Added subscript function for vectors

Redefining a typedef is a C11 feature:

    In file included from src/hnsw.c:10:
    src/hnsw.h:147:5: warning: redefinition of typedef 'HnswElementData' is a C11 feature [-Wtypedef-redefinition]
    }                       HnswElementData;
                            ^
    src/hnsw.h:118:32: note: previous definition is here
    typedef struct HnswElementData HnswElementData;
                                   ^
    src/hnsw.h:163:5: warning: redefinition of typedef 'HnswNeighborArray' is a C11 feature [-Wtypedef-redefinition]
    }                       HnswNeighborArray;
                            ^
    src/hnsw.h:119:34: note: previous definition is here
    typedef struct HnswNeighborArray HnswNeighborArray;
                                     ^
    2 warnings generated.

I got these warnings when I built PostgreSQL with "CC=clang
CFLAGS=-std=gnu99"; other similar options would surely produce the
warnings too.

.github/workflows/build.yml

@@ -73,6 +73,7 @@ jobs:
           postgres-version: 14
       - run: |
           call "C:\Program Files\Microsoft Visual Studio\2022\Enterprise\VC\Auxiliary\Build\vcvars64.bat" && ^
+          cd %TEMP% && ^
           nmake /NOLOGO /F Makefile.win && ^
           nmake /NOLOGO /F Makefile.win install && ^
           nmake /NOLOGO /F Makefile.win installcheck && ^

CHANGELOG.md

@@ -1,3 +1,11 @@
+## 0.7.0 (unreleased)
+
+- Added subscript function for vectors
+
+## 0.6.2 (unreleased)
+
+- Reduced lock contention with parallel HNSW index builds
+
 ## 0.6.1 (2024-03-04)
 
 - Fixed error with `ANALYZE` and vectors with different dimensions

README.md

@@ -26,7 +26,7 @@ make
 make install # may need sudo
 ```
 
-See the [installation notes](#installation-notes) if you run into issues
+See the [installation notes](#installation-notes---linux-and-mac) if you run into issues
 
 You can also install it with [Docker](#docker), [Homebrew](#homebrew), [PGXN](#pgxn), [APT](#apt), [Yum](#yum), [pkg](#pkg), or [conda-forge](#conda-forge), and it comes preinstalled with [Postgres.app](#postgresapp) and many [hosted providers](#hosted-postgres). There are also instructions for [GitHub Actions](https://github.com/pgvector/setup-pgvector).
 
@@ -44,12 +44,15 @@ Then use `nmake` to build:
 
 ```cmd
 set "PGROOT=C:\Program Files\PostgreSQL\16"
+cd %TEMP%
 git clone --branch v0.6.1 https://github.com/pgvector/pgvector.git
 cd pgvector
 nmake /F Makefile.win
 nmake /F Makefile.win install
 ```
 
+See the [installation notes](#installation-notes---windows) if you run into issues
+
 You can also install it with [Docker](#docker) or [conda-forge](#conda-forge).
 
 ## Getting Started
@@ -410,13 +413,39 @@ You can use [Reciprocal Rank Fusion](https://github.com/pgvector/pgvector-python
 
 ## Performance
 
+### Tuning
+
+Use a tool like [PgTune](https://pgtune.leopard.in.ua/) to set initial values for Postgres server parameters.
+
+### Loading
+
+Use `COPY` for bulk loading data ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/bulk_loading.py)).
+
+```sql
+COPY items (embedding) FROM STDIN WITH (FORMAT BINARY);
+```
+
+Add any indexes *after* loading the initial data for best performance.
+
+### Indexing
+
+See index build time for [HNSW](#index-build-time) and [IVFFlat](#index-build-time-1).
+
+In production environments, create indexes concurrently to avoid blocking writes.
+
+```sql
+CREATE INDEX CONCURRENTLY ...
+```
+
+### Querying
+
 Use `EXPLAIN ANALYZE` to debug performance.
 
 ```sql
 EXPLAIN ANALYZE SELECT * FROM items ORDER BY embedding <-> '[3,1,2]' LIMIT 5;
 ```
 
-### Exact Search
+#### Exact Search
 
 To speed up queries without an index, increase `max_parallel_workers_per_gather`.
 
@@ -430,7 +459,7 @@ If vectors are normalized to length 1 (like [OpenAI embeddings](https://platform
 SELECT * FROM items ORDER BY embedding <#> '[3,1,2]' LIMIT 5;
 ```
 
-### Approximate Search
+#### Approximate Search
 
 To speed up queries with an IVFFlat index, increase the number of inverted lists (at the expense of recall).
 
@@ -438,7 +467,7 @@ To speed up queries with an IVFFlat index, increase the number of inverted lists
 CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 1000);
 ```
 
-## Vacuuming
+### Vacuuming
 
 Vacuuming can take a while for HNSW indexes. Speed it up by reindexing first.
 
@@ -447,6 +476,41 @@ REINDEX INDEX CONCURRENTLY index_name;
 VACUUM table_name;
 ```
 
+## Monitoring
+
+Monitor performance with [pg_stat_statements](https://www.postgresql.org/docs/current/pgstatstatements.html) (be sure to add it to `shared_preload_libraries`).
+
+```sql
+CREATE EXTENSION pg_stat_statements;
+```
+
+Get the most time-consuming queries with:
+
+```sql
+SELECT query, calls, ROUND((total_plan_time + total_exec_time) / calls) AS avg_time_ms,
+    ROUND((total_plan_time + total_exec_time) / 60000) AS total_time_min
+    FROM pg_stat_statements ORDER BY total_plan_time + total_exec_time DESC LIMIT 20;
+```
+
+Note: Replace `total_plan_time + total_exec_time` with `total_time` for Postgres < 13
+
+Monitor recall by comparing results from approximate search with exact search.
+
+```sql
+BEGIN;
+SET LOCAL enable_indexscan = off; -- use exact search
+SELECT ...
+COMMIT;
+```
+
+## Scaling
+
+Scale pgvector the same way you scale Postgres.
+
+Scale vertically by increasing memory, CPU, and storage on a single instance. Use existing tools to [tune parameters](#tuning) and [monitor performance](#monitoring).
+
+Scale horizontally with [replicas](https://www.postgresql.org/docs/current/hot-standby.html), or use [Citus](https://github.com/citusdata/citus) or another approach for sharding ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/citus.py)).
+
 ## Languages
 
 Use pgvector from any language with a Postgres client. You can even generate and store vectors in one language and query them in another.
@@ -552,7 +616,17 @@ SELECT pg_size_pretty(pg_relation_size('index_name'));
 
 #### Why isn’t a query using an index?
 
-The cost estimation in pgvector < 0.4.3 does not always work well with the planner. You can encourage the planner to use an index for a query with:
+The query needs to have an `ORDER BY` and `LIMIT`, and the `ORDER BY` must be the result of a distance operator, not an expression.
+
+```sql
+-- index
+ORDER BY embedding <=> '[3,1,2]' LIMIT 5;
+
+-- no index
+ORDER BY 1 - (embedding <=> '[3,1,2]') DESC LIMIT 5;
+```
+
+You can encourage the planner to use an index for a query with:
 
 ```sql
 BEGIN;
@@ -581,6 +655,10 @@ or choose to store vectors inline:
 ALTER TABLE items ALTER COLUMN embedding SET STORAGE PLAIN;
 ```
 
+#### Why are there less results for a query after adding an HNSW index?
+
+Results are limited by the size of the dynamic candidate list (`hnsw.ef_search`). There may be even less results due to dead tuples or filtering conditions in the query. We recommend setting `hnsw.ef_search` to at least twice the `LIMIT` of the query. If you need more than 500 results, use an IVFFlat index instead.
+
 #### Why are there less results for a query after adding an IVFFlat index?
 
 The index was likely created with too little data for the number of lists. Drop the index until the table has more data.
@@ -589,6 +667,8 @@ The index was likely created with too little data for the number of lists. Drop
 DROP INDEX index_name;
 ```
 
+Results can also be limited by the number of probes (`ivfflat.probes`).
+
 ## Reference
 
 ### Vector Type
@@ -624,7 +704,7 @@ Function | Description | Added
 avg(vector) → vector | average |
 sum(vector) → vector | sum | 0.5.0
 
-## Installation Notes
+## Installation Notes - Linux and Mac
 
 ### Postgres Location
 
@@ -666,12 +746,24 @@ If compilation fails and the output includes `warning: no such sysroot directory
 
 ### Portability
 
+By default, pgvector compiles with `-march=native` on some platforms for best performance. However, this can lead to `Illegal instruction` errors if trying to run the compiled extension on a different machine.
+
 To compile for portability, use:
 
 ```sh
 make OPTFLAGS=""
 ```
 
+## Installation Notes - Windows
+
+### Missing Header
+
+If compilation fails with `Cannot open include file: 'postgres.h': No such file or directory`, make sure `PGROOT` is correct.
+
+### Permissions
+
+If installation fails with `Access is denied`, re-run the installation instructions as an administrator.
+
 ## Additional Installation Methods
 
 ### Docker
@@ -856,6 +948,12 @@ make installcheck REGRESS=functions                            # regression test
 make prove_installcheck PROVE_TESTS=test/t/001_ivfflat_wal.pl  # TAP test
 ```
 
+To enable assertions:
+
+```sh
+make clean && PG_CFLAGS="-DUSE_ASSERT_CHECKING" make && make install
+```
+
 To enable benchmarking:
 
 ```sh
@@ -868,12 +966,6 @@ To show memory usage:
 make clean && PG_CFLAGS="-DHNSW_MEMORY -DIVFFLAT_MEMORY" make && make install
 ```
 
-To enable assertions:
-
-```sh
-make clean && PG_CFLAGS="-DUSE_ASSERT_CHECKING" make && make install
-```
-
 To get k-means metrics:
 
 ```sh

sql/vector--0.6.2--0.7.0.sql

@@ -0,0 +1,7 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.7.0'" to load this file. \quit
+
+CREATE FUNCTION vector_subscript(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+ALTER TYPE vector SET (SUBSCRIPT = vector_subscript);

sql/vector.sql

@@ -20,12 +20,16 @@ CREATE FUNCTION vector_recv(internal, oid, integer) RETURNS vector
 CREATE FUNCTION vector_send(vector) RETURNS bytea
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION vector_subscript(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE TYPE vector (
 	INPUT     = vector_in,
 	OUTPUT    = vector_out,
 	TYPMOD_IN = vector_typmod_in,
 	RECEIVE   = vector_recv,
 	SEND      = vector_send,
+	SUBSCRIPT = vector_subscript,
 	STORAGE   = external
 );
 

src/hnsw.h

@@ -129,7 +129,7 @@ HnswPtrDeclare(HnswNeighborArray, HnswNeighborArrayRelptr, HnswNeighborArrayPtr)
 HnswPtrDeclare(HnswNeighborArrayPtr, HnswNeighborsRelptr, HnswNeighborsPtr);
 HnswPtrDeclare(char, DatumRelptr, DatumPtr);
 
-typedef struct HnswElementData
+struct HnswElementData
 {
 	HnswElementPtr next;
 	ItemPointerData heaptids[HNSW_HEAPTIDS];
@@ -144,7 +144,7 @@ typedef struct HnswElementData
 	BlockNumber neighborPage;
 	DatumPtr	value;
 	LWLock		lock;
-}			HnswElementData;
+};
 
 typedef HnswElementData * HnswElement;
 
@@ -155,12 +155,12 @@ typedef struct HnswCandidate
 	bool		closer;
 }			HnswCandidate;
 
-typedef struct HnswNeighborArray
+struct HnswNeighborArray
 {
 	int			length;
 	bool		closerSet;
 	HnswCandidate items[FLEXIBLE_ARRAY_MEMBER];
-}			HnswNeighborArray;
+};
 
 typedef struct HnswPairingHeapNode
 {
@@ -185,6 +185,7 @@ typedef struct HnswGraph
 
 	/* Entry state */
 	LWLock		entryLock;
+	LWLock		entryWaitLock;
 	HnswElementPtr entryPoint;
 
 	/* Allocations state */

src/hnswbuild.c

@@ -431,10 +431,15 @@ InsertTupleInMemory(HnswBuildState * buildstate, HnswElement element)
 	HnswGraph  *graph = buildstate->graph;
 	HnswElement entryPoint;
 	LWLock	   *entryLock = &graph->entryLock;
+	LWLock	   *entryWaitLock = &graph->entryWaitLock;
 	int			efConstruction = buildstate->efConstruction;
 	int			m = buildstate->m;
 	char	   *base = buildstate->hnswarea;
 
+	/* Wait if another process needs exclusive lock on entry lock */
+	LWLockAcquire(entryWaitLock, LW_EXCLUSIVE);
+	LWLockRelease(entryWaitLock);
+
 	/* Get entry point */
 	LWLockAcquire(entryLock, LW_SHARED);
 	entryPoint = HnswPtrAccess(base, graph->entryPoint);
@@ -445,8 +450,10 @@ InsertTupleInMemory(HnswBuildState * buildstate, HnswElement element)
 		/* Release shared lock */
 		LWLockRelease(entryLock);
 
-		/* Get exclusive lock */
+		/* Tell other processes to wait and get exclusive lock */
+		LWLockAcquire(entryWaitLock, LW_EXCLUSIVE);
 		LWLockAcquire(entryLock, LW_EXCLUSIVE);
+		LWLockRelease(entryWaitLock);
 
 		/* Get latest entry point after lock is acquired */
 		entryPoint = HnswPtrAccess(base, graph->entryPoint);
@@ -612,6 +619,7 @@ InitGraph(HnswGraph * graph, char *base, long memoryTotal)
 	graph->indtuples = 0;
 	SpinLockInit(&graph->lock);
 	LWLockInitialize(&graph->entryLock, hnsw_lock_tranche_id);
+	LWLockInitialize(&graph->entryWaitLock, hnsw_lock_tranche_id);
 	LWLockInitialize(&graph->allocatorLock, hnsw_lock_tranche_id);
 	LWLockInitialize(&graph->flushLock, hnsw_lock_tranche_id);
 }

src/vector.c

@@ -4,11 +4,18 @@
 
 #include "catalog/pg_type.h"
 #include "common/shortest_dec.h"
+#include "executor/execExpr.h"
 #include "fmgr.h"
 #include "hnsw.h"
 #include "ivfflat.h"
 #include "lib/stringinfo.h"
 #include "libpq/pqformat.h"
+#include "nodes/makefuncs.h"
+#include "nodes/nodeFuncs.h"
+#include "nodes/subscripting.h"
+#include "parser/parse_coerce.h"
+#include "parser/parse_expr.h"
+#include "parser/parse_node.h"
 #include "port.h"				/* for strtof() */
 #include "utils/array.h"
 #include "utils/builtins.h"
@@ -418,6 +425,180 @@ vector_send(PG_FUNCTION_ARGS)
 	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
 }
 
+/*
+ * Transform the subscript expressions
+ */
+static void
+vector_subscript_transform(SubscriptingRef *sbsref, List *indirection, ParseState *pstate, bool isSlice, bool isAssignment)
+{
+	A_Indices  *ai;
+	Node	   *subexpr;
+
+	if (list_length(indirection) != 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				 errmsg("vector allows only one subscript"),
+				 parser_errposition(pstate,
+									exprLocation((Node *) indirection))));
+
+	ai = linitial_node(A_Indices, indirection);
+
+	if (isSlice)
+	{
+		if (ai->lidx)
+		{
+			subexpr = transformExpr(pstate, ai->lidx, pstate->p_expr_kind);
+			/* If it's not int4 already, try to coerce */
+			subexpr = coerce_to_target_type(pstate,
+											subexpr, exprType(subexpr),
+											INT4OID, -1,
+											COERCION_ASSIGNMENT,
+											COERCE_IMPLICIT_CAST,
+											-1);
+			if (subexpr == NULL)
+				ereport(ERROR,
+						(errcode(ERRCODE_DATATYPE_MISMATCH),
+						 errmsg("vector subscript must have type integer"),
+						 parser_errposition(pstate, exprLocation(ai->lidx))));
+		}
+		else if (!ai->is_slice)
+		{
+			/* Make a constant 1 */
+			subexpr = (Node *) makeConst(INT4OID,
+										 -1,
+										 InvalidOid,
+										 sizeof(int32),
+										 Int32GetDatum(1),
+										 false,
+										 true); /* pass by value */
+		}
+		else
+		{
+			/* Slice with omitted lower bound, put NULL into the list */
+			subexpr = NULL;
+		}
+		sbsref->reflowerindexpr = list_make1(subexpr);
+	}
+	else
+		Assert(ai->lidx == NULL && !ai->is_slice);
+
+	if (ai->uidx)
+	{
+		subexpr = transformExpr(pstate, ai->uidx, pstate->p_expr_kind);
+		/* If it's not int4 already, try to coerce */
+		subexpr = coerce_to_target_type(pstate,
+										subexpr, exprType(subexpr),
+										INT4OID, -1,
+										COERCION_ASSIGNMENT,
+										COERCE_IMPLICIT_CAST,
+										-1);
+		if (subexpr == NULL)
+			ereport(ERROR,
+					(errcode(ERRCODE_DATATYPE_MISMATCH),
+					 errmsg("array subscript must have type integer"),
+					 parser_errposition(pstate, exprLocation(ai->uidx))));
+	}
+	else
+	{
+		/* Slice with omitted upper bound, put NULL into the list */
+		Assert(isSlice && ai->is_slice);
+		subexpr = NULL;
+	}
+	sbsref->refupperindexpr = list_make1(subexpr);
+
+	if (isSlice)
+		sbsref->refrestype = sbsref->refcontainertype;
+	else
+		sbsref->refrestype = FLOAT4OID;
+}
+
+/*
+ * Fetch a vector element
+ */
+static void
+vector_subscript_fetch(ExprState *state, ExprEvalStep *op, ExprContext *econtext)
+{
+	SubscriptingRefState *sbsrefstate = op->d.sbsref.state;
+	Vector	   *vec = DatumGetVector(*op->resvalue);
+	int			index = DatumGetInt32(sbsrefstate->upperindex[0]);
+
+	if (index < 1 || index > vec->dim)
+		*op->resnull = true;
+	else
+		*op->resvalue = Float4GetDatum(vec->x[index - 1]);
+}
+
+/*
+ * Fetch a vector slice
+ */
+static void
+vector_subscript_fetch_slice(ExprState *state, ExprEvalStep *op, ExprContext *econtext)
+{
+	SubscriptingRefState *sbsrefstate = op->d.sbsref.state;
+
+	if (sbsrefstate->upperprovided[0] && sbsrefstate->upperindexnull[0])
+		*op->resnull = true;
+	else if (sbsrefstate->lowerprovided[0] && sbsrefstate->lowerindexnull[0])
+		*op->resnull = true;
+	else
+	{
+		Vector	   *vec = DatumGetVector(*op->resvalue);
+		int			upperindex = sbsrefstate->upperprovided[0] ? DatumGetInt32(sbsrefstate->upperindex[0]) : vec->dim;
+		int			lowerindex = sbsrefstate->lowerprovided[0] ? DatumGetInt32(sbsrefstate->lowerindex[0]) : 1;
+		int			dim;
+		Vector	   *result;
+
+		if (upperindex > vec->dim)
+			upperindex = vec->dim;
+
+		if (lowerindex < 1)
+			lowerindex = 1;
+
+		dim = upperindex - lowerindex + 1;
+
+		CheckDim(dim);
+
+		result = InitVector(dim);
+		for (int i = 0; i < dim; i++)
+			result->x[i] = vec->x[lowerindex + i - 1];
+
+		*op->resvalue = PointerGetDatum(result);
+	}
+}
+
+/*
+ * Set up execution state for a vector subscript operation
+ */
+static void
+vector_exec_setup(const SubscriptingRef *sbsref, SubscriptingRefState *sbsrefstate, SubscriptExecSteps *methods)
+{
+	methods->sbs_check_subscripts = NULL;
+	if (sbsrefstate->numlower != 0)
+		methods->sbs_fetch = vector_subscript_fetch_slice;
+	else
+		methods->sbs_fetch = vector_subscript_fetch;
+	methods->sbs_assign = NULL;
+	methods->sbs_fetch_old = NULL;
+}
+
+/*
+ * Subscript handler
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_subscript);
+Datum
+vector_subscript(PG_FUNCTION_ARGS)
+{
+	static const SubscriptRoutines sbsroutines = {
+		.transform = vector_subscript_transform,
+		.exec_setup = vector_exec_setup,
+		.fetch_strict = true,	/* fetch returns NULL for NULL inputs */
+		.fetch_leakproof = true,	/* fetch returns NULL for bad subscript */
+		.store_leakproof = false	/* ... but assignment throws error */
+	};
+
+	PG_RETURN_POINTER(&sbsroutines);
+}
+
 /*
  * Convert vector to vector
  * This is needed to check the type modifier

test/expected/functions.out

@@ -24,6 +24,112 @@ SELECT '[1e37]'::vector * '[1e37]';
 ERROR:  value out of range: overflow
 SELECT '[1e-37]'::vector * '[1e-37]';
 ERROR:  value out of range: underflow
+SELECT ('[1,2,3]'::vector)[0];
+ vector 
+--------
+       
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[1];
+ vector 
+--------
+      1
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[2];
+ vector 
+--------
+      2
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[3];
+ vector 
+--------
+      3
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[4];
+ vector 
+--------
+       
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[1:1];
+ vector 
+--------
+ [1]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[1:2];
+ vector 
+--------
+ [1,2]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[2:4];
+ vector 
+--------
+ [2,3]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[-2:2];
+ vector 
+--------
+ [1,2]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[2:1];
+ERROR:  vector must have at least 1 dimension
+SELECT ('[1,2,3]'::vector)[:];
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[:2];
+ vector 
+--------
+ [1,2]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[2:];
+ vector 
+--------
+ [2,3]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[:4];
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[-2:];
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[NULL];
+ vector 
+--------
+       
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[NULL:2];
+ vector 
+--------
+ 
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[2:NULL];
+ vector 
+--------
+ 
+(1 row)
+
+SELECT ('[1,2,3]'::vector)[1][1];
+ERROR:  vector allows only one subscript
 SELECT '[1,2,3]'::vector = '[1,2,3]';
  ?column? 
 ----------

test/sql/functions.sql

@@ -6,6 +6,26 @@ SELECT '[1,2,3]'::vector * '[4,5,6]';
 SELECT '[1e37]'::vector * '[1e37]';
 SELECT '[1e-37]'::vector * '[1e-37]';
 
+SELECT ('[1,2,3]'::vector)[0];
+SELECT ('[1,2,3]'::vector)[1];
+SELECT ('[1,2,3]'::vector)[2];
+SELECT ('[1,2,3]'::vector)[3];
+SELECT ('[1,2,3]'::vector)[4];
+SELECT ('[1,2,3]'::vector)[1:1];
+SELECT ('[1,2,3]'::vector)[1:2];
+SELECT ('[1,2,3]'::vector)[2:4];
+SELECT ('[1,2,3]'::vector)[-2:2];
+SELECT ('[1,2,3]'::vector)[2:1];
+SELECT ('[1,2,3]'::vector)[:];
+SELECT ('[1,2,3]'::vector)[:2];
+SELECT ('[1,2,3]'::vector)[2:];
+SELECT ('[1,2,3]'::vector)[:4];
+SELECT ('[1,2,3]'::vector)[-2:];
+SELECT ('[1,2,3]'::vector)[NULL];
+SELECT ('[1,2,3]'::vector)[NULL:2];
+SELECT ('[1,2,3]'::vector)[2:NULL];
+SELECT ('[1,2,3]'::vector)[1][1];
+
 SELECT '[1,2,3]'::vector = '[1,2,3]';
 SELECT '[1,2,3]'::vector = '[1,2]';