Use DSA

Spinlocks should be held only for a few instructions, for multiple
reasons:

- You have to be very careful not to elog() out while holding a
  spinlock, because there is no mechanism to release the spinlock on
  error.

- Waiters can waste a lot of cycles spinning if the lock is
  contended. I you wait on a spinlock for too long, the PostgreSQL
  implementation will actually PANIC, see s_lock_stuck().

The flushLock is particularly problematic. It is held in exclusive
mode, which means it holds a spinlock, over the call to
FlushPages(). FlushPages() performs lots of I/O so it can take a very
long time (>= minutes), and can also easily error out for various
reasons.

allocatorLock would perhaps be OK as a spinlocks, but even that feels
a bit heavy, so I converted that to an LWLock, too.

entryLock is usually held for a very short time, in shared mode, so
that would be fine as a spinlock. However, in the rare case that the
entry point is updated, it's held for a very long time. An LWLock used
in shared mode is about as fast a spinlock, that path is pretty
heavily optimized.

I think we have some problems with the per-element spinlocks too. In
HnswUpdateNeighborPagesInMemory(), it's held over a call to
HnswUpdateConnection(), but HnswUpdateConnection() can error out at
least in case of an out-of-memory error (it uses lappend(), which
calls palloc()). It also calls the distance function, and I don't
think they are guaranteed to be ereport-free either. However, I didn't
address that in this PR, it needs a bit more thinking.

.github/workflows/build.yml

@@ -62,7 +62,7 @@ jobs:
           wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_14_5.tar.gz
           tar xf REL_14_5.tar.gz
       - run: make prove_installcheck PROVE_FLAGS="-I ./postgres-REL_14_5/src/test/perl" PERL5LIB="/Users/runner/perl5/lib/perl5"
-      - run: make clean && /usr/local/opt/llvm@15/bin/scan-build --status-bugs make
+      - run: make clean && /usr/local/opt/llvm@15/bin/scan-build --status-bugs make PG_CFLAGS="-DUSE_ASSERT_CHECKING"
   windows:
     runs-on: windows-latest
     if: ${{ !startsWith(github.ref_name, 'mac') }}

CHANGELOG.md

@@ -1,7 +1,8 @@
 ## 0.5.2 (unreleased)
 
 - Improved performance of HNSW
-- Added support for on-disk parallel index builds for HNSW
+- Added support for parallel index builds for HNSW
+- Reduced memory usage for HNSW index builds
 - Reduced WAL generation for HNSW index builds
 - Fixed `invalid memory alloc request size` error with HNSW index build
 

README.md

@@ -161,8 +161,97 @@ You can add an index to use approximate nearest neighbor search, which trades so
 
 Supported index types are:
 
-- [IVFFlat](#ivfflat)
 - [HNSW](#hnsw) - added in 0.5.0
+- [IVFFlat](#ivfflat)
+
+## HNSW
+
+An HNSW index creates a multilayer graph. It has better query performance than IVFFlat (in terms of speed-recall tradeoff), but has slower build times and uses more memory. Also, an index can be created without any data in the table since there isn’t a training step like IVFFlat.
+
+Add an index for each distance function you want to use.
+
+L2 distance
+
+```sql
+CREATE INDEX ON items USING hnsw (embedding vector_l2_ops);
+```
+
+Inner product
+
+```sql
+CREATE INDEX ON items USING hnsw (embedding vector_ip_ops);
+```
+
+Cosine distance
+
+```sql
+CREATE INDEX ON items USING hnsw (embedding vector_cosine_ops);
+```
+
+Vectors with up to 2,000 dimensions can be indexed.
+
+### Index Options
+
+Specify HNSW parameters
+
+- `m` - the max number of connections per layer (16 by default)
+- `ef_construction` - the size of the dynamic candidate list for constructing the graph (64 by default)
+
+```sql
+CREATE INDEX ON items USING hnsw (embedding vector_l2_ops) WITH (m = 16, ef_construction = 64);
+```
+
+A higher value of `ef_construction` provides better recall at the cost of index build time / insert speed.
+
+### Query Options
+
+Specify the size of the dynamic candidate list for search (40 by default)
+
+```sql
+SET hnsw.ef_search = 100;
+```
+
+A higher value provides better recall at the cost of speed.
+
+Use `SET LOCAL` inside a transaction to set it for a single query
+
+```sql
+BEGIN;
+SET LOCAL hnsw.ef_search = 100;
+SELECT ...
+COMMIT;
+```
+
+### Index Build Time
+
+Indexes build significantly faster when the graph fits into `maintenance_work_mem`
+
+```sql
+SET maintenance_work_mem = '8GB';
+```
+
+A notice is shown when the graph no longer fits
+
+```text
+NOTICE:  hnsw graph no longer fits into maintenance_work_mem after 100000 tuples
+DETAIL:  Building will take significantly more time.
+HINT:  Increase maintenance_work_mem to speed up builds.
+```
+
+Note: Do not set `maintenance_work_mem` so high that it exhausts the memory on the server
+
+### Indexing Progress
+
+Check [indexing progress](https://www.postgresql.org/docs/current/progress-reporting.html#CREATE-INDEX-PROGRESS-REPORTING) with Postgres 12+
+
+```sql
+SELECT phase, round(100.0 * blocks_done / nullif(blocks_total, 0), 1) AS "%" FROM pg_stat_progress_create_index;
+```
+
+The phases for HNSW are:
+
+1. `initializing`
+2. `loading tuples`
 
 ## IVFFlat
 
@@ -232,77 +321,6 @@ The phases for IVFFlat are:
 
 Note: `%` is only populated during the `loading tuples` phase
 
-## HNSW
-
-An HNSW index creates a multilayer graph. It has slower build times and uses more memory than IVFFlat, but has better query performance (in terms of speed-recall tradeoff). There’s no training step like IVFFlat, so the index can be created without any data in the table.
-
-Add an index for each distance function you want to use.
-
-L2 distance
-
-```sql
-CREATE INDEX ON items USING hnsw (embedding vector_l2_ops);
-```
-
-Inner product
-
-```sql
-CREATE INDEX ON items USING hnsw (embedding vector_ip_ops);
-```
-
-Cosine distance
-
-```sql
-CREATE INDEX ON items USING hnsw (embedding vector_cosine_ops);
-```
-
-Vectors with up to 2,000 dimensions can be indexed.
-
-### Index Options
-
-Specify HNSW parameters
-
-- `m` - the max number of connections per layer (16 by default)
-- `ef_construction` - the size of the dynamic candidate list for constructing the graph (64 by default)
-
-```sql
-CREATE INDEX ON items USING hnsw (embedding vector_l2_ops) WITH (m = 16, ef_construction = 64);
-```
-
-A higher value of `ef_construction` provides better recall at the cost of index build time / insert speed.
-
-### Query Options
-
-Specify the size of the dynamic candidate list for search (40 by default)
-
-```sql
-SET hnsw.ef_search = 100;
-```
-
-A higher value provides better recall at the cost of speed.
-
-Use `SET LOCAL` inside a transaction to set it for a single query
-
-```sql
-BEGIN;
-SET LOCAL hnsw.ef_search = 100;
-SELECT ...
-COMMIT;
-```
-
-### Indexing Progress
-
-Check [indexing progress](https://www.postgresql.org/docs/current/progress-reporting.html#CREATE-INDEX-PROGRESS-REPORTING) with Postgres 12+
-
-```sql
-SELECT phase, round(100.0 * blocks_done / nullif(blocks_total, 0), 1) AS "%" FROM pg_stat_progress_create_index;
-```
-
-The phases for HNSW are:
-
-1. `initializing`
-2. `loading tuples`
-
 ## Filtering
 
 There are a few ways to index nearest neighbor queries with a `WHERE` clause
@@ -320,8 +338,7 @@ CREATE INDEX ON items (category_id);
 Or a [partial index](https://www.postgresql.org/docs/current/indexes-partial.html) on the vector column for approximate search
 
 ```sql
-CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 100)
-    WHERE (category_id = 123);
+CREATE INDEX ON items USING hnsw (embedding vector_l2_ops) WHERE (category_id = 123);
 ```
 
 Use [partitioning](https://www.postgresql.org/docs/current/ddl-partitioning.html) for approximate search on many different values of the `WHERE` columns
@@ -571,10 +588,10 @@ If compilation fails with `fatal error: postgres.h: No such file or directory`,
 For Ubuntu and Debian, use:
 
 ```sh
-sudo apt install postgresql-server-dev-15
+sudo apt install postgresql-server-dev-16
 ```
 
-Note: Replace `15` with your Postgres server version
+Note: Replace `16` with your Postgres server version
 
 ### Windows
 
@@ -589,7 +606,7 @@ Note: The exact path will vary depending on your Visual Studio version and editi
 Then use `nmake` to build:
 
 ```cmd
-set "PGROOT=C:\Program Files\PostgreSQL\15"
+set "PGROOT=C:\Program Files\PostgreSQL\16"
 git clone --branch v0.5.1 https://github.com/pgvector/pgvector.git
 cd pgvector
 nmake /F Makefile.win
@@ -639,22 +656,22 @@ pgxn install vector
 Debian and Ubuntu packages are available from the [PostgreSQL APT Repository](https://wiki.postgresql.org/wiki/Apt). Follow the [setup instructions](https://wiki.postgresql.org/wiki/Apt#Quickstart) and run:
 
 ```sh
-sudo apt install postgresql-15-pgvector
+sudo apt install postgresql-16-pgvector
 ```
 
-Note: Replace `15` with your Postgres server version
+Note: Replace `16` with your Postgres server version
 
 ### Yum
 
 RPM packages are available from the [PostgreSQL Yum Repository](https://yum.postgresql.org/). Follow the [setup instructions](https://www.postgresql.org/download/linux/redhat/) for your distribution and run:
 
 ```sh
-sudo yum install pgvector_15
+sudo yum install pgvector_16
 # or
-sudo dnf install pgvector_15
+sudo dnf install pgvector_16
 ```
 
-Note: Replace `15` with your Postgres server version
+Note: Replace `16` with your Postgres server version
 
 ### conda-forge
 

src/hnsw.c

@@ -14,15 +14,45 @@
 #endif
 
 int			hnsw_ef_search;
-bool		hnsw_enable_parallel_build;
+int			hnsw_lock_tranche_id;
 static relopt_kind hnsw_relopt_kind;
 
+/*
+ * Assign a tranche ID for our LWLocks. This only needs to be done by one
+ * backend, as the tranche ID is remembered in shared memory.
+ *
+ * This shared memory area is very small, so we just allocate it from the
+ * "slop" that PostgreSQL reserves for small allocations like this. If
+ * this grows bigger, we should use a shmem_request_hook and
+ * RequestAddinShmemSpace() to pre-reserve space for this.
+ */
+static void
+HnswInitLockTranche(void)
+{
+	int		   *tranche_ids;
+	bool		found;
+
+	LWLockAcquire(AddinShmemInitLock, LW_EXCLUSIVE);
+	tranche_ids = ShmemInitStruct("hnsw LWLock ids",
+								  sizeof(int) * 1,
+								  &found);
+	if (!found)
+		tranche_ids[0] = LWLockNewTrancheId();
+	hnsw_lock_tranche_id = tranche_ids[0];
+	LWLockRelease(AddinShmemInitLock);
+
+	/* Per-backend registration of the tranche ID */
+	LWLockRegisterTranche(hnsw_lock_tranche_id, "HnswBuild");
+}
+
 /*
  * Initialize index options and variables
  */
 void
 HnswInit(void)
 {
+	HnswInitLockTranche();
+
 	hnsw_relopt_kind = add_reloption_kind();
 	add_int_reloption(hnsw_relopt_kind, "m", "Max number of connections",
 					  HNSW_DEFAULT_M, HNSW_MIN_M, HNSW_MAX_M
@@ -40,11 +70,6 @@ HnswInit(void)
 	DefineCustomIntVariable("hnsw.ef_search", "Sets the size of the dynamic candidate list for search",
 							"Valid range is 1..1000.", &hnsw_ef_search,
 							HNSW_DEFAULT_EF_SEARCH, HNSW_MIN_EF_SEARCH, HNSW_MAX_EF_SEARCH, PGC_USERSET, 0, NULL, NULL, NULL);
-
-	/* Behind a variable for now since can be slower than building in memory */
-	DefineCustomBoolVariable("hnsw.enable_parallel_build", "Enables or disables building indexes in parallel",
-							 NULL, &hnsw_enable_parallel_build,
-							 false, PGC_USERSET, 0, NULL, NULL, NULL);
 }
 
 /*

src/hnsw.h

@@ -8,6 +8,7 @@
 #include "access/reloptions.h"
 #include "nodes/execnodes.h"
 #include "port.h"				/* for random() */
+#include "utils/relptr.h"
 #include "utils/sampling.h"
 #include "vector.h"
 
@@ -72,8 +73,10 @@
 
 #if PG_VERSION_NUM >= 150000
 #define RandomDouble() pg_prng_double(&pg_global_prng_state)
+#define SeedRandom(seed) pg_prng_seed(&pg_global_prng_state, seed)
 #else
 #define RandomDouble() (((double) random()) / MAX_RANDOM_VALUE)
+#define SeedRandom(seed) srandom(seed)
 #endif
 
 #if PG_VERSION_NUM < 130000
@@ -91,33 +94,66 @@
 #define HnswGetMl(m) (1 / log(m))
 
 /* Ensure fits on page and in uint8 */
-#define HnswGetMaxLevel(m) Min(((BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - offsetof(HnswNeighborTupleData, indextids) - sizeof(ItemIdData)) / (sizeof(ItemPointerData)) / m) - 2, 255)
+#define HnswGetMaxLevel(m) Min(((BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - offsetof(HnswNeighborTupleData, indextids) - sizeof(ItemIdData)) / (sizeof(ItemPointerData)) / (m)) - 2, 255)
+
+#define HnswGetValue(base, element) PointerGetDatum(HnswPtrAccess(base, (element)->value))
+
+#if PG_VERSION_NUM < 140005
+#define relptr_offset(rp) ((rp).relptr_off - 1)
+#endif
+
+/* Pointer macros */
+#define HnswPtrAccess(base, hp) ((base) == NULL ? (hp).ptr : relptr_access(base, (hp).relptr))
+#define HnswPtrStore(base, hp, value) ((base) == NULL ? (void) ((hp).ptr = (value)) : (void) relptr_store(base, (hp).relptr, value))
+#define HnswPtrIsNull(base, hp) ((base) == NULL ? (hp).ptr == NULL : relptr_is_null((hp).relptr))
+#define HnswPtrEqual(base, hp1, hp2) ((base) == NULL ? (hp1).ptr == (hp2).ptr : relptr_offset((hp1).relptr) == relptr_offset((hp2).relptr))
+
+/* For code paths dedicated to each type */
+#define HnswPtrPointer(hp) (hp).ptr
+#define HnswPtrOffset(hp) relptr_offset((hp).relptr)
 
 /* Variables */
 extern int	hnsw_ef_search;
-extern bool hnsw_enable_parallel_build;
 
+/* This is initialized when the module is loaded */
+extern int	hnsw_lock_tranche_id;
+
+typedef struct HnswElementData HnswElementData;
 typedef struct HnswNeighborArray HnswNeighborArray;
 
+#define HnswPtrDeclare(type, relptrtype, ptrtype) \
+	relptr_declare(type, relptrtype); \
+	typedef union { type *ptr; relptrtype relptr; } ptrtype;
+
+/* Pointers that can be absolute or relative */
+/* Use char for DatumPtr so works with Pointer */
+HnswPtrDeclare(HnswElementData, HnswElementRelptr, HnswElementPtr);
+HnswPtrDeclare(HnswNeighborArray, HnswNeighborArrayRelptr, HnswNeighborArrayPtr);
+HnswPtrDeclare(HnswNeighborArrayPtr, HnswNeighborsRelptr, HnswNeighborsPtr);
+HnswPtrDeclare(char, DatumRelptr, DatumPtr);
+
 typedef struct HnswElementData
 {
-	List	   *heaptids;
+	HnswElementPtr next;
+	ItemPointerData heaptids[HNSW_HEAPTIDS];
+	uint8		heaptidsLength;
 	uint8		level;
 	uint8		deleted;
 	uint32		hash;
-	HnswNeighborArray *neighbors;
+	HnswNeighborsPtr neighbors;
 	BlockNumber blkno;
 	OffsetNumber offno;
 	OffsetNumber neighborOffno;
 	BlockNumber neighborPage;
-	Datum		value;
+	DatumPtr	value;
+	LWLock		lock;
 }			HnswElementData;
 
 typedef HnswElementData * HnswElement;
 
 typedef struct HnswCandidate
 {
-	HnswElement element;
+	HnswElementPtr element;
 	float		distance;
 	bool		closer;
 }			HnswCandidate;
@@ -126,7 +162,7 @@ typedef struct HnswNeighborArray
 {
 	int			length;
 	bool		closerSet;
-	HnswCandidate *items;
+	HnswCandidate items[FLEXIBLE_ARRAY_MEMBER];
 }			HnswNeighborArray;
 
 typedef struct HnswPairingHeapNode
@@ -143,6 +179,27 @@ typedef struct HnswOptions
 	int			efConstruction; /* size of dynamic candidate list */
 }			HnswOptions;
 
+typedef struct HnswGraph
+{
+	/* Graph state */
+	slock_t		lock;
+	HnswElementPtr head;
+	double		indtuples;
+
+	/* Entry state */
+	LWLock		entryLock;
+	HnswElementPtr entryPoint;
+
+	/* Allocations state */
+	LWLock		allocatorLock;
+	long		memoryUsed;
+	long		memoryTotal;
+
+	/* Flushed state */
+	LWLock		flushLock;
+	bool		flushed;
+}			HnswGraph;
+
 typedef struct HnswSpool
 {
 	Relation	heap;
@@ -156,6 +213,7 @@ typedef struct HnswShared
 	Oid			indexrelid;
 	bool		isconcurrent;
 	int			scantuplesortstates;
+	dsa_pointer dsaptr;
 
 	/* Worker progress */
 	ConditionVariable workersdonecv;
@@ -166,7 +224,7 @@ typedef struct HnswShared
 	/* Mutable state */
 	int			nparticipantsdone;
 	double		reltuples;
-	double		indtuples;
+	HnswGraph	graphData;
 
 #if PG_VERSION_NUM < 120000
 	ParallelHeapScanDescData heapdesc;	/* must come last */
@@ -184,8 +242,15 @@ typedef struct HnswLeader
 	int			nparticipanttuplesorts;
 	HnswShared *hnswshared;
 	Snapshot	snapshot;
+	char	   *hnswarea;
 }			HnswLeader;
 
+typedef struct HnswAllocator
+{
+	void	   *(*alloc) (Size size, void *state);
+	void	   *state;
+}			HnswAllocator;
+
 typedef struct HnswBuildState
 {
 	/* Info */
@@ -209,20 +274,21 @@ typedef struct HnswBuildState
 	Oid			collation;
 
 	/* Variables */
-	List	   *elements;
-	HnswElement entryPoint;
+	HnswGraph	graphData;
+	HnswGraph  *graph;
 	double		ml;
 	int			maxLevel;
-	long		memoryLeft;
-	bool		flushed;
 	Vector	   *normvec;
 
 	/* Memory */
+	MemoryContext graphCtx;
 	MemoryContext tmpCtx;
+	HnswAllocator allocator;
 
 	/* Parallel builds */
 	HnswLeader *hnswleader;
 	HnswShared *hnswshared;
+	char	   *hnswarea;
 }			HnswBuildState;
 
 typedef struct HnswMetaPageData
@@ -321,25 +387,24 @@ bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * re
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);
 void		HnswInit(void);
-List	   *HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement);
+List	   *HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement);
 HnswElement HnswGetEntryPoint(Relation index);
 void		HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
-HnswElement HnswInitElement(ItemPointer tid, int m, double ml, int maxLevel);
-void		HnswFreeElement(HnswElement element);
+void	   *HnswAlloc(HnswAllocator * allocator, Size size);
+HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
 HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
-void		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		HnswInsertElement(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
+HnswCandidate *HnswEntryCandidate(char *base, HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
 void		HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum, bool building);
-void		HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m);
+void		HnswSetNeighborTuple(char *base, 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, bool building);
+void		HnswInitNeighbors(char *base, HnswElement element, int m, HnswAllocator * alloc);
+bool		HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel, bool building);
 void		HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building);
 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		HnswSetElementTuple(char *base, HnswElementTuple etup, HnswElement element);
+void		HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int m, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation);
 void		HnswLoadNeighbors(HnswElement element, Relation index, int m);
 PGDLLEXPORT void HnswParallelBuildMain(dsm_segment *seg, shm_toc *toc);
 
@@ -359,6 +424,16 @@ void		hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys,
 bool		hnswgettuple(IndexScanDesc scan, ScanDirection dir);
 void		hnswendscan(IndexScanDesc scan);
 
+static inline HnswNeighborArray *
+HnswGetNeighbors(char *base, HnswElement element, int lc)
+{
+	HnswNeighborArrayPtr *neighborList = HnswPtrAccess(base, element->neighbors);
+
+	Assert(element->level >= lc);
+
+	return HnswPtrAccess(base, neighborList[lc]);
+}
+
 /* Hash tables */
 typedef struct TidHashEntry
 {
@@ -386,4 +461,17 @@ typedef struct PointerHashEntry
 #define SH_DECLARE
 #include "lib/simplehash.h"
 
+typedef struct OffsetHashEntry
+{
+	Size		offset;
+	char		status;
+}			OffsetHashEntry;
+
+#define SH_PREFIX offsethash
+#define SH_ELEMENT_TYPE OffsetHashEntry
+#define SH_KEY_TYPE Size
+#define SH_SCOPE extern
+#define SH_DECLARE
+#include "lib/simplehash.h"
+
 #endif

src/hnswbuild.c

@@ -54,9 +54,12 @@
 #endif
 
 #define PARALLEL_KEY_HNSW_SHARED		UINT64CONST(0xA000000000000001)
-#define PARALLEL_KEY_QUERY_TEXT			UINT64CONST(0xA000000000000002)
+#define PARALLEL_KEY_HNSW_AREA			UINT64CONST(0xA000000000000002)
+#define PARALLEL_KEY_QUERY_TEXT			UINT64CONST(0xA000000000000003)
 
-#define LIST_MAX_LENGTH ((1 << 26) - 1)
+#if PG_VERSION_NUM < 130000
+#define GENERATIONCHUNK_RAWSIZE (SIZEOF_SIZE_T + SIZEOF_VOID_P * 2)
+#endif
 
 /*
  * Create the metapage
@@ -88,6 +91,7 @@ CreateMetaPage(HnswBuildState * buildstate)
 	((PageHeader) page)->pd_lower =
 		((char *) metap + sizeof(HnswMetaPageData)) - (char *) page;
 
+	MarkBufferDirty(buf);
 	UnlockReleaseBuffer(buf);
 }
 
@@ -104,6 +108,7 @@ HnswBuildAppendPage(Relation index, Buffer *buf, Page *page, ForkNumber forkNum)
 	HnswPageGetOpaque(*page)->nextblkno = BufferGetBlockNumber(newbuf);
 
 	/* Commit */
+	MarkBufferDirty(*buf);
 	UnlockReleaseBuffer(*buf);
 
 	/* Can take a while, so ensure we can interrupt */
@@ -131,9 +136,11 @@ CreateElementPages(HnswBuildState * buildstate)
 	HnswElementTuple etup;
 	HnswNeighborTuple ntup;
 	BlockNumber insertPage;
+	HnswElement entryPoint;
 	Buffer		buf;
 	Page		page;
-	ListCell   *lc;
+	HnswElementPtr iter = buildstate->graph->head;
+	char	   *base = buildstate->hnswarea;
 
 	/* Calculate sizes */
 	etupAllocSize = BLCKSZ;
@@ -148,18 +155,22 @@ CreateElementPages(HnswBuildState * buildstate)
 	page = BufferGetPage(buf);
 	HnswInitPage(buf, page);
 
-	foreach(lc, buildstate->elements)
+	while (!HnswPtrIsNull(base, iter))
 	{
-		HnswElement element = lfirst(lc);
+		HnswElement element = HnswPtrAccess(base, iter);
 		Size		etupSize;
 		Size		ntupSize;
 		Size		combinedSize;
+		void	   *valuePtr = HnswPtrAccess(base, element->value);
+
+		/* Update iterator */
+		iter = element->next;
 
 		/* Zero memory for each element */
 		MemSet(etup, 0, etupAllocSize);
 
 		/* Calculate sizes */
-		etupSize = HNSW_ELEMENT_TUPLE_SIZE(VARSIZE_ANY(DatumGetPointer(element->value)));
+		etupSize = HNSW_ELEMENT_TUPLE_SIZE(VARSIZE_ANY(valuePtr));
 		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(element->level, buildstate->m);
 		combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
 
@@ -167,7 +178,7 @@ CreateElementPages(HnswBuildState * buildstate)
 		if (etupSize > etupAllocSize)
 			elog(ERROR, "index tuple too large");
 
-		HnswSetElementTuple(etup, element);
+		HnswSetElementTuple(base, etup, element);
 
 		/* Keep element and neighbors on the same page if possible */
 		if (PageGetFreeSpace(page) < etupSize || (combinedSize <= maxSize && PageGetFreeSpace(page) < combinedSize))
@@ -205,9 +216,11 @@ CreateElementPages(HnswBuildState * buildstate)
 	insertPage = BufferGetBlockNumber(buf);
 
 	/* Commit */
+	MarkBufferDirty(buf);
 	UnlockReleaseBuffer(buf);
 
-	HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_ALWAYS, buildstate->entryPoint, insertPage, forkNum, true);
+	entryPoint = HnswPtrAccess(base, buildstate->graph->entryPoint);
+	HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_ALWAYS, entryPoint, insertPage, forkNum, true);
 
 	pfree(etup);
 	pfree(ntup);
@@ -222,19 +235,23 @@ CreateNeighborPages(HnswBuildState * buildstate)
 	Relation	index = buildstate->index;
 	ForkNumber	forkNum = buildstate->forkNum;
 	int			m = buildstate->m;
-	ListCell   *lc;
+	HnswElementPtr iter = buildstate->graph->head;
+	char	   *base = buildstate->hnswarea;
 	HnswNeighborTuple ntup;
 
 	/* Allocate once */
 	ntup = palloc0(BLCKSZ);
 
-	foreach(lc, buildstate->elements)
+	while (!HnswPtrIsNull(base, iter))
 	{
-		HnswElement e = lfirst(lc);
+		HnswElement e = HnswPtrAccess(base, iter);
 		Buffer		buf;
 		Page		page;
 		Size		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(e->level, m);
 
+		/* Update iterator */
+		iter = e->next;
+
 		/* Can take a while, so ensure we can interrupt */
 		/* Needs to be called when no buffer locks are held */
 		CHECK_FOR_INTERRUPTS();
@@ -243,58 +260,166 @@ CreateNeighborPages(HnswBuildState * buildstate)
 		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
 		page = BufferGetPage(buf);
 
-		HnswSetNeighborTuple(ntup, e, m);
+		HnswSetNeighborTuple(base, ntup, e, m);
 
 		if (!PageIndexTupleOverwrite(page, e->neighborOffno, (Item) ntup, ntupSize))
 			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
 		/* Commit */
+		MarkBufferDirty(buf);
 		UnlockReleaseBuffer(buf);
 	}
 
 	pfree(ntup);
 }
 
-/*
- * Free elements
- */
-static void
-FreeElements(HnswBuildState * buildstate)
-{
-	ListCell   *lc;
-
-	foreach(lc, buildstate->elements)
-		HnswFreeElement(lfirst(lc));
-
-	list_free(buildstate->elements);
-}
-
 /*
  * Flush pages
  */
 static void
 FlushPages(HnswBuildState * buildstate)
 {
+#ifdef HNSW_MEMORY
+	elog(INFO, "memory: %zu MB", buildstate->graph->memoryUsed / (1024 * 1024));
+#endif
+
 	CreateMetaPage(buildstate);
 	CreateElementPages(buildstate);
 	CreateNeighborPages(buildstate);
 
-	buildstate->flushed = true;
-	FreeElements(buildstate);
+	buildstate->graph->flushed = true;
+	MemoryContextReset(buildstate->graphCtx);
+}
+
+/*
+ * Add a heap TID to an existing element
+ */
+static bool
+HnswAddDuplicateInMemory(HnswElement element, HnswElement dup)
+{
+	LWLockAcquire(&dup->lock, LW_EXCLUSIVE);
+
+	if (dup->heaptidsLength == HNSW_HEAPTIDS)
+	{
+		LWLockRelease(&dup->lock);
+		return false;
+	}
+
+	HnswAddHeapTid(dup, &element->heaptids[0]);
+
+	LWLockRelease(&dup->lock);
+
+	return true;
+}
+
+/*
+ * Find duplicate element
+ */
+static bool
+HnswFindDuplicateInMemory(char *base, HnswElement element)
+{
+	HnswNeighborArray *neighbors = HnswGetNeighbors(base, element, 0);
+
+	for (int i = 0; i < neighbors->length; i++)
+	{
+		HnswCandidate *neighbor = &neighbors->items[i];
+		HnswElement neighborElement = HnswPtrAccess(base, neighbor->element);
+		Datum		value = HnswGetValue(base, element);
+		Datum		neighborValue = HnswGetValue(base, neighborElement);
+
+		/* Exit early since ordered by distance */
+		if (!datumIsEqual(value, neighborValue, false, -1))
+			return false;
+
+		/* Check for space */
+		if (HnswAddDuplicateInMemory(element, neighborElement))
+			return true;
+	}
+
+	return false;
+}
+
+/*
+ * Add to element and neighbor pages
+ */
+static void
+WriteNewElementPagesInMemory(char *base, HnswGraph * graph, HnswElement element)
+{
+	SpinLockAcquire(&graph->lock);
+	element->next = graph->head;
+	HnswPtrStore(base, graph->head, element);
+	SpinLockRelease(&graph->lock);
+}
+
+/*
+ * Update neighbors
+ */
+static void
+HnswUpdateNeighborPagesInMemory(char *base, FmgrInfo *procinfo, Oid collation, HnswElement e, int m)
+{
+	for (int lc = e->level; lc >= 0; lc--)
+	{
+		int			lm = HnswGetLayerM(m, lc);
+		HnswNeighborArray *neighbors = HnswGetNeighbors(base, e, lc);
+
+		for (int i = 0; i < neighbors->length; i++)
+		{
+			HnswCandidate *hc = &neighbors->items[i];
+			HnswElement neighborElement = HnswPtrAccess(base, hc->element);
+
+			/* Keep scan-build happy on Mac x86-64 */
+			Assert(neighborElement);
+
+			/* Use element for lock instead of hc since hc can be replaced */
+			LWLockAcquire(&neighborElement->lock, LW_EXCLUSIVE);
+			HnswUpdateConnection(base, e, hc, lm, lc, NULL, NULL, procinfo, collation);
+			LWLockRelease(&neighborElement->lock);
+		}
+	}
+}
+
+/*
+ * Write changes in memory
+ */
+static void
+WriteElementInMemory(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement entryPoint, HnswBuildState * buildstate, HnswGraph * graph, bool updateEntryPoint)
+{
+	char	   *base = buildstate->hnswarea;
+
+	/* Try to add to existing page */
+	if (HnswFindDuplicateInMemory(base, element))
+		return;
+
+	/* Write element and neighbor tuples */
+	WriteNewElementPagesInMemory(base, graph, element);
+
+	/* Update neighbors */
+	HnswUpdateNeighborPagesInMemory(base, procinfo, collation, element, m);
+
+	/* Update entry point if needed (already have lock) */
+	if (updateEntryPoint)
+		HnswPtrStore(base, graph->entryPoint, element);
 }
 
 /*
  * Insert tuple
  */
 static bool
-InsertTuple(Relation index, Datum *values, HnswElement element, HnswBuildState * buildstate, HnswElement * dup, MemoryContext outerCtx)
+InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, HnswBuildState * buildstate)
 {
 	FmgrInfo   *procinfo = buildstate->procinfo;
 	Oid			collation = buildstate->collation;
-	HnswElement entryPoint = buildstate->entryPoint;
+	HnswGraph  *graph = buildstate->graph;
+	HnswElement entryPoint;
 	int			efConstruction = buildstate->efConstruction;
 	int			m = buildstate->m;
-	MemoryContext oldCtx;
+	HnswElement element;
+	HnswAllocator *allocator = &buildstate->allocator;
+	Size		valueSize;
+	Pointer		valuePtr;
+	bool		updateEntryPoint;
+	LWLock	   *flushLock = &graph->flushLock;
+	char	   *base = buildstate->hnswarea;
 
 	/* Detoast once for all calls */
 	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
@@ -306,52 +431,82 @@ InsertTuple(Relation index, Datum *values, HnswElement element, HnswBuildState *
 			return false;
 	}
 
-	/* Copy value to element so accessible outside of memory context */
-	oldCtx = MemoryContextSwitchTo(outerCtx);
-	element->value = datumCopy(value, false, -1);
-	MemoryContextSwitchTo(oldCtx);
+	/* Get datum size */
+	valueSize = VARSIZE_ANY(DatumGetPointer(value));
 
-	/* Insert element in graph */
-	HnswInsertElement(element, entryPoint, NULL, procinfo, collation, m, efConstruction, false);
+	/* Ensure graph not flushed when inserting */
+	LWLockAcquire(flushLock, LW_SHARED);
 
-	/* Look for duplicate */
-	*dup = HnswFindDuplicate(element);
-
-	/* Update neighbors if needed */
-	if (*dup == NULL)
+	if (graph->flushed)
 	{
-		for (int lc = element->level; lc >= 0; lc--)
-		{
-			int			lm = HnswGetLayerM(m, lc);
-			HnswNeighborArray *neighbors = &element->neighbors[lc];
+		LWLockRelease(flushLock);
 
-			for (int i = 0; i < neighbors->length; i++)
-				HnswUpdateConnection(element, &neighbors->items[i], lm, lc, NULL, NULL, procinfo, collation);
-		}
+		return HnswInsertTupleOnDisk(index, value, values, isnull, heaptid, buildstate->heap, true);
 	}
 
-	/* Update entry point if needed */
-	if (*dup == NULL && (entryPoint == NULL || element->level > entryPoint->level))
-		buildstate->entryPoint = element;
+	/* Get lock for allocator */
+	LWLockAcquire(&graph->allocatorLock, LW_EXCLUSIVE);
 
-	UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++buildstate->indtuples);
+	/* Flush pages if needed */
+	if (graph->memoryUsed >= graph->memoryTotal)
+	{
+		LWLockRelease(&graph->allocatorLock);
 
-	return *dup == NULL;
-}
+		LWLockRelease(flushLock);
+		LWLockAcquire(flushLock, LW_EXCLUSIVE);
 
-/*
- * Get the memory used by an element
- */
-static long
-HnswElementMemory(HnswElement e, int m)
-{
-	long		elementSize = sizeof(HnswElementData);
+		if (!graph->flushed)
+		{
+			ereport(NOTICE,
+					(errmsg("hnsw graph no longer fits into maintenance_work_mem after " INT64_FORMAT " tuples", (int64) graph->indtuples),
+					 errdetail("Building will take significantly more time."),
+					 errhint("Increase maintenance_work_mem to speed up builds.")));
 
-	elementSize += sizeof(HnswNeighborArray) * (e->level + 1);
-	elementSize += sizeof(HnswCandidate) * (m * (e->level + 2));
-	elementSize += sizeof(ItemPointerData);
-	elementSize += VARSIZE_ANY(DatumGetPointer(e->value));
-	return elementSize;
+			FlushPages(buildstate);
+		}
+
+		LWLockRelease(flushLock);
+
+		return HnswInsertTupleOnDisk(index, value, values, isnull, heaptid, buildstate->heap, true);
+	}
+
+	/* Create an element */
+	element = HnswInitElement(base, heaptid, buildstate->m, buildstate->ml, buildstate->maxLevel, allocator);
+	valuePtr = HnswAlloc(allocator, valueSize);
+
+	/* Release allocator lock */
+	LWLockRelease(&graph->allocatorLock);
+
+	/* Copy datum */
+	memcpy(valuePtr, DatumGetPointer(value), valueSize);
+	HnswPtrStore(base, element->value, valuePtr);
+
+	/* Create element lock */
+	LWLockInitialize(&element->lock, hnsw_lock_tranche_id);
+
+	/* Get entry point */
+	LWLockAcquire(&graph->entryLock, LW_EXCLUSIVE);
+	entryPoint = HnswPtrAccess(base, graph->entryPoint);
+	updateEntryPoint = entryPoint == NULL || element->level > entryPoint->level;
+
+	/* Release lock if not updating entry point */
+	if (!updateEntryPoint)
+		LWLockRelease(&graph->entryLock);
+
+	/* Insert element in graph */
+	HnswInsertElement(base, element, entryPoint, NULL, procinfo, collation, m, efConstruction, false);
+
+	/* Write to memory */
+	WriteElementInMemory(index, procinfo, collation, element, m, efConstruction, entryPoint, buildstate, graph, updateEntryPoint);
+
+	/* Release lock if needed */
+	if (updateEntryPoint)
+		LWLockRelease(&graph->entryLock);
+
+	/* Release flush lock */
+	LWLockRelease(flushLock);
+
+	return true;
 }
 
 /*
@@ -362,10 +517,8 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 			  bool *isnull, bool tupleIsAlive, void *state)
 {
 	HnswBuildState *buildstate = (HnswBuildState *) state;
+	HnswGraph  *graph = buildstate->graph;
 	MemoryContext oldCtx;
-	HnswElement element;
-	HnswElement dup = NULL;
-	bool		inserted;
 
 #if PG_VERSION_NUM < 130000
 	ItemPointer tid = &hup->t_self;
@@ -375,70 +528,80 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	if (isnull[0])
 		return;
 
-	if (buildstate->flushed || buildstate->memoryLeft <= 0 || list_length(buildstate->elements) == LIST_MAX_LENGTH)
-	{
-		if (!buildstate->flushed)
-		{
-			if (buildstate->memoryLeft <= 0)
-				ereport(NOTICE,
-						(errmsg("hnsw graph no longer fits into maintenance_work_mem after " INT64_FORMAT " tuples", (int64) buildstate->indtuples),
-						 errdetail("Building will take significantly more time."),
-						 errhint("Increase maintenance_work_mem to speed up builds.")));
-
-			FlushPages(buildstate);
-		}
-
-		oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
-
-		if (HnswInsertTuple(buildstate->index, values, isnull, tid, buildstate->heap, true))
-		{
-			if (buildstate->hnswshared)
-			{
-				HnswShared *hnswshared = buildstate->hnswshared;
-
-				SpinLockAcquire(&hnswshared->mutex);
-				UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++hnswshared->indtuples);
-				SpinLockRelease(&hnswshared->mutex);
-			}
-			else
-				UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++buildstate->indtuples);
-		}
-
-		/* Reset memory context */
-		MemoryContextSwitchTo(oldCtx);
-		MemoryContextReset(buildstate->tmpCtx);
-
-		return;
-	}
-
-	/* Allocate necessary memory outside of memory context */
-	element = HnswInitElement(tid, buildstate->m, buildstate->ml, buildstate->maxLevel);
-
-	/* Use memory context since detoast can allocate */
+	/* Use memory context */
 	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
 
 	/* Insert tuple */
-	inserted = InsertTuple(index, values, element, buildstate, &dup, oldCtx);
+	if (InsertTuple(index, values, isnull, tid, buildstate))
+	{
+		/* Update progress */
+		SpinLockAcquire(&graph->lock);
+		UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++graph->indtuples);
+		SpinLockRelease(&graph->lock);
+	}
 
 	/* Reset memory context */
 	MemoryContextSwitchTo(oldCtx);
 	MemoryContextReset(buildstate->tmpCtx);
+}
 
-	/* Add outside memory context */
-	if (dup != NULL)
-	{
-		HnswAddHeapTid(dup, tid);
-		buildstate->memoryLeft -= sizeof(ItemPointerData);
-	}
+/*
+ * Initialize the graph
+ */
+static void
+InitGraph(HnswGraph * graph, char *base, long memoryTotal)
+{
+	HnswPtrStore(base, graph->head, (HnswElement) NULL);
+	HnswPtrStore(base, graph->entryPoint, (HnswElement) NULL);
+	graph->memoryUsed = 0;
+	graph->memoryTotal = memoryTotal;
+	graph->flushed = false;
+	graph->indtuples = 0;
+	SpinLockInit(&graph->lock);
+	LWLockInitialize(&graph->entryLock, hnsw_lock_tranche_id);
+	LWLockInitialize(&graph->allocatorLock, hnsw_lock_tranche_id);
+	LWLockInitialize(&graph->flushLock, hnsw_lock_tranche_id);
+}
 
-	/* Add to buildstate or free */
-	if (inserted)
-	{
-		buildstate->elements = lappend(buildstate->elements, element);
-		buildstate->memoryLeft -= HnswElementMemory(element, buildstate->m);
-	}
-	else
-		HnswFreeElement(element);
+/*
+ * Initialize an allocator
+ */
+static void
+InitAllocator(HnswAllocator * allocator, void *(*alloc) (Size size, void *state), void *state)
+{
+	allocator->alloc = alloc;
+	allocator->state = state;
+}
+
+/*
+ * Memory context allocator
+ */
+static void *
+HnswMemoryContextAlloc(Size size, void *state)
+{
+	HnswBuildState *buildstate = (HnswBuildState *) state;
+	void	   *chunk = MemoryContextAlloc(buildstate->graphCtx, size);
+
+#if PG_VERSION_NUM >= 130000
+	buildstate->graphData.memoryUsed = MemoryContextMemAllocated(buildstate->graphCtx, false);
+#else
+	buildstate->graphData.memoryUsed += MAXALIGN(size);
+#endif
+
+	return chunk;
+}
+
+/*
+ * Shared memory allocator
+ */
+static void *
+HnswSharedMemoryAlloc(Size size, void *state)
+{
+	HnswBuildState *buildstate = (HnswBuildState *) state;
+	void	   *chunk = buildstate->hnswarea + buildstate->graph->memoryUsed;
+
+	buildstate->graph->memoryUsed += MAXALIGN(size);
+	return chunk;
 }
 
 /*
@@ -474,22 +637,29 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	buildstate->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
 	buildstate->collation = index->rd_indcollation[0];
 
-	buildstate->elements = NIL;
-	buildstate->entryPoint = NULL;
+	InitGraph(&buildstate->graphData, NULL, maintenance_work_mem * 1024L);
+	buildstate->graph = &buildstate->graphData;
 	buildstate->ml = HnswGetMl(buildstate->m);
 	buildstate->maxLevel = HnswGetMaxLevel(buildstate->m);
-	buildstate->memoryLeft = maintenance_work_mem * 1024L;
-	buildstate->flushed = false;
 
 	/* Reuse for each tuple */
 	buildstate->normvec = InitVector(buildstate->dimensions);
 
+	buildstate->graphCtx = GenerationContextCreate(CurrentMemoryContext,
+												   "Hnsw build graph context",
+#if PG_VERSION_NUM >= 150000
+												   1024 * 1024, 1024 * 1024,
+#endif
+												   1024 * 1024);
 	buildstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 											   "Hnsw build temporary context",
 											   ALLOCSET_DEFAULT_SIZES);
 
+	InitAllocator(&buildstate->allocator, &HnswMemoryContextAlloc, buildstate);
+
 	buildstate->hnswleader = NULL;
 	buildstate->hnswshared = NULL;
+	buildstate->hnswarea = NULL;
 }
 
 /*
@@ -499,6 +669,7 @@ static void
 FreeBuildState(HnswBuildState * buildstate)
 {
 	pfree(buildstate->normvec);
+	MemoryContextDelete(buildstate->graphCtx);
 	MemoryContextDelete(buildstate->tmpCtx);
 }
 
@@ -518,7 +689,8 @@ ParallelHeapScan(HnswBuildState * buildstate)
 		SpinLockAcquire(&hnswshared->mutex);
 		if (hnswshared->nparticipantsdone == nparticipanttuplesorts)
 		{
-			buildstate->indtuples = hnswshared->indtuples;
+			buildstate->graph = &hnswshared->graphData;
+			buildstate->hnswarea = buildstate->hnswleader->hnswarea;
 			reltuples = hnswshared->reltuples;
 			SpinLockRelease(&hnswshared->mutex);
 			break;
@@ -538,7 +710,7 @@ ParallelHeapScan(HnswBuildState * buildstate)
  * Perform a worker's portion of a parallel insert
  */
 static void
-HnswParallelScanAndInsert(HnswSpool * hnswspool, HnswShared * hnswshared, bool progress)
+HnswParallelScanAndInsert(HnswSpool * hnswspool, HnswShared * hnswshared, char *hnswarea, bool progress)
 {
 	HnswBuildState buildstate;
 #if PG_VERSION_NUM >= 120000
@@ -553,10 +725,9 @@ HnswParallelScanAndInsert(HnswSpool * hnswspool, HnswShared * hnswshared, bool p
 	indexInfo = BuildIndexInfo(hnswspool->index);
 	indexInfo->ii_Concurrent = hnswshared->isconcurrent;
 	InitBuildState(&buildstate, hnswspool->heap, hnswspool->index, indexInfo, MAIN_FORKNUM);
-	/* TODO Support in-memory builds */
-	buildstate.memoryLeft = 0;
-	buildstate.flushed = true;
-	buildstate.hnswshared = hnswshared;
+	buildstate.graph = &hnswshared->graphData;
+	buildstate.hnswarea = hnswarea;
+	InitAllocator(&buildstate.allocator, &HnswSharedMemoryAlloc, &buildstate);
 #if PG_VERSION_NUM >= 120000
 	scan = table_beginscan_parallel(hnswspool->heap,
 									ParallelTableScanFromHnswShared(hnswshared));
@@ -597,6 +768,9 @@ HnswParallelBuildMain(dsm_segment *seg, shm_toc *toc)
 	char	   *sharedquery;
 	HnswSpool  *hnswspool;
 	HnswShared *hnswshared;
+	dsa_area   *dsa;
+	void	   *dsaspace;
+	char	   *hnswarea;
 	Relation	heapRel;
 	Relation	indexRel;
 	LOCKMODE	heapLockmode;
@@ -637,8 +811,12 @@ HnswParallelBuildMain(dsm_segment *seg, shm_toc *toc)
 	hnswspool->heap = heapRel;
 	hnswspool->index = indexRel;
 
+	dsaspace = shm_toc_lookup(toc, PARALLEL_KEY_HNSW_AREA, false);
+	dsa = dsa_attach_in_place(dsaspace, seg);
+	hnswarea = dsa_get_address(dsa, hnswshared->dsaptr);
+
 	/* Perform inserts */
-	HnswParallelScanAndInsert(hnswspool, hnswshared, false);
+	HnswParallelScanAndInsert(hnswspool, hnswshared, hnswarea, false);
 
 	/* Close relations within worker */
 	index_close(indexRel, indexLockmode);
@@ -701,7 +879,7 @@ HnswLeaderParticipateAsWorker(HnswBuildState * buildstate)
 	leaderworker->index = buildstate->index;
 
 	/* Perform work common to all participants */
-	HnswParallelScanAndInsert(leaderworker, hnswleader->hnswshared, true);
+	HnswParallelScanAndInsert(leaderworker, hnswleader->hnswshared, hnswleader->hnswarea, true);
 }
 
 /*
@@ -714,7 +892,12 @@ HnswBeginParallel(HnswBuildState * buildstate, bool isconcurrent, int request)
 	int			scantuplesortstates;
 	Snapshot	snapshot;
 	Size		esthnswshared;
+	Size		esthnswarea;
+	Size		estdsaspace;
 	HnswShared *hnswshared;
+	void	   *dsaspace;
+	dsa_area   *dsa;
+	char	   *hnswarea;
 	HnswLeader *hnswleader = (HnswLeader *) palloc0(sizeof(HnswLeader));
 	bool		leaderparticipates = true;
 	int			querylen;
@@ -743,7 +926,11 @@ HnswBeginParallel(HnswBuildState * buildstate, bool isconcurrent, int request)
 	/* Estimate size of workspaces */
 	esthnswshared = ParallelEstimateShared(buildstate->heap, snapshot);
 	shm_toc_estimate_chunk(&pcxt->estimator, esthnswshared);
-	shm_toc_estimate_keys(&pcxt->estimator, 1);
+
+	/* Start with a minimal DSA so InitializeParallelDSM does not fail */
+	estdsaspace = dsa_minimum_size();
+	shm_toc_estimate_chunk(&pcxt->estimator, estdsaspace);
+	shm_toc_estimate_keys(&pcxt->estimator, 2);
 
 	/* Finally, estimate PARALLEL_KEY_QUERY_TEXT space */
 	if (debug_query_string)
@@ -780,7 +967,6 @@ HnswBeginParallel(HnswBuildState * buildstate, bool isconcurrent, int request)
 	/* Initialize mutable state */
 	hnswshared->nparticipantsdone = 0;
 	hnswshared->reltuples = 0;
-	hnswshared->indtuples = 0;
 #if PG_VERSION_NUM >= 120000
 	table_parallelscan_initialize(buildstate->heap,
 								  ParallelTableScanFromHnswShared(hnswshared),
@@ -789,7 +975,28 @@ HnswBeginParallel(HnswBuildState * buildstate, bool isconcurrent, int request)
 	heap_parallelscan_initialize(&hnswshared->heapdesc, buildstate->heap, snapshot);
 #endif
 
+	dsaspace = shm_toc_allocate(pcxt->toc, estdsaspace);
+	dsa = dsa_create_in_place(dsaspace, estdsaspace, hnsw_lock_tranche_id, pcxt->seg);
+
+	esthnswarea = maintenance_work_mem * 1024L;
+	hnswshared->dsaptr = dsa_allocate_extended(dsa, esthnswarea, DSA_ALLOC_HUGE | DSA_ALLOC_NO_OOM);
+
+	/* If not enough shared memory, back out (do serial build) */
+	if (!DsaPointerIsValid(hnswshared->dsaptr))
+	{
+		if (IsMVCCSnapshot(snapshot))
+			UnregisterSnapshot(snapshot);
+		DestroyParallelContext(pcxt);
+		ExitParallelMode();
+		return;
+	}
+
+	hnswarea = dsa_get_address(dsa, hnswshared->dsaptr);
+	/* Report less than allocated so never fails */
+	InitGraph(&hnswshared->graphData, hnswarea, esthnswarea - 1024 * 1024);
+
 	shm_toc_insert(pcxt->toc, PARALLEL_KEY_HNSW_SHARED, hnswshared);
+	shm_toc_insert(pcxt->toc, PARALLEL_KEY_HNSW_AREA, dsaspace);
 
 	/* Store query string for workers */
 	if (debug_query_string)
@@ -809,6 +1016,7 @@ HnswBeginParallel(HnswBuildState * buildstate, bool isconcurrent, int request)
 		hnswleader->nparticipanttuplesorts++;
 	hnswleader->hnswshared = hnswshared;
 	hnswleader->snapshot = snapshot;
+	hnswleader->hnswarea = hnswarea;
 
 	/* If no workers were successfully launched, back out (do serial build) */
 	if (pcxt->nworkers_launched == 0)
@@ -831,6 +1039,27 @@ HnswBeginParallel(HnswBuildState * buildstate, bool isconcurrent, int request)
 	WaitForParallelWorkersToAttach(pcxt);
 }
 
+/*
+ * Compute parallel workers
+ */
+static int
+ComputeParallelWorkers(Relation heap, Relation index)
+{
+	int			parallel_workers;
+
+	/* Make sure it's safe to use parallel workers */
+	parallel_workers = plan_create_index_workers(RelationGetRelid(heap), RelationGetRelid(index));
+	if (parallel_workers == 0)
+		return 0;
+
+	/* Use parallel_workers storage parameter on table if set */
+	parallel_workers = RelationGetParallelWorkers(heap, -1);
+	if (parallel_workers != -1)
+		return Min(parallel_workers, max_parallel_maintenance_workers);
+
+	return max_parallel_maintenance_workers;
+}
+
 /*
  * Build graph
  */
@@ -842,30 +1071,35 @@ BuildGraph(HnswBuildState * buildstate, ForkNumber forkNum)
 	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_HNSW_PHASE_LOAD);
 
 	/* Calculate parallel workers */
-	if (hnsw_enable_parallel_build)
-		parallel_workers = plan_create_index_workers(RelationGetRelid(buildstate->heap), RelationGetRelid(buildstate->index));
+	if (buildstate->heap != NULL)
+		parallel_workers = ComputeParallelWorkers(buildstate->heap, buildstate->index);
 
 	/* Attempt to launch parallel worker scan when required */
 	if (parallel_workers > 0)
-	{
-		/* TODO Support in-memory builds */
-		FlushPages(buildstate);
 		HnswBeginParallel(buildstate, buildstate->indexInfo->ii_Concurrent, parallel_workers);
+
+	/* Add tuples to graph */
+	if (buildstate->heap != NULL)
+	{
+		if (buildstate->hnswleader)
+			buildstate->reltuples = ParallelHeapScan(buildstate);
+		else
+		{
+#if PG_VERSION_NUM >= 120000
+			buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+														   true, true, BuildCallback, (void *) buildstate, NULL);
+#else
+			buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+													   true, BuildCallback, (void *) buildstate, NULL);
+#endif
+		}
+
+		buildstate->indtuples = buildstate->graph->indtuples;
 	}
 
-	/* Add tuples to sort */
-	if (buildstate->hnswleader)
-		buildstate->reltuples = ParallelHeapScan(buildstate);
-	else
-	{
-#if PG_VERSION_NUM >= 120000
-		buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-													   true, true, BuildCallback, (void *) buildstate, NULL);
-#else
-		buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-												   true, BuildCallback, (void *) buildstate, NULL);
-#endif
-	}
+	/* Flush pages */
+	if (!buildstate->graph->flushed)
+		FlushPages(buildstate);
 
 	/* End parallel build */
 	if (buildstate->hnswleader)
@@ -895,13 +1129,13 @@ static void
 BuildIndex(Relation heap, Relation index, IndexInfo *indexInfo,
 		   HnswBuildState * buildstate, ForkNumber forkNum)
 {
+#ifdef HNSW_MEMORY
+	SeedRandom(42);
+#endif
+
 	InitBuildState(buildstate, heap, index, indexInfo, forkNum);
 
-	if (buildstate->heap != NULL)
-		BuildGraph(buildstate, forkNum);
-
-	if (!buildstate->flushed)
-		FlushPages(buildstate);
+	BuildGraph(buildstate, forkNum);
 
 	if (RelationNeedsWAL(index))
 		log_newpage_range(index, forkNum, 0, RelationGetNumberOfBlocks(index), true);

src/hnswinsert.c

@@ -5,6 +5,7 @@
 #include "hnsw.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
+#include "utils/datum.h"
 #include "utils/memutils.h"
 
 /*
@@ -133,9 +134,10 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	OffsetNumber freeOffno = InvalidOffsetNumber;
 	OffsetNumber freeNeighborOffno = InvalidOffsetNumber;
 	BlockNumber newInsertPage = InvalidBlockNumber;
+	char	   *base = NULL;
 
 	/* Calculate sizes */
-	etupSize = HNSW_ELEMENT_TUPLE_SIZE(VARSIZE_ANY(DatumGetPointer(e->value)));
+	etupSize = HNSW_ELEMENT_TUPLE_SIZE(VARSIZE_ANY(HnswPtrAccess(base, e->value)));
 	ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(e->level, m);
 	combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
 	maxSize = HNSW_MAX_SIZE;
@@ -143,11 +145,11 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 
 	/* Prepare element tuple */
 	etup = palloc0(etupSize);
-	HnswSetElementTuple(etup, e);
+	HnswSetElementTuple(base, etup, e);
 
 	/* Prepare neighbor tuple */
 	ntup = palloc0(ntupSize);
-	HnswSetNeighborTuple(ntup, e, m);
+	HnswSetNeighborTuple(base, ntup, e, m);
 
 	/* Find a page (or two if needed) to insert the tuples */
 	for (;;)
@@ -219,7 +221,9 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 			HnswInsertAppendPage(index, &newbuf, &newpage, state, page, building);
 
 			/* Commit */
-			if (!building)
+			if (building)
+				MarkBufferDirty(buf);
+			else
 				GenericXLogFinish(state);
 
 			/* Unlock previous buffer */
@@ -294,7 +298,13 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	}
 
 	/* Commit */
-	if (!building)
+	if (building)
+	{
+		MarkBufferDirty(buf);
+		if (nbuf != buf)
+			MarkBufferDirty(nbuf);
+	}
+	else
 		GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 	if (nbuf != buf)
@@ -331,10 +341,12 @@ ConnectionExists(HnswElement e, HnswNeighborTuple ntup, int startIdx, int lm)
 void
 HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building)
 {
+	char	   *base = NULL;
+
 	for (int lc = e->level; lc >= 0; lc--)
 	{
 		int			lm = HnswGetLayerM(m, lc);
-		HnswNeighborArray *neighbors = &e->neighbors[lc];
+		HnswNeighborArray *neighbors = HnswGetNeighbors(base, e, lc);
 
 		for (int i = 0; i < neighbors->length; i++)
 		{
@@ -347,11 +359,12 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
 			Size		ntupSize;
 			int			idx = -1;
 			int			startIdx;
-			OffsetNumber offno = hc->element->neighborOffno;
+			HnswElement neighborElement = HnswPtrAccess(base, hc->element);
+			OffsetNumber offno = neighborElement->neighborOffno;
 
 			/* Get latest neighbors since they may have changed */
 			/* Do not lock yet since selecting neighbors can take time */
-			HnswLoadNeighbors(hc->element, index, m);
+			HnswLoadNeighbors(neighborElement, index, m);
 
 			/*
 			 * Could improve performance for vacuuming by checking neighbors
@@ -361,14 +374,14 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
 			 */
 
 			/* Select neighbors */
-			HnswUpdateConnection(e, hc, lm, lc, &idx, index, procinfo, collation);
+			HnswUpdateConnection(NULL, 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);
+			buf = ReadBuffer(index, neighborElement->neighborPage);
 			LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
 			if (building)
 			{
@@ -387,7 +400,7 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
 			ntupSize = ItemIdGetLength(itemid);
 
 			/* Calculate index for update */
-			startIdx = (hc->element->level - lc) * m;
+			startIdx = (neighborElement->level - lc) * m;
 
 			/* Check for existing connection */
 			if (checkExisting && ConnectionExists(e, ntup, startIdx, lm))
@@ -421,7 +434,9 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
 					elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
 				/* Commit */
-				if (!building)
+				if (building)
+					MarkBufferDirty(buf);
+				else
 					GenericXLogFinish(state);
 			}
 			else if (!building)
@@ -480,34 +495,60 @@ HnswAddDuplicate(Relation index, HnswElement element, HnswElement dup, bool buil
 	}
 
 	/* Add heap TID */
-	etup->heaptids[i] = *((ItemPointer) linitial(element->heaptids));
+	etup->heaptids[i] = element->heaptids[0];
 
 	/* Overwrite tuple */
 	if (!PageIndexTupleOverwrite(page, dup->offno, (Item) etup, etupSize))
 		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
 	/* Commit */
-	if (!building)
+	if (building)
+		MarkBufferDirty(buf);
+	else
 		GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 
 	return true;
 }
 
+/*
+ * Find duplicate element
+ */
+static bool
+HnswFindDuplicate(Relation index, HnswElement element, bool building)
+{
+	char	   *base = NULL;
+	HnswNeighborArray *neighbors = HnswGetNeighbors(base, element, 0);
+
+	for (int i = 0; i < neighbors->length; i++)
+	{
+		HnswCandidate *neighbor = &neighbors->items[i];
+		HnswElement neighborElement = HnswPtrAccess(base, neighbor->element);
+		Datum		value = HnswGetValue(base, element);
+		Datum		neighborValue = HnswGetValue(base, neighborElement);
+
+		/* Exit early since ordered by distance */
+		if (!datumIsEqual(value, neighborValue, false, -1))
+			return false;
+
+		if (HnswAddDuplicate(index, element, neighborElement, building))
+			return true;
+	}
+
+	return false;
+}
+
 /*
  * Write changes to disk
  */
 static void
-WriteElement(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement dup, HnswElement entryPoint, bool building)
+WriteElement(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement entryPoint, bool building)
 {
 	BlockNumber newInsertPage = InvalidBlockNumber;
 
-	/* Try to add to existing page */
-	if (dup != NULL)
-	{
-		if (HnswAddDuplicate(index, element, dup, building))
-			return;
-	}
+	/* Look for duplicate */
+	if (HnswFindDuplicate(index, element, building))
+		return;
 
 	/* Write element and neighbor tuples */
 	WriteNewElementPages(index, element, m, GetInsertPage(index), &newInsertPage, building);
@@ -519,7 +560,7 @@ WriteElement(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement elem
 	/* Update neighbors */
 	HnswUpdateNeighborPages(index, procinfo, collation, element, m, false, building);
 
-	/* Update metapage if needed */
+	/* Update entry point if needed */
 	if (entryPoint == NULL || element->level > entryPoint->level)
 		HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM, building);
 }
@@ -528,29 +569,16 @@ WriteElement(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement elem
  * Insert a tuple into the index
  */
 bool
-HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel, bool building)
+HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel, bool building)
 {
-	Datum		value;
-	FmgrInfo   *normprocinfo;
 	HnswElement entryPoint;
 	HnswElement element;
 	int			m;
 	int			efConstruction = HnswGetEfConstruction(index);
 	FmgrInfo   *procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
 	Oid			collation = index->rd_indcollation[0];
-	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;
-	}
+	char	   *base = NULL;
 
 	/*
 	 * Get a shared lock. This allows vacuum to ensure no in-flight inserts
@@ -563,8 +591,8 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
 
 	/* Create an element */
-	element = HnswInitElement(heap_tid, m, HnswGetMl(m), HnswGetMaxLevel(m));
-	element->value = value;
+	element = HnswInitElement(base, heap_tid, m, HnswGetMl(m), HnswGetMaxLevel(m), NULL);
+	HnswPtrStore(base, element->value, DatumGetPointer(value));
 
 	/* Prevent concurrent inserts when likely updating entry point */
 	if (entryPoint == NULL || element->level > entryPoint->level)
@@ -581,13 +609,10 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	}
 
 	/* Insert element in graph */
-	HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, false);
-
-	/* Look for duplicate */
-	dup = HnswFindDuplicate(element);
+	HnswInsertElement(base, element, entryPoint, index, procinfo, collation, m, efConstruction, false);
 
 	/* Write to disk */
-	WriteElement(index, procinfo, collation, element, m, efConstruction, dup, entryPoint, building);
+	WriteElement(index, procinfo, collation, element, m, efConstruction, entryPoint, building);
 
 	/* Release lock */
 	UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
@@ -595,6 +620,30 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	return true;
 }
 
+/*
+ * Insert a tuple into the index
+ */
+static void
+HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel)
+{
+	Datum		value;
+	FmgrInfo   *normprocinfo;
+	Oid			collation = index->rd_indcollation[0];
+
+	/* 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;
+	}
+
+	HnswInsertTupleOnDisk(index, value, values, isnull, heap_tid, heapRel, false);
+}
+
 /*
  * Insert a tuple into the index
  */
@@ -621,7 +670,7 @@ hnswinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid,
 	oldCtx = MemoryContextSwitchTo(insertCtx);
 
 	/* Insert tuple */
-	HnswInsertTuple(index, values, isnull, heap_tid, heap, false);
+	HnswInsertTuple(index, values, isnull, heap_tid, heap);
 
 	/* Delete memory context */
 	MemoryContextSwitchTo(oldCtx);

src/hnswscan.c

@@ -21,6 +21,7 @@ GetScanItems(IndexScanDesc scan, Datum q)
 	List	   *w;
 	int			m;
 	HnswElement entryPoint;
+	char	   *base = NULL;
 
 	/* Get m and entry point */
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
@@ -28,15 +29,15 @@ GetScanItems(IndexScanDesc scan, Datum q)
 	if (entryPoint == NULL)
 		return NIL;
 
-	ep = list_make1(HnswEntryCandidate(entryPoint, q, index, procinfo, collation, false));
+	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, false));
 
 	for (int lc = entryPoint->level; lc >= 1; lc--)
 	{
-		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, m, false, NULL);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, false, NULL);
 		ep = w;
 	}
 
-	return HnswSearchLayer(q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
 }
 
 /*
@@ -184,19 +185,19 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 
 	while (list_length(so->w) > 0)
 	{
+		char	   *base = NULL;
 		HnswCandidate *hc = llast(so->w);
+		HnswElement element = HnswPtrAccess(base, hc->element);
 		ItemPointer heaptid;
 
 		/* Move to next element if no valid heap TIDs */
-		if (list_length(hc->element->heaptids) == 0)
+		if (element->heaptidsLength == 0)
 		{
 			so->w = list_delete_last(so->w);
 			continue;
 		}
 
-		heaptid = llast(hc->element->heaptids);
-
-		hc->element->heaptids = list_delete_last(hc->element->heaptids);
+		heaptid = &element->heaptids[--element->heaptidsLength];
 
 		MemoryContextSwitchTo(oldCtx);
 

src/hnswutils.c

@@ -84,9 +84,40 @@ hash_pointer(uintptr_t ptr)
 #define SH_DEFINE
 #include "lib/simplehash.h"
 
+/* Needed to include simplehash.h again */
+#if PG_VERSION_NUM < 120000
+#undef SH_EQUAL
+#undef sh_log2
+#undef sh_pow2
+#define sh_log2 offsethash_sh_log2
+#define sh_pow2 offsethash_sh_pow2
+#endif
+
+/* Offset hash table */
+static uint32
+hash_offset(Size offset)
+{
+#if SIZEOF_SIZE_T == 8
+	return murmurhash64((uint64) offset);
+#else
+	return murmurhash32((uint32) offset);
+#endif
+}
+
+#define SH_PREFIX		offsethash
+#define SH_ELEMENT_TYPE	OffsetHashEntry
+#define SH_KEY_TYPE		Size
+#define	SH_KEY			offset
+#define SH_HASH_KEY(tb, key)	hash_offset(key)
+#define SH_EQUAL(tb, a, b)		(a == b)
+#define	SH_SCOPE		extern
+#define SH_DEFINE
+#include "lib/simplehash.h"
+
 typedef union
 {
 	pointerhash_hash *pointers;
+	offsethash_hash *offsets;
 	tidhash_hash *tids;
 }			visited_hash;
 
@@ -188,42 +219,46 @@ HnswInitPage(Buffer buf, Page page)
  * Allocate neighbors
  */
 void
-HnswInitNeighbors(HnswElement element, int m)
+HnswInitNeighbors(char *base, HnswElement element, int m, HnswAllocator * allocator)
 {
 	int			level = element->level;
 
-	element->neighbors = palloc(sizeof(HnswNeighborArray) * (level + 1));
+	HnswNeighborArrayPtr *neighborList = (HnswNeighborArrayPtr *) HnswAlloc(allocator, sizeof(HnswNeighborArrayPtr) * (level + 1));
+
+	HnswPtrStore(base, element->neighbors, neighborList);
 
 	for (int lc = 0; lc <= level; lc++)
 	{
 		HnswNeighborArray *a;
 		int			lm = HnswGetLayerM(m, lc);
 
-		a = &element->neighbors[lc];
+		HnswPtrStore(base, neighborList[lc], (HnswNeighborArray *) HnswAlloc(allocator, offsetof(HnswNeighborArray, items) + sizeof(HnswCandidate) * lm));
+
+		a = HnswGetNeighbors(base, element, lc);
 		a->length = 0;
-		a->items = palloc(sizeof(HnswCandidate) * lm);
 		a->closerSet = false;
 	}
 }
 
 /*
- * Free neighbors
+ * Allocate memory from the allocator
  */
-static void
-HnswFreeNeighbors(HnswElement element)
+void *
+HnswAlloc(HnswAllocator * allocator, Size size)
 {
-	for (int lc = 0; lc <= element->level; lc++)
-		pfree(element->neighbors[lc].items);
-	pfree(element->neighbors);
+	if (allocator)
+		return (*(allocator)->alloc) (size, (allocator)->state);
+
+	return palloc(size);
 }
 
 /*
  * Allocate an element
  */
 HnswElement
-HnswInitElement(ItemPointer heaptid, int m, double ml, int maxLevel)
+HnswInitElement(char *base, ItemPointer heaptid, int m, double ml, int maxLevel, HnswAllocator * allocator)
 {
-	HnswElement element = palloc(sizeof(HnswElementData));
+	HnswElement element = HnswAlloc(allocator, sizeof(HnswElementData));
 
 	int			level = (int) (-log(RandomDouble()) * ml);
 
@@ -231,42 +266,26 @@ HnswInitElement(ItemPointer heaptid, int m, double ml, int maxLevel)
 	if (level > maxLevel)
 		level = maxLevel;
 
-	element->heaptids = NIL;
+	element->heaptidsLength = 0;
 	HnswAddHeapTid(element, heaptid);
 
 	element->level = level;
 	element->deleted = 0;
 
-	HnswInitNeighbors(element, m);
+	HnswInitNeighbors(base, element, m, allocator);
 
-	element->value = PointerGetDatum(NULL);
+	HnswPtrStore(base, element->value, (Pointer) NULL);
 
 	return element;
 }
 
-/*
- * Free an element
- */
-void
-HnswFreeElement(HnswElement element)
-{
-	HnswFreeNeighbors(element);
-	list_free_deep(element->heaptids);
-	if (DatumGetPointer(element->value))
-		pfree(DatumGetPointer(element->value));
-	pfree(element);
-}
-
 /*
  * Add a heap TID to an element
  */
 void
 HnswAddHeapTid(HnswElement element, ItemPointer heaptid)
 {
-	ItemPointer copy = palloc(sizeof(ItemPointerData));
-
-	ItemPointerCopy(heaptid, copy);
-	element->heaptids = lappend(element->heaptids, copy);
+	element->heaptids[element->heaptidsLength++] = *heaptid;
 }
 
 /*
@@ -276,11 +295,12 @@ HnswElement
 HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno)
 {
 	HnswElement element = palloc(sizeof(HnswElementData));
+	char	   *base = NULL;
 
 	element->blkno = blkno;
 	element->offno = offno;
-	element->neighbors = NULL;
-	element->value = PointerGetDatum(NULL);
+	HnswPtrStore(base, element->neighbors, (HnswNeighborArrayPtr *) NULL);
+	HnswPtrStore(base, element->value, (Pointer) NULL);
 	return element;
 }
 
@@ -379,7 +399,9 @@ HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, Bloc
 
 	HnswUpdateMetaPageInfo(page, updateEntry, entryPoint, insertPage);
 
-	if (!building)
+	if (building)
+		MarkBufferDirty(buf);
+	else
 		GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 }
@@ -388,26 +410,28 @@ HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, Bloc
  * Set element tuple, except for neighbor info
  */
 void
-HnswSetElementTuple(HnswElementTuple etup, HnswElement element)
+HnswSetElementTuple(char *base, HnswElementTuple etup, HnswElement element)
 {
+	Pointer		valuePtr = HnswPtrAccess(base, element->value);
+
 	etup->type = HNSW_ELEMENT_TUPLE_TYPE;
 	etup->level = element->level;
 	etup->deleted = 0;
 	for (int i = 0; i < HNSW_HEAPTIDS; i++)
 	{
-		if (i < list_length(element->heaptids))
-			etup->heaptids[i] = *((ItemPointer) list_nth(element->heaptids, i));
+		if (i < element->heaptidsLength)
+			etup->heaptids[i] = element->heaptids[i];
 		else
 			ItemPointerSetInvalid(&etup->heaptids[i]);
 	}
-	memcpy(&etup->data, DatumGetPointer(element->value), VARSIZE_ANY(DatumGetPointer(element->value)));
+	memcpy(&etup->data, valuePtr, VARSIZE_ANY(valuePtr));
 }
 
 /*
  * Set neighbor tuple
  */
 void
-HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m)
+HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m)
 {
 	int			idx = 0;
 
@@ -415,7 +439,7 @@ HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m)
 
 	for (int lc = e->level; lc >= 0; lc--)
 	{
-		HnswNeighborArray *neighbors = &e->neighbors[lc];
+		HnswNeighborArray *neighbors = HnswGetNeighbors(base, e, lc);
 		int			lm = HnswGetLayerM(m, lc);
 
 		for (int i = 0; i < lm; i++)
@@ -425,8 +449,9 @@ HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m)
 			if (i < neighbors->length)
 			{
 				HnswCandidate *hc = &neighbors->items[i];
+				HnswElement hce = HnswPtrAccess(base, hc->element);
 
-				ItemPointerSet(indextid, hc->element->blkno, hc->element->offno);
+				ItemPointerSet(indextid, hce->blkno, hce->offno);
 			}
 			else
 				ItemPointerSetInvalid(indextid);
@@ -442,12 +467,14 @@ HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m)
 static void
 LoadNeighborsFromPage(HnswElement element, Relation index, Page page, int m)
 {
+	char	   *base = NULL;
+
 	HnswNeighborTuple ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
 	int			neighborCount = (element->level + 2) * m;
 
 	Assert(HnswIsNeighborTuple(ntup));
 
-	HnswInitNeighbors(element, m);
+	HnswInitNeighbors(base, element, m, NULL);
 
 	/* Ensure expected neighbors */
 	if (ntup->count != neighborCount)
@@ -473,9 +500,9 @@ LoadNeighborsFromPage(HnswElement element, Relation index, Page page, int m)
 		if (level < 0)
 			level = 0;
 
-		neighbors = &element->neighbors[level];
+		neighbors = HnswGetNeighbors(base, element, level);
 		hc = &neighbors->items[neighbors->length++];
-		hc->element = e;
+		HnswPtrStore(base, hc->element, e);
 	}
 }
 
@@ -507,7 +534,7 @@ HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHe
 	element->deleted = etup->deleted;
 	element->neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
 	element->neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
-	element->heaptids = NIL;
+	element->heaptidsLength = 0;
 
 	if (loadHeaptids)
 	{
@@ -522,7 +549,12 @@ HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHe
 	}
 
 	if (loadVec)
-		element->value = datumCopy(PointerGetDatum(&etup->data), false, -1);
+	{
+		char	   *base = NULL;
+		Datum		value = datumCopy(PointerGetDatum(&etup->data), false, -1);
+
+		HnswPtrStore(base, element->value, DatumGetPointer(value));
+	}
 }
 
 /*
@@ -558,24 +590,27 @@ HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index,
  * Get the distance for a candidate
  */
 static float
-GetCandidateDistance(HnswCandidate * hc, Datum q, FmgrInfo *procinfo, Oid collation)
+GetCandidateDistance(char *base, HnswCandidate * hc, Datum q, FmgrInfo *procinfo, Oid collation)
 {
-	return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, q, hc->element->value));
+	HnswElement hce = HnswPtrAccess(base, hc->element);
+	Datum		value = HnswGetValue(base, hce);
+
+	return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, q, value));
 }
 
 /*
  * Create a candidate for the entry point
  */
 HnswCandidate *
-HnswEntryCandidate(HnswElement entryPoint, Datum q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec)
+HnswEntryCandidate(char *base, HnswElement entryPoint, Datum q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec)
 {
 	HnswCandidate *hc = palloc(sizeof(HnswCandidate));
 
-	hc->element = entryPoint;
+	HnswPtrStore(base, hc->element, entryPoint);
 	if (index == NULL)
-		hc->distance = GetCandidateDistance(hc, q, procinfo, collation);
+		hc->distance = GetCandidateDistance(base, hc, q, procinfo, collation);
 	else
-		HnswLoadElement(hc->element, &hc->distance, &q, index, procinfo, collation, loadVec);
+		HnswLoadElement(entryPoint, &hc->distance, &q, index, procinfo, collation, loadVec);
 	return hc;
 }
 
@@ -625,44 +660,85 @@ CreatePairingHeapNode(HnswCandidate * c)
  * Add to visited
  */
 static inline void
-AddToVisited(visited_hash v, HnswCandidate * hc, Relation index, bool *found)
+AddToVisited(char *base, visited_hash v, HnswCandidate * hc, Relation index, bool *found)
 {
-	if (index == NULL)
+	if (index != NULL)
+	{
+		HnswElement element = HnswPtrAccess(base, hc->element);
+		ItemPointerData indextid;
+
+		ItemPointerSet(&indextid, element->blkno, element->offno);
+		tidhash_insert(v.tids, indextid, found);
+	}
+	else if (base != NULL)
 	{
 #if PG_VERSION_NUM >= 130000
-		pointerhash_insert_hash(v.pointers, (uintptr_t) hc->element, hc->element->hash, found);
+		HnswElement element = HnswPtrAccess(base, hc->element);
+
+		offsethash_insert_hash(v.offsets, HnswPtrOffset(hc->element), element->hash, found);
 #else
-		pointerhash_insert(v.pointers, (uintptr_t) hc->element, found);
+		offsethash_insert(v.offsets, HnswPtrOffset(hc->element), found);
 #endif
 	}
 	else
 	{
-		ItemPointerData indextid;
+#if PG_VERSION_NUM >= 130000
+		HnswElement element = HnswPtrAccess(base, hc->element);
 
-		ItemPointerSet(&indextid, hc->element->blkno, hc->element->offno);
-		tidhash_insert(v.tids, indextid, found);
+		pointerhash_insert_hash(v.pointers, (uintptr_t) HnswPtrPointer(hc->element), element->hash, found);
+#else
+		pointerhash_insert(v.pointers, (uintptr_t) HnswPtrPointer(hc->element), found);
+#endif
 	}
 }
 
+/*
+ * Count element towards ef
+ */
+static inline bool
+CountElement(char *base, HnswElement skipElement, HnswCandidate * hc)
+{
+	HnswElement e;
+
+	if (skipElement == NULL)
+		return true;
+
+	/* Ensure does not access heaptidsLength during in-memory build */
+	pg_memory_barrier();
+
+	e = HnswPtrAccess(base, hc->element);
+	return e->heaptidsLength != 0;
+}
+
 /*
  * Algorithm 2 from paper
  */
 List *
-HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement)
+HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement)
 {
-	ListCell   *lc2;
-
 	List	   *w = NIL;
 	pairingheap *C = pairingheap_allocate(CompareNearestCandidates, NULL);
 	pairingheap *W = pairingheap_allocate(CompareFurthestCandidates, NULL);
 	int			wlen = 0;
 	visited_hash v;
+	ListCell   *lc2;
+	HnswNeighborArray *neighborhoodData = NULL;
+	Size		neighborhoodSize;
 
 	/* Create hash table */
-	if (index == NULL)
-		v.pointers = pointerhash_create(CurrentMemoryContext, ef * m * 2, NULL);
-	else
+	if (index != NULL)
 		v.tids = tidhash_create(CurrentMemoryContext, ef * m * 2, NULL);
+	else if (base != NULL)
+		v.offsets = offsethash_create(CurrentMemoryContext, ef * m * 2, NULL);
+	else
+		v.pointers = pointerhash_create(CurrentMemoryContext, ef * m * 2, NULL);
+
+	/* Create local memory for neighborhood if needed */
+	if (index == NULL)
+	{
+		neighborhoodSize = offsetof(HnswNeighborArray, items) + sizeof(HnswCandidate) * HnswGetLayerM(m, lc);
+		neighborhoodData = palloc(neighborhoodSize);
+	}
 
 	/* Add entry points to v, C, and W */
 	foreach(lc2, ep)
@@ -670,7 +746,7 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 		HnswCandidate *hc = (HnswCandidate *) lfirst(lc2);
 		bool		found;
 
-		AddToVisited(v, hc, index, &found);
+		AddToVisited(base, v, hc, index, &found);
 
 		pairingheap_add(C, &(CreatePairingHeapNode(hc)->ph_node));
 		pairingheap_add(W, &(CreatePairingHeapNode(hc)->ph_node));
@@ -680,7 +756,7 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 		 * 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)
+		if (CountElement(base, skipElement, hc))
 			wlen++;
 	}
 
@@ -689,38 +765,51 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 		HnswNeighborArray *neighborhood;
 		HnswCandidate *c = ((HnswPairingHeapNode *) pairingheap_remove_first(C))->inner;
 		HnswCandidate *f = ((HnswPairingHeapNode *) pairingheap_first(W))->inner;
+		HnswElement cElement;
 
 		if (c->distance > f->distance)
 			break;
 
-		if (c->element->neighbors == NULL)
-			HnswLoadNeighbors(c->element, index, m);
+		cElement = HnswPtrAccess(base, c->element);
+
+		if (HnswPtrIsNull(base, cElement->neighbors))
+			HnswLoadNeighbors(cElement, index, m);
 
 		/* Get the neighborhood at layer lc */
-		neighborhood = &c->element->neighbors[lc];
+		neighborhood = HnswGetNeighbors(base, cElement, lc);
+
+		/* Copy neighborhood to local memory if needed */
+		if (index == NULL)
+		{
+			LWLockAcquire(&cElement->lock, LW_EXCLUSIVE);
+			memcpy(neighborhoodData, neighborhood, neighborhoodSize);
+			LWLockRelease(&cElement->lock);
+			neighborhood = neighborhoodData;
+		}
 
 		for (int i = 0; i < neighborhood->length; i++)
 		{
 			HnswCandidate *e = &neighborhood->items[i];
 			bool		visited;
 
-			AddToVisited(v, e, index, &visited);
+			AddToVisited(base, v, e, index, &visited);
 
 			if (!visited)
 			{
 				float		eDistance;
+				HnswElement eElement = HnswPtrAccess(base, e->element);
 
 				f = ((HnswPairingHeapNode *) pairingheap_first(W))->inner;
 
 				if (index == NULL)
-					eDistance = GetCandidateDistance(e, q, procinfo, collation);
+					eDistance = GetCandidateDistance(base, e, q, procinfo, collation);
 				else
-					HnswLoadElement(e->element, &eDistance, &q, index, procinfo, collation, inserting);
+					HnswLoadElement(eElement, &eDistance, &q, index, procinfo, collation, inserting);
 
-				Assert(!e->element->deleted);
+				Assert(!eElement->deleted);
 
 				/* Make robust to issues */
-				if (e->element->level < lc)
+				if (eElement->level < lc)
 					continue;
 
 				if (eDistance < f->distance || wlen < ef)
@@ -728,7 +817,7 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 					/* Copy e */
 					HnswCandidate *ec = palloc(sizeof(HnswCandidate));
 
-					ec->element = e->element;
+					HnswPtrStore(base, ec->element, eElement);
 					ec->distance = eDistance;
 
 					pairingheap_add(C, &(CreatePairingHeapNode(ec)->ph_node));
@@ -739,7 +828,7 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 					 * 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)
+					if (CountElement(base, skipElement, e))
 					{
 						wlen++;
 
@@ -764,7 +853,7 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 }
 
 /*
- * Compare candidate distances
+ * Compare candidate distances with pointer tie-breaker
  */
 static int
 #if PG_VERSION_NUM >= 130000
@@ -782,10 +871,38 @@ CompareCandidateDistances(const void *a, const void *b)
 	if (hca->distance > hcb->distance)
 		return -1;
 
-	if (hca->element < hcb->element)
+	if (HnswPtrPointer(hca->element) < HnswPtrPointer(hcb->element))
 		return 1;
 
-	if (hca->element > hcb->element)
+	if (HnswPtrPointer(hca->element) > HnswPtrPointer(hcb->element))
+		return -1;
+
+	return 0;
+}
+
+/*
+ * Compare candidate distances with offset tie-breaker
+ */
+static int
+#if PG_VERSION_NUM >= 130000
+CompareCandidateDistancesOffset(const ListCell *a, const ListCell *b)
+#else
+CompareCandidateDistancesOffset(const void *a, const void *b)
+#endif
+{
+	HnswCandidate *hca = lfirst((ListCell *) a);
+	HnswCandidate *hcb = lfirst((ListCell *) b);
+
+	if (hca->distance < hcb->distance)
+		return 1;
+
+	if (hca->distance > hcb->distance)
+		return -1;
+
+	if (HnswPtrOffset(hca->element) < HnswPtrOffset(hcb->element))
+		return 1;
+
+	if (HnswPtrOffset(hca->element) > HnswPtrOffset(hcb->element))
 		return -1;
 
 	return 0;
@@ -795,46 +912,59 @@ CompareCandidateDistances(const void *a, const void *b)
  * Calculate the distance between elements
  */
 static float
-HnswGetDistance(HnswElement a, HnswElement b, int lc, FmgrInfo *procinfo, Oid collation)
+HnswGetDistance(char *base, HnswElement a, HnswElement b, int lc, FmgrInfo *procinfo, Oid collation)
 {
+	Datum		aValue;
+	Datum		bValue;
+
 	/* Look for cached distance */
-	if (a->neighbors != NULL)
+	if (!HnswPtrIsNull(base, a->neighbors))
 	{
-		Assert(a->level >= lc);
+		HnswNeighborArray *neighbors = HnswGetNeighbors(base, a, lc);
 
-		for (int i = 0; i < a->neighbors[lc].length; i++)
+		for (int i = 0; i < neighbors->length; i++)
 		{
-			if (a->neighbors[lc].items[i].element == b)
-				return a->neighbors[lc].items[i].distance;
+			HnswElement element = HnswPtrAccess(base, neighbors->items[i].element);
+
+			if (element == b)
+				return neighbors->items[i].distance;
 		}
 	}
 
-	if (b->neighbors != NULL)
+	if (!HnswPtrIsNull(base, b->neighbors))
 	{
-		Assert(b->level >= lc);
+		HnswNeighborArray *neighbors = HnswGetNeighbors(base, b, lc);
 
-		for (int i = 0; i < b->neighbors[lc].length; i++)
+		for (int i = 0; i < neighbors->length; i++)
 		{
-			if (b->neighbors[lc].items[i].element == a)
-				return b->neighbors[lc].items[i].distance;
+			HnswElement element = HnswPtrAccess(base, neighbors->items[i].element);
+
+			if (element == a)
+				return neighbors->items[i].distance;
 		}
 	}
 
-	return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, a->value, b->value));
+	aValue = HnswGetValue(base, a);
+	bValue = HnswGetValue(base, b);
+
+	return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, aValue, bValue));
 }
 
 /*
  * Check if an element is closer to q than any element from R
  */
 static bool
-CheckElementCloser(HnswCandidate * e, List *r, int lc, FmgrInfo *procinfo, Oid collation)
+CheckElementCloser(char *base, HnswCandidate * e, List *r, int lc, FmgrInfo *procinfo, Oid collation)
 {
+	HnswElement eElement = HnswPtrAccess(base, e->element);
 	ListCell   *lc2;
 
 	foreach(lc2, r)
 	{
 		HnswCandidate *ri = lfirst(lc2);
-		float		distance = HnswGetDistance(e->element, ri->element, lc, procinfo, collation);
+		HnswElement riElement = HnswPtrAccess(base, ri->element);
+
+		float		distance = HnswGetDistance(base, eElement, riElement, lc, procinfo, collation);
 
 		if (distance <= e->distance)
 			return false;
@@ -847,12 +977,13 @@ CheckElementCloser(HnswCandidate * e, List *r, int lc, FmgrInfo *procinfo, Oid c
  * Algorithm 4 from paper
  */
 static List *
-SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswElement e2, HnswCandidate * newCandidate, HnswCandidate * *pruned, bool sortCandidates)
+SelectNeighbors(char *base, List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswElement e2, HnswCandidate * newCandidate, HnswCandidate * *pruned, bool sortCandidates)
 {
 	List	   *r = NIL;
 	List	   *w = list_copy(c);
 	pairingheap *wd;
-	bool		mustCalculate = !e2->neighbors[lc].closerSet;
+	HnswNeighborArray *neighbors = HnswGetNeighbors(base, e2, lc);
+	bool		mustCalculate = !neighbors->closerSet;
 	List	   *added = NIL;
 	bool		removedAny = false;
 
@@ -863,7 +994,12 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswE
 
 	/* Ensure order of candidates is deterministic for closer caching */
 	if (sortCandidates)
-		list_sort(w, CompareCandidateDistances);
+	{
+		if (base == NULL)
+			list_sort(w, CompareCandidateDistances);
+		else
+			list_sort(w, CompareCandidateDistancesOffset);
+	}
 
 	while (list_length(w) > 0 && list_length(r) < m)
 	{
@@ -874,7 +1010,7 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswE
 
 		/* Use previous state of r and wd to skip work when possible */
 		if (mustCalculate)
-			e->closer = CheckElementCloser(e, r, lc, procinfo, collation);
+			e->closer = CheckElementCloser(base, e, r, lc, procinfo, collation);
 		else if (list_length(added) > 0)
 		{
 			/*
@@ -883,7 +1019,7 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswE
 			 */
 			if (e->closer)
 			{
-				e->closer = CheckElementCloser(e, added, lc, procinfo, collation);
+				e->closer = CheckElementCloser(base, e, added, lc, procinfo, collation);
 
 				if (!e->closer)
 					removedAny = true;
@@ -896,7 +1032,7 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswE
 				 */
 				if (removedAny)
 				{
-					e->closer = CheckElementCloser(e, r, lc, procinfo, collation);
+					e->closer = CheckElementCloser(base, e, r, lc, procinfo, collation);
 					if (e->closer)
 						added = lappend(added, e);
 				}
@@ -904,7 +1040,7 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswE
 		}
 		else if (e == newCandidate)
 		{
-			e->closer = CheckElementCloser(e, r, lc, procinfo, collation);
+			e->closer = CheckElementCloser(base, e, r, lc, procinfo, collation);
 			if (e->closer)
 				added = lappend(added, e);
 		}
@@ -916,7 +1052,7 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswE
 	}
 
 	/* Cached value can only be used in future if sorted deterministically */
-	e2->neighbors[lc].closerSet = sortCandidates;
+	neighbors->closerSet = sortCandidates;
 
 	/* Keep pruned connections */
 	while (!pairingheap_is_empty(wd) && list_length(r) < m)
@@ -934,38 +1070,14 @@ SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswE
 	return r;
 }
 
-/*
- * Find duplicate element
- */
-HnswElement
-HnswFindDuplicate(HnswElement e)
-{
-	HnswNeighborArray *neighbors = &e->neighbors[0];
-
-	for (int i = 0; i < neighbors->length; i++)
-	{
-		HnswCandidate *neighbor = &neighbors->items[i];
-
-		/* Exit early since ordered by distance */
-		if (!datumIsEqual(e->value, neighbor->element->value, false, -1))
-			break;
-
-		/* Check for space */
-		if (list_length(neighbor->element->heaptids) < HNSW_HEAPTIDS)
-			return neighbor->element;
-	}
-
-	return NULL;
-}
-
 /*
  * Add connections
  */
 static void
-AddConnections(HnswElement element, List *neighbors, int m, int lc)
+AddConnections(char *base, HnswElement element, List *neighbors, int m, int lc)
 {
 	ListCell   *lc2;
-	HnswNeighborArray *a = &element->neighbors[lc];
+	HnswNeighborArray *a = HnswGetNeighbors(base, element, lc);
 
 	foreach(lc2, neighbors)
 		a->items[a->length++] = *((HnswCandidate *) lfirst(lc2));
@@ -975,13 +1087,13 @@ AddConnections(HnswElement element, List *neighbors, int m, int lc)
  * Update connections
  */
 void
-HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation)
+HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int m, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation)
 {
-	HnswNeighborArray *currentNeighbors = &hc->element->neighbors[lc];
-
+	HnswElement hce = HnswPtrAccess(base, hc->element);
+	HnswNeighborArray *currentNeighbors = HnswGetNeighbors(base, hce, lc);
 	HnswCandidate hc2;
 
-	hc2.element = element;
+	HnswPtrStore(base, hc2.element, element);
 	hc2.distance = hc->distance;
 
 	if (currentNeighbors->length < m)
@@ -1000,19 +1112,20 @@ HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int
 		/* Load elements on insert */
 		if (index != NULL)
 		{
-			Datum		q = hc->element->value;
+			Datum		q = HnswGetValue(base, hce);
 
 			for (int i = 0; i < currentNeighbors->length; i++)
 			{
 				HnswCandidate *hc3 = &currentNeighbors->items[i];
+				HnswElement hc3Element = HnswPtrAccess(base, hc3->element);
 
-				if (DatumGetPointer(hc3->element->value) == NULL)
-					HnswLoadElement(hc3->element, &hc3->distance, &q, index, procinfo, collation, true);
+				if (HnswPtrIsNull(base, hc3Element->value))
+					HnswLoadElement(hc3Element, &hc3->distance, &q, index, procinfo, collation, true);
 				else
-					hc3->distance = GetCandidateDistance(hc3, q, procinfo, collation);
+					hc3->distance = GetCandidateDistance(base, hc3, q, procinfo, collation);
 
 				/* Prune element if being deleted */
-				if (list_length(hc3->element->heaptids) == 0)
+				if (hc3Element->heaptidsLength == 0)
 				{
 					pruned = &currentNeighbors->items[i];
 					break;
@@ -1029,7 +1142,7 @@ HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int
 				c = lappend(c, &currentNeighbors->items[i]);
 			c = lappend(c, &hc2);
 
-			SelectNeighbors(c, m, lc, procinfo, collation, hc->element, &hc2, &pruned, true);
+			SelectNeighbors(base, c, m, lc, procinfo, collation, hce, &hc2, &pruned, true);
 
 			/* Should not happen */
 			if (pruned == NULL)
@@ -1039,7 +1152,7 @@ HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int
 		/* Find and replace the pruned element */
 		for (int i = 0; i < currentNeighbors->length; i++)
 		{
-			if (currentNeighbors->items[i].element == pruned->element)
+			if (HnswPtrEqual(base, currentNeighbors->items[i].element, pruned->element))
 			{
 				currentNeighbors->items[i] = hc2;
 
@@ -1057,43 +1170,65 @@ HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int
  * Remove elements being deleted or skipped
  */
 static List *
-RemoveElements(List *w, HnswElement skipElement)
+RemoveElements(char *base, List *w, HnswElement skipElement)
 {
 	ListCell   *lc2;
 	List	   *w2 = NIL;
 
+	/* Ensure does not access heaptidsLength during in-memory build */
+	pg_memory_barrier();
+
 	foreach(lc2, w)
 	{
 		HnswCandidate *hc = (HnswCandidate *) lfirst(lc2);
+		HnswElement hce = HnswPtrAccess(base, hc->element);
 
 		/* Skip self for vacuuming update */
-		if (skipElement != NULL && hc->element->blkno == skipElement->blkno && hc->element->offno == skipElement->offno)
+		if (skipElement != NULL && hce->blkno == skipElement->blkno && hce->offno == skipElement->offno)
 			continue;
 
-		if (list_length(hc->element->heaptids) != 0)
+		if (hce->heaptidsLength != 0)
 			w2 = lappend(w2, hc);
 	}
 
 	return w2;
 }
 
+#if PG_VERSION_NUM >= 130000
+/*
+ * Precompute hash
+ */
+static void
+PrecomputeHash(char *base, HnswElement element)
+{
+	HnswElementPtr ptr;
+
+	HnswPtrStore(base, ptr, element);
+
+	if (base == NULL)
+		element->hash = hash_pointer((uintptr_t) HnswPtrPointer(ptr));
+	else
+		element->hash = hash_offset(HnswPtrOffset(ptr));
+}
+#endif
+
 /*
  * Algorithm 1 from paper
  */
 void
-HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing)
+HnswInsertElement(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing)
 {
 	List	   *ep;
 	List	   *w;
 	int			level = element->level;
 	int			entryLevel;
-	Datum		q = element->value;
+	Datum		q = HnswGetValue(base, element);
 	HnswElement skipElement = existing ? element : NULL;
 
 #if PG_VERSION_NUM >= 130000
 	/* Precompute hash */
 	if (index == NULL)
-		element->hash = hash_pointer((uintptr_t) element);
+		PrecomputeHash(base, element);
 #endif
 
 	/* No neighbors if no entry point */
@@ -1101,13 +1236,13 @@ HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, F
 		return;
 
 	/* Get entry point and level */
-	ep = list_make1(HnswEntryCandidate(entryPoint, q, index, procinfo, collation, true));
+	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, true));
 	entryLevel = entryPoint->level;
 
 	/* 1st phase: greedy search to insert level */
 	for (int lc = entryLevel; lc >= level + 1; lc--)
 	{
-		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, m, true, skipElement);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, true, skipElement);
 		ep = w;
 	}
 
@@ -1125,12 +1260,12 @@ HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, F
 		List	   *neighbors;
 		List	   *lw;
 
-		w = HnswSearchLayer(q, ep, efConstruction, lc, index, procinfo, collation, m, true, skipElement);
+		w = HnswSearchLayer(base, q, ep, efConstruction, lc, index, procinfo, collation, m, true, skipElement);
 
 		/* Elements being deleted or skipped can help with search */
 		/* but should be removed before selecting neighbors */
 		if (index != NULL)
-			lw = RemoveElements(w, skipElement);
+			lw = RemoveElements(base, w, skipElement);
 		else
 			lw = w;
 
@@ -1139,9 +1274,9 @@ HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, F
 		 * sortCandidates to true for in-memory builds to enable closer
 		 * caching, but there does not seem to be a difference in performance.
 		 */
-		neighbors = SelectNeighbors(lw, lm, lc, procinfo, collation, element, NULL, NULL, false);
+		neighbors = SelectNeighbors(base, lw, lm, lc, procinfo, collation, element, NULL, NULL, false);
 
-		AddConnections(element, neighbors, lm, lc);
+		AddConnections(base, element, neighbors, lm, lc);
 
 		ep = w;
 	}

src/hnswvacuum.c

@@ -205,15 +205,15 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 		return;
 
 	/* Init fields */
-	HnswInitNeighbors(element, m);
-	element->heaptids = NIL;
+	HnswInitNeighbors(NULL, element, m, NULL);
+	element->heaptidsLength = 0;
 
 	/* Add element to graph, skipping itself */
-	HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, true);
+	HnswInsertElement(NULL, element, entryPoint, index, procinfo, collation, m, efConstruction, true);
 
 	/* Update neighbor tuple */
 	/* Do this before getting page to minimize locking */
-	HnswSetNeighborTuple(ntup, element, m);
+	HnswSetNeighborTuple(NULL, ntup, element, m);
 
 	/* Get neighbor page */
 	buf = ReadBufferExtended(index, MAIN_FORKNUM, element->neighborPage, RBM_NORMAL, bas);
@@ -301,7 +301,7 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 			{
 				/* Reset neighbors from previous update */
 				if (highestPoint != NULL)
-					highestPoint->neighbors = NULL;
+					HnswPtrStore((char *) NULL, highestPoint->neighbors, (HnswNeighborArrayPtr *) NULL);
 
 				RepairGraphElement(vacuumstate, entryPoint, highestPoint);
 			}

src/ivfbuild.c

@@ -543,10 +543,10 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	pfree(list);
 }
 
+#ifdef IVFFLAT_KMEANS_DEBUG
 /*
  * Print k-means metrics
  */
-#ifdef IVFFLAT_KMEANS_DEBUG
 static void
 PrintKmeansMetrics(IvfflatBuildState * buildstate)
 {

src/ivfkmeans.c

@@ -6,6 +6,10 @@
 #include "ivfflat.h"
 #include "miscadmin.h"
 
+#ifdef IVFFLAT_MEMORY
+#include "utils/memutils.h"
+#endif
+
 /*
  * Initialize with kmeans++
  *
@@ -151,6 +155,23 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	}
 }
 
+#ifdef IVFFLAT_MEMORY
+/*
+ * Show memory usage
+ */
+static void
+ShowMemoryUsage(Size estimatedSize)
+{
+#if PG_VERSION_NUM >= 130000
+	elog(INFO, "total memory: %zu MB",
+		 MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
+#else
+	MemoryContextStats(CurrentMemoryContext);
+#endif
+	elog(INFO, "estimated memory: %zu MB", estimatedSize / (1024 * 1024));
+}
+#endif
+
 /*
  * Use Elkan for performance. This requires distance function to satisfy triangle inequality.
  *
@@ -231,6 +252,10 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		vec->dim = dimensions;
 	}
 
+#ifdef IVFFLAT_MEMORY
+	ShowMemoryUsage(totalSize);
+#endif
+
 	/* Pick initial centers */
 	InitCenters(index, samples, centers, lowerBound);
 

test/t/012_hnsw_build_recall.pl

@@ -95,11 +95,10 @@ for my $i (0 .. $#operators)
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");
 
-	# Build index in parallel
+	# Build index in parallel in memory
 	my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
 		SET client_min_messages = DEBUG;
 		SET min_parallel_table_scan_size = 1;
-		SET hnsw.enable_parallel_build = on;
 		CREATE INDEX idx ON tst USING hnsw (v $opclass);
 	));
 	is($ret, 0, $stderr);
@@ -109,6 +108,21 @@ for my $i (0 .. $#operators)
 	test_recall($min, $operator);
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel on disk
+	# Set parallel_workers on table to use workers with low maintenance_work_mem
+	($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		ALTER TABLE tst SET (parallel_workers = 2);
+		SET client_min_messages = DEBUG;
+		SET maintenance_work_mem = '4MB';
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+		ALTER TABLE tst RESET (parallel_workers);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+	like($stderr, qr/hnsw graph no longer fits into maintenance_work_mem/);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
 }
 
 done_testing();