
+) SELECT * FROM nearest_results WHERE distance < 5 ORDER BY distance;
+```
+
+Note: Place any other filters inside the CTE
+
+### Iterative Scan Options
+
+Since scanning a large portion of an approximate index is expensive, there are options to control when a scan ends
+
+#### HNSW
+
+Specify the max number of tuples to visit (20,000 by default)
+
+```sql
+SET hnsw.max_scan_tuples = 20000;
+```
+
+Note: This is approximate and does not affect the initial scan
+
+Specify the max amount of memory to use, as a multiple of `work_mem` (1 by default)
+
+```sql
+SET hnsw.scan_mem_multiplier = 2;
+```
+
+You can see when increasing this is needed by enabling debug messages
+
+```sql
+SET client_min_messages = debug1;
+```
+
+which will show when a scan reaches the memory limit
+
+```text
+DEBUG:  hnsw index scan reached memory limit after 20000 tuples
+HINT:  Increase hnsw.scan_mem_multiplier to scan more tuples.
+```
+
+#### IVFFlat
+
+Specify the max number of probes
+
+```sql
+SET ivfflat.max_probes = 100;
+```
+
+Note: If this is lower than `ivfflat.probes`, `ivfflat.probes` will be used
+
 ## Half-Precision Vectors
 
 *Added in 0.7.0*

sql/vector--0.7.4--0.8.0.sql

@@ -24,5 +24,3 @@ CREATE CAST (double precision[] AS sparsevec)
 
 CREATE CAST (numeric[] AS sparsevec)
 	WITH FUNCTION array_to_sparsevec(numeric[], integer, boolean) AS ASSIGNMENT;
-
--- TODO add ivfflat attributes

sql/vector.sql

@@ -916,13 +916,3 @@ CREATE OPERATOR CLASS sparsevec_l1_ops
 	OPERATOR 1 <+> (sparsevec, sparsevec) FOR ORDER BY float_ops,
 	FUNCTION 1 l1_distance(sparsevec, sparsevec),
 	FUNCTION 3 hnsw_sparsevec_support(internal);
-
--- ivfflat attributes
-
-CREATE OPERATOR CLASS vector_integer_ops
-	DEFAULT FOR TYPE integer USING ivfflat AS
-	OPERATOR 2 < ,
-	OPERATOR 3 <= ,
-	OPERATOR 4 = ,
-	OPERATOR 5 >= ,
-	OPERATOR 6 > ;

src/hnsw.c

@@ -18,7 +18,17 @@
 #define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
 #endif
 
+static const struct config_enum_entry hnsw_iterative_scan_options[] = {
+	{"off", HNSW_ITERATIVE_SCAN_OFF, false},
+	{"relaxed_order", HNSW_ITERATIVE_SCAN_RELAXED, false},
+	{"strict_order", HNSW_ITERATIVE_SCAN_STRICT, false},
+	{NULL, 0, false}
+};
+
 int			hnsw_ef_search;
+int			hnsw_iterative_scan;
+int			hnsw_max_scan_tuples;
+double		hnsw_scan_mem_multiplier;
 int			hnsw_lock_tranche_id;
 static relopt_kind hnsw_relopt_kind;
 
@@ -67,7 +77,21 @@ HnswInit(void)
 
 	DefineCustomIntVariable("hnsw.ef_search", "Sets the size of the dynamic candidate list for search",
 							"Valid range is 1..1000.", &hnsw_ef_search,
-							HNSW_DEFAULT_EF_SEARCH, HNSW_MIN_EF_SEARCH, HNSW_MAX_EF_SEARCH, PGC_USERSET, 0, NULL, NULL, NULL);
+							HNSW_DEFAULT_EF_SEARCH, HNSW_MIN_EF_SEARCH, HNSW_MAX_EF_SEARCH, PGC_USERSET, GUC_EXPLAIN, NULL, NULL, NULL);
+
+	DefineCustomEnumVariable("hnsw.iterative_scan", "Sets the mode for iterative scans",
+							 NULL, &hnsw_iterative_scan,
+							 HNSW_ITERATIVE_SCAN_OFF, hnsw_iterative_scan_options, PGC_USERSET, GUC_EXPLAIN, NULL, NULL, NULL);
+
+	/* This is approximate and does not affect the initial scan */
+	DefineCustomIntVariable("hnsw.max_scan_tuples", "Sets the max number of tuples to visit for iterative scans",
+							NULL, &hnsw_max_scan_tuples,
+							20000, 1, INT_MAX, PGC_USERSET, GUC_EXPLAIN, NULL, NULL, NULL);
+
+	/* Same range as hash_mem_multiplier */
+	DefineCustomRealVariable("hnsw.scan_mem_multiplier", "Sets the multiple of work_mem to use for iterative scans",
+							 NULL, &hnsw_scan_mem_multiplier,
+							 1, 1, 1000, PGC_USERSET, GUC_EXPLAIN, NULL, NULL, NULL);
 
 	MarkGUCPrefixReserved("hnsw");
 }
@@ -113,6 +137,10 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 		*indexSelectivity = 0;
 		*indexCorrelation = 0;
 		*indexPages = 0;
+#if PG_VERSION_NUM >= 180000
+		/* See "On disable_cost" thread on pgsql-hackers */
+		path->path.disabled_nodes = 2;
+#endif
 		return;
 	}
 

src/hnsw.h

@@ -109,8 +109,18 @@
 
 /* Variables */
 extern int	hnsw_ef_search;
+extern int	hnsw_iterative_scan;
+extern int	hnsw_max_scan_tuples;
+extern double hnsw_scan_mem_multiplier;
 extern int	hnsw_lock_tranche_id;
 
+typedef enum HnswIterativeScanMode
+{
+	HNSW_ITERATIVE_SCAN_OFF,
+	HNSW_ITERATIVE_SCAN_RELAXED,
+	HNSW_ITERATIVE_SCAN_STRICT
+}			HnswIterativeScanMode;
+
 typedef struct HnswElementData HnswElementData;
 typedef struct HnswNeighborArray HnswNeighborArray;
 
@@ -132,6 +142,7 @@ struct HnswElementData
 	uint8		heaptidsLength;
 	uint8		level;
 	uint8		deleted;
+	uint8		version;
 	uint32		hash;
 	HnswNeighborsPtr neighbors;
 	BlockNumber blkno;
@@ -319,10 +330,10 @@ typedef struct HnswElementTupleData
 	uint8		type;
 	uint8		level;
 	uint8		deleted;
-	uint8		unused;
+	uint8		version;
 	ItemPointerData heaptids[HNSW_HEAPTIDS];
 	ItemPointerData neighbortid;
-	uint16		unused2;
+	uint16		unused;
 	Vector		data;
 }			HnswElementTupleData;
 
@@ -331,7 +342,7 @@ typedef HnswElementTupleData * HnswElementTuple;
 typedef struct HnswNeighborTupleData
 {
 	uint8		type;
-	uint8		unused;
+	uint8		version;
 	uint16		count;
 	ItemPointerData indextids[FLEXIBLE_ARRAY_MEMBER];
 }			HnswNeighborTupleData;
@@ -356,6 +367,13 @@ typedef struct HnswScanOpaqueData
 	const		HnswTypeInfo *typeInfo;
 	bool		first;
 	List	   *w;
+	visited_hash v;
+	pairingheap *discarded;
+	HnswQuery	q;
+	int			m;
+	int64		tuples;
+	double		previousDistance;
+	Size		maxMemory;
 	MemoryContext tmpCtx;
 
 	/* Support functions */
@@ -399,7 +417,7 @@ bool		HnswCheckNorm(HnswSupport * support, Datum value);
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);
 void		HnswInit(void);
-List	   *HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement);
+List	   *HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples);
 HnswElement HnswGetEntryPoint(Relation index);
 void		HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
 void	   *HnswAlloc(HnswAllocator * allocator, Size size);

src/hnswinsert.c

@@ -36,7 +36,7 @@ GetInsertPage(Relation index)
  * Check for a free offset
  */
 static bool
-HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size etupSize, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *newInsertPage)
+HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size etupSize, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *newInsertPage, uint8 *tupleVersion)
 {
 	OffsetNumber offno;
 	OffsetNumber maxoffno = PageGetMaxOffsetNumber(page);
@@ -98,6 +98,7 @@ HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size
 			{
 				*freeOffno = offno;
 				*freeNeighborOffno = neighborOffno;
+				*tupleVersion = etup->version;
 				return true;
 			}
 			else if (*nbuf != buf)
@@ -153,6 +154,7 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 	OffsetNumber freeOffno = InvalidOffsetNumber;
 	OffsetNumber freeNeighborOffno = InvalidOffsetNumber;
 	BlockNumber newInsertPage = InvalidBlockNumber;
+	uint8		tupleVersion;
 	char	   *base = NULL;
 
 	/* Calculate sizes */
@@ -202,7 +204,7 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 		}
 
 		/* Next, try space from a deleted element */
-		if (HnswFreeOffset(index, buf, page, e, etupSize, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage))
+		if (HnswFreeOffset(index, buf, page, e, etupSize, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage, &tupleVersion))
 		{
 			if (nbuf != buf)
 			{
@@ -212,6 +214,10 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 					npage = GenericXLogRegisterBuffer(state, nbuf, 0);
 			}
 
+			/* Set tuple version */
+			etup->version = tupleVersion;
+			ntup->version = tupleVersion;
+
 			break;
 		}
 

src/hnswscan.c

@@ -5,6 +5,7 @@
 #include "pgstat.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
+#include "utils/float.h"
 #include "utils/memutils.h"
 
 /*
@@ -21,25 +22,57 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	int			m;
 	HnswElement entryPoint;
 	char	   *base = NULL;
-	HnswQuery	q;
-
-	q.value = value;
+	HnswQuery  *q = &so->q;
 
 	/* Get m and entry point */
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
 
+	q->value = value;
+	so->m = m;
+
 	if (entryPoint == NULL)
 		return NIL;
 
-	ep = list_make1(HnswEntryCandidate(base, entryPoint, &q, index, support, false));
+	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, support, false));
 
 	for (int lc = entryPoint->level; lc >= 1; lc--)
 	{
-		w = HnswSearchLayer(base, &q, ep, 1, lc, index, support, m, false, NULL);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, support, m, false, NULL, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
-	return HnswSearchLayer(base, &q, ep, hnsw_ef_search, 0, index, support, m, false, NULL);
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, support, m, false, NULL, &so->v, hnsw_iterative_scan != HNSW_ITERATIVE_SCAN_OFF ? &so->discarded : NULL, true, &so->tuples);
+}
+
+/*
+ * Resume scan at ground level with discarded candidates
+ */
+static List *
+ResumeScanItems(IndexScanDesc scan)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	Relation	index = scan->indexRelation;
+	List	   *ep = NIL;
+	char	   *base = NULL;
+	int			batch_size = hnsw_ef_search;
+
+	if (pairingheap_is_empty(so->discarded))
+		return NIL;
+
+	/* Get next batch of candidates */
+	for (int i = 0; i < batch_size; i++)
+	{
+		HnswSearchCandidate *sc;
+
+		if (pairingheap_is_empty(so->discarded))
+			break;
+
+		sc = HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded));
+
+		ep = lappend(ep, sc);
+	}
+
+	return HnswSearchLayer(base, &so->q, ep, batch_size, 0, index, &so->support, so->m, false, NULL, &so->v, &so->discarded, false, &so->tuples);
 }
 
 /*
@@ -69,6 +102,17 @@ GetScanValue(IndexScanDesc scan)
 	return value;
 }
 
+#if defined(HNSW_MEMORY)
+/*
+ * Show memory usage
+ */
+static void
+ShowMemoryUsage(HnswScanOpaque so)
+{
+	elog(INFO, "memory: %zu KB, tuples: " INT64_FORMAT, MemoryContextMemAllocated(so->tmpCtx, false) / 1024, so->tuples);
+}
+#endif
+
 /*
  * Prepare for an index scan
  */
@@ -77,19 +121,29 @@ hnswbeginscan(Relation index, int nkeys, int norderbys)
 {
 	IndexScanDesc scan;
 	HnswScanOpaque so;
+	double		maxMemory;
 
 	scan = RelationGetIndexScan(index, nkeys, norderbys);
 
 	so = (HnswScanOpaque) palloc(sizeof(HnswScanOpaqueData));
 	so->typeInfo = HnswGetTypeInfo(index);
-	so->first = true;
-	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
-									   "Hnsw scan temporary context",
-									   ALLOCSET_DEFAULT_SIZES);
 
 	/* Set support functions */
 	HnswInitSupport(&so->support, index);
 
+	/*
+	 * Use a lower max allocation size than default to allow scanning more
+	 * tuples for iterative search before exceeding work_mem
+	 */
+	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+									   "Hnsw scan temporary context",
+									   0, 8 * 1024, 256 * 1024);
+
+	/* Calculate max memory */
+	/* Add 256 extra bytes to fill last block when close */
+	maxMemory = (double) work_mem * hnsw_scan_mem_multiplier * 1024.0 + 256;
+	so->maxMemory = Min(maxMemory, (double) SIZE_MAX);
+
 	scan->opaque = so;
 
 	return scan;
@@ -104,6 +158,11 @@ hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int no
 	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
 
 	so->first = true;
+	/* v and discarded are allocated in tmpCtx */
+	so->v.tids = NULL;
+	so->discarded = NULL;
+	so->tuples = 0;
+	so->previousDistance = -get_float8_infinity();
 	MemoryContextReset(so->tmpCtx);
 
 	if (keys && scan->numberOfKeys > 0)
@@ -161,26 +220,104 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		so->first = false;
 
 #if defined(HNSW_MEMORY)
-		elog(INFO, "memory: %zu KB", MemoryContextMemAllocated(so->tmpCtx, false) / 1024);
+		ShowMemoryUsage(so);
 #endif
 	}
 
-	while (list_length(so->w) > 0)
+	for (;;)
 	{
 		char	   *base = NULL;
-		HnswSearchCandidate *sc = llast(so->w);
-		HnswElement element = HnswPtrAccess(base, sc->element);
+		HnswSearchCandidate *sc;
+		HnswElement element;
 		ItemPointer heaptid;
 
+		if (list_length(so->w) == 0)
+		{
+			if (hnsw_iterative_scan == HNSW_ITERATIVE_SCAN_OFF)
+				break;
+
+			/* Empty index */
+			if (so->discarded == NULL)
+				break;
+
+			/* Reached max number of tuples */
+			if (so->tuples >= hnsw_max_scan_tuples)
+			{
+				if (pairingheap_is_empty(so->discarded))
+					break;
+
+				/* Return remaining tuples */
+				so->w = lappend(so->w, HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded)));
+			}
+			/* Prevent scans from consuming too much memory */
+			else if (MemoryContextMemAllocated(so->tmpCtx, false) > so->maxMemory)
+			{
+				if (pairingheap_is_empty(so->discarded))
+				{
+					ereport(DEBUG1,
+							(errmsg("hnsw index scan reached memory limit after " INT64_FORMAT " tuples", so->tuples),
+							 errhint("Increase hnsw.scan_mem_multiplier to scan more tuples.")));
+
+					break;
+				}
+
+				/* Return remaining tuples */
+				so->w = lappend(so->w, HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded)));
+			}
+			else
+			{
+				/*
+				 * Locking ensures when neighbors are read, the elements they
+				 * reference will not be deleted (and replaced) during the
+				 * iteration.
+				 *
+				 * Elements loaded into memory on previous iterations may have
+				 * been deleted (and replaced), so when reading neighbors, the
+				 * element version must be checked.
+				 */
+				LockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+				so->w = ResumeScanItems(scan);
+
+				UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+#if defined(HNSW_MEMORY)
+				ShowMemoryUsage(so);
+#endif
+			}
+
+			if (list_length(so->w) == 0)
+				break;
+		}
+
+		sc = llast(so->w);
+		element = HnswPtrAccess(base, sc->element);
+
 		/* Move to next element if no valid heap TIDs */
 		if (element->heaptidsLength == 0)
 		{
 			so->w = list_delete_last(so->w);
+
+			/* Mark memory as free for next iteration */
+			if (hnsw_iterative_scan != HNSW_ITERATIVE_SCAN_OFF)
+			{
+				pfree(element);
+				pfree(sc);
+			}
+
 			continue;
 		}
 
 		heaptid = &element->heaptids[--element->heaptidsLength];
 
+		if (hnsw_iterative_scan == HNSW_ITERATIVE_SCAN_STRICT)
+		{
+			if (sc->distance < so->previousDistance)
+				continue;
+
+			so->previousDistance = sc->distance;
+		}
+
 		MemoryContextSwitchTo(oldCtx);
 
 		scan->xs_heaptid = *heaptid;

src/hnswutils.c

@@ -251,6 +251,8 @@ HnswInitElement(char *base, ItemPointer heaptid, int m, double ml, int maxLevel,
 
 	element->level = level;
 	element->deleted = 0;
+	/* Start at one to make it easier to find issues */
+	element->version = 1;
 
 	HnswInitNeighbors(base, element, m, allocator);
 
@@ -430,6 +432,7 @@ HnswSetElementTuple(char *base, HnswElementTuple etup, HnswElement element)
 	etup->type = HNSW_ELEMENT_TUPLE_TYPE;
 	etup->level = element->level;
 	etup->deleted = 0;
+	etup->version = element->version;
 	for (int i = 0; i < HNSW_HEAPTIDS; i++)
 	{
 		if (i < element->heaptidsLength)
@@ -472,6 +475,7 @@ HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m)
 	}
 
 	ntup->count = idx;
+	ntup->version = e->version;
 }
 
 /*
@@ -482,6 +486,7 @@ HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHe
 {
 	element->level = etup->level;
 	element->deleted = etup->deleted;
+	element->version = etup->version;
 	element->neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
 	element->neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
 	element->heaptidsLength = 0;
@@ -576,21 +581,34 @@ GetElementDistance(char *base, HnswElement element, HnswQuery * q, HnswSupport *
 	return HnswGetDistance(q->value, value, support);
 }
 
+/*
+ * Allocate a search candidate
+ */
+static HnswSearchCandidate *
+HnswInitSearchCandidate(char *base, HnswElement element, double distance)
+{
+	HnswSearchCandidate *sc = palloc(sizeof(HnswSearchCandidate));
+
+	HnswPtrStore(base, sc->element, element);
+	sc->distance = distance;
+	return sc;
+}
+
 /*
  * Create a candidate for the entry point
  */
 HnswSearchCandidate *
 HnswEntryCandidate(char *base, HnswElement entryPoint, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec)
 {
-	HnswSearchCandidate *sc = palloc(sizeof(HnswSearchCandidate));
 	bool		inMemory = index == NULL;
+	double		distance;
 
-	HnswPtrStore(base, sc->element, entryPoint);
 	if (inMemory)
-		sc->distance = GetElementDistance(base, entryPoint, q, support);
+		distance = GetElementDistance(base, entryPoint, q, support);
 	else
-		HnswLoadElement(entryPoint, &sc->distance, q, index, support, loadVec, NULL);
-	return sc;
+		HnswLoadElement(entryPoint, &distance, q, index, support, loadVec, NULL);
+
+	return HnswInitSearchCandidate(base, entryPoint, distance);
 }
 
 /*
@@ -608,6 +626,21 @@ CompareNearestCandidates(const pairingheap_node *a, const pairingheap_node *b, v
 	return 0;
 }
 
+/*
+ * Compare discarded candidate distances
+ */
+static int
+CompareNearestDiscardedCandidates(const pairingheap_node *a, const pairingheap_node *b, void *arg)
+{
+	if (HnswGetSearchCandidateConst(w_node, a)->distance < HnswGetSearchCandidateConst(w_node, b)->distance)
+		return 1;
+
+	if (HnswGetSearchCandidateConst(w_node, a)->distance > HnswGetSearchCandidateConst(w_node, b)->distance)
+		return -1;
+
+	return 0;
+}
+
 /*
  * Compare candidate distances
  */
@@ -728,8 +761,11 @@ HnswLoadNeighborTids(HnswElement element, ItemPointerData *indextids, Relation i
 
 	ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
 
-	/* Ensure expected neighbors */
-	if (ntup->count != (element->level + 2) * m)
+	/*
+	 * Ensure the neighbor tuple has not been deleted or replaced between
+	 * index scan iterations
+	 */
+	if (ntup->version != element->version || ntup->count != (element->level + 2) * m)
 	{
 		UnlockReleaseBuffer(buf);
 		return false;
@@ -775,13 +811,13 @@ HnswLoadUnvisitedFromDisk(HnswElement element, HnswUnvisited * unvisited, int *u
  * Algorithm 2 from paper
  */
 List *
-HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement)
+HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples)
 {
 	List	   *w = NIL;
 	pairingheap *C = pairingheap_allocate(CompareNearestCandidates, NULL);
 	pairingheap *W = pairingheap_allocate(CompareFurthestCandidates, NULL);
 	int			wlen = 0;
-	visited_hash v;
+	visited_hash vh;
 	ListCell   *lc2;
 	HnswNeighborArray *localNeighborhood = NULL;
 	Size		neighborhoodSize = 0;
@@ -790,7 +826,19 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 	int			unvisitedLength;
 	bool		inMemory = index == NULL;
 
-	InitVisited(base, &v, inMemory, ef, m);
+	if (v == NULL)
+	{
+		v = &vh;
+		initVisited = true;
+	}
+
+	if (initVisited)
+	{
+		InitVisited(base, v, inMemory, ef, m);
+
+		if (discarded != NULL)
+			*discarded = pairingheap_allocate(CompareNearestDiscardedCandidates, NULL);
+	}
 
 	/* Create local memory for neighborhood if needed */
 	if (inMemory)
@@ -805,7 +853,14 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 		HnswSearchCandidate *sc = (HnswSearchCandidate *) lfirst(lc2);
 		bool		found;
 
-		AddToVisited(base, &v, sc->element, inMemory, &found);
+		if (initVisited)
+		{
+			AddToVisited(base, v, sc->element, inMemory, &found);
+
+			/* OK to count elements instead of tuples */
+			if (tuples != NULL)
+				(*tuples)++;
+		}
 
 		pairingheap_add(C, &sc->c_node);
 		pairingheap_add(W, &sc->w_node);
@@ -831,9 +886,13 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 		cElement = HnswPtrAccess(base, c->element);
 
 		if (inMemory)
-			HnswLoadUnvisitedFromMemory(base, cElement, unvisited, &unvisitedLength, &v, lc, localNeighborhood, neighborhoodSize);
+			HnswLoadUnvisitedFromMemory(base, cElement, unvisited, &unvisitedLength, v, lc, localNeighborhood, neighborhoodSize);
 		else
-			HnswLoadUnvisitedFromDisk(cElement, unvisited, &unvisitedLength, &v, index, m, lm, lc);
+			HnswLoadUnvisitedFromDisk(cElement, unvisited, &unvisitedLength, v, index, m, lm, lc);
+
+		/* OK to count elements instead of tuples */
+		if (tuples != NULL)
+			(*tuples) += unvisitedLength;
 
 		for (int i = 0; i < unvisitedLength; i++)
 		{
@@ -857,25 +916,30 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 
 				/* Avoid any allocations if not adding */
 				eElement = NULL;
-				HnswLoadElementImpl(blkno, offno, &eDistance, q, index, support, inserting, alwaysAdd ? NULL : &f->distance, &eElement);
+				HnswLoadElementImpl(blkno, offno, &eDistance, q, index, support, inserting, alwaysAdd || discarded != NULL ? NULL : &f->distance, &eElement);
 
 				if (eElement == NULL)
 					continue;
 			}
 
-			if (!(eDistance < f->distance || alwaysAdd))
-				continue;
+			if (eElement == NULL || !(eDistance < f->distance || alwaysAdd))
+			{
+				if (discarded != NULL)
+				{
+					/* Create a new candidate */
+					e = HnswInitSearchCandidate(base, eElement, eDistance);
+					pairingheap_add(*discarded, &e->w_node);
+				}
 
-			Assert(!eElement->deleted);
+				continue;
+			}
 
 			/* Make robust to issues */
 			if (eElement->level < lc)
 				continue;
 
 			/* Create a new candidate */
-			e = palloc(sizeof(HnswSearchCandidate));
-			HnswPtrStore(base, e->element, eElement);
-			e->distance = eDistance;
+			e = HnswInitSearchCandidate(base, eElement, eDistance);
 			pairingheap_add(C, &e->c_node);
 			pairingheap_add(W, &e->w_node);
 
@@ -890,7 +954,12 @@ HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation in
 
 				/* No need to decrement wlen */
 				if (wlen > ef)
-					pairingheap_remove_first(W);
+				{
+					HnswSearchCandidate *d = HnswGetSearchCandidate(w_node, pairingheap_remove_first(W));
+
+					if (discarded != NULL)
+						pairingheap_add(*discarded, &d->w_node);
+				}
 			}
 		}
 	}
@@ -1225,7 +1294,7 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 	/* 1st phase: greedy search to insert level */
 	for (int lc = entryLevel; lc >= level + 1; lc--)
 	{
-		w = HnswSearchLayer(base, &q, ep, 1, lc, index, support, m, true, skipElement);
+		w = HnswSearchLayer(base, &q, ep, 1, lc, index, support, m, true, skipElement, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
@@ -1244,7 +1313,7 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 		List	   *lw = NIL;
 		ListCell   *lc2;
 
-		w = HnswSearchLayer(base, &q, ep, efConstruction, lc, index, support, m, true, skipElement);
+		w = HnswSearchLayer(base, &q, ep, efConstruction, lc, index, support, m, true, skipElement, NULL, NULL, true, NULL);
 
 		/* Convert search candidates to candidates */
 		foreach(lc2, w)

src/hnswvacuum.c

@@ -527,6 +527,14 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 			for (int i = 0; i < ntup->count; i++)
 				ItemPointerSetInvalid(&ntup->indextids[i]);
 
+			/* Increment version */
+			/* This is used to avoid incorrect reads for iterative scans */
+			/* Reserve some bits for future use */
+			etup->version++;
+			if (etup->version > 15)
+				etup->version = 1;
+			ntup->version = etup->version;
+
 			/*
 			 * We modified the tuples in place, no need to call
 			 * PageIndexTupleOverwrite

src/ivfbuild.c

@@ -138,7 +138,7 @@ SampleRows(IvfflatBuildState * buildstate)
  * Add tuple to sort
  */
 static void
-AddTupleToSort(Relation index, ItemPointer tid, Datum *values, bool *isnull, IvfflatBuildState * buildstate)
+AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState * buildstate)
 {
 	double		distance;
 	double		minDistance = DBL_MAX;
@@ -184,11 +184,6 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, bool *isnull, Ivf
 	slot->tts_isnull[1] = false;
 	slot->tts_values[2] = value;
 	slot->tts_isnull[2] = false;
-	for (int i = 1; i < buildstate->tupdesc->natts; i++)
-	{
-		slot->tts_values[2 + i] = values[i];
-		slot->tts_isnull[2 + i] = isnull[i];
-	}
 	ExecStoreVirtualTuple(slot);
 
 	/*
@@ -220,7 +215,7 @@ BuildCallback(Relation index, ItemPointer tid, Datum *values,
 	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
 
 	/* Add tuple to sort */
-	AddTupleToSort(index, tid, values, isnull, buildstate);
+	AddTupleToSort(index, tid, values, buildstate);
 
 	/* Reset memory context */
 	MemoryContextSwitchTo(oldCtx);
@@ -231,20 +226,19 @@ BuildCallback(Relation index, ItemPointer tid, Datum *values,
  * Get index tuple from sort state
  */
 static inline void
-GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot, Datum *values, bool *isnull, IndexTuple *itup, int *list)
+GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot, IndexTuple *itup, int *list)
 {
 	if (tuplesort_gettupleslot(sortstate, true, false, slot, NULL))
 	{
-		bool		unused;
+		Datum		value;
+		bool		isnull;
 
-		*list = DatumGetInt32(slot_getattr(slot, 1, &unused));
-
-		for (int i = 0; i < tupdesc->natts; i++)
-			values[i] = slot_getattr(slot, 3 + i, &isnull[i]);
+		*list = DatumGetInt32(slot_getattr(slot, 1, &isnull));
+		value = slot_getattr(slot, 3, &isnull);
 
 		/* Form the index tuple */
-		*itup = index_form_tuple(tupdesc, values, isnull);
-		(*itup)->t_tid = *((ItemPointer) DatumGetPointer(slot_getattr(slot, 2, &unused)));
+		*itup = index_form_tuple(tupdesc, &value, &isnull);
+		(*itup)->t_tid = *((ItemPointer) DatumGetPointer(slot_getattr(slot, 2, &isnull)));
 	}
 	else
 		*list = -1;
@@ -262,14 +256,12 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 
 	TupleTableSlot *slot = MakeSingleTupleTableSlot(buildstate->sortdesc, &TTSOpsMinimalTuple);
 	TupleDesc	tupdesc = buildstate->tupdesc;
-	Datum	   *values = palloc(tupdesc->natts * sizeof(Datum));
-	bool	   *isnull = palloc(tupdesc->natts * sizeof(bool));
 
 	pgstat_progress_update_param(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_LOAD);
 
 	pgstat_progress_update_param(PROGRESS_CREATEIDX_TUPLES_TOTAL, buildstate->indtuples);
 
-	GetNextTuple(buildstate->sortstate, tupdesc, slot, values, isnull, &itup, &list);
+	GetNextTuple(buildstate->sortstate, tupdesc, slot, &itup, &list);
 
 	for (int i = 0; i < buildstate->centers->length; i++)
 	{
@@ -305,7 +297,7 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 
 			pgstat_progress_update_param(PROGRESS_CREATEIDX_TUPLES_DONE, ++inserted);
 
-			GetNextTuple(buildstate->sortstate, tupdesc, slot, values, isnull, &itup, &list);
+			GetNextTuple(buildstate->sortstate, tupdesc, slot, &itup, &list);
 		}
 
 		insertPage = BufferGetBlockNumber(buf);
@@ -315,9 +307,6 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 		/* Set the start and insert pages */
 		IvfflatUpdateList(index, buildstate->listInfo[i], insertPage, InvalidBlockNumber, startPage, forkNum);
 	}
-
-	pfree(values);
-	pfree(isnull);
 }
 
 /*
@@ -341,19 +330,6 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
 				 errmsg("type not supported for ivfflat index")));
 
-	/* TODO See if needed */
-	if (IndexRelationGetNumberOfKeyAttributes(index) > 3)
-		elog(ERROR, "index cannot have more than three columns");
-
-	if (!OidIsValid(index_getprocid(index, 1, IVFFLAT_DISTANCE_PROC)))
-		elog(ERROR, "first column must be a vector");
-
-	for (int i = 1; i < IndexRelationGetNumberOfKeyAttributes(index); i++)
-	{
-		if (OidIsValid(index_getprocid(index, i + 1, IVFFLAT_DISTANCE_PROC)))
-			elog(ERROR, "column %d cannot be a vector", i + 1);
-	}
-
 	/* Require column to have dimensions to be indexed */
 	if (buildstate->dimensions < 0)
 		ereport(ERROR,
@@ -381,11 +357,10 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 				 errmsg("dimensions must be greater than one for this opclass")));
 
 	/* Create tuple description for sorting */
-	buildstate->sortdesc = CreateTemplateTupleDesc(2 + buildstate->tupdesc->natts);
+	buildstate->sortdesc = CreateTemplateTupleDesc(3);
 	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 1, "list", INT4OID, -1, 0);
 	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
-	for (int i = 0; i < buildstate->tupdesc->natts; i++)
-		TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) (3 + i), NULL, buildstate->tupdesc->attrs[i].atttypid, -1, 0);
+	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 3, "vector", buildstate->tupdesc->attrs[0].atttypid, -1, 0);
 
 	buildstate->slot = MakeSingleTupleTableSlot(buildstate->sortdesc, &TTSOpsVirtual);
 

src/ivfflat.c

@@ -17,8 +17,16 @@
 #endif
 
 int			ivfflat_probes;
+int			ivfflat_iterative_scan;
+int			ivfflat_max_probes;
 static relopt_kind ivfflat_relopt_kind;
 
+static const struct config_enum_entry ivfflat_iterative_scan_options[] = {
+	{"off", IVFFLAT_ITERATIVE_SCAN_OFF, false},
+	{"relaxed_order", IVFFLAT_ITERATIVE_SCAN_RELAXED, false},
+	{NULL, 0, false}
+};
+
 /*
  * Initialize index options and variables
  */
@@ -31,7 +39,16 @@ IvfflatInit(void)
 
 	DefineCustomIntVariable("ivfflat.probes", "Sets the number of probes",
 							"Valid range is 1..lists.", &ivfflat_probes,
-							IVFFLAT_DEFAULT_PROBES, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
+							IVFFLAT_DEFAULT_PROBES, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS, PGC_USERSET, GUC_EXPLAIN, NULL, NULL, NULL);
+
+	DefineCustomEnumVariable("ivfflat.iterative_scan", "Sets the mode for iterative scans",
+							 NULL, &ivfflat_iterative_scan,
+							 IVFFLAT_ITERATIVE_SCAN_OFF, ivfflat_iterative_scan_options, PGC_USERSET, GUC_EXPLAIN, NULL, NULL, NULL);
+
+	/* If this is less than probes, probes is used */
+	DefineCustomIntVariable("ivfflat.max_probes", "Sets the max number of probes for iterative scans",
+							NULL, &ivfflat_max_probes,
+							IVFFLAT_MAX_LISTS, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS, PGC_USERSET, GUC_EXPLAIN, NULL, NULL, NULL);
 
 	MarkGUCPrefixReserved("ivfflat");
 }
@@ -82,6 +99,10 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 		*indexSelectivity = 0;
 		*indexCorrelation = 0;
 		*indexPages = 0;
+#if PG_VERSION_NUM >= 180000
+		/* See "On disable_cost" thread on pgsql-hackers */
+		path->path.disabled_nodes = 2;
+#endif
 		return;
 	}
 
@@ -167,7 +188,7 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	amroutine->amcanorderbyop = true;
 	amroutine->amcanbackward = false;	/* can change direction mid-scan */
 	amroutine->amcanunique = false;
-	amroutine->amcanmulticol = true;
+	amroutine->amcanmulticol = false;
 	amroutine->amoptionalkey = true;
 	amroutine->amsearcharray = false;
 	amroutine->amsearchnulls = false;

src/ivfflat.h

@@ -80,6 +80,14 @@
 
 /* Variables */
 extern int	ivfflat_probes;
+extern int	ivfflat_iterative_scan;
+extern int	ivfflat_max_probes;
+
+typedef enum IvfflatIterativeScanMode
+{
+	IVFFLAT_ITERATIVE_SCAN_OFF,
+	IVFFLAT_ITERATIVE_SCAN_RELAXED
+}			IvfflatIterativeScanMode;
 
 typedef struct VectorArrayData
 {
@@ -248,8 +256,11 @@ typedef struct IvfflatScanOpaqueData
 {
 	const		IvfflatTypeInfo *typeInfo;
 	int			probes;
+	int			maxProbes;
 	int			dimensions;
 	bool		first;
+	Datum		value;
+	MemoryContext tmpCtx;
 
 	/* Sorting */
 	Tuplesortstate *sortstate;
@@ -266,7 +277,9 @@ typedef struct IvfflatScanOpaqueData
 
 	/* Lists */
 	pairingheap *listQueue;
-	IvfflatScanList lists[FLEXIBLE_ARRAY_MEMBER];	/* must come last */
+	BlockNumber *listPages;
+	int			listIndex;
+	IvfflatScanList *lists;
 }			IvfflatScanOpaqueData;
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;

src/ivfinsert.c

@@ -78,8 +78,6 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 	BlockNumber insertPage = InvalidBlockNumber;
 	ListInfo	listInfo;
 	BlockNumber originalInsertPage;
-	TupleDesc	tupdesc = RelationGetDescr(index);
-	Datum	   *newValues = palloc(tupdesc->natts * sizeof(Datum));
 
 	/* Detoast once for all calls */
 	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
@@ -104,12 +102,8 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 	Assert(BlockNumberIsValid(insertPage));
 	originalInsertPage = insertPage;
 
-	newValues[0] = value;
-	for (int i = 1; i < tupdesc->natts; i++)
-		newValues[i] = values[i];
-
 	/* Form tuple */
-	itup = index_form_tuple(tupdesc, newValues, isnull);
+	itup = index_form_tuple(RelationGetDescr(index), &value, isnull);
 	itup->t_tid = *heap_tid;
 
 	/* Get tuple size */

src/ivfscan.c

@@ -10,10 +10,7 @@
 #include "miscadmin.h"
 #include "pgstat.h"
 #include "storage/bufmgr.h"
-
-#ifdef IVFFLAT_MEMORY
 #include "utils/memutils.h"
-#endif
 
 #define GetScanList(ptr) pairingheap_container(IvfflatScanList, ph_node, ptr)
 #define GetScanListConst(ptr) pairingheap_const_container(IvfflatScanList, ph_node, ptr)
@@ -65,7 +62,7 @@ GetScanLists(IndexScanDesc scan, Datum value)
 			/* Use procinfo from the index instead of scan key for performance */
 			distance = DatumGetFloat8(so->distfunc(so->procinfo, so->collation, PointerGetDatum(&list->center), value));
 
-			if (listCount < so->probes)
+			if (listCount < so->maxProbes)
 			{
 				IvfflatScanList *scanlist;
 
@@ -78,7 +75,7 @@ GetScanLists(IndexScanDesc scan, Datum value)
 				pairingheap_add(so->listQueue, &scanlist->ph_node);
 
 				/* Calculate max distance */
-				if (listCount == so->probes)
+				if (listCount == so->maxProbes)
 					maxDistance = GetScanList(pairingheap_first(so->listQueue))->distance;
 			}
 			else if (distance < maxDistance)
@@ -102,34 +99,11 @@ GetScanLists(IndexScanDesc scan, Datum value)
 
 		UnlockReleaseBuffer(cbuf);
 	}
-}
 
-/*
- * Check if matches scan keys
- */
-static bool
-MatchesScanKeys(IndexScanDesc scan, IndexTuple itup, TupleDesc tupdesc)
-{
-	for (int i = 0; i < scan->numberOfKeys; i++)
-	{
-		ScanKey		key = &scan->keyData[i];
-		bool		attnull = key->sk_flags & SK_ISNULL;
-		bool		isnull;
-		Datum		value = index_getattr(itup, key->sk_attno, tupdesc, &isnull);
+	for (int i = listCount - 1; i >= 0; i--)
+		so->listPages[i] = GetScanList(pairingheap_remove_first(so->listQueue))->startPage;
 
-		if (isnull || attnull)
-		{
-			if (isnull != attnull)
-				return false;
-		}
-		else
-		{
-			if (!DatumGetBool(FunctionCall2Coll(&key->sk_func, key->sk_collation, value, key->sk_argument)))
-				return false;
-		}
-	}
-
-	return true;
+	Assert(pairingheap_is_empty(so->listQueue));
 }
 
 /*
@@ -142,11 +116,14 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	TupleDesc	tupdesc = RelationGetDescr(scan->indexRelation);
 	double		tuples = 0;
 	TupleTableSlot *slot = so->vslot;
+	int			batchProbes = 0;
+
+	tuplesort_reset(so->sortstate);
 
 	/* Search closest probes lists */
-	while (!pairingheap_is_empty(so->listQueue))
+	while (so->listIndex < so->maxProbes && (++batchProbes) <= so->probes)
 	{
-		BlockNumber searchPage = GetScanList(pairingheap_remove_first(so->listQueue))->startPage;
+		BlockNumber searchPage = so->listPages[so->listIndex++];
 
 		/* Search all entry pages for list */
 		while (BlockNumberIsValid(searchPage))
@@ -168,10 +145,6 @@ GetScanItems(IndexScanDesc scan, Datum value)
 				ItemId		itemid = PageGetItemId(page, offno);
 
 				itup = (IndexTuple) PageGetItem(page, itemid);
-
-				if (!MatchesScanKeys(scan, itup, tupdesc))
-					continue;
-
 				datum = index_getattr(itup, 1, tupdesc, &isnull);
 
 				/*
@@ -198,13 +171,17 @@ GetScanItems(IndexScanDesc scan, Datum value)
 		}
 	}
 
-	if (tuples < 100)
+	if (tuples < 100 && ivfflat_iterative_scan == IVFFLAT_ITERATIVE_SCAN_OFF)
 		ereport(DEBUG1,
 				(errmsg("index scan found few tuples"),
 				 errdetail("Index may have been created with little data."),
 				 errhint("Recreate the index and possibly decrease lists.")));
 
 	tuplesort_performsort(so->sortstate);
+
+#if defined(IVFFLAT_MEMORY)
+	elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
+#endif
 }
 
 /*
@@ -241,7 +218,13 @@ GetScanValue(IndexScanDesc scan)
 
 		/* Normalize if needed */
 		if (so->normprocinfo != NULL)
+		{
+			MemoryContext oldCtx = MemoryContextSwitchTo(so->tmpCtx);
+
 			value = IvfflatNormValue(so->typeInfo, so->collation, value);
+
+			MemoryContextSwitchTo(oldCtx);
+		}
 	}
 
 	return value;
@@ -272,19 +255,30 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	int			lists;
 	int			dimensions;
 	int			probes = ivfflat_probes;
+	int			maxProbes;
+	MemoryContext oldCtx;
 
 	scan = RelationGetIndexScan(index, nkeys, norderbys);
 
 	/* Get lists and dimensions from metapage */
 	IvfflatGetMetaPageInfo(index, &lists, &dimensions);
 
+	if (ivfflat_iterative_scan != IVFFLAT_ITERATIVE_SCAN_OFF)
+		maxProbes = Max(ivfflat_max_probes, probes);
+	else
+		maxProbes = probes;
+
 	if (probes > lists)
 		probes = lists;
 
-	so = (IvfflatScanOpaque) palloc(offsetof(IvfflatScanOpaqueData, lists) + probes * sizeof(IvfflatScanList));
+	if (maxProbes > lists)
+		maxProbes = lists;
+
+	so = (IvfflatScanOpaque) palloc(sizeof(IvfflatScanOpaqueData));
 	so->typeInfo = IvfflatGetTypeInfo(index);
 	so->first = true;
 	so->probes = probes;
+	so->maxProbes = maxProbes;
 	so->dimensions = dimensions;
 
 	/* Set support functions */
@@ -292,6 +286,12 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	so->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	so->collation = index->rd_indcollation[0];
 
+	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+									   "Ivfflat scan temporary context",
+									   ALLOCSET_DEFAULT_SIZES);
+
+	oldCtx = MemoryContextSwitchTo(so->tmpCtx);
+
 	/* Create tuple description for sorting */
 	so->tupdesc = CreateTemplateTupleDesc(2);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
@@ -312,6 +312,11 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	so->bas = GetAccessStrategy(BAS_BULKREAD);
 
 	so->listQueue = pairingheap_allocate(CompareLists, scan);
+	so->listPages = palloc(maxProbes * sizeof(BlockNumber));
+	so->listIndex = 0;
+	so->lists = palloc(maxProbes * sizeof(IvfflatScanList));
+
+	MemoryContextSwitchTo(oldCtx);
 
 	scan->opaque = so;
 
@@ -326,11 +331,9 @@ ivfflatrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 
-	if (!so->first)
-		tuplesort_reset(so->sortstate);
-
 	so->first = true;
 	pairingheap_reset(so->listQueue);
+	so->listIndex = 0;
 
 	if (keys && scan->numberOfKeys > 0)
 		memmove(scan->keyData, keys, scan->numberOfKeys * sizeof(ScanKeyData));
@@ -346,6 +349,8 @@ bool
 ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
+	ItemPointer heaptid;
+	bool		isnull;
 
 	/*
 	 * Index can be used to scan backward, but Postgres doesn't support
@@ -373,28 +378,23 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
 		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;
-
-#if defined(IVFFLAT_MEMORY)
-		elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
-#endif
-
-		/* Clean up if we allocated a new value */
-		if (value != scan->orderByData->sk_argument)
-			pfree(DatumGetPointer(value));
+		so->value = value;
 	}
 
-	if (tuplesort_gettupleslot(so->sortstate, true, false, so->mslot, NULL))
+	while (!tuplesort_gettupleslot(so->sortstate, true, false, so->mslot, NULL))
 	{
-		bool		isnull;
-		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->mslot, 2, &isnull));
+		if (so->listIndex == so->maxProbes)
+			return false;
 
-		scan->xs_heaptid = *heaptid;
-		scan->xs_recheck = false;
-		scan->xs_recheckorderby = false;
-		return true;
+		IvfflatBench("GetScanItems", GetScanItems(scan, so->value));
 	}
 
-	return false;
+	heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->mslot, 2, &isnull));
+
+	scan->xs_heaptid = *heaptid;
+	scan->xs_recheck = false;
+	scan->xs_recheckorderby = false;
+	return true;
 }
 
 /*
@@ -405,12 +405,10 @@ ivfflatendscan(IndexScanDesc scan)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 
-	pairingheap_free(so->listQueue);
+	/* Free any temporary files */
 	tuplesort_end(so->sortstate);
-	FreeAccessStrategy(so->bas);
-	FreeTupleDesc(so->tupdesc);
 
-	/* TODO Free vslot and mslot without freeing TupleDesc */
+	MemoryContextDelete(so->tmpCtx);
 
 	pfree(so);
 	scan->opaque = NULL;

src/ivfvacuum.c

@@ -26,7 +26,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 		Page		cpage;
 		OffsetNumber coffno;
 		OffsetNumber cmaxoffno;
-		BlockNumber startPages[MaxOffsetNumber];
+		BlockNumber listPages[MaxOffsetNumber];
 		ListInfo	listInfo;
 
 		cbuf = ReadBuffer(index, blkno);
@@ -40,7 +40,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 		{
 			IvfflatList list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, coffno));
 
-			startPages[coffno - FirstOffsetNumber] = list->startPage;
+			listPages[coffno - FirstOffsetNumber] = list->startPage;
 		}
 
 		listInfo.blkno = blkno;
@@ -50,7 +50,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 
 		for (coffno = FirstOffsetNumber; coffno <= cmaxoffno; coffno = OffsetNumberNext(coffno))
 		{
-			BlockNumber searchPage = startPages[coffno - FirstOffsetNumber];
+			BlockNumber searchPage = listPages[coffno - FirstOffsetNumber];
 			BlockNumber insertPage = InvalidBlockNumber;
 
 			/* Iterate over entry pages */

test/expected/hnsw_vector.out

@@ -99,6 +99,32 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::vector)) t2
      4
 (1 row)
 
+DROP TABLE t;
+-- iterative
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops);
+SET hnsw.iterative_scan = strict_order;
+SET hnsw.ef_search = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+SET hnsw.iterative_scan = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+RESET hnsw.iterative_scan;
+RESET hnsw.ef_search;
 DROP TABLE t;
 -- unlogged
 CREATE UNLOGGED TABLE t (val vector(3));
@@ -139,4 +165,29 @@ SET hnsw.ef_search = 0;
 ERROR:  0 is outside the valid range for parameter "hnsw.ef_search" (1 .. 1000)
 SET hnsw.ef_search = 1001;
 ERROR:  1001 is outside the valid range for parameter "hnsw.ef_search" (1 .. 1000)
+SHOW hnsw.iterative_scan;
+ hnsw.iterative_scan 
+---------------------
+ off
+(1 row)
+
+SET hnsw.iterative_scan = on;
+ERROR:  invalid value for parameter "hnsw.iterative_scan": "on"
+HINT:  Available values: off, relaxed_order, strict_order.
+SHOW hnsw.max_scan_tuples;
+ hnsw.max_scan_tuples 
+----------------------
+ 20000
+(1 row)
+
+SET hnsw.max_scan_tuples = 0;
+ERROR:  0 is outside the valid range for parameter "hnsw.max_scan_tuples" (1 .. 2147483647)
+SHOW hnsw.scan_mem_multiplier;
+ hnsw.scan_mem_multiplier 
+--------------------------
+ 1
+(1 row)
+
+SET hnsw.scan_mem_multiplier = 0;
+ERROR:  0 is outside the valid range for parameter "hnsw.scan_mem_multiplier" (1 .. 1000)
 DROP TABLE t;

test/expected/ivfflat_vector.out

@@ -81,6 +81,37 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2
      3
 (1 row)
 
+DROP TABLE t;
+-- iterative
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 3);
+SET ivfflat.iterative_scan = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+SET ivfflat.max_probes = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+(1 row)
+
+SET ivfflat.max_probes = 2;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+(2 rows)
+
+RESET ivfflat.iterative_scan;
+RESET ivfflat.max_probes;
 DROP TABLE t;
 -- unlogged
 CREATE UNLOGGED TABLE t (val vector(3));
@@ -109,4 +140,27 @@ SHOW ivfflat.probes;
  1
 (1 row)
 
+SET ivfflat.probes = 0;
+ERROR:  0 is outside the valid range for parameter "ivfflat.probes" (1 .. 32768)
+SET ivfflat.probes = 32769;
+ERROR:  32769 is outside the valid range for parameter "ivfflat.probes" (1 .. 32768)
+SHOW ivfflat.iterative_scan;
+ ivfflat.iterative_scan 
+------------------------
+ off
+(1 row)
+
+SET ivfflat.iterative_scan = on;
+ERROR:  invalid value for parameter "ivfflat.iterative_scan": "on"
+HINT:  Available values: off, relaxed_order.
+SHOW ivfflat.max_probes;
+ ivfflat.max_probes 
+--------------------
+ 32768
+(1 row)
+
+SET ivfflat.max_probes = 0;
+ERROR:  0 is outside the valid range for parameter "ivfflat.max_probes" (1 .. 32768)
+SET ivfflat.max_probes = 32769;
+ERROR:  32769 is outside the valid range for parameter "ivfflat.max_probes" (1 .. 32768)
 DROP TABLE t;

test/sql/hnsw_vector.sql

@@ -57,6 +57,23 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::vector)) t2
 
 DROP TABLE t;
 
+-- iterative
+
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops);
+
+SET hnsw.iterative_scan = strict_order;
+SET hnsw.ef_search = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+SET hnsw.iterative_scan = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+RESET hnsw.iterative_scan;
+RESET hnsw.ef_search;
+DROP TABLE t;
+
 -- unlogged
 
 CREATE UNLOGGED TABLE t (val vector(3));
@@ -81,4 +98,16 @@ SHOW hnsw.ef_search;
 SET hnsw.ef_search = 0;
 SET hnsw.ef_search = 1001;
 
+SHOW hnsw.iterative_scan;
+
+SET hnsw.iterative_scan = on;
+
+SHOW hnsw.max_scan_tuples;
+
+SET hnsw.max_scan_tuples = 0;
+
+SHOW hnsw.scan_mem_multiplier;
+
+SET hnsw.scan_mem_multiplier = 0;
+
 DROP TABLE t;

test/sql/ivfflat_vector.sql

@@ -44,6 +44,25 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2
 
 DROP TABLE t;
 
+-- iterative
+
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 3);
+
+SET ivfflat.iterative_scan = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+SET ivfflat.max_probes = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+SET ivfflat.max_probes = 2;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+RESET ivfflat.iterative_scan;
+RESET ivfflat.max_probes;
+DROP TABLE t;
+
 -- unlogged
 
 CREATE UNLOGGED TABLE t (val vector(3));
@@ -62,4 +81,16 @@ CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 32769);
 
 SHOW ivfflat.probes;
 
+SET ivfflat.probes = 0;
+SET ivfflat.probes = 32769;
+
+SHOW ivfflat.iterative_scan;
+
+SET ivfflat.iterative_scan = on;
+
+SHOW ivfflat.max_probes;
+
+SET ivfflat.max_probes = 0;
+SET ivfflat.max_probes = 32769;
+
 DROP TABLE t;

test/t/041_ivfflat_inline_filtering.pl

@@ -1,197 +0,0 @@
-use strict;
-use warnings FATAL => 'all';
-use PostgreSQL::Test::Cluster;
-use PostgreSQL::Test::Utils;
-use Test::More;
-
-my $node;
-my @queries = ();
-my @where = ();
-my @expected;
-my $limit = 20;
-my $dim = 3;
-my $array_sql = join(",", ('random()') x $dim);
-my $nc = 100;
-my $nc2 = 10;
-
-sub test_recall
-{
-	my ($probes, $min, $operator) = @_;
-	my $correct = 0;
-	my $total = 0;
-
-	for my $j (0 .. 2)
-	{
-		my $explain = $node->safe_psql("postgres", qq(
-			SET enable_seqscan = off;
-			SET ivfflat.probes = $probes;
-			EXPLAIN ANALYZE SELECT i FROM tst WHERE $where[$j] ORDER BY v $operator '$queries[$j]' LIMIT $limit;
-		));
-		like($explain, qr/Index Cond/);
-	}
-
-	for my $i (0 .. $#queries)
-	{
-		my $actual = $node->safe_psql("postgres", qq(
-			SET enable_seqscan = off;
-			SET ivfflat.probes = $probes;
-			SELECT i FROM tst WHERE $where[$i] ORDER BY v $operator '$queries[$i]' LIMIT $limit;
-		));
-		my @actual_ids = split("\n", $actual);
-		my %actual_set = map { $_ => 1 } @actual_ids;
-
-		is(scalar(@actual_ids), $limit);
-
-		my @expected_ids = split("\n", $expected[$i]);
-
-		foreach (@expected_ids)
-		{
-			if (exists($actual_set{$_}))
-			{
-				$correct++;
-			}
-			$total++;
-		}
-	}
-
-	cmp_ok($correct / $total, ">=", $min, $operator);
-}
-
-# Initialize node
-$node = PostgreSQL::Test::Cluster->new('node');
-$node->init;
-$node->start;
-
-# Create table
-$node->safe_psql("postgres", "CREATE EXTENSION vector;");
-$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim), c int4, c2 int4);");
-$node->safe_psql("postgres",
-	"INSERT INTO tst SELECT i, ARRAY[$array_sql], i % $nc, i % $nc2 FROM generate_series(1, 50000) i;"
-);
-
-# Generate queries
-for my $i (1 .. 100)
-{
-	my @r = ();
-	for (1 .. $dim)
-	{
-		push(@r, rand());
-	}
-	push(@queries, "[" . join(",", @r) . "]");
-
-	if ($i % 3 == 0)
-	{
-		my $c = int(rand() * $nc);
-		push(@where, "c = $c");
-	}
-	elsif ($i % 3 == 1)
-	{
-		my $c2 = int(rand() * $nc2);
-		push(@where, "c2 = $c2");
-	}
-	else
-	{
-		# use c2 to ensure results
-		my $c2 = int(rand() * $nc2);
-		push(@where, "c = $c2 AND c2 = $c2");
-	}
-}
-
-# Add index
-$node->safe_psql("postgres", qq(
-	CREATE INDEX ON tst USING ivfflat (v vector_l2_ops, c, c2) WITH (lists = 100);
-));
-
-# Insert more rows
-$node->safe_psql("postgres",
-	"INSERT INTO tst SELECT i, ARRAY[$array_sql], i % $nc, i % $nc2 FROM generate_series(1, 50000) i;"
-);
-
-# Get exact results
-@expected = ();
-for my $i (0 .. $#queries)
-{
-	my $res = $node->safe_psql("postgres", qq(
-		SET enable_indexscan = off;
-		SELECT i FROM tst WHERE $where[$i] ORDER BY v <-> '$queries[$i]' LIMIT $limit;
-	));
-	push(@expected, $res);
-}
-
-# Test recall
-test_recall(10, 0.99, '<->');
-
-# Test vacuum
-$node->safe_psql("postgres", "DELETE FROM tst WHERE c > 5;");
-$node->safe_psql("postgres", "VACUUM tst;");
-
-# Test less than
-my $explain = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	EXPLAIN ANALYZE SELECT i FROM tst WHERE c < 10 ORDER BY v <-> '$queries[0]' LIMIT $limit;
-));
-like($explain, qr/Index Cond: \(c < 10\)/);
-
-# Test less than or equal
-$explain = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	EXPLAIN ANALYZE SELECT i FROM tst WHERE c <= 10 ORDER BY v <-> '$queries[0]' LIMIT $limit;
-));
-like($explain, qr/Index Cond: \(c <= 10\)/);
-
-# Test greater than or equal
-$explain = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	EXPLAIN ANALYZE SELECT i FROM tst WHERE c >= 90 ORDER BY v <-> '$queries[0]' LIMIT $limit;
-));
-like($explain, qr/Index Cond: \(c >= 90\)/);
-
-# Test greater than
-$explain = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	EXPLAIN ANALYZE SELECT i FROM tst WHERE c > 90 ORDER BY v <-> '$queries[0]' LIMIT $limit;
-));
-like($explain, qr/Index Cond: \(c > 90\)/);
-
-# Test multiple attribute columns
-$explain = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = 1 AND c2 = 1 ORDER BY v <-> '$queries[0]' LIMIT $limit;
-));
-like($explain, qr/Index Cond: \(\(c = 1\) AND \(c2 = 1\)\)/);
-
-# Test only last attribute column
-$explain = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	EXPLAIN ANALYZE SELECT i FROM tst WHERE c2 = 1 ORDER BY v <-> '$queries[0]' LIMIT $limit;
-));
-like($explain, qr/Index Cond: \(c2 = 1\)/);
-
-# Test only vector column
-$explain = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$queries[0]' LIMIT $limit;
-));
-like($explain, qr/Index Scan/);
-
-# Test only attribute columns
-$explain = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = 1;
-));
-like($explain, qr/Seq Scan/);
-
-# Test columns
-my ($ret, $stdout, $stderr) = $node->psql("postgres", "CREATE INDEX ON tst USING ivfflat (c);");
-like($stderr, qr/first column must be a vector/);
-
-($ret, $stdout, $stderr) = $node->psql("postgres", "CREATE INDEX ON tst USING ivfflat (c, v vector_cosine_ops);");
-like($stderr, qr/first column must be a vector/);
-
-($ret, $stdout, $stderr) = $node->psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_cosine_ops, c, c, c);");
-like($stderr, qr/index cannot have more than three columns/);
-
-($ret, $stdout, $stderr) = $node->psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_cosine_ops, v vector_cosine_ops);");
-like($stderr, qr/column 2 cannot be a vector/);
-
-done_testing();

test/t/041_ivfflat_iterative_scan.pl

@@ -0,0 +1,54 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $dim = 3;
+my $array_sql = join(",", ('random()') x $dim);
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4 PRIMARY KEY, v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
+);
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_l2_ops);");
+
+my $count = $node->safe_psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET ivfflat.probes = 10;
+	SET ivfflat.iterative_scan = relaxed_order;
+	SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst LIMIT 1) LIMIT 11) t;
+));
+is($count, 10);
+
+foreach ((30, 50, 70))
+{
+	my $max_probes = $_;
+	my $expected = $max_probes / 10;
+	my $sum = 0;
+
+	for my $i (1 .. 20)
+	{
+		$count = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET ivfflat.probes = 10;
+			SET ivfflat.iterative_scan = relaxed_order;
+			SET ivfflat.max_probes = $max_probes;
+			SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst WHERE i = $i) LIMIT 11) t;
+		));
+		$sum += $count;
+	}
+
+	my $avg = $sum / 20;
+	cmp_ok($avg, '>', $expected - 2);
+	cmp_ok($avg, '<', $expected + 2);
+}
+
+done_testing();

test/t/042_ivfflat_iterative_scan_recall.pl

@@ -0,0 +1,125 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my @cs = (100, 1000);
+
+sub test_recall
+{
+	my ($c, $probes, $min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET ivfflat.probes = $probes;
+		SET ivfflat.iterative_scan = relaxed_order;
+		EXPLAIN ANALYZE SELECT i FROM tst WHERE i % $c = 0 ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx on tst/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET ivfflat.probes = $probes;
+			SET ivfflat.iterative_scan = relaxed_order;
+			SELECT i FROM tst WHERE i % $c = 0 ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+
+		my @expected_ids = split("\n", $expected[$i]);
+		my %expected_set = map { $_ => 1 } @expected_ids;
+
+		foreach (@actual_ids)
+		{
+			if (exists($expected_set{$_}))
+			{
+				$correct++;
+			}
+		}
+
+		$total += $limit;
+	}
+
+	cmp_ok($correct / $total, ">=", $min, "$operator $c");
+}
+
+# Initialize node
+$node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector(3));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 100000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "[$r1,$r2,$r3]");
+}
+
+# Check each index type
+my @operators = ("<->", "<=>");
+my @opclasses = ("vector_l2_ops", "vector_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING ivfflat (v $opclass);");
+
+	foreach (@cs)
+	{
+		my $c = $_;
+
+		# Get exact results
+		@expected = ();
+		foreach (@queries)
+		{
+			my $res = $node->safe_psql("postgres", qq(
+				SET enable_indexscan = off;
+				WITH top AS (
+					SELECT v $operator '$_' AS distance FROM tst WHERE i % $c = 0 ORDER BY distance LIMIT $limit
+				)
+				SELECT i FROM tst WHERE (v $operator '$_') <= (SELECT MAX(distance) FROM top)
+			));
+			push(@expected, $res);
+		}
+
+		if ($c == 100)
+		{
+			test_recall($c, 1, 0.57, $operator);
+			test_recall($c, 10, 0.98, $operator);
+		}
+		else
+		{
+			if ($operator eq "<->")
+			{
+				test_recall($c, 1, 0.80, $operator);
+			}
+			else
+			{
+				test_recall($c, 1, 0.88, $operator);
+			}
+		}
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();

test/t/043_hnsw_iterative_scan.pl

@@ -0,0 +1,68 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $dim = 3;
+my $array_sql = join(",", ('random()') x $dim);
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4 PRIMARY KEY, v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
+);
+$node->safe_psql("postgres", qq(
+	SET maintenance_work_mem = '128MB';
+	SET max_parallel_maintenance_workers = 2;
+	CREATE INDEX ON tst USING hnsw (v vector_l2_ops)
+));
+
+my $count = $node->safe_psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET hnsw.iterative_scan = relaxed_order;
+	SET hnsw.max_scan_tuples = 100000;
+	SET hnsw.scan_mem_multiplier = 2;
+	SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst LIMIT 1) LIMIT 11) t;
+));
+is($count, 10);
+
+foreach ((30000, 50000, 70000))
+{
+	my $max_tuples = $_;
+	my $expected = $max_tuples / 10000;
+	my $sum = 0;
+
+	for my $i (1 .. 20)
+	{
+		$count = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.iterative_scan = relaxed_order;
+			SET hnsw.max_scan_tuples = $max_tuples;
+			SET hnsw.scan_mem_multiplier = 2;
+			SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst WHERE i = $i) LIMIT 11) t;
+		));
+		$sum += $count;
+	}
+
+	my $avg = $sum / 20;
+	cmp_ok($avg, '>', $expected - 2);
+	cmp_ok($avg, '<', $expected + 2);
+}
+
+my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET hnsw.iterative_scan = relaxed_order;
+	SET client_min_messages = debug1;
+	SET work_mem = '1MB';
+	SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst LIMIT 1) LIMIT 11) t;
+));
+like($stderr, qr/hnsw index scan reached memory limit after \d+ tuples/);
+
+done_testing();

test/t/044_hnsw_iterative_scan_recall.pl

@@ -0,0 +1,118 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 3;
+my $array_sql = join(",", ('random()') x $dim);
+my @cs = (50, 500);
+
+sub test_recall
+{
+	my ($c, $ef_search, $min, $operator, $mode) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = $ef_search;
+		SET hnsw.iterative_scan = $mode;
+		EXPLAIN ANALYZE SELECT i FROM tst WHERE i % $c = 0 ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx on tst/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = $ef_search;
+			SET hnsw.iterative_scan = $mode;
+			SELECT i FROM tst WHERE i % $c = 0 ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+
+		my @expected_ids = split("\n", $expected[$i]);
+		my %expected_set = map { $_ => 1 } @expected_ids;
+
+		foreach (@actual_ids)
+		{
+			if (exists($expected_set{$_}))
+			{
+				$correct++;
+			}
+		}
+
+		$total += $limit;
+	}
+
+	cmp_ok($correct / $total, ">=", $min, "$operator $mode $c");
+}
+
+# Initialize node
+$node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 50000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each index type
+my @operators = ("<->", "<=>");
+my @opclasses = ("vector_l2_ops", "vector_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	$node->safe_psql("postgres", qq(
+		SET maintenance_work_mem = '128MB';
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+
+	foreach (@cs)
+	{
+		my $c = $_;
+
+		# Get exact results
+		@expected = ();
+		foreach (@queries)
+		{
+			my $res = $node->safe_psql("postgres", qq(
+				SET enable_indexscan = off;
+				WITH top AS (
+					SELECT v $operator '$_' AS distance FROM tst WHERE i % $c = 0 ORDER BY distance LIMIT $limit
+				)
+				SELECT i FROM tst WHERE (v $operator '$_') <= (SELECT MAX(distance) FROM top)
+			));
+			push(@expected, $res);
+		}
+
+		test_recall($c, 40, 0.99, $operator, "strict_order");
+		test_recall($c, 40, 0.99, $operator, "relaxed_order");
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();