Use normalize_l2 for ivfflat

Merge branch 'normalize_l2' into hnsw-normalize
Fixed precision on Windows
2026-07-22 12:07:34 +08:00 · 2023-10-16 17:56:50 -07:00 · 2023-10-16 17:09:20 -07:00 · 2023-10-16 17:08:19 -07:00 · 2023-10-16 16:53:40 -07:00 · 2023-10-16 16:42:40 -07:00
51 changed files with 697 additions and 1108 deletions
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -78,7 +78,6 @@ jobs:
          nmake /NOLOGO /F Makefile.win uninstall
        shell: cmd
  i386:
-    if: ${{ !startsWith(github.ref_name, 'mac') && !startsWith(github.ref_name, 'windows') }}
    runs-on: ubuntu-latest
    container:
      image: debian:11
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -3,6 +3,7 @@
 - Added HNSW index type
 - Added support for parallel index builds
 - Added `l1_distance` function
+- Added `normalize_l2` function
 - Added element-wise multiplication for vectors
 - Added `sum` aggregate
 - Improved performance of distance functions
--- a/1
+++ b/1
@@ -4,7 +4,6 @@ EXTVERSION = 0.4.4
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
 OBJS = src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
-HEADERS = src/vector.h

 TESTS = $(wildcard test/sql/*.sql)
 REGRESS = $(patsubst test/sql/%.sql,%,$(TESTS))
--- a/Makefile.win
+++ b/Makefile.win
@@ -2,7 +2,6 @@ EXTENSION = vector
 EXTVERSION = 0.4.4

 OBJS = src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\vector.obj
-HEADERS = src\vector.h

 REGRESS = btree cast copy functions input ivfflat_cosine ivfflat_ip ivfflat_l2 ivfflat_options ivfflat_unlogged
 REGRESS_OPTS = --inputdir=test --load-extension=vector
@@ -55,8 +54,6 @@ install:
 	copy $(SHLIB) "$(PKGLIBDIR)"
 	copy $(EXTENSION).control "$(SHAREDIR)\extension"
 	copy sql\$(EXTENSION)--*.sql "$(SHAREDIR)\extension"
-	mkdir "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
-	copy $(HEADERS) "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"

 installcheck:
 	"$(BINDIR)\pg_regress" --bindir="$(BINDIR)" $(REGRESS_OPTS) $(REGRESS)
@@ -64,9 +61,7 @@ installcheck:
 uninstall:
 	del /f "$(PKGLIBDIR)\$(SHLIB)"
 	del /f "$(SHAREDIR)\extension\$(EXTENSION).control"
-	del /f "$(SHAREDIR)\extension\$(EXTENSION)--*.sql"
-	del /f "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)\*.h"
-	rmdir "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
+	del /f "$(SHAREDIR)\extension\vector--*.sql"

 clean:
 	del /f $(SHLIB) $(EXTENSION).lib $(EXTENSION).exp
--- a/README.md
+++ b/README.md
@@ -2,7 +2,7 @@

 Open-source vector similarity search for Postgres

-Store your vectors with the rest of your data. Supports:
+Store all of your application data in one place. Supports:

 - exact and approximate nearest neighbor search
 - L2 distance, inner product, and cosine distance
@@ -392,6 +392,7 @@ cosine_distance(vector, vector) → double precision | cosine distance
 inner_product(vector, vector) → double precision | inner product
 l2_distance(vector, vector) → double precision | Euclidean distance
 l1_distance(vector, vector) → double precision | taxicab distance [unreleased]
+normalize_l2(vector) → vector | normalize with Euclidean norm [unreleased]
 vector_dims(vector) → integer | number of dimensions
 vector_norm(vector) → double precision | Euclidean norm

--- a/sql/vector--0.4.4--0.5.0.sql
+++ b/sql/vector--0.4.4--0.5.0.sql
@@ -4,6 +4,9 @@
 CREATE FUNCTION l1_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;

+CREATE FUNCTION normalize_l2(vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;

--- a/sql/vector.sql
+++ b/sql/vector.sql
@@ -49,6 +49,9 @@ CREATE FUNCTION vector_dims(vector) RETURNS integer
 CREATE FUNCTION vector_norm(vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;

+CREATE FUNCTION normalize_l2(vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE FUNCTION vector_add(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;

@@ -265,15 +268,15 @@ CREATE OPERATOR CLASS vector_ip_ops
 	OPERATOR 1 <#> (vector, vector) FOR ORDER BY float_ops,
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
 	FUNCTION 3 vector_spherical_distance(vector, vector),
-	FUNCTION 4 vector_norm(vector);
+	FUNCTION 6 normalize_l2(vector);

 CREATE OPERATOR CLASS vector_cosine_ops
 	FOR TYPE vector USING ivfflat AS
 	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
-	FUNCTION 2 vector_norm(vector),
 	FUNCTION 3 vector_spherical_distance(vector, vector),
-	FUNCTION 4 vector_norm(vector);
+	FUNCTION 5 normalize_l2(vector),
+	FUNCTION 6 normalize_l2(vector);

 CREATE OPERATOR CLASS vector_l2_ops
 	FOR TYPE vector USING hnsw AS
@@ -289,4 +292,4 @@ CREATE OPERATOR CLASS vector_cosine_ops
 	FOR TYPE vector USING hnsw AS
 	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
-	FUNCTION 2 vector_norm(vector);
+	FUNCTION 3 normalize_l2(vector);
--- a/src/hnsw.c
+++ b/src/hnsw.c
@@ -37,7 +37,7 @@ HnswInit(void)
 		);

 	DefineCustomIntVariable("hnsw.ef_search", "Sets the size of the dynamic candidate list for search",
-							"Valid range is 1..1000.", &hnsw_ef_search,
+							"Valid range is 10..1000.", &hnsw_ef_search,
 							HNSW_DEFAULT_EF_SEARCH, HNSW_MIN_EF_SEARCH, HNSW_MAX_EF_SEARCH, PGC_USERSET, 0, NULL, NULL, NULL);
 }

@@ -167,7 +167,7 @@ hnswhandler(PG_FUNCTION_ARGS)
 	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);

 	amroutine->amstrategies = 0;
-	amroutine->amsupport = 2;
+	amroutine->amsupport = 3;
 #if PG_VERSION_NUM >= 130000
 	amroutine->amoptsprocnum = 0;
 #endif
--- a/src/hnsw.h
+++ b/src/hnsw.h
@@ -19,40 +19,32 @@
 /* Support functions */
 #define HNSW_DISTANCE_PROC 1
 #define HNSW_NORM_PROC 2
+#define HNSW_NORMALIZE_PROC 3

 #define HNSW_VERSION	1
 #define HNSW_MAGIC_NUMBER 0xA953A953
-#define HNSW_PAGE_ID	0xFF90
+#define HNSW_PAGE_ID	0xFF85

 /* Preserved page numbers */
 #define HNSW_METAPAGE_BLKNO	0
 #define HNSW_HEAD_BLKNO		1	/* first element page */

-/* Must correspond to page numbers since page lock is used */
-#define HNSW_UPDATE_LOCK 	0
-#define HNSW_SCAN_LOCK		1
-
-/* HNSW parameters */
 #define HNSW_DEFAULT_M	16
-#define HNSW_MIN_M	2
+#define HNSW_MIN_M	4
 #define HNSW_MAX_M		100
 #define HNSW_DEFAULT_EF_CONSTRUCTION	40
-#define HNSW_MIN_EF_CONSTRUCTION	4
+#define HNSW_MIN_EF_CONSTRUCTION	10
 #define HNSW_MAX_EF_CONSTRUCTION		1000
 #define HNSW_DEFAULT_EF_SEARCH	40
-#define HNSW_MIN_EF_SEARCH		1
+#define HNSW_MIN_EF_SEARCH		10
 #define HNSW_MAX_EF_SEARCH		1000

-/* Tuple types */
 #define HNSW_ELEMENT_TUPLE_TYPE  1
 #define HNSW_NEIGHBOR_TUPLE_TYPE 2

 /* Make graph robust against non-HOT updates */
 #define HNSW_HEAPTIDS 10

-#define HNSW_UPDATE_ENTRY_GREATER 1
-#define HNSW_UPDATE_ENTRY_ALWAYS 2
-
 /* Build phases */
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
 #define PROGRESS_HNSW_PHASE_LOAD		2
@@ -77,13 +69,10 @@
 #define HnswIsElementTuple(tup) ((tup)->type == HNSW_ELEMENT_TUPLE_TYPE)
 #define HnswIsNeighborTuple(tup) ((tup)->type == HNSW_NEIGHBOR_TUPLE_TYPE)

-/* 2 * M connections for ground layer */
-#define HnswGetLayerM(m, layer) (layer == 0 ? (m) * 2 : (m))
-
-/* Optimal ML from paper */
+#define HnswGetLayerM(m, layer) (layer == 0 ? m * 2 : m)
 #define HnswGetMl(m) (1 / log(m))

-/* Ensure fits on page and in uint8 */
+/* Ensure fits in uint8 */
 #define HnswGetMaxLevel(m) Min(((BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - offsetof(HnswNeighborTupleData, indextids) - sizeof(ItemIdData)) / (sizeof(ItemPointerData)) / m) - 2, 255)

 /* Variables */
@@ -118,6 +107,13 @@ typedef struct HnswNeighborArray
 	HnswCandidate *items;
 }			HnswNeighborArray;

+typedef struct HnswUpdate
+{
+	HnswCandidate hc;
+	int			level;
+	int			index;
+}			HnswUpdate;
+
 typedef struct HnswPairingHeapNode
 {
 	pairingheap_node ph_node;
@@ -152,6 +148,7 @@ typedef struct HnswBuildState
 	/* Support functions */
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;

 	/* Variables */
@@ -225,6 +222,7 @@ typedef struct HnswScanOpaqueData
 	/* Support functions */
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;
 }			HnswScanOpaqueData;

@@ -260,31 +258,25 @@ typedef struct HnswVacuumState
 int			HnswGetM(Relation index);
 int			HnswGetEfConstruction(Relation index);
 FmgrInfo   *HnswOptionalProcInfo(Relation rel, uint16 procnum);
-bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+void		HnswNormValue(FmgrInfo *procinfo, FmgrInfo *normalizeprocinfo, Oid collation, Datum *value, Vector * result);
 void		HnswCommitBuffer(Buffer buf, GenericXLogState *state);
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);
 void		HnswInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state);
 void		HnswInit(void);
-List	   *HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, bool inserting, HnswElement skipElement);
+List	   *HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, bool inserting, BlockNumber *skipPage, OffsetNumber *skipOffno);
 HnswElement HnswGetEntryPoint(Relation index);
 HnswElement HnswInitElement(ItemPointer tid, int m, double ml, int maxLevel);
 void		HnswFreeElement(HnswElement element);
-HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
-void		HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
-HnswElement HnswFindDuplicate(HnswElement e);
-HnswCandidate *HnswEntryCandidate(HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
-void		HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum);
+HnswElement HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, List **updates, bool vacuuming);
+HnswCandidate *HnswEntryCandidate(HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadvec);
+void		HnswUpdateMetaPage(Relation index, bool updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum);
 void		HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m);
 void		HnswAddHeapTid(HnswElement element, ItemPointer heaptid);
 void		HnswInitNeighbors(HnswElement element, int m);
 bool		HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel);
-void		HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting);
-void		HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHeaptids, bool loadVec);
 void		HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec);
 void		HnswSetElementTuple(HnswElementTuple etup, HnswElement element);
-void		HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation);
-void		HnswLoadNeighbors(HnswElement element, Relation index);

 /* Index access methods */
 IndexBuildResult *hnswbuild(Relation heap, Relation index, IndexInfo *indexInfo);
--- a/src/hnswbuild.c
+++ b/src/hnswbuild.c
@@ -60,7 +60,6 @@ CreateMetaPage(HnswBuildState * buildstate)
 	metap->efConstruction = buildstate->efConstruction;
 	metap->entryBlkno = InvalidBlockNumber;
 	metap->entryOffno = InvalidOffsetNumber;
-	metap->entryLevel = -1;
 	metap->insertPage = InvalidBlockNumber;
 	((PageHeader) page)->pd_lower =
 		((char *) metap + sizeof(HnswMetaPageData)) - (char *) page;
@@ -183,7 +182,7 @@ CreateElementPages(HnswBuildState * buildstate)
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);

-	HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_ALWAYS, buildstate->entryPoint, insertPage, forkNum);
+	HnswUpdateMetaPage(index, true, buildstate->entryPoint, insertPage, forkNum);

 	pfree(etup);
 	pfree(ntup);
@@ -279,33 +278,13 @@ InsertTuple(Relation index, Datum *values, HnswElement element, HnswBuildState *
 	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));

 	/* Normalize if needed */
-	if (buildstate->normprocinfo != NULL)
-	{
-		if (!HnswNormValue(buildstate->normprocinfo, collation, &value, buildstate->normvec))
-			return false;
-	}
+	HnswNormValue(buildstate->normprocinfo, buildstate->normalizeprocinfo, collation, &value, buildstate->normvec);

 	/* Copy value to element so accessible outside of memory context */
 	memcpy(element->vec, DatumGetVector(value), VECTOR_SIZE(buildstate->dimensions));

 	/* Insert element in graph */
-	HnswInsertElement(element, entryPoint, NULL, procinfo, collation, m, efConstruction, false);
-
-	/* Look for duplicate */
-	*dup = HnswFindDuplicate(element);
-
-	/* Update neighbors if needed */
-	if (*dup == NULL)
-	{
-		for (int lc = element->level; lc >= 0; lc--)
-		{
-			int			lm = HnswGetLayerM(m, lc);
-			HnswNeighborArray *neighbors = &element->neighbors[lc];
-
-			for (int i = 0; i < neighbors->length; i++)
-				HnswUpdateConnection(element, &neighbors->items[i], lm, lc, NULL, NULL, procinfo, collation);
-		}
-	}
+	*dup = HnswInsertElement(element, entryPoint, NULL, procinfo, collation, m, efConstruction, NULL, false);

 	/* Update entry point if needed */
 	if (*dup == NULL && (entryPoint == NULL || element->level > entryPoint->level))
@@ -424,15 +403,13 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	if (buildstate->dimensions > HNSW_MAX_DIM)
 		elog(ERROR, "column cannot have more than %d dimensions for hnsw index", HNSW_MAX_DIM);

-	if (buildstate->efConstruction < 2 * buildstate->m)
-		elog(ERROR, "ef_construction must be greater than or equal to 2 * m");
-
 	buildstate->reltuples = 0;
 	buildstate->indtuples = 0;

 	/* Get support functions */
 	buildstate->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
 	buildstate->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	buildstate->normalizeprocinfo = HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC);
 	buildstate->collation = index->rd_indcollation[0];

 	buildstate->elements = NIL;
--- a/src/hnswinsert.c
+++ b/src/hnswinsert.c
@@ -34,7 +34,7 @@ GetInsertPage(Relation index)
 * Check for a free offset
 */
 static bool
-HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *newInsertPage)
+HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *firstFreePage)
 {
 	OffsetNumber offno;
 	OffsetNumber maxoffno = PageGetMaxOffsetNumber(page);
@@ -49,15 +49,14 @@ HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size

 		if (etup->deleted)
 		{
-			BlockNumber elementPage = BufferGetBlockNumber(buf);
 			BlockNumber neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
 			OffsetNumber neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
 			ItemId		itemid;

-			if (!BlockNumberIsValid(*newInsertPage))
-				*newInsertPage = elementPage;
+			if (!BlockNumberIsValid(*firstFreePage))
+				*firstFreePage = neighborPage;

-			if (neighborPage == elementPage)
+			if (neighborPage == BufferGetBlockNumber(buf))
 			{
 				*nbuf = buf;
 				*npage = page;
@@ -111,7 +110,7 @@ HnswInsertAppendPage(Relation index, Buffer *nbuf, Page *npage, GenericXLogState
 * Add to element and neighbor pages
 */
 static void
-WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPage, BlockNumber *updatedInsertPage)
+WriteNewElementPages(Relation index, HnswElement e, int m)
 {
 	Buffer		buf;
 	Page		page;
@@ -119,24 +118,21 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	Size		etupSize;
 	Size		ntupSize;
 	Size		combinedSize;
-	Size		maxSize;
-	Size		minCombinedSize;
 	HnswElementTuple etup;
-	BlockNumber currentPage = insertPage;
+	BlockNumber insertPage = GetInsertPage(index);
+	BlockNumber originalInsertPage = insertPage;
 	int			dimensions = e->vec->dim;
 	HnswNeighborTuple ntup;
 	Buffer		nbuf;
 	Page		npage;
 	OffsetNumber freeOffno = InvalidOffsetNumber;
 	OffsetNumber freeNeighborOffno = InvalidOffsetNumber;
-	BlockNumber newInsertPage = InvalidBlockNumber;
+	BlockNumber firstFreePage = InvalidBlockNumber;

 	/* Calculate sizes */
 	etupSize = HNSW_ELEMENT_TUPLE_SIZE(dimensions);
 	ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(e->level, m);
 	combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
-	maxSize = BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData));
-	minCombinedSize = etupSize + HNSW_NEIGHBOR_TUPLE_SIZE(0, m) + sizeof(ItemIdData);

 	/* Prepare element tuple */
 	etup = palloc0(etupSize);
@@ -146,22 +142,16 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	ntup = palloc0(ntupSize);
 	HnswSetNeighborTuple(ntup, e, m);

-	/* Find a page (or two if needed) to insert the tuples */
+	/* Find a page to insert the item */
 	for (;;)
 	{
-		buf = ReadBuffer(index, currentPage);
+		buf = ReadBuffer(index, insertPage);
 		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);

 		state = GenericXLogStart(index);
 		page = GenericXLogRegisterBuffer(state, buf, 0);

-		/* Keep track of first page where element at level 0 can fit */
-		if (!BlockNumberIsValid(newInsertPage) && PageGetFreeSpace(page) >= minCombinedSize)
-			newInsertPage = currentPage;
-
-		/* First, try the fastest path */
-		/* Space for both tuples on the current page */
-		/* This can split existing tuples in rare cases */
+		/* Space for both */
 		if (PageGetFreeSpace(page) >= combinedSize)
 		{
 			nbuf = buf;
@@ -169,8 +159,15 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 			break;
 		}

-		/* Next, try space from a deleted element */
-		if (HnswFreeOffset(index, buf, page, e, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage))
+		/* Space for element but not neighbors and last page */
+		if (PageGetFreeSpace(page) >= etupSize && !BlockNumberIsValid(HnswPageGetOpaque(page)->nextblkno))
+		{
+			HnswInsertAppendPage(index, &nbuf, &npage, state, page);
+			break;
+		}
+
+		/* Space from deleted item */
+		if (HnswFreeOffset(index, buf, page, e, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &firstFreePage))
 		{
 			if (nbuf != buf)
 				npage = GenericXLogRegisterBuffer(state, nbuf, 0);
@@ -178,17 +175,9 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 			break;
 		}

-		/* Finally, try space for element only if last page */
-		/* Skip if both tuples can fit on the same page */
-		if (combinedSize > maxSize && PageGetFreeSpace(page) >= etupSize && !BlockNumberIsValid(HnswPageGetOpaque(page)->nextblkno))
-		{
-			HnswInsertAppendPage(index, &nbuf, &npage, state, page);
-			break;
-		}
+		insertPage = HnswPageGetOpaque(page)->nextblkno;

-		currentPage = HnswPageGetOpaque(page)->nextblkno;
-
-		if (BlockNumberIsValid(currentPage))
+		if (BlockNumberIsValid(insertPage))
 		{
 			/* Move to next page */
 			GenericXLogAbort(state);
@@ -230,10 +219,7 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	e->blkno = BufferGetBlockNumber(buf);
 	e->neighborPage = BufferGetBlockNumber(nbuf);

-	/* Added tuple to new page if newInsertPage is not set */
-	/* So can set to neighbor page instead of element page */
-	if (!BlockNumberIsValid(newInsertPage))
-		newInsertPage = e->neighborPage;
+	insertPage = e->neighborPage;

 	if (OffsetNumberIsValid(freeOffno))
 	{
@@ -279,126 +265,75 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 		UnlockReleaseBuffer(nbuf);

 	/* Update the insert page */
-	if (BlockNumberIsValid(newInsertPage) && newInsertPage != insertPage)
-		*updatedInsertPage = newInsertPage;
+	if (insertPage != originalInsertPage && (!OffsetNumberIsValid(freeOffno) || firstFreePage == insertPage))
+		HnswUpdateMetaPage(index, false, NULL, insertPage, MAIN_FORKNUM);
 }

 /*
- * Check if connection already exists
+ * Calculate index for update
 */
-static bool
-ConnectionExists(HnswElement e, HnswNeighborTuple ntup, int startIdx, int lm)
+static int
+HnswGetIndex(HnswUpdate * update, int m)
 {
-	for (int i = 0; i < lm; i++)
-	{
-		ItemPointer indextid = &ntup->indextids[startIdx + i];
-
-		if (!ItemPointerIsValid(indextid))
-			break;
-
-		if (ItemPointerGetBlockNumber(indextid) == e->blkno && ItemPointerGetOffsetNumber(indextid) == e->offno)
-			return true;
-	}
-
-	return false;
+	return (update->hc.element->level - update->level) * m + update->index;
 }

 /*
 * Update neighbors
 */
-void
-HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting)
+static void
+UpdateNeighborPages(Relation index, HnswElement e, int m, List *updates)
 {
-	for (int lc = e->level; lc >= 0; lc--)
+	ListCell   *lc;
+
+	/* Could update multiple at once for same element */
+	/* but should only happen a low percent of time, so keep simple for now */
+	foreach(lc, updates)
 	{
-		int			lm = HnswGetLayerM(m, lc);
-		HnswNeighborArray *neighbors = &e->neighbors[lc];
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		HnswUpdate *update = lfirst(lc);
+		ItemId		itemid;
+		HnswNeighborTuple ntup;
+		Size		ntupSize;
+		int			idx;
+		OffsetNumber offno = update->hc.element->neighborOffno;

-		for (int i = 0; i < neighbors->length; i++)
+		/* Register page */
+		buf = ReadBuffer(index, update->hc.element->neighborPage);
+		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+
+		/* Get tuple */
+		itemid = PageGetItemId(page, offno);
+		ntup = (HnswNeighborTuple) PageGetItem(page, itemid);
+		ntupSize = ItemIdGetLength(itemid);
+
+		/* Calculate index */
+		idx = HnswGetIndex(update, m);
+
+		/* Make robust to issues */
+		if (idx < ntup->count)
 		{
-			HnswCandidate *hc = &neighbors->items[i];
-			Buffer		buf;
-			Page		page;
-			GenericXLogState *state;
-			ItemId		itemid;
-			HnswNeighborTuple ntup;
-			Size		ntupSize;
-			int			idx = -1;
-			int			startIdx;
-			OffsetNumber offno = hc->element->neighborOffno;
+			ItemPointer indextid = &ntup->indextids[idx];

-			/* Get latest neighbors since they may have changed */
-			/* Do not lock yet since selecting neighbors can take time */
-			HnswLoadNeighbors(hc->element, index);
+			/* Update neighbor */
+			ItemPointerSet(indextid, e->blkno, e->offno);

-			/*
-			 * Could improve performance for vacuuming by checking neighbors
-			 * against list of elements being deleted to find index. It's
-			 * important to exclude already deleted elements for this since
-			 * they can be replaced at any time.
-			 */
+			/* Overwrite tuple */
+			if (!PageIndexTupleOverwrite(page, offno, (Item) ntup, ntupSize))
+				elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));

-			/* Select neighbors */
-			HnswUpdateConnection(e, hc, lm, lc, &idx, index, procinfo, collation);
-
-			/* New element was not selected as a neighbor */
-			if (idx == -1)
-				continue;
-
-			/* Register page */
-			buf = ReadBuffer(index, hc->element->neighborPage);
-			LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
-			state = GenericXLogStart(index);
-			page = GenericXLogRegisterBuffer(state, buf, 0);
-
-			/* Get tuple */
-			itemid = PageGetItemId(page, offno);
-			ntup = (HnswNeighborTuple) PageGetItem(page, itemid);
-			ntupSize = ItemIdGetLength(itemid);
-
-			/* Calculate index for update */
-			startIdx = (hc->element->level - lc) * m;
-
-			/* Check for existing connection */
-			if (checkExisting && ConnectionExists(e, ntup, startIdx, lm))
-				idx = -1;
-			else if (idx == -2)
-			{
-				/* Find free offset if still exists */
-				/* TODO Retry updating connections if not */
-				for (int j = 0; j < lm; j++)
-				{
-					if (!ItemPointerIsValid(&ntup->indextids[startIdx + j]))
-					{
-						idx = startIdx + j;
-						break;
-					}
-				}
-			}
-			else
-				idx += startIdx;
-
-			/* Make robust to issues */
-			if (idx >= 0 && idx < ntup->count)
-			{
-				ItemPointer indextid = &ntup->indextids[idx];
-
-				/* Update neighbor */
-				ItemPointerSet(indextid, e->blkno, e->offno);
-
-				/* Overwrite tuple */
-				if (!PageIndexTupleOverwrite(page, offno, (Item) ntup, ntupSize))
-					elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
-
-				/* Commit */
-				MarkBufferDirty(buf);
-				GenericXLogFinish(state);
-			}
-			else
-				GenericXLogAbort(state);
-
-			UnlockReleaseBuffer(buf);
+			/* Commit */
+			MarkBufferDirty(buf);
+			GenericXLogFinish(state);
 		}
+		else
+			GenericXLogAbort(state);
+
+		UnlockReleaseBuffer(buf);
 	}
 }

@@ -456,10 +391,8 @@ HnswAddDuplicate(Relation index, HnswElement element, HnswElement dup)
 * Write changes to disk
 */
 static void
-WriteElement(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement dup, HnswElement entryPoint)
+WriteElement(Relation index, HnswElement element, int m, List *updates, HnswElement dup, HnswElement entryPoint)
 {
-	BlockNumber newInsertPage = InvalidBlockNumber;
-
 	/* Try to add to existing page */
 	if (dup != NULL)
 	{
@@ -467,19 +400,13 @@ WriteElement(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement elem
 			return;
 	}

-	/* Write element and neighbor tuples */
-	WriteNewElementPages(index, element, m, GetInsertPage(index), &newInsertPage);
-
-	/* Update insert page if needed */
-	if (BlockNumberIsValid(newInsertPage))
-		HnswUpdateMetaPage(index, 0, NULL, newInsertPage, MAIN_FORKNUM);
-
-	/* Update neighbors */
-	HnswUpdateNeighborPages(index, procinfo, collation, element, m, false);
+	/* If fails, take this path */
+	WriteNewElementPages(index, element, m);
+	UpdateNeighborPages(index, element, m, updates);

 	/* Update metapage if needed */
 	if (entryPoint == NULL || element->level > entryPoint->level)
-		HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM);
+		HnswUpdateMetaPage(index, true, element, InvalidBlockNumber, MAIN_FORKNUM);
 }

 /*
@@ -490,6 +417,7 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 {
 	Datum		value;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	HnswElement entryPoint;
 	HnswElement element;
 	int			m = HnswGetM(index);
@@ -497,59 +425,29 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	double		ml = HnswGetMl(m);
 	FmgrInfo   *procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
 	Oid			collation = index->rd_indcollation[0];
+	List	   *updates = NIL;
 	HnswElement dup;
-	LOCKMODE	lockmode = ShareLock;

 	/* Detoast once for all calls */
 	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));

 	/* Normalize if needed */
 	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
-	if (normprocinfo != NULL)
-	{
-		if (!HnswNormValue(normprocinfo, collation, &value, NULL))
-			return false;
-	}
+	normalizeprocinfo = HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC);
+	HnswNormValue(normprocinfo, normalizeprocinfo, collation, &value, NULL);

 	/* Create an element */
 	element = HnswInitElement(heap_tid, m, ml, HnswGetMaxLevel(m));
 	element->vec = DatumGetVector(value);

-	/*
-	 * Get a shared lock. This allows vacuum to ensure no in-flight inserts
-	 * before repairing graph. Use a page lock so it does not interfere with
-	 * buffer lock (or reads when vacuuming).
-	 */
-	LockPage(index, HNSW_UPDATE_LOCK, lockmode);
-
 	/* Get entry point */
 	entryPoint = HnswGetEntryPoint(index);

-	/* Prevent concurrent inserts when likely updating entry point */
-	if (entryPoint == NULL || element->level > entryPoint->level)
-	{
-		/* Release shared lock */
-		UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
-
-		/* Get exclusive lock */
-		lockmode = ExclusiveLock;
-		LockPage(index, HNSW_UPDATE_LOCK, lockmode);
-
-		/* Get latest entry point after lock is acquired */
-		entryPoint = HnswGetEntryPoint(index);
-	}
-
 	/* Insert element in graph */
-	HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, false);
-
-	/* Look for duplicate */
-	dup = HnswFindDuplicate(element);
+	dup = HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, &updates, false);

 	/* Write to disk */
-	WriteElement(index, procinfo, collation, element, m, efConstruction, dup, entryPoint);
-
-	/* Release lock */
-	UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
+	WriteElement(index, element, m, updates, dup, entryPoint);

 	return true;
 }
--- a/src/hnswscan.c
+++ b/src/hnswscan.c
@@ -4,35 +4,34 @@
 #include "hnsw.h"
 #include "pgstat.h"
 #include "storage/bufmgr.h"
-#include "storage/lmgr.h"
 #include "utils/memutils.h"

 /*
 * Algorithm 5 from paper
 */
-static List *
+static void
 GetScanItems(IndexScanDesc scan, Datum q)
 {
 	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
 	Relation	index = scan->indexRelation;
 	FmgrInfo   *procinfo = so->procinfo;
 	Oid			collation = so->collation;
-	List	   *ep;
+	List	   *ep = NIL;
 	List	   *w;
 	HnswElement entryPoint = HnswGetEntryPoint(index);

 	if (entryPoint == NULL)
-		return NIL;
+		return;

-	ep = list_make1(HnswEntryCandidate(entryPoint, q, index, procinfo, collation, false));
+	ep = lappend(ep, HnswEntryCandidate(entryPoint, q, index, procinfo, collation, false));

 	for (int lc = entryPoint->level; lc >= 1; lc--)
 	{
-		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, false, NULL);
+		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, false, NULL, NULL);
 		ep = w;
 	}

-	return HnswSearchLayer(q, ep, hnsw_ef_search, 0, index, procinfo, collation, false, NULL);
+	so->w = HnswSearchLayer(q, ep, hnsw_ef_search, 0, index, procinfo, collation, false, NULL, NULL);
 }

 /*
@@ -79,6 +78,7 @@ hnswbeginscan(Relation index, int nkeys, int norderbys)
 	/* Set support functions */
 	so->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
 	so->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	so->normalizeprocinfo = HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC);
 	so->collation = index->rd_indcollation[0];

 	scan->opaque = so;
@@ -141,21 +141,10 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 			Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));

 			/* Fine if normalization fails */
-			if (so->normprocinfo != NULL)
-				HnswNormValue(so->normprocinfo, so->collation, &value, NULL);
+			HnswNormValue(so->normprocinfo, so->normalizeprocinfo, so->collation, &value, NULL);
 		}

-		/*
-		 * Get a shared lock. This allows vacuum to ensure no in-flight scans
-		 * before marking tuples as deleted.
-		 */
-		LockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
-
-		so->w = GetScanItems(scan, value);
-
-		/* Release shared lock */
-		UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
-
+		GetScanItems(scan, value);
 		so->first = false;
 	}

--- a/src/hnswutils.c
+++ b/src/hnswutils.c
@@ -7,7 +7,7 @@
 #include "vector.h"

 /*
- * Get the max number of connections in an upper layer for each element in the index
+ * Get the number of connection in the index
 */
 int
 HnswGetM(Relation index)
@@ -47,17 +47,26 @@ HnswOptionalProcInfo(Relation rel, uint16 procnum)
 }

 /*
- * Divide by the norm
- *
- * Returns false if value should not be indexed
+ * Normalize a vector
 *
 * The caller needs to free the pointer stored in value
 * if it's different than the original value
 */
-bool
-HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result)
+void
+HnswNormValue(FmgrInfo *procinfo, FmgrInfo *normalizeprocinfo, Oid collation, Datum *value, Vector * result)
 {
-	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
+	double		norm;
+
+	if (normalizeprocinfo != NULL)
+	{
+		*value = FunctionCall1Coll(normalizeprocinfo, collation, *value);
+		return;
+	}
+
+	if (procinfo == NULL)
+		return;
+
+	norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));

 	if (norm > 0)
 	{
@@ -70,11 +79,7 @@ HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result)
 			result->x[i] = v->x[i] / norm;

 		*value = PointerGetDatum(result);
-
-		return true;
 	}
-
-	return false;
 }

 /*
@@ -197,8 +202,8 @@ HnswAddHeapTid(HnswElement element, ItemPointer heaptid)
 /*
 * Allocate an element from block and offset numbers
 */
-HnswElement
-HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno)
+static HnswElement
+InitElementFromBlock(BlockNumber blkno, OffsetNumber offno)
 {
 	HnswElement element = palloc(sizeof(HnswElementData));

@@ -226,7 +231,7 @@ HnswGetEntryPoint(Relation index)
 	metap = HnswPageGetMeta(page);

 	if (BlockNumberIsValid(metap->entryBlkno))
-		entryPoint = HnswInitElementFromBlock(metap->entryBlkno, metap->entryOffno);
+		entryPoint = InitElementFromBlock(metap->entryBlkno, metap->entryOffno);

 	UnlockReleaseBuffer(buf);

@@ -234,12 +239,22 @@ HnswGetEntryPoint(Relation index)
 }

 /*
- * Update the metapage info
+ * Update the metapage
 */
-static void
-HnswUpdateMetaPageInfo(Page page, int updateEntry, HnswElement entryPoint, BlockNumber insertPage)
+void
+HnswUpdateMetaPage(Relation index, bool updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum)
 {
-	HnswMetaPage metap = HnswPageGetMeta(page);
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	HnswMetaPage metap;
+
+	buf = ReadBufferExtended(index, forkNum, HNSW_METAPAGE_BLKNO, RBM_NORMAL, NULL);
+	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+	state = GenericXLogStart(index);
+	page = GenericXLogRegisterBuffer(state, buf, 0);
+
+	metap = HnswPageGetMeta(page);

 	if (updateEntry)
 	{
@@ -249,7 +264,7 @@ HnswUpdateMetaPageInfo(Page page, int updateEntry, HnswElement entryPoint, Block
 			metap->entryOffno = InvalidOffsetNumber;
 			metap->entryLevel = -1;
 		}
-		else if (entryPoint->level > metap->entryLevel || updateEntry == HNSW_UPDATE_ENTRY_ALWAYS)
+		else
 		{
 			metap->entryBlkno = entryPoint->blkno;
 			metap->entryOffno = entryPoint->offno;
@@ -259,24 +274,6 @@ HnswUpdateMetaPageInfo(Page page, int updateEntry, HnswElement entryPoint, Block

 	if (BlockNumberIsValid(insertPage))
 		metap->insertPage = insertPage;
-}
-
-/*
- * Update the metapage
- */
-void
-HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum)
-{
-	Buffer		buf;
-	Page		page;
-	GenericXLogState *state;
-
-	buf = ReadBufferExtended(index, forkNum, HNSW_METAPAGE_BLKNO, RBM_NORMAL, NULL);
-	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
-	state = GenericXLogStart(index);
-	page = GenericXLogRegisterBuffer(state, buf, 0);
-
-	HnswUpdateMetaPageInfo(page, updateEntry, entryPoint, insertPage);

 	HnswCommitBuffer(buf, state);
 }
@@ -364,7 +361,7 @@ LoadNeighborsFromPage(HnswElement element, Relation index, Page page)
 		if (!ItemPointerIsValid(indextid))
 			continue;

-		e = HnswInitElementFromBlock(ItemPointerGetBlockNumber(indextid), ItemPointerGetOffsetNumber(indextid));
+		e = InitElementFromBlock(ItemPointerGetBlockNumber(indextid), ItemPointerGetOffsetNumber(indextid));

 		/* Calculate level based on offset */
 		level = element->level - i / m;
@@ -380,8 +377,8 @@ LoadNeighborsFromPage(HnswElement element, Relation index, Page page)
 /*
 * Load neighbors
 */
-void
-HnswLoadNeighbors(HnswElement element, Relation index)
+static void
+LoadNeighbors(HnswElement element, Relation index)
 {
 	Buffer		buf;
 	Page		page;
@@ -395,37 +392,6 @@ HnswLoadNeighbors(HnswElement element, Relation index)
 	UnlockReleaseBuffer(buf);
 }

-/*
- * Load an element from a tuple
- */
-void
-HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHeaptids, bool loadVec)
-{
-	element->level = etup->level;
-	element->deleted = etup->deleted;
-	element->neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
-	element->neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
-	element->heaptids = NIL;
-
-	if (loadHeaptids)
-	{
-		for (int i = 0; i < HNSW_HEAPTIDS; i++)
-		{
-			/* Can stop at first invalid */
-			if (!ItemPointerIsValid(&etup->heaptids[i]))
-				break;
-
-			HnswAddHeapTid(element, &etup->heaptids[i]);
-		}
-	}
-
-	if (loadVec)
-	{
-		element->vec = palloc(VECTOR_SIZE(etup->vec.dim));
-		memcpy(element->vec, &etup->vec, VECTOR_SIZE(etup->vec.dim));
-	}
-}
-
 /*
 * Load an element and optionally get its distance from q
 */
@@ -446,7 +412,25 @@ HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index,
 	Assert(HnswIsElementTuple(etup));

 	/* Load element */
-	HnswLoadElementFromTuple(element, etup, true, loadVec);
+	element->heaptids = NIL;
+	for (int i = 0; i < HNSW_HEAPTIDS; i++)
+	{
+		/* Can stop at first invalid */
+		if (!ItemPointerIsValid(&etup->heaptids[i]))
+			break;
+
+		HnswAddHeapTid(element, &etup->heaptids[i]);
+	}
+	element->level = etup->level;
+	element->neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
+	element->neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
+	element->deleted = etup->deleted;
+
+	if (loadVec)
+	{
+		element->vec = palloc(VECTOR_SIZE(etup->vec.dim));
+		memcpy(element->vec, &etup->vec, VECTOR_SIZE(etup->vec.dim));
+	}

 	/* Calculate distance */
 	if (distance != NULL)
@@ -468,7 +452,7 @@ GetCandidateDistance(HnswCandidate * hc, Datum q, FmgrInfo *procinfo, Oid collat
 * Create a candidate for the entry point
 */
 HnswCandidate *
-HnswEntryCandidate(HnswElement entryPoint, Datum q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec)
+HnswEntryCandidate(HnswElement entryPoint, Datum q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadvec)
 {
 	HnswCandidate *hc = palloc(sizeof(HnswCandidate));

@@ -476,7 +460,7 @@ HnswEntryCandidate(HnswElement entryPoint, Datum q, Relation index, FmgrInfo *pr
 	if (index == NULL)
 		hc->distance = GetCandidateDistance(hc, q, procinfo, collation);
 	else
-		HnswLoadElement(hc->element, &hc->distance, &q, index, procinfo, collation, loadVec);
+		HnswLoadElement(hc->element, &hc->distance, &q, index, procinfo, collation, loadvec);
 	return hc;
 }

@@ -543,7 +527,7 @@ AddToVisited(HTAB *v, HnswCandidate * hc, Relation index, bool *found)
 * Algorithm 2 from paper
 */
 List *
-HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, bool inserting, HnswElement skipElement)
+HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, bool inserting, BlockNumber *skipPage, OffsetNumber *skipOffno)
 {
 	ListCell   *lc2;

@@ -579,13 +563,7 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 		pairingheap_add(C, &(CreatePairingHeapNode(hc)->ph_node));
 		pairingheap_add(W, &(CreatePairingHeapNode(hc)->ph_node));

-		/*
-		 * Do not count elements being deleted towards ef when vacuuming. It
-		 * would be ideal to do this for inserts as well, but this could
-		 * affect insert performance.
-		 */
-		if (skipElement == NULL || list_length(hc->element->heaptids) != 0)
-			wlen++;
+		wlen++;
 	}

 	while (!pairingheap_is_empty(C))
@@ -598,7 +576,7 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 			break;

 		if (c->element->neighbors == NULL)
-			HnswLoadNeighbors(c->element, index);
+			LoadNeighbors(c->element, index);

 		/* Get the neighborhood at layer lc */
 		neighborhood = &c->element->neighbors[lc];
@@ -621,10 +599,16 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 				else
 					HnswLoadElement(e->element, &eDistance, &q, index, procinfo, collation, inserting);

-				Assert(!e->element->deleted);
+				/* Skip if fully deleted */
+				if (e->element->deleted)
+					continue;
+
+				/* Skip for inserts if deleting */
+				if (inserting && list_length(e->element->heaptids) == 0)
+					continue;

 				/* Skip self for vacuuming update */
-				if (skipElement != NULL && e->element->blkno == skipElement->blkno && e->element->offno == skipElement->offno)
+				if (skipPage != NULL && e->element->neighborPage == *skipPage && e->element->neighborOffno == *skipOffno)
 					continue;

 				/* Make robust to issues */
@@ -641,20 +625,11 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro

 					pairingheap_add(C, &(CreatePairingHeapNode(ec)->ph_node));
 					pairingheap_add(W, &(CreatePairingHeapNode(ec)->ph_node));
+					wlen++;

-					/*
-					 * Do not count elements being deleted towards ef when
-					 * vacuuming. It would be ideal to do this for inserts as
-					 * well, but this could affect insert performance.
-					 */
-					if (skipElement == NULL || list_length(e->element->heaptids) != 0)
-					{
-						wlen++;
-
-						/* No need to decrement wlen */
-						if (wlen > ef)
-							pairingheap_remove_first(W);
-					}
+					/* No need to decrement wlen */
+					if (wlen > ef)
+						pairingheap_remove_first(W);
 				}
 			}
 		}
@@ -733,7 +708,7 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswC
 	List	   *w = list_copy(c);
 	pairingheap *wd;

-	if (list_length(w) <= m)
+	if (list_length(w) < m)
 		return w;

 	wd = pairingheap_allocate(CompareNearestCandidates, NULL);
@@ -773,14 +748,14 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswC
 /*
 * Find duplicate element
 */
-HnswElement
-HnswFindDuplicate(HnswElement e)
+static HnswElement
+HnswFindDuplicate(HnswElement e, List *neighbors)
 {
-	HnswNeighborArray *neighbors = &e->neighbors[0];
+	ListCell   *lc;

-	for (int i = 0; i < neighbors->length; i++)
+	foreach(lc, neighbors)
 	{
-		HnswCandidate *neighbor = &neighbors->items[i];
+		HnswCandidate *neighbor = lfirst(lc);

 		/* Exit early since ordered by distance */
 		if (vector_cmp_internal(e->vec, neighbor->element->vec) != 0)
@@ -829,134 +804,144 @@ CompareCandidateDistances(const void *a, const void *b)
 	return 0;
 }

+/*
+ * Create update
+ */
+static HnswUpdate *
+CreateUpdate(HnswCandidate * hc, int level, int index)
+{
+	HnswUpdate *update = palloc(sizeof(HnswUpdate));
+
+	update->hc = *hc;
+	update->level = level;
+	update->index = index;
+	return update;
+}
+
 /*
 * Update connections
 */
-void
-HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation)
+static void
+UpdateConnections(HnswElement element, List *neighbors, int m, int lc, List **updates, Relation index, FmgrInfo *procinfo, Oid collation)
 {
-	HnswNeighborArray *currentNeighbors = &hc->element->neighbors[lc];
+	ListCell   *lc2;

-	HnswCandidate hc2;
-
-	hc2.element = element;
-	hc2.distance = hc->distance;
-
-	if (currentNeighbors->length < m)
+	foreach(lc2, neighbors)
 	{
-		currentNeighbors->items[currentNeighbors->length++] = hc2;
+		HnswCandidate *hc = (HnswCandidate *) lfirst(lc2);
+		HnswNeighborArray *currentNeighbors = &hc->element->neighbors[lc];

-		/* Track update */
-		if (updateIdx != NULL)
-			*updateIdx = -2;
-	}
-	else
-	{
-		/* Shrink connections */
-		HnswCandidate *pruned = NULL;
+		HnswCandidate hc2;

-		/* Load elements on insert */
-		if (index != NULL)
+		hc2.element = element;
+		hc2.distance = hc->distance;
+
+		if (currentNeighbors->length < m)
 		{
-			Datum		q = PointerGetDatum(hc->element->vec);
+			currentNeighbors->items[currentNeighbors->length++] = hc2;

+			/* Track updates */
+			if (updates != NULL)
+				*updates = lappend(*updates, CreateUpdate(hc, lc, currentNeighbors->length - 1));
+		}
+		else
+		{
+			/* Shrink connections */
+			HnswCandidate *pruned = NULL;
+			List	   *c = NIL;
+
+			/* Load elements on insert */
+			if (index != NULL)
+			{
+				Datum		q = PointerGetDatum(hc->element->vec);
+
+				for (int i = 0; i < currentNeighbors->length; i++)
+				{
+					HnswCandidate *hc3 = &currentNeighbors->items[i];
+
+					if (hc3->element->vec == NULL)
+						HnswLoadElement(hc3->element, &hc3->distance, &q, index, procinfo, collation, true);
+					else
+						hc3->distance = GetCandidateDistance(hc3, q, procinfo, collation);
+
+					/* Prune element if being deleted */
+					if (list_length(hc3->element->heaptids) == 0)
+					{
+						pruned = &currentNeighbors->items[i];
+						break;
+					}
+				}
+			}
+
+			if (pruned == NULL)
+			{
+				/* Add and sort candidates */
+				for (int i = 0; i < currentNeighbors->length; i++)
+					c = lappend(c, &currentNeighbors->items[i]);
+				c = lappend(c, &hc2);
+				list_sort(c, CompareCandidateDistances);
+
+				SelectNeighbors(c, m, lc, procinfo, collation, &pruned);
+
+				/* Should not happen */
+				if (pruned == NULL)
+					continue;
+			}
+
+			/* Find and replace the pruned element */
 			for (int i = 0; i < currentNeighbors->length; i++)
 			{
-				HnswCandidate *hc3 = &currentNeighbors->items[i];
-
-				if (hc3->element->vec == NULL)
-					HnswLoadElement(hc3->element, &hc3->distance, &q, index, procinfo, collation, true);
-				else
-					hc3->distance = GetCandidateDistance(hc3, q, procinfo, collation);
-
-				/* Prune element if being deleted */
-				if (list_length(hc3->element->heaptids) == 0)
+				if (currentNeighbors->items[i].element == pruned->element)
 				{
-					pruned = &currentNeighbors->items[i];
+					currentNeighbors->items[i] = hc2;
+
+					/* Track updates */
+					if (updates != NULL)
+						*updates = lappend(*updates, CreateUpdate(hc, lc, i));
+
 					break;
 				}
 			}
 		}
-
-		if (pruned == NULL)
-		{
-			List	   *c = NIL;
-
-			/* Add and sort candidates */
-			for (int i = 0; i < currentNeighbors->length; i++)
-				c = lappend(c, &currentNeighbors->items[i]);
-			c = lappend(c, &hc2);
-			list_sort(c, CompareCandidateDistances);
-
-			SelectNeighbors(c, m, lc, procinfo, collation, &pruned);
-
-			/* Should not happen */
-			if (pruned == NULL)
-				return;
-		}
-
-		/* Find and replace the pruned element */
-		for (int i = 0; i < currentNeighbors->length; i++)
-		{
-			if (currentNeighbors->items[i].element == pruned->element)
-			{
-				currentNeighbors->items[i] = hc2;
-
-				/* Track update */
-				if (updateIdx != NULL)
-					*updateIdx = i;
-
-				break;
-			}
-		}
 	}
 }

-/*
- * Remove elements being deleted
- */
-static List *
-RemoveElementsBeingDeleted(List *w)
-{
-	ListCell   *lc2;
-	List	   *w2 = NIL;
-
-	foreach(lc2, w)
-	{
-		HnswCandidate *hc = (HnswCandidate *) lfirst(lc2);
-
-		if (list_length(hc->element->heaptids) != 0)
-			w2 = lappend(w2, hc);
-	}
-
-	return w2;
-}
-
 /*
 * Algorithm 1 from paper
 */
-void
-HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing)
+HnswElement
+HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, List **updates, bool vacuuming)
 {
-	List	   *ep;
+	List	   *ep = NIL;
 	List	   *w;
 	int			level = element->level;
 	int			entryLevel;
+	List	  **newNeighbors = palloc(sizeof(List *) * (level + 1));
 	Datum		q = PointerGetDatum(element->vec);
-	HnswElement skipElement = existing ? element : NULL;
-
-	/* No neighbors if no entry point */
-	if (entryPoint == NULL)
-		return;
+	HnswElement dup;
+	BlockNumber *skipPage = vacuuming ? &element->neighborPage : NULL;
+	OffsetNumber *skipOffno = vacuuming ? &element->neighborOffno : NULL;
+	bool		removeEntryPoint;
+	HnswCandidate *entryCandidate;

 	/* Get entry point and level */
-	ep = list_make1(HnswEntryCandidate(entryPoint, q, index, procinfo, collation, true));
-	entryLevel = entryPoint->level;
+	if (entryPoint != NULL)
+	{
+		entryCandidate = HnswEntryCandidate(entryPoint, q, index, procinfo, collation, true);
+		ep = lappend(ep, entryCandidate);
+		entryLevel = entryPoint->level;
+		removeEntryPoint = vacuuming && list_length(entryPoint->heaptids) == 0;
+	}
+	else
+	{
+		entryLevel = -1;
+		removeEntryPoint = false;
+	}

 	/* 1st phase: greedy search to insert level */
 	for (int lc = entryLevel; lc >= level + 1; lc--)
 	{
-		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, true, skipElement);
+		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, true, skipPage, skipOffno);
 		ep = w;
 	}

@@ -967,19 +952,35 @@ HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, F
 	for (int lc = level; lc >= 0; lc--)
 	{
 		int			lm = HnswGetLayerM(m, lc);
-		List	   *neighbors;

-		w = HnswSearchLayer(q, ep, efConstruction, lc, index, procinfo, collation, true, skipElement);
+		w = HnswSearchLayer(q, ep, efConstruction, lc, index, procinfo, collation, true, skipPage, skipOffno);

-		/* Elements being deleted can help with search */
-		/* but should be removed before selecting neighbors */
-		if (index != NULL)
-			w = RemoveElementsBeingDeleted(w);
-
-		neighbors = SelectNeighbors(w, lm, lc, procinfo, collation, NULL);
-
-		AddConnections(element, neighbors, lm, lc);
+		/* Remove entry point if it's being deleted */
+		if (removeEntryPoint)
+			w = list_delete_ptr(w, entryCandidate);

+		newNeighbors[lc] = SelectNeighbors(w, lm, lc, procinfo, collation, NULL);
 		ep = w;
 	}
+
+	/* Look for duplicate */
+	if (level >= 0 && !vacuuming)
+	{
+		dup = HnswFindDuplicate(element, newNeighbors[0]);
+		if (dup != NULL)
+			return dup;
+	}
+
+	/* Update connections */
+	for (int lc = level; lc >= 0; lc--)
+	{
+		int			lm = HnswGetLayerM(m, lc);
+
+		AddConnections(element, newNeighbors[lc], lm, lc);
+
+		if (!vacuuming)
+			UpdateConnections(element, newNeighbors[lc], lm, lc, updates, index, procinfo, collation);
+	}
+
+	return NULL;
 }
--- a/src/hnswvacuum.c
+++ b/src/hnswvacuum.c
@@ -5,11 +5,10 @@
 #include "commands/vacuum.h"
 #include "hnsw.h"
 #include "storage/bufmgr.h"
-#include "storage/lmgr.h"
 #include "utils/memutils.h"

 /*
- * Check if deleted list contains an index TID
+ * Check if deleted list contains an index tid
 */
 static bool
 DeletedContains(HTAB *deleted, ItemPointer indextid)
@@ -33,7 +32,6 @@ RemoveHeapTids(HnswVacuumState * vacuumstate)
 	Relation	index = vacuumstate->index;
 	BufferAccessStrategy bas = vacuumstate->bas;
 	HnswElement entryPoint = HnswGetEntryPoint(vacuumstate->index);
-	IndexBulkDeleteResult *stats = vacuumstate->stats;

 	/* Store separately since highestPoint.level is uint8 */
 	int			highestLevel = -1;
@@ -79,15 +77,11 @@ RemoveHeapTids(HnswVacuumState * vacuumstate)
 						break;

 					if (vacuumstate->callback(&etup->heaptids[i], vacuumstate->callback_state))
-					{
 						itemUpdated = true;
-						stats->tuples_removed++;
-					}
 					else
 					{
 						/* Move to front of list */
 						etup->heaptids[idx++] = etup->heaptids[i];
-						stats->num_index_tuples++;
 					}
 				}

@@ -115,7 +109,7 @@ RemoveHeapTids(HnswVacuumState * vacuumstate)

 				(void) hash_search(vacuumstate->deleted, &ip, HASH_ENTER, NULL);
 			}
-			else if (etup->level > highestLevel && !(entryPoint != NULL && blkno == entryPoint->blkno && offno == entryPoint->offno))
+			else if (etup->level > highestLevel && !(blkno == entryPoint->blkno && offno == entryPoint->offno))
 			{
 				/* Keep track of highest non-entry point */
 				highestPoint->blkno = blkno;
@@ -175,11 +169,6 @@ NeedsUpdated(HnswVacuumState * vacuumstate, HnswElement element)
 		}
 	}

-	/* Also update if layer 0 is not full */
-	/* This could indicate too many candidates being deleted during insert */
-	if (!needsUpdated)
-		needsUpdated = !ItemPointerIsValid(&ntup->indextids[ntup->count - 1]);
-
 	UnlockReleaseBuffer(buf);

 	return needsUpdated;
@@ -189,7 +178,7 @@ NeedsUpdated(HnswVacuumState * vacuumstate, HnswElement element)
 * Repair graph for a single element
 */
 static void
-RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswElement entryPoint)
+RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element)
 {
 	Relation	index = vacuumstate->index;
 	Buffer		buf;
@@ -199,20 +188,42 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	int			efConstruction = vacuumstate->efConstruction;
 	FmgrInfo   *procinfo = vacuumstate->procinfo;
 	Oid			collation = vacuumstate->collation;
+	HnswElement entryPoint;
 	BufferAccessStrategy bas = vacuumstate->bas;
 	HnswNeighborTuple ntup = vacuumstate->ntup;
 	Size		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(element->level, m);

-	/* Skip if element is entry point */
-	if (entryPoint != NULL && element->blkno == entryPoint->blkno && element->offno == entryPoint->offno)
+	/* Check if any neighbors point to deleted values */
+	if (!NeedsUpdated(vacuumstate, element))
 		return;

+	/* Refresh entry point for each element */
+	entryPoint = HnswGetEntryPoint(index);
+
+	/* Special case for entry point */
+	if (element->blkno == entryPoint->blkno && element->offno == entryPoint->offno)
+	{
+		if (BlockNumberIsValid(vacuumstate->highestPoint.blkno))
+		{
+			/* Already updated */
+			if (vacuumstate->highestPoint.blkno == element->blkno && vacuumstate->highestPoint.offno == element->offno)
+				return;
+
+			entryPoint = &vacuumstate->highestPoint;
+
+			/* Reset neighbors from previous update */
+			entryPoint->neighbors = NULL;
+		}
+		else
+			entryPoint = NULL;
+	}
+
 	/* Init fields */
 	HnswInitNeighbors(element, m);
 	element->heaptids = NIL;

 	/* Add element to graph, skipping itself */
-	HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, true);
+	HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, NULL, true);

 	/* Update neighbor tuple */
 	/* Do this before getting page to minimize locking */
@@ -232,9 +243,6 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	MarkBufferDirty(buf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
-
-	/* Update neighbors */
-	HnswUpdateNeighborPages(index, procinfo, collation, element, m, true);
 }

 /*
@@ -248,35 +256,16 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 	HnswElement entryPoint;
 	MemoryContext oldCtx = MemoryContextSwitchTo(vacuumstate->tmpCtx);

-	if (!BlockNumberIsValid(highestPoint->blkno))
-		highestPoint = NULL;
-
-	/*
-	 * Repair graph for highest non-entry point. Highest point may be outdated
-	 * due to inserts that happen during and after RemoveHeapTids.
-	 */
-	if (highestPoint != NULL)
+	/* Repair graph for highest non-entry point */
+	/* This may not be the highest with new inserts, but should be fine */
+	if (BlockNumberIsValid(highestPoint->blkno))
 	{
-		/* Get a shared lock */
-		LockPage(index, HNSW_UPDATE_LOCK, ShareLock);
-
-		/* Load element */
 		HnswLoadElement(highestPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true);
-
-		/* Repair if needed */
-		if (NeedsUpdated(vacuumstate, highestPoint))
-			RepairGraphElement(vacuumstate, highestPoint, HnswGetEntryPoint(index));
-
-		/* Release lock */
-		UnlockPage(index, HNSW_UPDATE_LOCK, ShareLock);
+		RepairGraphElement(vacuumstate, highestPoint);
 	}

-	/* Prevent concurrent inserts when possibly updating entry point */
-	LockPage(index, HNSW_UPDATE_LOCK, ExclusiveLock);
-
-	/* Get latest entry point */
+	/* See if entry point needs updated */
 	entryPoint = HnswGetEntryPoint(index);
-
 	if (entryPoint != NULL)
 	{
 		ItemPointerData epData;
@@ -284,37 +273,15 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 		ItemPointerSet(&epData, entryPoint->blkno, entryPoint->offno);

 		if (DeletedContains(vacuumstate->deleted, &epData))
-		{
-			/*
-			 * Replace the entry point with the highest point. If highest
-			 * point is outdated and empty, the entry point will be empty
-			 * until an element is repaired.
-			 */
-			HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_ALWAYS, highestPoint, InvalidBlockNumber, MAIN_FORKNUM);
-		}
+			HnswUpdateMetaPage(index, true, highestPoint, InvalidBlockNumber, MAIN_FORKNUM);
 		else
 		{
-			/*
-			 * Repair the entry point with the highest point. If highest point
-			 * is outdated, this can remove connections at higher levels in
-			 * the graph until they are repaired, but this should be fine.
-			 */
+			/* Highest point will be used to repair */
 			HnswLoadElement(entryPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true);
-
-			if (NeedsUpdated(vacuumstate, entryPoint))
-			{
-				/* Reset neighbors from previous update */
-				if (highestPoint != NULL)
-					highestPoint->neighbors = NULL;
-
-				RepairGraphElement(vacuumstate, entryPoint, highestPoint);
-			}
+			RepairGraphElement(vacuumstate, entryPoint);
 		}
 	}

-	/* Release lock */
-	UnlockPage(index, HNSW_UPDATE_LOCK, ExclusiveLock);
-
 	/* Reset memory context */
 	MemoryContextSwitchTo(oldCtx);
 	MemoryContextReset(vacuumstate->tmpCtx);
@@ -330,11 +297,6 @@ RepairGraph(HnswVacuumState * vacuumstate)
 	BufferAccessStrategy bas = vacuumstate->bas;
 	BlockNumber blkno = HNSW_HEAD_BLKNO;

-	/* Wait for inserts to complete */
-	LockPage(index, HNSW_UPDATE_LOCK, ExclusiveLock);
-	UnlockPage(index, HNSW_UPDATE_LOCK, ExclusiveLock);
-
-	/* Repair entry point first */
 	RepairGraphEntryPoint(vacuumstate);

 	while (BlockNumberIsValid(blkno))
@@ -371,8 +333,14 @@ RepairGraph(HnswVacuumState * vacuumstate)
 				continue;

 			/* Create an element */
-			element = HnswInitElementFromBlock(blkno, offno);
-			HnswLoadElementFromTuple(element, etup, false, true);
+			element = palloc(sizeof(HnswElementData));
+			element->neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
+			element->neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
+			element->level = etup->level;
+			element->blkno = blkno;
+			element->offno = offno;
+			element->vec = palloc(VECTOR_SIZE(etup->vec.dim));
+			memcpy(element->vec, &etup->vec, VECTOR_SIZE(etup->vec.dim));

 			elements = lappend(elements, element);
 		}
@@ -383,48 +351,7 @@ RepairGraph(HnswVacuumState * vacuumstate)

 		/* Update neighbor pages */
 		foreach(lc2, elements)
-		{
-			HnswElement element = (HnswElement) lfirst(lc2);
-			HnswElement entryPoint;
-			LOCKMODE	lockmode = ShareLock;
-
-			/* Check if any neighbors point to deleted values */
-			if (!NeedsUpdated(vacuumstate, element))
-				continue;
-
-			/* Get a shared lock */
-			LockPage(index, HNSW_UPDATE_LOCK, lockmode);
-
-			/* Refresh entry point for each element */
-			entryPoint = HnswGetEntryPoint(index);
-
-			/* Prevent concurrent inserts when likely updating entry point */
-			if (entryPoint == NULL || element->level > entryPoint->level)
-			{
-				/* Release shared lock */
-				UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
-
-				/* Get exclusive lock */
-				lockmode = ExclusiveLock;
-				LockPage(index, HNSW_UPDATE_LOCK, lockmode);
-
-				/* Get latest entry point after lock is acquired */
-				entryPoint = HnswGetEntryPoint(index);
-			}
-
-			/* Repair connections */
-			RepairGraphElement(vacuumstate, element, entryPoint);
-
-			/*
-			 * Update metapage if needed. Should only happen if entry point
-			 * was replaced and highest point was outdated.
-			 */
-			if (entryPoint == NULL || element->level > entryPoint->level)
-				HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM);
-
-			/* Release lock */
-			UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
-		}
+			RepairGraphElement(vacuumstate, (HnswElement) lfirst(lc2));

 		/* Reset memory context */
 		MemoryContextSwitchTo(oldCtx);
@@ -442,10 +369,7 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 	BlockNumber insertPage = InvalidBlockNumber;
 	Relation	index = vacuumstate->index;
 	BufferAccessStrategy bas = vacuumstate->bas;
-
-	/* Wait for selects to complete */
-	LockPage(index, HNSW_SCAN_LOCK, ExclusiveLock);
-	UnlockPage(index, HNSW_SCAN_LOCK, ExclusiveLock);
+	IndexBulkDeleteResult *stats = vacuumstate->stats;

 	while (BlockNumberIsValid(blkno))
 	{
@@ -489,17 +413,17 @@ MarkDeleted(HnswVacuumState * vacuumstate)

 			/* Skip deleted tuples */
 			if (etup->deleted)
-			{
-				/* Set to first free page */
-				if (!BlockNumberIsValid(insertPage))
-					insertPage = blkno;
-
 				continue;
-			}

 			/* Skip live tuples */
 			if (ItemPointerIsValid(&etup->heaptids[0]))
+			{
+				stats->num_index_tuples++;
 				continue;
+			}
+
+			/* Update stats */
+			stats->tuples_removed++;

 			/* Calculate sizes */
 			etupSize = HNSW_ELEMENT_TUPLE_SIZE(etup->vec.dim);
@@ -562,8 +486,7 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 		UnlockReleaseBuffer(buf);
 	}

-	/* Update insert page last, after everything has been marked as deleted */
-	HnswUpdateMetaPage(index, 0, NULL, insertPage, MAIN_FORKNUM);
+	HnswUpdateMetaPage(index, false, NULL, insertPage, MAIN_FORKNUM);
 }

 /*
@@ -611,67 +534,6 @@ FreeVacuumState(HnswVacuumState * vacuumstate)
 	MemoryContextDelete(vacuumstate->tmpCtx);
 }

-/*
- * Print graph
- */
-#ifdef HNSW_DEBUG
-static void
-PrintGraph(HnswVacuumState * vacuumstate)
-{
-	BlockNumber blkno = HNSW_HEAD_BLKNO;
-	Relation	index = vacuumstate->index;
-
-	while (BlockNumberIsValid(blkno))
-	{
-		Buffer		buf;
-		Page		page;
-		OffsetNumber offno;
-		OffsetNumber maxoffno;
-
-		buf = ReadBuffer(index, blkno);
-		LockBuffer(buf, BUFFER_LOCK_SHARE);
-		page = BufferGetPage(buf);
-		maxoffno = PageGetMaxOffsetNumber(page);
-
-		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
-		{
-			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
-			HnswElement element;
-
-			/* Skip neighbor tuples */
-			if (!HnswIsElementTuple(etup))
-				continue;
-
-			/* Skip deleted tuples */
-			if (etup->deleted)
-				continue;
-
-			element = HnswInitElementFromBlock(blkno, offno);
-			HnswLoadElementFromTuple(element, etup, false, true);
-			HnswLoadNeighbors(element, index);
-
-			elog(INFO, "element (%d,%d)", element->blkno, element->offno);
-
-			for (int lc = element->level; lc >= 0; lc--)
-			{
-				HnswNeighborArray *neighbors = &element->neighbors[lc];
-
-				for (int i = 0; i < neighbors->length; i++)
-				{
-					HnswElement e = neighbors->items[i].element;
-
-					elog(INFO, "%d: (%d,%d)", lc, e->blkno, e->offno);
-				}
-			}
-		}
-
-		blkno = HnswPageGetOpaque(page)->nextblkno;
-
-		UnlockReleaseBuffer(buf);
-	}
-}
-#endif
-
 /*
 * Bulk delete tuples from the index
 */
@@ -692,10 +554,6 @@ hnswbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 	/* Pass 3: Mark as deleted */
 	MarkDeleted(&vacuumstate);

-#ifdef HNSW_DEBUG
-	PrintGraph(&vacuumstate);
-#endif
-
 	FreeVacuumState(&vacuumstate);

 	return vacuumstate.stats;
--- a/src/ivfbuild.c
+++ b/src/ivfbuild.c
@@ -75,11 +75,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 	 * Normalize with KMEANS_NORM_PROC since spherical distance function
 	 * expects unit vectors
 	 */
-	if (buildstate->kmeansnormprocinfo != NULL)
-	{
-		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->normvec))
-			return;
-	}
+	IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->kmeansnormalizeprocinfo, buildstate->collation, &value, buildstate->normvec);

 	if (samples->length < targsamples)
 	{
@@ -176,11 +172,7 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState
 	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));

 	/* Normalize if needed */
-	if (buildstate->normprocinfo != NULL)
-	{
-		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->normvec))
-			return;
-	}
+	IvfflatNormValue(buildstate->normprocinfo, buildstate->normalizeprocinfo, buildstate->collation, &value, buildstate->normvec);

 	/* Find the list that minimizes the distance */
 	for (int i = 0; i < centers->length; i++)
@@ -368,6 +360,8 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
 	buildstate->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	buildstate->kmeansnormprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
+	buildstate->normalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC);
+	buildstate->kmeansnormalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORMALIZE_PROC);
 	buildstate->collation = index->rd_indcollation[0];

 	/* Require more than one dimension for spherical k-means */
--- a/src/ivfflat.c
+++ b/src/ivfflat.c
@@ -24,7 +24,7 @@ IvfflatInit(void)
 {
 	ivfflat_relopt_kind = add_reloption_kind();
 	add_int_reloption(ivfflat_relopt_kind, "lists", "Number of inverted lists",
-					  IVFFLAT_DEFAULT_LISTS, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS
+					  IVFFLAT_DEFAULT_LISTS, 1, IVFFLAT_MAX_LISTS
 #if PG_VERSION_NUM >= 130000
 					  ,AccessExclusiveLock
 #endif
@@ -32,7 +32,7 @@ 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);
+							1, 1, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
 }

 /*
@@ -194,7 +194,7 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);

 	amroutine->amstrategies = 0;
-	amroutine->amsupport = 4;
+	amroutine->amsupport = 6;
 #if PG_VERSION_NUM >= 130000
 	amroutine->amoptsprocnum = 0;
 #endif
--- a/src/ivfflat.h
+++ b/src/ivfflat.h
@@ -31,6 +31,8 @@
 #define IVFFLAT_NORM_PROC 2
 #define IVFFLAT_KMEANS_DISTANCE_PROC 3
 #define IVFFLAT_KMEANS_NORM_PROC 4
+#define IVFFLAT_NORMALIZE_PROC 5
+#define IVFFLAT_KMEANS_NORMALIZE_PROC 6

 #define IVFFLAT_VERSION	1
 #define IVFFLAT_MAGIC_NUMBER 0x14FF1A7
@@ -40,11 +42,8 @@
 #define IVFFLAT_METAPAGE_BLKNO	0
 #define IVFFLAT_HEAD_BLKNO		1	/* first list page */

-/* IVFFlat parameters */
 #define IVFFLAT_DEFAULT_LISTS	100
-#define IVFFLAT_MIN_LISTS		1
 #define IVFFLAT_MAX_LISTS		32768
-#define IVFFLAT_DEFAULT_PROBES	1

 /* Build phases */
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
@@ -175,6 +174,8 @@ typedef struct IvfflatBuildState
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
 	FmgrInfo   *kmeansnormprocinfo;
+	FmgrInfo   *normalizeprocinfo;
+	FmgrInfo   *kmeansnormalizeprocinfo;
 	Oid			collation;

 	/* Variables */
@@ -256,6 +257,7 @@ typedef struct IvfflatScanOpaqueData
 	/* Support functions */
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;

 	/* Lists */
@@ -276,7 +278,7 @@ void		VectorArrayFree(VectorArray arr);
 void		PrintVectorArray(char *msg, VectorArray arr);
 void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
 FmgrInfo   *IvfflatOptionalProcInfo(Relation rel, uint16 procnum);
-bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+void		IvfflatNormValue(FmgrInfo *procinfo, FmgrInfo *normalizeprocinfo, Oid collation, Datum *value, Vector * result);
 int			IvfflatGetLists(Relation index);
 void		IvfflatUpdateList(Relation index, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);
 void		IvfflatCommitBuffer(Buffer buf, GenericXLogState *state);
--- a/src/ivfinsert.c
+++ b/src/ivfinsert.c
@@ -68,6 +68,7 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 	IndexTuple	itup;
 	Datum		value;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
@@ -81,11 +82,8 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel

 	/* Normalize if needed */
 	normprocinfo = IvfflatOptionalProcInfo(rel, IVFFLAT_NORM_PROC);
-	if (normprocinfo != NULL)
-	{
-		if (!IvfflatNormValue(normprocinfo, rel->rd_indcollation[0], &value, NULL))
-			return;
-	}
+	normalizeprocinfo = IvfflatOptionalProcInfo(rel, IVFFLAT_NORMALIZE_PROC);
+	IvfflatNormValue(normprocinfo, normalizeprocinfo, rel->rd_indcollation[0], &value, NULL);

 	/* Find the insert page - sets the page and list info */
 	FindInsertPage(rel, values, &insertPage, &listInfo);
--- a/src/ivfscan.c
+++ b/src/ivfscan.c
@@ -232,6 +232,7 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	/* Set support functions */
 	so->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
 	so->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
+	so->normalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC);
 	so->collation = index->rd_indcollation[0];

 	/* Create tuple description for sorting */
@@ -319,8 +320,7 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 			Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));

 			/* Fine if normalization fails */
-			if (so->normprocinfo != NULL)
-				IvfflatNormValue(so->normprocinfo, so->collation, &value, NULL);
+			IvfflatNormValue(so->normprocinfo, so->normalizeprocinfo, so->collation, &value, NULL);
 		}

 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
--- a/src/ivfutils.c
+++ b/src/ivfutils.c
@@ -66,17 +66,26 @@ IvfflatOptionalProcInfo(Relation rel, uint16 procnum)
 }

 /*
- * Divide by the norm
- *
- * Returns false if value should not be indexed
+ * Normalize a vector
 *
 * The caller needs to free the pointer stored in value
 * if it's different than the original value
 */
-bool
-IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result)
+void
+IvfflatNormValue(FmgrInfo *procinfo, FmgrInfo *normalizeprocinfo, Oid collation, Datum *value, Vector * result)
 {
-	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
+	double		norm;
+
+	if (normalizeprocinfo != NULL)
+	{
+		*value = FunctionCall1Coll(normalizeprocinfo, collation, *value);
+		return;
+	}
+
+	if (procinfo == NULL)
+		return;
+
+	norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));

 	if (norm > 0)
 	{
@@ -89,11 +98,7 @@ IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * resul
 			result->x[i] = v->x[i] / norm;

 		*value = PointerGetDatum(result);
-
-		return true;
 	}
-
-	return false;
 }

 /*
--- a/src/vector.c
+++ b/src/vector.c
@@ -15,10 +15,6 @@
 #include "utils/numeric.h"
 #include "vector.h"

-#if PG_VERSION_NUM >= 160000
-#include "varatt.h"
-#endif
-
 #if PG_VERSION_NUM >= 120000
 #include "common/shortest_dec.h"
 #include "utils/float.h"
@@ -39,7 +35,6 @@ PG_MODULE_MAGIC;
 /*
 * Initialize index options and variables
 */
-PGDLLEXPORT void _PG_init(void);
 void
 _PG_init(void)
 {
@@ -105,23 +100,6 @@ CheckElement(float value)
 				 errmsg("infinite value not allowed in vector")));
 }

-/*
- * Allocate and initialize a new vector
- */
-Vector *
-InitVector(int dim)
-{
-	Vector	   *result;
-	int			size;
-
-	size = VECTOR_SIZE(dim);
-	result = (Vector *) palloc0(size);
-	SET_VARSIZE(result, size);
-	result->dim = dim;
-
-	return result;
-}
-
 /*
 * Check for whitespace, since array_isspace() is static
 */
@@ -755,16 +733,62 @@ vector_dims(PG_FUNCTION_ARGS)
 PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_norm);
 Datum
 vector_norm(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	float	   *ax = a->x;
+	float		norm = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		norm += ax[i] * ax[i];
+
+	PG_RETURN_FLOAT8(sqrt((double) norm));
+}
+
+/*
+ * Normalize a vector with the L2 norm
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(normalize_l2);
+Datum
+normalize_l2(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	float	   *ax = a->x;
 	double		norm = 0.0;
+#ifdef _MSC_VER
+	/* Fix precision on Windows */
+	double		normf;
+#else
+	float		normf;
+#endif
+	Vector	   *result;
+	float	   *rx;
+
+	result = InitVector(a->dim);
+	rx = result->x;

 	/* Auto-vectorized */
 	for (int i = 0; i < a->dim; i++)
 		norm += (double) ax[i] * (double) ax[i];

-	PG_RETURN_FLOAT8(sqrt(norm));
+	norm = sqrt(norm);
+	normf = norm;
+
+	if (normf > 0)
+	{
+		/* Auto-vectorized */
+		for (int i = 0, imax = a->dim; i < imax; i++)
+			rx[i] = ax[i] / normf;
+
+		/* Check for overflow */
+		for (int i = 0, imax = a->dim; i < imax; i++)
+		{
+			if (isinf(rx[i]))
+				float_overflow_error();
+		}
+	}
+
+	PG_RETURN_POINTER(result);
 }

 /*
--- a/src/vector.h
+++ b/src/vector.h
@@ -1,6 +1,12 @@
 #ifndef VECTOR_H
 #define VECTOR_H

+#include "postgres.h"
+
+#if PG_VERSION_NUM >= 160000
+#include "varatt.h"
+#endif
+
 #define VECTOR_MAX_DIM 16000

 #define VECTOR_SIZE(_dim)		(offsetof(Vector, x) + sizeof(float)*(_dim))
@@ -8,6 +14,9 @@
 #define PG_GETARG_VECTOR_P(x)	DatumGetVector(PG_GETARG_DATUM(x))
 #define PG_RETURN_VECTOR_P(x)	PG_RETURN_POINTER(x)

+/* Exported functions */
+PGDLLEXPORT void _PG_init(void);
+
 typedef struct Vector
 {
 	int32		vl_len_;		/* varlena header (do not touch directly!) */
@@ -16,8 +25,24 @@ typedef struct Vector
 	float		x[FLEXIBLE_ARRAY_MEMBER];
 }			Vector;

-Vector	   *InitVector(int dim);
 void		PrintVector(char *msg, Vector * vector);
 int			vector_cmp_internal(Vector * a, Vector * b);

+/*
+ * Allocate and initialize a new vector
+ */
+static inline Vector *
+InitVector(int dim)
+{
+	Vector	   *result;
+	int			size;
+
+	size = VECTOR_SIZE(dim);
+	result = (Vector *) palloc0(size);
+	SET_VARSIZE(result, size);
+	result->dim = dim;
+
+	return result;
+}
+
 #endif
--- a/test/expected/functions.out
+++ b/test/expected/functions.out
@@ -48,10 +48,34 @@ SELECT vector_norm('[0,1]');
           1
 (1 row)

-SELECT vector_norm('[3e37,4e37]')::real;
- vector_norm 
-------------
-       5e+37
+SELECT normalize_l2('[3,4]');
+ normalize_l2 
+--------------
+ [0.6,0.8]
+(1 row)
+
+SELECT normalize_l2('[3,0]');
+ normalize_l2 
+--------------
+ [1,0]
+(1 row)
+
+SELECT normalize_l2('[0,0.1]');
+ normalize_l2 
+--------------
+ [0,1]
+(1 row)
+
+SELECT normalize_l2('[0,0]');
+ normalize_l2 
+--------------
+ [0,0]
+(1 row)
+
+SELECT normalize_l2('[3e38]');
+ normalize_l2 
+--------------
+ [1]
 (1 row)

 SELECT l2_distance('[0,0]', '[3,4]');
--- a/test/expected/hnsw_cosine.out
+++ b/test/expected/hnsw_cosine.out
@@ -9,18 +9,19 @@ SELECT * FROM t ORDER BY val <=> '[3,3,3]';
 [1,1,1]
 [1,2,3]
 [1,2,4]
-(3 rows)
+ [0,0,0]
+(4 rows)

 SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
 count 
 -------
-     3
+     4
 (1 row)

 SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2;
 count 
 -------
-     3
+     4
 (1 row)

 DROP TABLE t;
--- a/test/expected/hnsw_l2.out
+++ b/test/expected/hnsw_l2.out
@@ -27,10 +27,4 @@ SELECT COUNT(*) FROM t;
     5
 (1 row)

-TRUNCATE t;
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
- val 
-----
-(0 rows)
-
 DROP TABLE t;
--- a/test/expected/hnsw_options.out
+++ b/test/expected/hnsw_options.out
@@ -1,26 +1,25 @@
+SET enable_seqscan = off;
 CREATE TABLE t (val vector(3));
-CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 1);
-ERROR:  value 1 out of bounds for option "m"
-DETAIL:  Valid values are between "2" and "100".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 3);
+ERROR:  value 3 out of bounds for option "m"
+DETAIL:  Valid values are between "4" and "100".
 CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 101);
 ERROR:  value 101 out of bounds for option "m"
-DETAIL:  Valid values are between "2" and "100".
-CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 3);
-ERROR:  value 3 out of bounds for option "ef_construction"
-DETAIL:  Valid values are between "4" and "1000".
+DETAIL:  Valid values are between "4" and "100".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 9);
+ERROR:  value 9 out of bounds for option "ef_construction"
+DETAIL:  Valid values are between "10" and "1000".
 CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 1001);
 ERROR:  value 1001 out of bounds for option "ef_construction"
-DETAIL:  Valid values are between "4" and "1000".
-CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 16, ef_construction = 31);
-ERROR:  ef_construction must be greater than or equal to 2 * m
+DETAIL:  Valid values are between "10" and "1000".
 SHOW hnsw.ef_search;
 hnsw.ef_search 
 ----------------
 40
 (1 row)

-SET hnsw.ef_search = 0;
-ERROR:  0 is outside the valid range for parameter "hnsw.ef_search" (1 .. 1000)
+SET hnsw.ef_search = 9;
+ERROR:  9 is outside the valid range for parameter "hnsw.ef_search" (10 .. 1000)
 SET hnsw.ef_search = 1001;
-ERROR:  1001 is outside the valid range for parameter "hnsw.ef_search" (1 .. 1000)
+ERROR:  1001 is outside the valid range for parameter "hnsw.ef_search" (10 .. 1000)
 DROP TABLE t;
--- a/test/expected/ivfflat_cosine.out
+++ b/test/expected/ivfflat_cosine.out
@@ -9,18 +9,19 @@ SELECT * FROM t ORDER BY val <=> '[3,3,3]';
 [1,1,1]
 [1,2,3]
 [1,2,4]
-(3 rows)
+ [0,0,0]
+(4 rows)

 SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
 count 
 -------
-     3
+     4
 (1 row)

 SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2;
 count 
 -------
-     3
+     4
 (1 row)

 DROP TABLE t;
--- a/test/expected/ivfflat_l2.out
+++ b/test/expected/ivfflat_l2.out
@@ -1,7 +1,7 @@
 SET enable_seqscan = off;
 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 = 1);
+CREATE INDEX ON t USING ivfflat (val) WITH (lists = 1);
 INSERT INTO t (val) VALUES ('[1,2,4]');
 SELECT * FROM t ORDER BY val <-> '[3,3,3]';
   val   
@@ -27,13 +27,4 @@ SELECT COUNT(*) FROM t;
     5
 (1 row)

-TRUNCATE t;
-NOTICE:  ivfflat index created with little data
-DETAIL:  This will cause low recall.
-HINT:  Drop the index until the table has more data.
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
- val 
-----
-(0 rows)
-
 DROP TABLE t;
--- a/test/expected/ivfflat_options.out
+++ b/test/expected/ivfflat_options.out
@@ -1,8 +1,9 @@
+SET enable_seqscan = off;
 CREATE TABLE t (val vector(3));
-CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 0);
+CREATE INDEX ON t USING ivfflat (val) WITH (lists = 0);
 ERROR:  value 0 out of bounds for option "lists"
 DETAIL:  Valid values are between "1" and "32768".
-CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 32769);
+CREATE INDEX ON t USING ivfflat (val) WITH (lists = 32769);
 ERROR:  value 32769 out of bounds for option "lists"
 DETAIL:  Valid values are between "1" and "32768".
 SHOW ivfflat.probes;
--- a/test/expected/ivfflat_unlogged.out
+++ b/test/expected/ivfflat_unlogged.out
@@ -1,7 +1,7 @@
 SET enable_seqscan = off;
 CREATE UNLOGGED 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 = 1);
+CREATE INDEX ON t USING ivfflat (val) WITH (lists = 1);
 SELECT * FROM t ORDER BY val <-> '[3,3,3]';
   val   
 ---------
--- a/test/sql/functions.sql
+++ b/test/sql/functions.sql
@@ -11,7 +11,12 @@ SELECT vector_dims('[1,2,3]');
 SELECT round(vector_norm('[1,1]')::numeric, 5);
 SELECT vector_norm('[3,4]');
 SELECT vector_norm('[0,1]');
-SELECT vector_norm('[3e37,4e37]')::real;
+
+SELECT normalize_l2('[3,4]');
+SELECT normalize_l2('[3,0]');
+SELECT normalize_l2('[0,0.1]');
+SELECT normalize_l2('[0,0]');
+SELECT normalize_l2('[3e38]');

 SELECT l2_distance('[0,0]', '[3,4]');
 SELECT l2_distance('[0,0]', '[0,1]');
--- a/test/sql/hnsw_l2.sql
+++ b/test/sql/hnsw_l2.sql
@@ -10,7 +10,4 @@ SELECT * FROM t ORDER BY val <-> '[3,3,3]';
 SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
 SELECT COUNT(*) FROM t;

-TRUNCATE t;
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-
 DROP TABLE t;
--- a/test/sql/hnsw_options.sql
+++ b/test/sql/hnsw_options.sql
@@ -1,13 +1,14 @@
+SET enable_seqscan = off;
+
 CREATE TABLE t (val vector(3));
-CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 1);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 3);
 CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 101);
-CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 3);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 9);
 CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 1001);
-CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 16, ef_construction = 31);

 SHOW hnsw.ef_search;

-SET hnsw.ef_search = 0;
+SET hnsw.ef_search = 9;
 SET hnsw.ef_search = 1001;

 DROP TABLE t;
--- a/test/sql/ivfflat_l2.sql
+++ b/test/sql/ivfflat_l2.sql
@@ -2,7 +2,7 @@ SET enable_seqscan = off;

 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 = 1);
+CREATE INDEX ON t USING ivfflat (val) WITH (lists = 1);

 INSERT INTO t (val) VALUES ('[1,2,4]');

@@ -10,7 +10,4 @@ SELECT * FROM t ORDER BY val <-> '[3,3,3]';
 SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
 SELECT COUNT(*) FROM t;

-TRUNCATE t;
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-
 DROP TABLE t;
--- a/test/sql/ivfflat_options.sql
+++ b/test/sql/ivfflat_options.sql
@@ -1,6 +1,8 @@
+SET enable_seqscan = off;
+
 CREATE TABLE t (val vector(3));
-CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 0);
-CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 32769);
+CREATE INDEX ON t USING ivfflat (val) WITH (lists = 0);
+CREATE INDEX ON t USING ivfflat (val) WITH (lists = 32769);

 SHOW ivfflat.probes;

--- a/test/sql/ivfflat_unlogged.sql
+++ b/test/sql/ivfflat_unlogged.sql
@@ -2,7 +2,7 @@ SET enable_seqscan = off;

 CREATE UNLOGGED 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 = 1);
+CREATE INDEX ON t USING ivfflat (val) WITH (lists = 1);

 SELECT * FROM t ORDER BY val <-> '[3,3,3]';

--- a/test/t/001_ivfflat_wal.pl
+++ b/test/t/001_ivfflat_wal.pl
@@ -26,8 +26,7 @@ sub test_index_replay
 	  or die "Timed out while waiting for replica 1 to catch up";

 	my @r = ();
-	for (1 .. $dim)
-	{
+	for (1 .. $dim) {
 		push(@r, rand());
 	}
 	my $sql = join(",", @r);
@@ -53,13 +52,11 @@ my $array_sql = join(",", ('random()') x $dim);
 # Initialize primary node
 $node_primary = get_new_node('primary');
 $node_primary->init(allows_streaming => 1);
-if ($dim > 32)
-{
+if ($dim > 32) {
 	# TODO use wal_keep_segments for Postgres < 13
 	$node_primary->append_conf('postgresql.conf', qq(wal_keep_size = 1GB));
 }
-if ($dim > 1500)
-{
+if ($dim > 1500) {
 	$node_primary->append_conf('postgresql.conf', qq(maintenance_work_mem = 128MB));
 }
 $node_primary->start;
@@ -70,7 +67,8 @@ $node_primary->backup($backup_name);

 # Create streaming replica linking to primary
 $node_replica = get_new_node('replica');
-$node_replica->init_from_backup($node_primary, $backup_name, has_streaming => 1);
+$node_replica->init_from_backup($node_primary, $backup_name,
+	has_streaming => 1);
 $node_replica->start;

 # Create ivfflat index on primary
@@ -79,7 +77,7 @@ $node_primary->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));
 $node_primary->safe_psql("postgres",
 	"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
 );
-$node_primary->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_l2_ops);");
+$node_primary->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v);");

 # Test that queries give same result
 test_index_replay('initial');
--- a/test/t/002_ivfflat_vacuum.pl
+++ b/test/t/002_ivfflat_vacuum.pl
@@ -7,8 +7,7 @@ use Test::More;
 my $dim = 3;

 my @r = ();
-for (1 .. $dim)
-{
+for (1 .. $dim) {
 	my $v = int(rand(1000)) + 1;
 	push(@r, "i % $v");
 }
@@ -25,7 +24,7 @@ $node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
 $node->safe_psql("postgres",
 	"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
 );
-$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_l2_ops);");
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v);");

 # Get size
 my $size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");
--- a/test/t/003_ivfflat_recall.pl
+++ b/test/t/003_ivfflat_recall.pl
@@ -22,8 +22,7 @@ sub test_recall
 	));
 	like($explain, qr/Index Scan using idx on tst/);

-	for my $i (0 .. $#queries)
-	{
+	for my $i (0 .. $#queries) {
 		my $actual = $node->safe_psql("postgres", qq(
 			SET enable_seqscan = off;
 			SET ivfflat.probes = $probes;
@@ -34,10 +33,8 @@ sub test_recall

 		my @expected_ids = split("\n", $expected[$i]);

-		foreach (@expected_ids)
-		{
-			if (exists($actual_set{$_}))
-			{
+		foreach (@expected_ids) {
+			if (exists($actual_set{$_})) {
 				$correct++;
 			}
 			$total++;
@@ -60,8 +57,7 @@ $node->safe_psql("postgres",
 );

 # Generate queries
-for (1 .. 20)
-{
+for (1..20) {
 	my $r1 = rand();
 	my $r2 = rand();
 	my $r3 = rand();
@@ -70,21 +66,26 @@ for (1 .. 20)

 # Check each index type
 my @operators = ("<->", "<#>", "<=>");
-my @opclasses = ("vector_l2_ops", "vector_ip_ops", "vector_cosine_ops");

-for my $i (0 .. $#operators)
-{
-	my $operator = $operators[$i];
-	my $opclass = $opclasses[$i];
+foreach (@operators) {
+	my $operator = $_;

 	# Get exact results
 	@expected = ();
-	foreach (@queries)
-	{
+	foreach (@queries) {
 		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
 		push(@expected, $res);
 	}

+	my $opclass;
+	if ($operator eq "<->") {
+		$opclass = "vector_l2_ops";
+	} elsif ($operator eq "<#>") {
+		$opclass = "vector_ip_ops";
+	} else {
+		$opclass = "vector_cosine_ops";
+	}
+
 	# Build index serially
 	$node->safe_psql("postgres", qq(
 		SET max_parallel_maintenance_workers = 0;
@@ -92,14 +93,13 @@ for my $i (0 .. $#operators)
 	));

 	# Test approximate results
-	if ($operator ne "<#>")
-	{
+	if ($operator ne "<#>") {
 		# TODO fix test
-		test_recall(1, 0.71, $operator);
+		test_recall(1, 0.75, $operator);
 		test_recall(10, 0.95, $operator);
 	}
 	# Account for equal distances
-	test_recall(100, 0.9925, $operator);
+	test_recall(100, 0.995, $operator);

 	$node->safe_psql("postgres", "DROP INDEX idx;");

@@ -113,14 +113,13 @@ for my $i (0 .. $#operators)
 	like($stderr, qr/using \d+ parallel workers/);

 	# Test approximate results
-	if ($operator ne "<#>")
-	{
+	if ($operator ne "<#>") {
 		# TODO fix test
-		test_recall(1, 0.71, $operator);
+		test_recall(1, 0.75, $operator);
 		test_recall(10, 0.95, $operator);
 	}
 	# Account for equal distances
-	test_recall(100, 0.9925, $operator);
+	test_recall(100, 0.995, $operator);

 	$node->safe_psql("postgres", "DROP INDEX idx;");
 }
--- a/test/t/004_ivfflat_centers.pl
+++ b/test/t/004_ivfflat_centers.pl
@@ -20,7 +20,7 @@ sub test_centers
 {
 	my ($lists, $min) = @_;

-	my ($ret, $stdout, $stderr) = $node->psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_l2_ops) WITH (lists = $lists);");
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", "CREATE INDEX ON tst USING ivfflat (v) WITH (lists = $lists);");
 	is($ret, 0, $stderr);
 }

--- a/test/t/005_ivfflat_query_recall.pl
+++ b/test/t/005_ivfflat_query_recall.pl
@@ -18,21 +18,24 @@ $node->safe_psql("postgres",

 # Check each index type
 my @operators = ("<->", "<#>", "<=>");
-my @opclasses = ("vector_l2_ops", "vector_ip_ops", "vector_cosine_ops");
-
-for my $i (0 .. $#operators)
-{
-	my $operator = $operators[$i];
-	my $opclass = $opclasses[$i];
+foreach (@operators) {
+	my $operator = $_;

 	# Add index
+	my $opclass;
+	if ($operator eq "<->") {
+		$opclass = "vector_l2_ops";
+	} elsif ($operator eq "<#>") {
+		$opclass = "vector_ip_ops";
+	} else {
+		$opclass = "vector_cosine_ops";
+	}
 	$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v $opclass);");

 	# Test 100% recall
-	for (1 .. 20)
-	{
-		my $id = int(rand() * 100000);
-		my $query = $node->safe_psql("postgres", "SELECT v FROM tst WHERE i = $id;");
+	for (1..20) {
+		my $i = int(rand() * 100000);
+		my $query = $node->safe_psql("postgres", "SELECT v FROM tst WHERE i = $i;");
 		my $res = $node->safe_psql("postgres", qq(
 			SET enable_seqscan = off;
 			SELECT v FROM tst ORDER BY v <-> '$query' LIMIT 1;
--- a/test/t/006_ivfflat_lists.pl
+++ b/test/t/006_ivfflat_lists.pl
@@ -16,8 +16,8 @@ $node->safe_psql("postgres",
 	"INSERT INTO tst SELECT ARRAY[random(), random(), random()] FROM generate_series(1, 100000) i;"
 );

-$node->safe_psql("postgres", "CREATE INDEX lists50 ON tst USING ivfflat (v vector_l2_ops) WITH (lists = 50);");
-$node->safe_psql("postgres", "CREATE INDEX lists100 ON tst USING ivfflat (v vector_l2_ops) WITH (lists = 100);");
+$node->safe_psql("postgres", "CREATE INDEX lists50 ON tst USING ivfflat (v) WITH (lists = 50);");
+$node->safe_psql("postgres", "CREATE INDEX lists100 ON tst USING ivfflat (v) WITH (lists = 100);");

 # Test prefers more lists
 my $res = $node->safe_psql("postgres", "EXPLAIN SELECT v FROM tst ORDER BY v <-> '[0.5,0.5,0.5]' LIMIT 10;");
@@ -26,7 +26,7 @@ unlike($res, qr/lists50/);

 # Test errors with too much memory
 my ($ret, $stdout, $stderr) = $node->psql("postgres",
-	"CREATE INDEX lists10000 ON tst USING ivfflat (v vector_l2_ops) WITH (lists = 10000);"
+	"CREATE INDEX lists10000 ON tst USING ivfflat (v) WITH (lists = 10000);"
 );
 like($stderr, qr/memory required is/);

--- a/test/t/007_ivfflat_inserts.pl
+++ b/test/t/007_ivfflat_inserts.pl
@@ -19,7 +19,7 @@ $node->safe_psql("postgres", "CREATE TABLE tst (v vector($dim));");
 $node->safe_psql("postgres",
 	"INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
 );
-$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_l2_ops);");
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v);");

 $node->pgbench(
 	"--no-vacuum --client=5 --transactions=100",
@@ -28,7 +28,7 @@ $node->pgbench(
 	[qr{^$}],
 	"concurrent INSERTs",
 	{
-		"007_ivfflat_inserts" => "INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 10) i;"
+		"007_inserts" => "INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 10) i;"
 	}
 );

--- a/test/t/008_aggregates.pl
+++ b/test/t/008_aggregates.pl
@@ -30,8 +30,7 @@ sub test_aggregate

 	# Test matches real for avg
 	# Cannot test sum since sum(real) varies between calls
-	if ($agg eq 'avg')
-	{
+	if ($agg eq 'avg') {
 		my $r1 = $node->safe_psql("postgres", "SELECT $agg(r1)::float4 FROM tst;");
 		my $r2 = $node->safe_psql("postgres", "SELECT $agg(r2)::float4 FROM tst;");
 		my $r3 = $node->safe_psql("postgres", "SELECT $agg(r3)::float4 FROM tst;");
--- a/test/t/010_hnsw_wal.pl
+++ b/test/t/010_hnsw_wal.pl
@@ -26,8 +26,7 @@ sub test_index_replay
 	  or die "Timed out while waiting for replica 1 to catch up";

 	my @r = ();
-	for (1 .. $dim)
-	{
+	for (1 .. $dim) {
 		push(@r, rand());
 	}
 	my $sql = join(",", @r);
@@ -53,13 +52,11 @@ my $array_sql = join(",", ('random()') x $dim);
 # Initialize primary node
 $node_primary = get_new_node('primary');
 $node_primary->init(allows_streaming => 1);
-if ($dim > 32)
-{
+if ($dim > 32) {
 	# TODO use wal_keep_segments for Postgres < 13
 	$node_primary->append_conf('postgresql.conf', qq(wal_keep_size = 1GB));
 }
-if ($dim > 1500)
-{
+if ($dim > 1500) {
 	$node_primary->append_conf('postgresql.conf', qq(maintenance_work_mem = 128MB));
 }
 $node_primary->start;
@@ -70,7 +67,8 @@ $node_primary->backup($backup_name);

 # Create streaming replica linking to primary
 $node_replica = get_new_node('replica');
-$node_replica->init_from_backup($node_primary, $backup_name, has_streaming => 1);
+$node_replica->init_from_backup($node_primary, $backup_name,
+	has_streaming => 1);
 $node_replica->start;

 # Create hnsw index on primary
--- a/test/t/011_hnsw_vacuum.pl
+++ b/test/t/011_hnsw_vacuum.pl
@@ -7,8 +7,7 @@ use Test::More;
 my $dim = 3;

 my @r = ();
-for (1 .. $dim)
-{
+for (1 .. $dim) {
 	my $v = int(rand(1000)) + 1;
 	push(@r, "i % $v");
 }
@@ -23,7 +22,7 @@ $node->start;
 $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, 10000) i;"
+	"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
 );
 $node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v vector_l2_ops);");

@@ -34,21 +33,11 @@ my $size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_id
 $node->safe_psql("postgres", "DELETE FROM tst;");
 $node->safe_psql("postgres", "VACUUM tst;");
 $node->safe_psql("postgres",
-	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
+	"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
 );

 # Check size
-# May increase some due to different levels
 my $new_size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");
-cmp_ok($new_size, "<=", $size * 1.02, "size does not increase too much");
-
-# Delete all but one
-$node->safe_psql("postgres", "DELETE FROM tst WHERE i != 123;");
-$node->safe_psql("postgres", "VACUUM tst;");
-my $res = $node->safe_psql("postgres", qq(
-	SET enable_seqscan = off;
-	SELECT i FROM tst ORDER BY v <-> '[0,0,0]' LIMIT 10;
-));
-is($res, 123);
+cmp_ok($new_size, "<=", $size * 1.01, "size does not increase too much");

 done_testing();
--- a/test/t/012_hnsw_build_recall.pl
+++ b/test/t/012_hnsw_build_recall.pl
@@ -21,8 +21,7 @@ sub test_recall
 	));
 	like($explain, qr/Index Scan/);

-	for my $i (0 .. $#queries)
-	{
+	for my $i (0 .. $#queries) {
 		my $actual = $node->safe_psql("postgres", qq(
 			SET enable_seqscan = off;
 			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
@@ -32,10 +31,8 @@ sub test_recall

 		my @expected_ids = split("\n", $expected[$i]);

-		foreach (@expected_ids)
-		{
-			if (exists($actual_set{$_}))
-			{
+		foreach (@expected_ids) {
+			if (exists($actual_set{$_})) {
 				$correct++;
 			}
 			$total++;
@@ -58,8 +55,7 @@ $node->safe_psql("postgres",
 );

 # Generate queries
-for (1 .. 20)
-{
+for (1..20) {
 	my $r1 = rand();
 	my $r2 = rand();
 	my $r3 = rand();
@@ -68,26 +64,33 @@ for (1 .. 20)

 # Check each index type
 my @operators = ("<->", "<#>", "<=>");
-my @opclasses = ("vector_l2_ops", "vector_ip_ops", "vector_cosine_ops");

-for my $i (0 .. $#operators)
-{
-	my $operator = $operators[$i];
-	my $opclass = $opclasses[$i];
+foreach (@operators) {
+	my $operator = $_;

 	# Get exact results
 	@expected = ();
-	foreach (@queries)
-	{
+	foreach (@queries) {
 		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
 		push(@expected, $res);
 	}

 	# Add index
+	my $opclass;
+	if ($operator eq "<->") {
+		$opclass = "vector_l2_ops";
+	} elsif ($operator eq "<#>") {
+		$opclass = "vector_ip_ops";
+	} else {
+		$opclass = "vector_cosine_ops";
+	}
 	$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v $opclass);");

-	my $min = $operator eq "<#>" ? 0.80 : 0.99;
-	test_recall($min, $operator);
+	if ($operator eq "<#>") {
+		test_recall(0.80, $operator);
+	} else {
+		test_recall(0.99, $operator);
+	}
 }

 done_testing();
--- a/test/t/013_hnsw_insert_recall.pl
+++ b/test/t/013_hnsw_insert_recall.pl
@@ -21,8 +21,7 @@ sub test_recall
 	));
 	like($explain, qr/Index Scan/);

-	for my $i (0 .. $#queries)
-	{
+	for my $i (0 .. $#queries) {
 		my $actual = $node->safe_psql("postgres", qq(
 			SET enable_seqscan = off;
 			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
@@ -32,10 +31,8 @@ sub test_recall

 		my @expected_ids = split("\n", $expected[$i]);

-		foreach (@expected_ids)
-		{
-			if (exists($actual_set{$_}))
-			{
+		foreach (@expected_ids) {
+			if (exists($actual_set{$_})) {
 				$correct++;
 			}
 			$total++;
@@ -52,11 +49,10 @@ $node->start;

 # Create table
 $node->safe_psql("postgres", "CREATE EXTENSION vector;");
-$node->safe_psql("postgres", "CREATE TABLE tst (i serial, v vector(3));");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector(3));");

 # Generate queries
-for (1 .. 20)
-{
+for (1..20) {
 	my $r1 = rand();
 	my $r2 = rand();
 	my $r3 = rand();
@@ -65,32 +61,28 @@ for (1 .. 20)

 # Check each index type
 my @operators = ("<->", "<#>", "<=>");
-my @opclasses = ("vector_l2_ops", "vector_ip_ops", "vector_cosine_ops");

-for my $i (0 .. $#operators)
-{
-	my $operator = $operators[$i];
-	my $opclass = $opclasses[$i];
+foreach (@operators) {
+	my $operator = $_;

 	# Add index
+	my $opclass;
+	if ($operator eq "<->") {
+		$opclass = "vector_l2_ops";
+	} elsif ($operator eq "<#>") {
+		$opclass = "vector_ip_ops";
+	} else {
+		$opclass = "vector_cosine_ops";
+	}
 	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v $opclass);");

-	# Use concurrent inserts
-	$node->pgbench(
-		"--no-vacuum --client=10 --transactions=1000",
-		0,
-		[qr{actually processed}],
-		[qr{^$}],
-		"concurrent INSERTs",
-		{
-			"013_hnsw_insert_recall_$opclass" => "INSERT INTO tst (v) VALUES (ARRAY[random(), random(), random()]);"
-		}
+	$node->safe_psql("postgres",
+		"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 10000) i;"
 	);

 	# Get exact results
 	@expected = ();
-	foreach (@queries)
-	{
+	foreach (@queries) {
 		my $res = $node->safe_psql("postgres", qq(
 			SET enable_indexscan = off;
 			SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;
@@ -98,8 +90,11 @@ for my $i (0 .. $#operators)
 		push(@expected, $res);
 	}

-	my $min = $operator eq "<#>" ? 0.80 : 0.99;
-	test_recall($min, $operator);
+	if ($operator eq "<#>") {
+		test_recall(0.80, $operator);
+	} else {
+		test_recall(0.99, $operator);
+	}

 	$node->safe_psql("postgres", "DROP INDEX idx;");
 	$node->safe_psql("postgres", "TRUNCATE tst;");
--- a/test/t/014_hnsw_inserts.pl
+++ b/test/t/014_hnsw_inserts.pl
@@ -17,8 +17,22 @@ $node->start;
 # Create table and index
 $node->safe_psql("postgres", "CREATE EXTENSION vector;");
 $node->safe_psql("postgres", "CREATE TABLE tst (v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 100) i;"
+);
 $node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v vector_l2_ops);");

+$node->pgbench(
+	"--no-vacuum --client=5 --transactions=100",
+	0,
+	[qr{actually processed}],
+	[qr{^$}],
+	"concurrent INSERTs",
+	{
+		"007_inserts" => "INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 10) i;"
+	}
+);
+
 sub idx_scan
 {
 	# Stats do not update instantaneously
@@ -27,48 +41,18 @@ sub idx_scan
 	$node->safe_psql("postgres", "SELECT idx_scan FROM pg_stat_user_indexes WHERE indexrelid = 'tst_v_idx'::regclass;");
 }

-for my $i (1 .. 20)
-{
-	$node->pgbench(
-		"--no-vacuum --client=10 --transactions=1",
-		0,
-		[qr{actually processed}],
-		[qr{^$}],
-		"concurrent INSERTs",
-		{
-			"014_hnsw_inserts_$i" => "INSERT INTO tst VALUES (ARRAY[$array_sql]);"
-		}
-	);
+my $expected = 100 + 5 * 100 * 10;

-	my $count = $node->safe_psql("postgres", qq(
-		SET enable_seqscan = off;
-		SELECT COUNT(*) FROM (SELECT v FROM tst ORDER BY v <-> (SELECT v FROM tst LIMIT 1)) t;
-	));
-	is($count, 10);
+my $count = $node->safe_psql("postgres", "SELECT COUNT(*) FROM tst;");
+is($count, $expected);
+is(idx_scan(), 0);

-	$node->safe_psql("postgres", "TRUNCATE tst;");
-}
-
-$node->pgbench(
-	"--no-vacuum --client=20 --transactions=5",
-	0,
-	[qr{actually processed}],
-	[qr{^$}],
-	"concurrent INSERTs",
-	{
-		"014_hnsw_inserts" => "INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 10) i;"
-	}
-);
-
-my $count = $node->safe_psql("postgres", qq(
+$count = $node->safe_psql("postgres", qq(
 	SET enable_seqscan = off;
-	SET hnsw.ef_search = 1000;
+	SET hnsw.ef_search = 400;
 	SELECT COUNT(*) FROM (SELECT v FROM tst ORDER BY v <-> (SELECT v FROM tst LIMIT 1)) t;
 ));
-# Elements may lose all incoming connections with the HNSW algorithm
-# Vacuuming can fix this if one of the elements neighbors is deleted
-cmp_ok($count, ">=", 997);
-
-is(idx_scan(), 21);
+is($count, 400);
+is(idx_scan(), 1);

 done_testing();
--- a/test/t/015_hnsw_duplicates.pl
+++ b/test/t/015_hnsw_duplicates.pl
@@ -1,58 +0,0 @@
-use strict;
-use warnings;
-use PostgresNode;
-use TestLib;
-use Test::More;
-
-# Initialize node
-my $node = get_new_node('node');
-$node->init;
-$node->start;
-
-# Create table
-$node->safe_psql("postgres", "CREATE EXTENSION vector;");
-$node->safe_psql("postgres", "CREATE TABLE tst (v vector(3));");
-
-sub insert_vectors
-{
-	for my $i (1 .. 20)
-	{
-		$node->safe_psql("postgres", "INSERT INTO tst VALUES ('[1,1,1]');");
-	}
-}
-
-sub test_duplicates
-{
-	my $res = $node->safe_psql("postgres", qq(
-		SET enable_seqscan = off;
-		SET hnsw.ef_search = 1;
-		SELECT COUNT(*) FROM (SELECT * FROM tst ORDER BY v <-> '[1,1,1]') t;
-	));
-	is($res, 10);
-}
-
-# Test duplicates with build
-insert_vectors();
-$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v vector_l2_ops);");
-test_duplicates();
-
-# Reset
-$node->safe_psql("postgres", "TRUNCATE tst;");
-
-# Test duplicates with inserts
-insert_vectors();
-test_duplicates();
-
-# Test fallback path for inserts
-$node->pgbench(
-	"--no-vacuum --client=5 --transactions=100",
-	0,
-	[qr{actually processed}],
-	[qr{^$}],
-	"concurrent INSERTs",
-	{
-		"015_hnsw_duplicates" => "INSERT INTO tst VALUES ('[1,1,1]');"
-	}
-);
-
-done_testing();
--- a/test/t/016_hnsw_vacuum_recall.pl
+++ b/test/t/016_hnsw_vacuum_recall.pl
@@ -1,97 +0,0 @@
-use strict;
-use warnings;
-use PostgresNode;
-use TestLib;
-use Test::More;
-
-my $node;
-my @queries = ();
-my @expected;
-my $limit = 20;
-
-sub test_recall
-{
-	my ($min, $ef_search, $test_name) = @_;
-	my $correct = 0;
-	my $total = 0;
-
-	my $explain = $node->safe_psql("postgres", qq(
-		SET enable_seqscan = off;
-		SET hnsw.ef_search = $ef_search;
-		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$queries[0]' LIMIT $limit;
-	));
-	like($explain, qr/Index Scan/);
-
-	for my $i (0 .. $#queries)
-	{
-		my $actual = $node->safe_psql("postgres", qq(
-			SET enable_seqscan = off;
-			SET hnsw.ef_search = $ef_search;
-			SELECT i FROM tst ORDER BY v <-> '$queries[$i]' LIMIT $limit;
-		));
-		my @actual_ids = split("\n", $actual);
-		my %actual_set = map { $_ => 1 } @actual_ids;
-
-		my @expected_ids = split("\n", $expected[$i]);
-
-		foreach (@expected_ids)
-		{
-			if (exists($actual_set{$_}))
-			{
-				$correct++;
-			}
-			$total++;
-		}
-	}
-
-	cmp_ok($correct / $total, ">=", $min, $test_name);
-}
-
-# Initialize node
-$node = get_new_node('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));");
-$node->safe_psql("postgres", "ALTER TABLE tst SET (autovacuum_enabled = false);");
-$node->safe_psql("postgres",
-	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 10000) i;"
-);
-
-# Add index
-$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v vector_l2_ops) WITH (m = 4, ef_construction = 8);");
-
-# Delete data
-$node->safe_psql("postgres", "DELETE FROM tst WHERE i > 2500;");
-
-# Generate queries
-for (1 .. 20)
-{
-	my $r1 = rand();
-	my $r2 = rand();
-	my $r3 = rand();
-	push(@queries, "[$r1,$r2,$r3]");
-}
-
-# Get exact results
-@expected = ();
-foreach (@queries)
-{
-	my $res = $node->safe_psql("postgres", qq(
-		SET enable_indexscan = off;
-		SELECT i FROM tst ORDER BY v <-> '$_' LIMIT $limit;
-	));
-	push(@expected, $res);
-}
-
-test_recall(0.20, $limit, "before vacuum");
-test_recall(0.95, 100, "before vacuum");
-
-# TODO test concurrent inserts with vacuum
-$node->safe_psql("postgres", "VACUUM tst;");
-
-test_recall(0.95, $limit, "after vacuum");
-
-done_testing();
Author	SHA1	Message	Date
Andrew Kane	a5bb59d9f6	Use normalize_l2 for ivfflat	2023-10-16 17:56:50 -07:00
Andrew Kane	dd609f200b	Merge branch 'normalize_l2' into hnsw-normalize	2023-10-16 17:09:20 -07:00
Andrew Kane	9514c152bc	Fixed precision on Windows	2023-10-16 17:08:19 -07:00
Andrew Kane	b391e40765	Always normalize	2023-10-16 16:53:40 -07:00
Andrew Kane	0054a9c40a	Use normalize_l2 for normalization	2023-10-16 16:42:40 -07:00
Andrew Kane	9ed7e63fb7	Prevent overflow at cost to speed	2023-08-09 12:36:29 -07:00
Andrew Kane	47e361a93d	Added normalize_l2 function	2023-08-09 11:29:14 -07:00