Added strict ordering [skip ci]

Previously, the cost estimation formula for a HNSW index scan utilized
a methodology that only factored in the entry level for an HNSW scan
and the "m" index parameter, which reflects the number of tuples (or
vectors) to scan at each step of a HNSW graph traversal. While this
would bias the PostgreSQL query planner to choose an HNSW index scan
over other available paths, this could lead to potential suboptimal
index selection, for example, choosing to use a HNSW index instead of
an available B-tree index that has better selectivity.

The number of tuples scanned during HNSW graph traversal is principally
influenced by these factors:

 * The number of tuples stored in the index
 * `m` - the number of tuples that are scanned in each step of the graph
   traversal
 * `hnsw.ef_search` - which influences the total number of steps it
   takes for the scan to converge on the approximated nearest neighbors

Through testing different source models for vectors, we also observed
that the correlation of vectors in mdoels would impact this convergence.
For this first iteration, we've opted to hardcode a constant scaling
factor and set it to `0.55`, though a future commit may turn this into
a configurable parameter.

The high-level formula for estimating the cost of a HNSW index scan is
as such:

```
(entryLevel * m) + (layer0TuplesMax * layer0Selectivity)
```

where

- `(entryLevel * m)` is the lower bound of tuples to scan, as it
accounts for the graph traversal to layer 0 (L0). (L1 and above has an ef=1)
- `layer0TuplesMax` is an estimate of the maximum number of tuples to
scan at L0. This accounts for tuples that may end up being discarded due
to them already being visited. Testing shows that the number of steps
until converge is similar to the value of `hnsw.ef_search`, thus we can
estimate tuples max at `hnsw.ef_search * m * 2`
- `layer0Selectivity` - estimates the percentage of tuples that will
actually be scanned during the index traversal, multipled by the scaling
factor

In addition to the `m` build parameter and `hsnw.ef_search`, costs
estimates can be influenced by standard PostgreSQL costing parameters,
though adjusting those (e.g. `random_page_cost`) should be done with
care.

Co-authored-by: @ankane

CHANGELOG.md

@@ -1,6 +1,8 @@
 ## 0.8.0 (unreleased)
 
+- Added support for iterative index scans
 - Added casts for arrays to `sparsevec`
+- Improved cost estimation
 - Reduced memory usage for HNSW index scans
 - Dropped support for Postgres 12
 

README.md

@@ -445,6 +445,63 @@ 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);
 ```
 
+## Streaming Queries [unreleased]
+
+*Added in 0.8.0*
+
+With approximate indexes, you can end up with less results than expected due to filtering conditions in the query.
+
+Starting with 0.8.0, you can enable streaming queries. If too few results from the initial index scan match the query filters, it will resume scanning until enough results are found. This can significantly improve recall (at the cost of speed).
+
+```tsql
+SET hnsw.streaming = on;
+-- or
+SET ivfflat.streaming = on;
+```
+
+### Streaming Options
+
+Since scanning a large portion of the index is expensive, there are options to control when the scan ends.
+
+#### HNSW
+
+Specify the max number of additional tuples visited
+
+```sql
+SET hnsw.ef_stream = 10000;
+```
+
+The scan will also end if reaches `work_mem`, at which point a notice is shown
+
+```text
+NOTICE:  hnsw index scan exceeded work_mem after 50000 tuples
+HINT:  Increase work_mem to scan more tuples.
+```
+
+Adjust this with:
+
+```sql
+SET work_mem = '8MB';
+```
+
+#### IVFFlat
+
+Specify the max number of probes
+
+```sql
+SET ivfflat.max_probes = 100;
+```
+
+### Streaming Order
+
+With streaming queries, it’s possible for rows to be slightly out of order by distance. For strict ordering, use:
+
+```sql
+WITH approx_order AS MATERIALIZED (
+    SELECT *, embedding <-> '[1,2,3]' AS distance FROM items WHERE ... ORDER BY distance LIMIT 5
+) SELECT * FROM approx_order ORDER BY distance;
+```
+
 ## Half-Precision Vectors
 
 *Added in 0.7.0*

src/halfvec.c

@@ -159,24 +159,6 @@ CheckStateArray(ArrayType *statearray, const char *caller)
 	return (float8 *) ARR_DATA_PTR(statearray);
 }
 
-#if PG_VERSION_NUM < 120003
-static pg_noinline void
-float_overflow_error(void)
-{
-	ereport(ERROR,
-			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-			 errmsg("value out of range: overflow")));
-}
-
-static pg_noinline void
-float_underflow_error(void)
-{
-	ereport(ERROR,
-			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-			 errmsg("value out of range: underflow")));
-}
-#endif
-
 /*
  * Convert textual representation to internal representation
  */

src/hnsw.c

@@ -12,13 +12,15 @@
 #include "utils/float.h"
 #include "utils/guc.h"
 #include "utils/selfuncs.h"
+#include "utils/spccache.h"
 
 #if PG_VERSION_NUM < 150000
 #define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
 #endif
 
 int			hnsw_ef_search;
-int			hnsw_time_budget;
+int			hnsw_ef_stream;
+bool		hnsw_streaming;
 int			hnsw_lock_tranche_id;
 static relopt_kind hnsw_relopt_kind;
 
@@ -69,9 +71,16 @@ HnswInit(void)
 							"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);
 
-	DefineCustomIntVariable("hnsw.time_budget", "Sets the time budget for search",
-							NULL, &hnsw_time_budget,
-							-1, -1, INT_MAX, PGC_USERSET, GUC_UNIT_MS, NULL, NULL, NULL);
+	/* TODO Figure out name */
+	DefineCustomBoolVariable("hnsw.streaming", "Use streaming mode",
+							 NULL, &hnsw_streaming,
+							 HNSW_DEFAULT_STREAMING, PGC_USERSET, 0, NULL, NULL, NULL);
+
+	/* TODO Figure out name */
+	/* TODO Use same value as ivfflat.max_probes for "all" */
+	DefineCustomIntVariable("hnsw.ef_stream", "Sets the max number of additional candidates to visit for streaming search",
+							"-1 means all", &hnsw_ef_stream,
+							HNSW_DEFAULT_EF_STREAM, HNSW_MIN_EF_STREAM, HNSW_MAX_EF_STREAM, PGC_USERSET, 0, NULL, NULL, NULL);
 
 	MarkGUCPrefixReserved("hnsw");
 }
@@ -93,6 +102,33 @@ hnswbuildphasename(int64 phasenum)
 	}
 }
 
+/*
+ * Estimate ef needed for iterative scans
+ */
+static int
+EstimateEf(PlannerInfo *root, IndexPath *path)
+{
+	double		selectivity = 1;
+	ListCell   *lc;
+
+	/* Cannot estimate without limit */
+	/* limit_tuples includes offset */
+	if (root->limit_tuples < 0)
+		return 0;
+
+	/* Get the selectivity of non-index conditions */
+	foreach(lc, path->indexinfo->indrestrictinfo)
+	{
+		RestrictInfo *rinfo = lfirst(lc);
+
+		/* Skip DEFAULT_INEQ_SEL since it may be a distance filter */
+		if (rinfo->norm_selec >= 0 && rinfo->norm_selec <= 1 && rinfo->norm_selec != (Selectivity) DEFAULT_INEQ_SEL)
+			selectivity *= rinfo->norm_selec;
+	}
+
+	return root->limit_tuples / Max(selectivity, 0.00001);
+}
+
 /*
  * Estimate the cost of an index scan
  */
@@ -104,7 +140,12 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 {
 	GenericCosts costs;
 	int			m;
+	int			ef;
 	int			entryLevel;
+	int			layer0TuplesMax;
+	double		layer0Selectivity;
+	double		scalingFactor = 0.55;
+	double		spc_seq_page_cost;
 	Relation	index;
 
 	/* Never use index without order */
@@ -124,15 +165,57 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	HnswGetMetaPageInfo(index, &m, NULL);
 	index_close(index, NoLock);
 
-	/* Approximate entry level */
-	entryLevel = (int) -log(1.0 / path->indexinfo->tuples) * HnswGetMl(m);
+	ef = hnsw_streaming ? Max(hnsw_ef_search, EstimateEf(root, path)) : hnsw_ef_search;
 
-	/* TODO Improve estimate of visited tuples (currently underestimates) */
-	/* Account for number of tuples (or entry level), m, and ef_search */
-	costs.numIndexTuples = (entryLevel + 2) * m;
+	/*
+	 * HNSW cost estimation follows a formula that accounts for the total
+	 * number of tuples indexed combined with the parameters that most
+	 * influence the duration of the index scan, namely: m - the number of
+	 * tuples that are scanned in each step of the HNSW graph traversal
+	 * ef_search - which influences the total number of steps taken at layer 0
+	 *
+	 * The source of the vector data can impact how many steps it takes to
+	 * converge on the set of vectors to return to the executor. Currently, we
+	 * use a hardcoded scaling factor (HNSWScanScalingFactor) to help
+	 * influence that, but this could later become a configurable parameter
+	 * based on the cost estimations.
+	 *
+	 * The tuple estimator formula is below:
+	 *
+	 * numIndexTuples = entryLevel * m + layer0TuplesMax * layer0Selectivity
+	 *
+	 * "entryLevel * m" represents the floor of tuples we need to scan to get
+	 * to layer 0 (L0).
+	 *
+	 * "layer0TuplesMax" is the estimated total number of tuples we'd scan at
+	 * L0 if we weren't discarding already visited tuples as part of the scan.
+	 *
+	 * "layer0Selectivity" estimates the percentage of tuples that are scanned
+	 * at L0, accounting for previously visited tuples, multiplied by the
+	 * "scalingFactor" (currently hardcoded).
+	 */
+	entryLevel = (int) (log(path->indexinfo->tuples + 1) * HnswGetMl(m));
+	layer0TuplesMax = HnswGetLayerM(m, 0) * ef;
+	layer0Selectivity = (scalingFactor * log(path->indexinfo->tuples + 1)) /
+		(log(m) * (1 + log(ef)));
+
+	costs.numIndexTuples = (entryLevel * m) +
+		(layer0TuplesMax * layer0Selectivity);
 
 	genericcostestimate(root, path, loop_count, &costs);
 
+	get_tablespace_page_costs(path->indexinfo->reltablespace, NULL, &spc_seq_page_cost);
+
+	/* Adjust cost if needed since TOAST not included in seq scan cost */
+	if (costs.numIndexPages > path->indexinfo->rel->pages)
+	{
+		/* Change all page cost from random to sequential */
+		costs.indexTotalCost -= costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+
+		/* Remove cost of extra pages */
+		costs.indexTotalCost -= (costs.numIndexPages - path->indexinfo->rel->pages) * spc_seq_page_cost;
+	}
+
 	/* Use total cost since most work happens before first tuple is returned */
 	*indexStartupCost = costs.indexTotalCost;
 	*indexTotalCost = costs.indexTotalCost;

src/hnsw.h

@@ -12,6 +12,10 @@
 #include "utils/sampling.h"
 #include "vector.h"
 
+#ifdef HNSW_BENCH
+#include "portability/instr_time.h"
+#endif
+
 #define HNSW_MAX_DIM 2000
 #define HNSW_MAX_NNZ 1000
 
@@ -42,6 +46,10 @@
 #define HNSW_DEFAULT_EF_SEARCH	40
 #define HNSW_MIN_EF_SEARCH		1
 #define HNSW_MAX_EF_SEARCH		1000
+#define HNSW_DEFAULT_STREAMING	false
+#define HNSW_DEFAULT_EF_STREAM	-1
+#define HNSW_MIN_EF_STREAM		-1
+#define HNSW_MAX_EF_STREAM		INT_MAX
 
 /* Tuple types */
 #define HNSW_ELEMENT_TUPLE_TYPE  1
@@ -68,6 +76,21 @@
 #define HnswPageGetOpaque(page)	((HnswPageOpaque) PageGetSpecialPointer(page))
 #define HnswPageGetMeta(page)	((HnswMetaPageData *) PageGetContents(page))
 
+#ifdef HNSW_BENCH
+#define HnswBench(name, code) \
+	do { \
+		instr_time	start; \
+		instr_time	duration; \
+		INSTR_TIME_SET_CURRENT(start); \
+		(code); \
+		INSTR_TIME_SET_CURRENT(duration); \
+		INSTR_TIME_SUBTRACT(duration, start); \
+		elog(INFO, "%s: %.3f ms", name, INSTR_TIME_GET_MILLISEC(duration)); \
+	} while (0)
+#else
+#define HnswBench(name, code) (code)
+#endif
+
 #if PG_VERSION_NUM >= 150000
 #define RandomDouble() pg_prng_double(&pg_global_prng_state)
 #define SeedRandom(seed) pg_prng_seed(&pg_global_prng_state, seed)
@@ -106,7 +129,8 @@
 
 /* Variables */
 extern int	hnsw_ef_search;
-extern int	hnsw_time_budget;
+extern int	hnsw_ef_stream;
+extern bool hnsw_streaming;
 extern int	hnsw_lock_tranche_id;
 
 typedef struct HnswElementData HnswElementData;
@@ -130,6 +154,7 @@ struct HnswElementData
 	uint8		heaptidsLength;
 	uint8		level;
 	uint8		deleted;
+	uint8		version;
 	uint32		hash;
 	HnswNeighborsPtr neighbors;
 	BlockNumber blkno;
@@ -156,12 +181,16 @@ struct HnswNeighborArray
 	HnswCandidate items[FLEXIBLE_ARRAY_MEMBER];
 };
 
-typedef struct HnswPairingHeapNode
+typedef struct HnswSearchCandidate
 {
-	HnswCandidate *inner;
 	pairingheap_node c_node;
 	pairingheap_node w_node;
-}			HnswPairingHeapNode;
+	HnswElementPtr element;
+	float		distance;
+}			HnswSearchCandidate;
+
+#define HnswGetSearchCandidate(membername, ptr) pairingheap_container(HnswSearchCandidate, membername, ptr)
+#define HnswGetSearchCandidateConst(membername, ptr) pairingheap_const_container(HnswSearchCandidate, membername, ptr)
 
 /* HNSW index options */
 typedef struct HnswOptions
@@ -306,10 +335,10 @@ 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;
 
@@ -318,20 +347,32 @@ typedef HnswElementTupleData * HnswElementTuple;
 typedef struct HnswNeighborTupleData
 {
 	uint8		type;
-	uint8		unused;
+	uint8		version;
 	uint16		count;
 	ItemPointerData indextids[FLEXIBLE_ARRAY_MEMBER];
 }			HnswNeighborTupleData;
 
 typedef HnswNeighborTupleData * HnswNeighborTuple;
 
+typedef union
+{
+	struct pointerhash_hash *pointers;
+	struct offsethash_hash *offsets;
+	struct tidhash_hash *tids;
+}			visited_hash;
+
 typedef struct HnswScanOpaqueData
 {
 	const		HnswTypeInfo *typeInfo;
 	bool		first;
 	List	   *w;
+	visited_hash v;
+	pairingheap *discarded;
+	Datum		q;
+	int			m;
+	int64		tuples;
+	double		previousDistance;
 	MemoryContext tmpCtx;
-	instr_time	start;
 
 	/* Support functions */
 	FmgrInfo   *procinfo;
@@ -376,14 +417,14 @@ bool		HnswCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value);
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);
 void		HnswInit(void);
-List	   *HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement, instr_time *start);
+List	   *HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, 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);
 HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
 HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
 void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
-HnswCandidate *HnswEntryCandidate(char *base, HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
+HnswSearchCandidate *HnswEntryCandidate(char *base, HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
 void		HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum, bool building);
 void		HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m);
 void		HnswAddHeapTid(HnswElement element, ItemPointer heaptid);

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

@@ -1,9 +1,10 @@
 #include "postgres.h"
 
+#include <float.h>
+
 #include "access/relscan.h"
 #include "hnsw.h"
 #include "pgstat.h"
-#include "portability/instr_time.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
 #include "utils/memutils.h"
@@ -23,11 +24,13 @@ GetScanItems(IndexScanDesc scan, Datum q)
 	int			m;
 	HnswElement entryPoint;
 	char	   *base = NULL;
-	instr_time *start = hnsw_time_budget == -1 ? NULL : &so->start;
 
 	/* Get m and entry point */
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
 
+	so->q = q;
+	so->m = m;
+
 	if (entryPoint == NULL)
 		return NIL;
 
@@ -35,11 +38,44 @@ GetScanItems(IndexScanDesc scan, Datum q)
 
 	for (int lc = entryPoint->level; lc >= 1; lc--)
 	{
-		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, false, NULL, start);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, false, NULL, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
-	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL, start);
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL, &so->v, hnsw_streaming ? &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;
+	FmgrInfo   *procinfo = so->procinfo;
+	Oid			collation = so->collation;
+	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 *hc;
+
+		if (pairingheap_is_empty(so->discarded))
+			break;
+
+		hc = HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded));
+
+		ep = lappend(ep, hc);
+	}
+
+	return HnswSearchLayer(base, so->q, ep, batch_size, 0, index, procinfo, collation, so->m, false, NULL, &so->v, &so->discarded, false, &so->tuples);
 }
 
 /*
@@ -83,6 +119,8 @@ hnswbeginscan(Relation index, int nkeys, int norderbys)
 	so = (HnswScanOpaque) palloc(sizeof(HnswScanOpaqueData));
 	so->typeInfo = HnswGetTypeInfo(index);
 	so->first = true;
+	so->v.tids = NULL;
+	so->discarded = NULL;
 	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 									   "Hnsw scan temporary context",
 									   ALLOCSET_DEFAULT_SIZES);
@@ -92,9 +130,6 @@ hnswbeginscan(Relation index, int nkeys, int norderbys)
 	so->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
 	so->collation = index->rd_indcollation[0];
 
-	if (hnsw_time_budget != -1)
-		INSTR_TIME_SET_CURRENT(so->start);
-
 	scan->opaque = so;
 
 	return scan;
@@ -108,7 +143,15 @@ hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int no
 {
 	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
 
+	if (so->v.tids != NULL)
+		tidhash_reset(so->v.tids);
+
+	if (so->discarded != NULL)
+		pairingheap_reset(so->discarded);
+
 	so->first = true;
+	so->tuples = 0;
+	so->previousDistance = -INFINITY;
 	MemoryContextReset(so->tmpCtx);
 
 	if (keys && scan->numberOfKeys > 0)
@@ -158,7 +201,7 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		 */
 		LockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
 
-		so->w = GetScanItems(scan, value);
+		HnswBench("scan iteration", so->w = GetScanItems(scan, value));
 
 		/* Release shared lock */
 		UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
@@ -166,26 +209,101 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		so->first = false;
 
 #if defined(HNSW_MEMORY)
-		elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(so->tmpCtx, false) / (1024 * 1024));
+		elog(INFO, "memory: %zu KB", MemoryContextMemAllocated(so->tmpCtx, false) / 1024);
 #endif
 	}
 
-	while (list_length(so->w) > 0)
+	for (;;)
 	{
 		char	   *base = NULL;
-		HnswCandidate *hc = llast(so->w);
-		HnswElement element = HnswPtrAccess(base, hc->element);
+		HnswSearchCandidate *hc;
+		HnswElement element;
 		ItemPointer heaptid;
 
+		if (list_length(so->w) == 0)
+		{
+			if (!hnsw_streaming)
+				break;
+
+			/* Empty index */
+			if (so->discarded == NULL)
+				break;
+
+			/* Reached max number of additional tuples */
+			if (hnsw_ef_stream != -1 && so->tuples >= hnsw_ef_search + hnsw_ef_stream)
+			{
+				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) > (Size) work_mem * 1024L)
+			{
+				if (pairingheap_is_empty(so->discarded))
+				{
+					ereport(NOTICE,
+							(errmsg("hnsw index scan exceeded work_mem after " INT64_FORMAT " tuples", so->tuples),
+							 errhint("Increase work_mem 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);
+
+				HnswBench("scan iteration", so->w = ResumeScanItems(scan));
+
+				UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+#if defined(HNSW_MEMORY)
+				elog(INFO, "memory: %zu KB", MemoryContextMemAllocated(so->tmpCtx, false) / 1024);
+#endif
+			}
+
+			if (list_length(so->w) == 0)
+				break;
+		}
+
+		hc = llast(so->w);
+		element = HnswPtrAccess(base, hc->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_streaming)
+			{
+				pfree(element);
+				pfree(hc);
+			}
+
 			continue;
 		}
 
 		heaptid = &element->heaptids[--element->heaptidsLength];
 
+		if (hc->distance < so->previousDistance)
+			continue;
+
+		so->previousDistance = hc->distance;
+
 		MemoryContextSwitchTo(oldCtx);
 
 		scan->xs_heaptid = *heaptid;

src/hnswutils.c

@@ -9,7 +9,6 @@
 #include "fmgr.h"
 #include "hnsw.h"
 #include "lib/pairingheap.h"
-#include "portability/instr_time.h"
 #include "sparsevec.h"
 #include "storage/bufmgr.h"
 #include "utils/datum.h"
@@ -101,13 +100,6 @@ hash_offset(Size offset)
 #define SH_DEFINE
 #include "lib/simplehash.h"
 
-typedef union
-{
-	pointerhash_hash *pointers;
-	offsethash_hash *offsets;
-	tidhash_hash *tids;
-}			visited_hash;
-
 typedef union
 {
 	HnswElement element;
@@ -254,6 +246,8 @@ 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);
 
@@ -406,6 +400,7 @@ 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)
@@ -448,6 +443,7 @@ HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m)
 	}
 
 	ntup->count = idx;
+	ntup->version = e->version;
 }
 
 /*
@@ -521,6 +517,7 @@ 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;
@@ -609,10 +606,10 @@ GetElementDistance(char *base, HnswElement element, Datum q, FmgrInfo *procinfo,
 /*
  * Create a candidate for the entry point
  */
-HnswCandidate *
+HnswSearchCandidate *
 HnswEntryCandidate(char *base, HnswElement entryPoint, Datum q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec)
 {
-	HnswCandidate *hc = palloc(sizeof(HnswCandidate));
+	HnswSearchCandidate *hc = palloc(sizeof(HnswSearchCandidate));
 
 	HnswPtrStore(base, hc->element, entryPoint);
 	if (index == NULL)
@@ -622,19 +619,31 @@ HnswEntryCandidate(char *base, HnswElement entryPoint, Datum q, Relation index,
 	return hc;
 }
 
-#define HnswGetPairingHeapCandidate(membername, ptr) (pairingheap_container(HnswPairingHeapNode, membername, ptr)->inner)
-#define HnswGetPairingHeapCandidateConst(membername, ptr) (pairingheap_const_container(HnswPairingHeapNode, membername, ptr)->inner)
-
 /*
  * Compare candidate distances
  */
 static int
 CompareNearestCandidates(const pairingheap_node *a, const pairingheap_node *b, void *arg)
 {
-	if (HnswGetPairingHeapCandidateConst(c_node, a)->distance < HnswGetPairingHeapCandidateConst(c_node, b)->distance)
+	if (HnswGetSearchCandidateConst(c_node, a)->distance < HnswGetSearchCandidateConst(c_node, b)->distance)
 		return 1;
 
-	if (HnswGetPairingHeapCandidateConst(c_node, a)->distance > HnswGetPairingHeapCandidateConst(c_node, b)->distance)
+	if (HnswGetSearchCandidateConst(c_node, a)->distance > HnswGetSearchCandidateConst(c_node, b)->distance)
+		return -1;
+
+	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;
@@ -646,27 +655,15 @@ CompareNearestCandidates(const pairingheap_node *a, const pairingheap_node *b, v
 static int
 CompareFurthestCandidates(const pairingheap_node *a, const pairingheap_node *b, void *arg)
 {
-	if (HnswGetPairingHeapCandidateConst(w_node, a)->distance < HnswGetPairingHeapCandidateConst(w_node, b)->distance)
+	if (HnswGetSearchCandidateConst(w_node, a)->distance < HnswGetSearchCandidateConst(w_node, b)->distance)
 		return -1;
 
-	if (HnswGetPairingHeapCandidateConst(w_node, a)->distance > HnswGetPairingHeapCandidateConst(w_node, b)->distance)
+	if (HnswGetSearchCandidateConst(w_node, a)->distance > HnswGetSearchCandidateConst(w_node, b)->distance)
 		return 1;
 
 	return 0;
 }
 
-/*
- * Create a pairing heap node for a candidate
- */
-static HnswPairingHeapNode *
-CreatePairingHeapNode(HnswCandidate * c)
-{
-	HnswPairingHeapNode *node = palloc(sizeof(HnswPairingHeapNode));
-
-	node->inner = c;
-	return node;
-}
-
 /*
  * Init visited
  */
@@ -767,20 +764,30 @@ HnswLoadUnvisitedFromDisk(HnswElement element, HnswUnvisited * unvisited, int *u
 	int			start;
 	ItemPointerData indextids[HNSW_MAX_M * 2];
 
+	*unvisitedLength = 0;
+
 	buf = ReadBuffer(index, element->neighborPage);
 	LockBuffer(buf, BUFFER_LOCK_SHARE);
 	page = BufferGetPage(buf);
 
 	ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
-	start = (element->level - lc) * 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;
+	}
 
 	/* Copy to minimize lock time */
+	start = (element->level - lc) * m;
 	memcpy(&indextids, ntup->indextids + start, lm * sizeof(ItemPointerData));
 
 	UnlockReleaseBuffer(buf);
 
-	*unvisitedLength = 0;
-
 	for (int i = 0; i < lm; i++)
 	{
 		ItemPointer indextid = &indextids[i];
@@ -800,13 +807,13 @@ HnswLoadUnvisitedFromDisk(HnswElement element, HnswUnvisited * unvisited, int *u
  * Algorithm 2 from paper
  */
 List *
-HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement, instr_time *start)
+HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, 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;
@@ -814,7 +821,19 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 	HnswUnvisited *unvisited = palloc(lm * sizeof(HnswUnvisited));
 	int			unvisitedLength;
 
-	InitVisited(base, &v, index, ef, m);
+	if (v == NULL)
+	{
+		v = &vh;
+		initVisited = true;
+	}
+
+	if (initVisited)
+	{
+		InitVisited(base, v, index, ef, m);
+
+		if (discarded != NULL)
+			*discarded = pairingheap_allocate(CompareNearestDiscardedCandidates, NULL);
+	}
 
 	/* Create local memory for neighborhood if needed */
 	if (index == NULL)
@@ -826,15 +845,19 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 	/* Add entry points to v, C, and W */
 	foreach(lc2, ep)
 	{
-		HnswCandidate *hc = (HnswCandidate *) lfirst(lc2);
+		HnswSearchCandidate *hc = (HnswSearchCandidate *) lfirst(lc2);
 		bool		found;
-		HnswPairingHeapNode *node;
 
-		AddToVisited(base, &v, hc->element, index, &found);
+		if (initVisited)
+		{
+			AddToVisited(base, v, hc->element, index, &found);
 
-		node = CreatePairingHeapNode(hc);
-		pairingheap_add(C, &node->c_node);
-		pairingheap_add(W, &node->w_node);
+			if (tuples != NULL)
+				(*tuples)++;
+		}
+
+		pairingheap_add(C, &hc->c_node);
+		pairingheap_add(W, &hc->w_node);
 
 		/*
 		 * Do not count elements being deleted towards ef when vacuuming. It
@@ -847,40 +870,31 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 
 	while (!pairingheap_is_empty(C))
 	{
-		HnswCandidate *c = HnswGetPairingHeapCandidate(c_node, pairingheap_remove_first(C));
-		HnswCandidate *f = HnswGetPairingHeapCandidate(w_node, pairingheap_first(W));
+		HnswSearchCandidate *c = HnswGetSearchCandidate(c_node, pairingheap_remove_first(C));
+		HnswSearchCandidate *f = HnswGetSearchCandidate(w_node, pairingheap_first(W));
 		HnswElement cElement;
 
-		/* Check time budget */
-		if (start != NULL)
-		{
-			instr_time	duration;
-
-			INSTR_TIME_SET_CURRENT(duration);
-			INSTR_TIME_SUBTRACT(duration, *start);
-			if (INSTR_TIME_GET_MILLISEC(duration) >= hnsw_time_budget)
-				break;
-		}
-
 		if (c->distance > f->distance)
 			break;
 
 		cElement = HnswPtrAccess(base, c->element);
 
 		if (index == NULL)
-			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);
+
+		if (tuples != NULL)
+			(*tuples) += unvisitedLength;
 
 		for (int i = 0; i < unvisitedLength; i++)
 		{
 			HnswElement eElement;
-			HnswCandidate *e;
-			HnswPairingHeapNode *node;
+			HnswSearchCandidate *e;
 			float		eDistance;
 			bool		alwaysAdd = wlen < ef;
 
-			f = HnswGetPairingHeapCandidate(w_node, pairingheap_first(W));
+			f = HnswGetSearchCandidate(w_node, pairingheap_first(W));
 
 			if (index == NULL)
 			{
@@ -895,29 +909,33 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 
 				/* Avoid any allocations if not adding */
 				eElement = NULL;
-				HnswLoadElementImpl(blkno, offno, &eDistance, &q, index, procinfo, collation, inserting, alwaysAdd ? NULL : &f->distance, &eElement);
-
-				if (eElement == NULL)
-					continue;
+				HnswLoadElementImpl(blkno, offno, &eDistance, &q, index, procinfo, collation, inserting, alwaysAdd || discarded != NULL ? NULL : &f->distance, &eElement);
 			}
 
-			if (!(eDistance < f->distance || alwaysAdd))
-				continue;
+			if (eElement == NULL || !(eDistance < f->distance || alwaysAdd))
+			{
+				if (discarded != NULL)
+				{
+					/* Create a new candidate */
+					e = palloc(sizeof(HnswSearchCandidate));
+					HnswPtrStore(base, e->element, eElement);
+					e->distance = 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(HnswCandidate));
+			e = palloc(sizeof(HnswSearchCandidate));
 			HnswPtrStore(base, e->element, eElement);
 			e->distance = eDistance;
-
-			node = CreatePairingHeapNode(e);
-			pairingheap_add(C, &node->c_node);
-			pairingheap_add(W, &node->w_node);
+			pairingheap_add(C, &e->c_node);
+			pairingheap_add(W, &e->w_node);
 
 			/*
 			 * Do not count elements being deleted towards ef when vacuuming.
@@ -930,7 +948,12 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 
 				/* 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);
+				}
 			}
 		}
 	}
@@ -938,7 +961,7 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 	/* Add each element of W to w */
 	while (!pairingheap_is_empty(W))
 	{
-		HnswCandidate *hc = HnswGetPairingHeapCandidate(w_node, pairingheap_remove_first(W));
+		HnswSearchCandidate *hc = HnswGetSearchCandidate(w_node, pairingheap_remove_first(W));
 
 		w = lappend(w, hc);
 	}
@@ -1303,7 +1326,7 @@ 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, procinfo, collation, m, true, skipElement, NULL);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, true, skipElement, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
@@ -1319,16 +1342,27 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 	{
 		int			lm = HnswGetLayerM(m, lc);
 		List	   *neighbors;
-		List	   *lw;
+		List	   *lw = NIL;
+		ListCell   *lc2;
 
-		w = HnswSearchLayer(base, q, ep, efConstruction, lc, index, procinfo, collation, m, true, skipElement, NULL);
+		w = HnswSearchLayer(base, q, ep, efConstruction, lc, index, procinfo, collation, m, true, skipElement, NULL, NULL, true, NULL);
+
+		/* Convert search candidates to candidates */
+		foreach(lc2, w)
+		{
+			HnswSearchCandidate *sc = lfirst(lc2);
+			HnswCandidate *hc = palloc(sizeof(HnswCandidate));
+
+			hc->element = sc->element;
+			hc->distance = sc->distance;
+
+			lw = lappend(lw, hc);
+		}
 
 		/* Elements being deleted or skipped can help with search */
 		/* but should be removed before selecting neighbors */
 		if (index != NULL)
-			lw = RemoveElements(base, w, skipElement);
-		else
-			lw = w;
+			lw = RemoveElements(base, lw, skipElement);
 
 		/*
 		 * Candidates are sorted, but not deterministically. Could set

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/ivfflat.c

@@ -120,13 +120,6 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 		costs.indexTotalCost -= 0.5 * costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
 	}
 
-	/*
-	 * If the list selectivity is lower than what is returned from the generic
-	 * cost estimator, use that.
-	 */
-	if (ratio < costs.indexSelectivity)
-		costs.indexSelectivity = ratio;
-
 	/* Use total cost since most work happens before first tuple is returned */
 	*indexStartupCost = costs.indexTotalCost;
 	*indexTotalCost = costs.indexTotalCost;

src/ivfflat.h

@@ -253,8 +253,9 @@ typedef struct IvfflatScanOpaqueData
 	/* Sorting */
 	Tuplesortstate *sortstate;
 	TupleDesc	tupdesc;
-	TupleTableSlot *slot;
-	bool		isnull;
+	TupleTableSlot *vslot;
+	TupleTableSlot *mslot;
+	BufferAccessStrategy bas;
 
 	/* Support functions */
 	FmgrInfo   *procinfo;

src/ivfscan.c

@@ -15,16 +15,19 @@
 #include "utils/memutils.h"
 #endif
 
+#define GetScanList(ptr) pairingheap_container(IvfflatScanList, ph_node, ptr)
+#define GetScanListConst(ptr) pairingheap_const_container(IvfflatScanList, ph_node, ptr)
+
 /*
  * Compare list distances
  */
 static int
 CompareLists(const pairingheap_node *a, const pairingheap_node *b, void *arg)
 {
-	if (((const IvfflatScanList *) a)->distance > ((const IvfflatScanList *) b)->distance)
+	if (GetScanListConst(a)->distance > GetScanListConst(b)->distance)
 		return 1;
 
-	if (((const IvfflatScanList *) a)->distance < ((const IvfflatScanList *) b)->distance)
+	if (GetScanListConst(a)->distance < GetScanListConst(b)->distance)
 		return -1;
 
 	return 0;
@@ -76,14 +79,14 @@ GetScanLists(IndexScanDesc scan, Datum value)
 
 				/* Calculate max distance */
 				if (listCount == so->probes)
-					maxDistance = ((IvfflatScanList *) pairingheap_first(so->listQueue))->distance;
+					maxDistance = GetScanList(pairingheap_first(so->listQueue))->distance;
 			}
 			else if (distance < maxDistance)
 			{
 				IvfflatScanList *scanlist;
 
 				/* Remove */
-				scanlist = (IvfflatScanList *) pairingheap_remove_first(so->listQueue);
+				scanlist = GetScanList(pairingheap_remove_first(so->listQueue));
 
 				/* Reuse */
 				scanlist->startPage = list->startPage;
@@ -91,7 +94,7 @@ GetScanLists(IndexScanDesc scan, Datum value)
 				pairingheap_add(so->listQueue, &scanlist->ph_node);
 
 				/* Update max distance */
-				maxDistance = ((IvfflatScanList *) pairingheap_first(so->listQueue))->distance;
+				maxDistance = GetScanList(pairingheap_first(so->listQueue))->distance;
 			}
 		}
 
@@ -110,19 +113,12 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 	TupleDesc	tupdesc = RelationGetDescr(scan->indexRelation);
 	double		tuples = 0;
-	TupleTableSlot *slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsVirtual);
-
-	/*
-	 * Reuse same set of shared buffers for scan
-	 *
-	 * See postgres/src/backend/storage/buffer/README for description
-	 */
-	BufferAccessStrategy bas = GetAccessStrategy(BAS_BULKREAD);
+	TupleTableSlot *slot = so->vslot;
 
 	/* Search closest probes lists */
 	while (!pairingheap_is_empty(so->listQueue))
 	{
-		BlockNumber searchPage = ((IvfflatScanList *) pairingheap_remove_first(so->listQueue))->startPage;
+		BlockNumber searchPage = GetScanList(pairingheap_remove_first(so->listQueue))->startPage;
 
 		/* Search all entry pages for list */
 		while (BlockNumberIsValid(searchPage))
@@ -131,7 +127,7 @@ GetScanItems(IndexScanDesc scan, Datum value)
 			Page		page;
 			OffsetNumber maxoffno;
 
-			buf = ReadBufferExtended(scan->indexRelation, MAIN_FORKNUM, searchPage, RBM_NORMAL, bas);
+			buf = ReadBufferExtended(scan->indexRelation, MAIN_FORKNUM, searchPage, RBM_NORMAL, so->bas);
 			LockBuffer(buf, BUFFER_LOCK_SHARE);
 			page = BufferGetPage(buf);
 			maxoffno = PageGetMaxOffsetNumber(page);
@@ -170,8 +166,6 @@ GetScanItems(IndexScanDesc scan, Datum value)
 		}
 	}
 
-	FreeAccessStrategy(bas);
-
 	if (tuples < 100)
 		ereport(DEBUG1,
 				(errmsg("index scan found few tuples"),
@@ -274,7 +268,16 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	/* Prep sort */
 	so->sortstate = InitScanSortState(so->tupdesc);
 
-	so->slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsMinimalTuple);
+	/* Need separate slots for puttuple and gettuple */
+	so->vslot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsVirtual);
+	so->mslot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsMinimalTuple);
+
+	/*
+	 * Reuse same set of shared buffers for scan
+	 *
+	 * See postgres/src/backend/storage/buffer/README for description
+	 */
+	so->bas = GetAccessStrategy(BAS_BULKREAD);
 
 	so->listQueue = pairingheap_allocate(CompareLists, scan);
 
@@ -348,9 +351,10 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 			pfree(DatumGetPointer(value));
 	}
 
-	if (tuplesort_gettupleslot(so->sortstate, true, false, so->slot, NULL))
+	if (tuplesort_gettupleslot(so->sortstate, true, false, so->mslot, NULL))
 	{
-		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->slot, 2, &so->isnull));
+		bool		isnull;
+		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->mslot, 2, &isnull));
 
 		scan->xs_heaptid = *heaptid;
 		scan->xs_recheck = false;
@@ -371,6 +375,10 @@ ivfflatendscan(IndexScanDesc scan)
 
 	pairingheap_free(so->listQueue);
 	tuplesort_end(so->sortstate);
+	FreeAccessStrategy(so->bas);
+	FreeTupleDesc(so->tupdesc);
+
+	/* TODO Free vslot and mslot without freeing TupleDesc */
 
 	pfree(so);
 	scan->opaque = NULL;

src/vector.c

@@ -155,24 +155,6 @@ CheckStateArray(ArrayType *statearray, const char *caller)
 	return (float8 *) ARR_DATA_PTR(statearray);
 }
 
-#if PG_VERSION_NUM < 120003
-static pg_noinline void
-float_overflow_error(void)
-{
-	ereport(ERROR,
-			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-			 errmsg("value out of range: overflow")));
-}
-
-static pg_noinline void
-float_underflow_error(void)
-{
-	ereport(ERROR,
-			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-			 errmsg("value out of range: underflow")));
-}
-#endif
-
 /*
  * Convert textual representation to internal representation
  */

test/t/009_ivfflat_filtering.pl

@@ -94,8 +94,7 @@ like($explain, qr/Seq Scan/);
 $explain = $node->safe_psql("postgres", qq(
 	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1 ORDER BY v <-> '$query';
 ));
-# TODO Do not use index
-like($explain, qr/Index Scan using idx/);
+like($explain, qr/Seq Scan/);
 
 # Test attribute index
 $node->safe_psql("postgres", "CREATE INDEX attribute_idx ON tst (c);");
@@ -110,7 +109,6 @@ $node->safe_psql("postgres", "CREATE INDEX partial_idx ON tst USING ivfflat (v v
 $explain = $node->safe_psql("postgres", qq(
 	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
 ));
-# TODO Use partial index
-like($explain, qr/Index Scan using idx/);
+like($explain, qr/Index Scan using partial_idx/);
 
 done_testing();

test/t/017_hnsw_filtering.pl

@@ -18,9 +18,13 @@ $node->start;
 # Create table and index
 $node->safe_psql("postgres", "CREATE EXTENSION vector;");
 $node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim), c int4, t text);");
+$node->safe_psql("postgres", "CREATE TABLE cat (i int4 PRIMARY KEY, t text, b boolean);");
 $node->safe_psql("postgres",
 	"INSERT INTO tst SELECT i, ARRAY[$array_sql], i % $nc, 'test ' || i FROM generate_series(1, 10000) i;"
 );
+$node->safe_psql("postgres",
+	"INSERT INTO cat SELECT i, 'cat ' || i, i % 5 = 0 FROM generate_series(1, $nc) i;"
+);
 $node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v vector_l2_ops);");
 $node->safe_psql("postgres", "ANALYZE tst;");
 
@@ -96,13 +100,25 @@ $explain = $node->safe_psql("postgres", qq(
 ));
 like($explain, qr/Seq Scan/);
 
+# Test join
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT cat.t FROM cat INNER JOIN tst ON cat.i = tst.c ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test join with attribute filtering
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT cat.t FROM cat INNER JOIN tst ON cat.i = tst.c WHERE cat.b = 't' ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
 # Test attribute index
 $node->safe_psql("postgres", "CREATE INDEX attribute_idx ON tst (c);");
 $explain = $node->safe_psql("postgres", qq(
 	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
 ));
-# TODO Use attribute index
-like($explain, qr/Index Scan using idx/);
+# Use attribute index
+like($explain, qr/Bitmap Index Scan on attribute_idx/);
 
 # Test partial index
 $node->safe_psql("postgres", "CREATE INDEX partial_idx ON tst USING hnsw (v vector_l2_ops) WHERE (c = $c);");

test/t/039_hnsw_cost.pl

@@ -0,0 +1,46 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my @dims = (384, 1536);
+my $limit = 10;
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+
+for my $dim (@dims)
+{
+	my $array_sql = join(",", ('random()') x $dim);
+	my $n = $dim == 384 ? 2000 : 1000;
+
+	# Create table and index
+	$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
+	$node->safe_psql("postgres",
+		"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, $n) i;"
+	);
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v vector_l2_ops);");
+	$node->safe_psql("postgres", "ANALYZE tst;");
+
+	# Generate query
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	my $query = "[" . join(",", @r) . "]";
+
+	my $explain = $node->safe_psql("postgres", qq(
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$query' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx/);
+
+	$node->safe_psql("postgres", "DROP TABLE tst;");
+}
+
+done_testing();

test/t/040_ivfflat_cost.pl

@@ -0,0 +1,45 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my @dims = (384, 1536);
+my $limit = 10;
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+
+for my $dim (@dims)
+{
+	my $array_sql = join(",", ('random()') x $dim);
+
+	# Create table and index
+	$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
+	$node->safe_psql("postgres",
+		"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 5000) i;"
+	);
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING ivfflat (v vector_l2_ops) WITH (lists = 5);");
+	$node->safe_psql("postgres", "ANALYZE tst;");
+
+	# Generate query
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	my $query = "[" . join(",", @r) . "]";
+
+	my $explain = $node->safe_psql("postgres", qq(
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$query' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx/);
+
+	$node->safe_psql("postgres", "DROP TABLE tst;");
+}
+
+done_testing();

test/t/041_hnsw_streaming.pl

@@ -0,0 +1,66 @@
+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 = $node->safe_psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET hnsw.streaming = on;
+	SET work_mem = '8MB';
+	SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst LIMIT 1) LIMIT 11) t;
+));
+is($count, 10);
+
+foreach ((30000, 50000, 70000))
+{
+	my $ef_stream = $_;
+	my $expected = $ef_stream / 10000;
+	my $sum = 0;
+
+	for my $i (1 .. 20)
+	{
+		$count = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.streaming = on;
+			SET hnsw.ef_stream = $ef_stream;
+			SET work_mem = '8MB';
+			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) = $node->psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET hnsw.streaming = on;
+	SET work_mem = '2MB';
+	SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst LIMIT 1) LIMIT 11) t;
+));
+like($stderr, qr/hnsw index scan exceeded work_mem after \d+ tuples/);
+
+done_testing();

test/t/042_hnsw_streaming_recall.pl

@@ -0,0 +1,131 @@
+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 $dim);
+my @cs = (100, 1000);
+
+sub test_recall
+{
+	my ($c, $ef_search, $min, $operator) = @_;
+	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.streaming = on;
+		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.streaming = on;
+			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, $operator);
+}
+
+# Initialize node
+$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, 100000) 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, $res);
+		}
+
+		if ($c == 100)
+		{
+			test_recall($c, 40, 0.99, $operator);
+		}
+		else
+		{
+			if ($operator eq "<->")
+			{
+				test_recall($c, 40, 0.99, $operator);
+			}
+			else
+			{
+				test_recall($c, 40, 0.99, $operator);
+			}
+		}
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();