Updated readme [skip ci]

This reverts commit 3f674c9994.

CHANGELOG.md

@@ -1,15 +1,15 @@
 ## 0.7.0 (unreleased)
 
-- Added concatenate operator for vectors
+- Added `halfvec` type
 
-## 0.6.2 (unreleased)
+## 0.6.2 (2024-03-18)
 
 - Reduced lock contention with parallel HNSW index builds
 
 ## 0.6.1 (2024-03-04)
 
 - Fixed error with `ANALYZE` and vectors with different dimensions
-- Fixed error with `shared_preload_libraries`
+- Fixed segmentation fault with `shared_preload_libraries`
 - Fixed vector subtraction being marked as commutative
 
 ## 0.6.0 (2024-01-29)

META.json

@@ -2,7 +2,7 @@
 	"name": "vector",
 	"abstract": "Open-source vector similarity search for Postgres",
 	"description": "Supports L2 distance, inner product, and cosine distance",
-	"version": "0.6.1",
+	"version": "0.6.2",
 	"maintainer": [
 		"Andrew Kane <andrew@ankane.org>"
 	],
@@ -20,7 +20,7 @@
 		"vector": {
 			"file": "sql/vector.sql",
 			"docfile": "README.md",
-			"version": "0.6.1",
+			"version": "0.6.2",
 			"abstract": "Open-source vector similarity search for Postgres"
 		}
 	},

Makefile

@@ -1,10 +1,10 @@
 EXTENSION = vector
-EXTVERSION = 0.6.1
+EXTVERSION = 0.6.2
 
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
-OBJS = src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
+OBJS = src/halfvec.o src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
-HEADERS = src/vector.h
+HEADERS = src/halfvec.h src/vector.h
 
 TESTS = $(wildcard test/sql/*.sql)
 REGRESS = $(patsubst test/sql/%.sql,%,$(TESTS))

Makefile.win

@@ -1,8 +1,8 @@
 EXTENSION = vector
-EXTVERSION = 0.6.1
+EXTVERSION = 0.6.2
 
-OBJS = src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\vector.obj
+OBJS = src\halfvec.obj src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\vector.obj
-HEADERS = src\vector.h
+HEADERS = src\halfvec.h src\vector.h
 
 REGRESS = btree cast copy functions input ivfflat_cosine ivfflat_ip ivfflat_l2 ivfflat_options ivfflat_unlogged
 REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)

README.md

@@ -20,7 +20,7 @@ Compile and install the extension (supports Postgres 12+)
 
 ```sh
 cd /tmp
-git clone --branch v0.6.1 https://github.com/pgvector/pgvector.git
+git clone --branch v0.6.2 https://github.com/pgvector/pgvector.git
 cd pgvector
 make
 make install # may need sudo
@@ -45,7 +45,7 @@ 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
+git clone --branch v0.6.2 https://github.com/pgvector/pgvector.git
 cd pgvector
 nmake /F Makefile.win
 nmake /F Makefile.win install
@@ -400,6 +400,29 @@ Use [partitioning](https://www.postgresql.org/docs/current/ddl-partitioning.html
 CREATE TABLE items (embedding vector(3), category_id int) PARTITION BY LIST(category_id);
 ```
 
+## Types
+
+- `vector`
+- `halfvec`
+
+## Half-Precision
+
+```sql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding halfvec(3));
+INSERT INTO items (embedding) VALUES ('[1,2,3]'), ('[4,5,6]');
+CREATE INDEX ON items USING hnsw ((embedding::halfvec(3)) halfvec_l2_ops);
+```
+
+```sql
+SELECT id FROM items ORDER BY embedding::halfvec(3) <-> '[1,2,3]' LIMIT 5;
+```
+
+```sql
+SELECT id FROM (
+    SELECT * FROM items ORDER BY embedding::halfvec(3) <-> '[1,2,3]' LIMIT 20
+) ORDER BY embedding <-> '[1,2,3]' LIMIT 5;
+```
+
 ## Hybrid Search
 
 Use together with Postgres [full-text search](https://www.postgresql.org/docs/current/textsearch-intro.html) for hybrid search.
@@ -604,6 +627,18 @@ and query with:
 SELECT * FROM items ORDER BY embedding::vector(3) <-> '[3,1,2]' LIMIT 5;
 ```
 
+#### Are binary vectors supported?
+
+You can store binary vectors and perform exact nearest neighbor search by Hamming distance in Postgres without an extension ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/hash_image_search.py)).
+
+```tsql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding bit(3));
+INSERT INTO items (embedding) VALUES (B'000'), (B'111');
+SELECT * FROM items ORDER BY bit_count(embedding # B'101') LIMIT 5;
+```
+
+Indexing is not currently supported.
+
 #### Do indexes need to fit into memory?
 
 No, but like other index types, you’ll likely see better performance if they do. You can get the size of an index with:
@@ -659,6 +694,8 @@ ALTER TABLE items ALTER COLUMN embedding SET STORAGE PLAIN;
 
 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.
 
+Also, note that `NULL` vectors are not indexed (as well as zero vectors for cosine distance).
+
 #### 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.
@@ -669,6 +706,8 @@ DROP INDEX index_name;
 
 Results can also be limited by the number of probes (`ivfflat.probes`).
 
+Also, note that `NULL` vectors are not indexed (as well as zero vectors for cosine distance).
+
 ## Reference
 
 ### Vector Type
@@ -682,7 +721,6 @@ Operator | Description | Added
 \+ | element-wise addition |
 \- | element-wise subtraction |
 \* | element-wise multiplication | 0.5.0
-\|\| | concatenate | 0.7.0
 <-> | Euclidean distance |
 <#> | negative inner product |
 <=> | cosine distance |
@@ -705,6 +743,27 @@ Function | Description | Added
 avg(vector) → vector | average |
 sum(vector) → vector | sum | 0.5.0
 
+### Halfvec Type
+
+Each half vector takes `2 * dimensions + 8` bytes of storage. Each element is a half-precision floating-point number, and all elements must be finite (no `NaN`, `Infinity` or `-Infinity`). Half vectors can have up to 16,000 dimensions.
+
+### Halfvec Operators
+
+Operator | Description | Added
+--- | --- | ---
+<-> | Euclidean distance | 0.7.0
+<#> | negative inner product | 0.7.0
+<=> | cosine distance | 0.7.0
+
+### Halfvec Functions
+
+Function | Description | Added
+--- | --- | ---
+cosine_distance(halfvec, halfvec) → double precision | cosine distance | 0.7.0
+inner_product(halfvec, halfvec) → double precision | inner product | 0.7.0
+l2_distance(halfvec, halfvec) → double precision | Euclidean distance | 0.7.0
+l1_distance(halfvec, halfvec) → double precision | taxicab distance | 0.7.0
+
 ## Installation Notes - Linux and Mac
 
 ### Postgres Location
@@ -780,7 +839,7 @@ This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (r
 You can also build the image manually:
 
 ```sh
-git clone --branch v0.6.1 https://github.com/pgvector/pgvector.git
+git clone --branch v0.6.2 https://github.com/pgvector/pgvector.git
 cd pgvector
 docker build --build-arg PG_MAJOR=16 -t myuser/pgvector .
 ```

sql/vector--0.6.1--0.6.2.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.6.2'" to load this file. \quit

sql/vector--0.6.2--0.7.0.sql

@@ -1,9 +1,128 @@
 -- 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_concat(vector, vector) RETURNS vector
+CREATE TYPE halfvec;
+
+CREATE FUNCTION halfvec_in(cstring, oid, integer) RETURNS halfvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE OPERATOR || (
+CREATE FUNCTION halfvec_out(halfvec) RETURNS cstring
-	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_recv(internal, oid, integer) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_send(halfvec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE halfvec (
+	INPUT     = halfvec_in,
+	OUTPUT    = halfvec_out,
+	TYPMOD_IN = halfvec_typmod_in,
+	RECEIVE   = halfvec_recv,
+	SEND      = halfvec_send,
+	STORAGE   = external
 );
+
+CREATE FUNCTION l2_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_norm(halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_l2_squared_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(integer[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(real[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(double precision[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(numeric[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_to_float4(halfvec, integer, boolean) RETURNS real[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (halfvec AS halfvec)
+	WITH FUNCTION halfvec(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (halfvec AS real[])
+	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (integer[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (real[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(real[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (double precision[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(double precision[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (numeric[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(numeric[], integer, boolean) AS ASSIGNMENT;
+
+CREATE OPERATOR <-> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+CREATE OPERATOR CLASS halfvec_l2_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_ip_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_cosine_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 2 halfvec_norm(halfvec);
+
+CREATE FUNCTION halfvec_to_vector(halfvec, integer, boolean) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_to_halfvec(vector, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (halfvec AS vector)
+	WITH FUNCTION halfvec_to_vector(halfvec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (vector AS halfvec)
+	WITH FUNCTION vector_to_halfvec(vector, integer, boolean) AS ASSIGNMENT;

sql/vector.sql

@@ -99,9 +99,6 @@ CREATE FUNCTION vector_avg(double precision[]) RETURNS vector
 CREATE FUNCTION vector_combine(double precision[], double precision[]) RETURNS double precision[]
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION vector_concat(vector, vector) RETURNS vector
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
 -- aggregates
 
 CREATE AGGREGATE avg(vector) (
@@ -227,10 +224,6 @@ CREATE OPERATOR > (
 	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
 );
 
-CREATE OPERATOR || (
-	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
-);
-
 -- access methods
 
 CREATE FUNCTION ivfflathandler(internal) RETURNS index_am_handler
@@ -294,3 +287,145 @@ CREATE OPERATOR CLASS vector_cosine_ops
 	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
 	FUNCTION 2 vector_norm(vector);
+
+-- halfvec type
+
+CREATE TYPE halfvec;
+
+CREATE FUNCTION halfvec_in(cstring, oid, integer) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_out(halfvec) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_recv(internal, oid, integer) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_send(halfvec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE halfvec (
+	INPUT     = halfvec_in,
+	OUTPUT    = halfvec_out,
+	TYPMOD_IN = halfvec_typmod_in,
+	RECEIVE   = halfvec_recv,
+	SEND      = halfvec_send,
+	STORAGE   = external
+);
+
+-- halfvec functions
+
+CREATE FUNCTION l2_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_norm(halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- halfvec private functions
+
+CREATE FUNCTION halfvec_l2_squared_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- halfvec cast functions
+
+CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(integer[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(real[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(double precision[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(numeric[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_to_float4(halfvec, integer, boolean) RETURNS real[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- halfvec casts
+
+CREATE CAST (halfvec AS halfvec)
+	WITH FUNCTION halfvec(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (halfvec AS real[])
+	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (integer[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (real[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(real[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (double precision[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(double precision[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (numeric[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(numeric[], integer, boolean) AS ASSIGNMENT;
+
+-- halfvec operators
+
+CREATE OPERATOR <-> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+-- halfvec opclasses
+
+CREATE OPERATOR CLASS halfvec_l2_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_ip_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_cosine_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 2 halfvec_norm(halfvec);
+
+-- extension casts
+
+CREATE FUNCTION halfvec_to_vector(halfvec, integer, boolean) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_to_halfvec(vector, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (halfvec AS vector)
+	WITH FUNCTION halfvec_to_vector(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (vector AS halfvec)
+	WITH FUNCTION vector_to_halfvec(vector, integer, boolean) AS IMPLICIT;

src/halfvec.c

@@ -0,0 +1,969 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "catalog/pg_type.h"
+#include "common/shortest_dec.h"
+#include "fmgr.h"
+#include "halfvec.h"
+#include "lib/stringinfo.h"
+#include "libpq/pqformat.h"
+#include "port.h"				/* for strtof() */
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "utils/float.h"
+#include "utils/lsyscache.h"
+#include "utils/numeric.h"
+#include "vector.h"
+
+#if PG_VERSION_NUM < 130000
+#define TYPALIGN_DOUBLE 'd'
+#define TYPALIGN_INT 'i'
+#endif
+
+/*
+ * Check if half is NaN
+ */
+static inline bool
+HalfIsNan(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isnan(num);
+#else
+	return (num & 0x7C00) == 0x7C00 && (num & 0x7FFF) != 0x7C00;
+#endif
+}
+
+/*
+ * Check if half is infinite
+ */
+static inline bool
+HalfIsInf(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isinf(num);
+#else
+	return (num & 0x7FFF) == 0x7C00;
+#endif
+}
+
+/*
+ * Check if half is zero
+ */
+static inline bool
+HalfIsZero(half num)
+{
+#ifdef FLT16_SUPPORT
+	return num == 0;
+#else
+	return (num & 0x7FFF) == 0x0000;
+#endif
+}
+
+/*
+ * Get a half from a message buffer
+ */
+static half
+pq_getmsghalf(StringInfo msg)
+{
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swap;
+
+	swap.i = pq_getmsgint(msg, 2);
+	return swap.h;
+}
+
+/*
+ * Append a half to a StringInfo buffer
+ */
+static void
+pq_sendhalf(StringInfo buf, half h)
+{
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swap;
+
+	swap.h = h;
+	pq_sendint16(buf, swap.i);
+}
+
+/*
+ * Convert a half to a float4
+ */
+float
+HalfToFloat4(half num)
+{
+#ifdef FLT16_SUPPORT
+	return (float) num;
+#else
+	/* TODO Improve performance */
+
+	/* Assumes same endianness for floats and integers */
+	union
+	{
+		float		f;
+		uint32		i;
+	}			swapfloat;
+
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swaphalf;
+
+	uint16		bin;
+	uint32		exponent;
+	uint32		mantissa;
+	uint32		result;
+
+	swaphalf.h = num;
+	bin = swaphalf.i;
+	exponent = (bin & 0x7C00) >> 10;
+	mantissa = bin & 0x03FF;
+
+	/* Sign */
+	result = (bin & 0x8000) << 16;
+
+	if (exponent == 31)
+	{
+		if (mantissa == 0)
+		{
+			/* Infinite */
+			result |= 0x7F800000;
+		}
+		else
+		{
+			/* NaN */
+			result |= 0x7FC00000;
+			result |= mantissa << 13;
+		}
+	}
+	else if (exponent == 0)
+	{
+		/* Subnormal */
+		if (mantissa != 0)
+		{
+			exponent = -14;
+
+			for (int i = 0; i < 10; i++)
+			{
+				mantissa <<= 1;
+				exponent -= 1;
+
+				if ((mantissa >> 10) % 2 == 1)
+				{
+					mantissa &= 0x03ff;
+					break;
+				}
+			}
+
+			result |= (exponent + 127) << 23;
+			result |= mantissa << 13;
+		}
+	}
+	else
+	{
+		/* Normal */
+		result |= (exponent - 15 + 127) << 23;
+		result |= mantissa << 13;
+	}
+
+	swapfloat.i = result;
+	return swapfloat.f;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+half
+Float4ToHalfUnchecked(float num)
+{
+#ifdef FLT16_SUPPORT
+	return (_Float16) num;
+#else
+	/* TODO Improve performance */
+
+	/* Assumes same endianness for floats and integers */
+	union
+	{
+		float		f;
+		uint32		i;
+	}			swapfloat;
+
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swaphalf;
+
+	uint32		bin;
+	int			exponent;
+	int			mantissa;
+	uint16		result;
+
+	swapfloat.f = num;
+	bin = swapfloat.i;
+	exponent = (bin & 0x7F800000) >> 23;
+	mantissa = bin & 0x007FFFFF;
+
+	/* Sign */
+	result = (bin & 0x80000000) >> 16;
+
+	if (isinf(num))
+	{
+		/* Infinite */
+		result |= 0x7C00;
+	}
+	else if (isnan(num))
+	{
+		/* NaN */
+		result |= 0x7E00;
+		result |= mantissa >> 13;
+	}
+	else if (exponent > 98)
+	{
+		int			m;
+		int			gr;
+		int			s;
+
+		exponent -= 127;
+		s = mantissa & 0x00000FFF;
+
+		/* Subnormal */
+		if (exponent < -14)
+		{
+			int			diff = -exponent - 14;
+
+			mantissa >>= diff;
+			mantissa += 1 << (23 - diff);
+			s |= mantissa & 0x00000FFF;
+		}
+
+		m = mantissa >> 13;
+
+		/* Round */
+		gr = (mantissa >> 12) % 4;
+		if (gr == 3 || (gr == 1 && s != 0))
+			m += 1;
+
+		if (m == 1024)
+		{
+			m = 0;
+			exponent += 1;
+		}
+
+		if (exponent > 15)
+		{
+			/* Infinite */
+			result |= 0x7C00;
+		}
+		else
+		{
+			if (exponent >= -14)
+				result |= (exponent + 15) << 10;
+
+			result |= m;
+		}
+	}
+
+	swaphalf.i = result;
+	return swaphalf.h;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+half
+Float4ToHalf(float num)
+{
+	half		result = Float4ToHalfUnchecked(num);
+
+	if (unlikely(HalfIsInf(result)) && !isinf(num))
+		float_overflow_error();
+	if (unlikely(HalfIsZero(result)) && num != 0.0)
+		float_underflow_error();
+
+	return result;
+}
+
+/*
+ * Ensure same dimensions
+ */
+static inline void
+CheckDims(HalfVector * a, HalfVector * b)
+{
+	if (a->dim != b->dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different halfvec dimensions %d and %d", a->dim, b->dim)));
+}
+
+/*
+ * Ensure expected dimensions
+ */
+static inline void
+CheckExpectedDim(int32 typmod, int dim)
+{
+	if (typmod != -1 && typmod != dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected %d dimensions, not %d", typmod, dim)));
+}
+
+/*
+ * Ensure valid dimensions
+ */
+static inline void
+CheckDim(int dim)
+{
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("halfvec must have at least 1 dimension")));
+
+	if (dim > HALFVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("halfvec cannot have more than %d dimensions", HALFVEC_MAX_DIM)));
+}
+
+/*
+ * Ensure finite element
+ */
+static inline void
+CheckElement(half value)
+{
+	if (HalfIsNan(value))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("NaN not allowed in halfvec")));
+
+	if (HalfIsInf(value))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("infinite value not allowed in halfvec")));
+}
+
+/*
+ * Allocate and initialize a new half vector
+ */
+HalfVector *
+InitHalfVector(int dim)
+{
+	HalfVector *result;
+	int			size;
+
+	size = HALFVEC_SIZE(dim);
+	result = (HalfVector *) palloc0(size);
+	SET_VARSIZE(result, size);
+	result->dim = dim;
+
+	return result;
+}
+
+/*
+ * Check for whitespace, since array_isspace() is static
+ */
+static inline bool
+halfvec_isspace(char ch)
+{
+	if (ch == ' ' ||
+		ch == '\t' ||
+		ch == '\n' ||
+		ch == '\r' ||
+		ch == '\v' ||
+		ch == '\f')
+		return true;
+	return false;
+}
+
+#if PG_VERSION_NUM < 120003
+static pg_noinline void
+float_overflow_error(void)
+{
+	ereport(ERROR,
+			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+			 errmsg("value out of range: overflow")));
+}
+
+static pg_noinline void
+float_underflow_error(void)
+{
+	ereport(ERROR,
+			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+			 errmsg("value out of range: underflow")));
+}
+#endif
+
+/*
+ * Convert textual representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_in);
+Datum
+halfvec_in(PG_FUNCTION_ARGS)
+{
+	char	   *lit = PG_GETARG_CSTRING(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	half		x[HALFVEC_MAX_DIM];
+	int			dim = 0;
+	char	   *pt;
+	char	   *stringEnd;
+	HalfVector *result;
+	char	   *litcopy = pstrdup(lit);
+	char	   *str = litcopy;
+
+	while (halfvec_isspace(*str))
+		str++;
+
+	if (*str != '[')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("malformed halfvec literal: \"%s\"", lit),
+				 errdetail("Vector contents must start with \"[\".")));
+
+	str++;
+	pt = strtok(str, ",");
+	stringEnd = pt;
+
+	while (pt != NULL && *stringEnd != ']')
+	{
+		if (dim == HALFVEC_MAX_DIM)
+			ereport(ERROR,
+					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+					 errmsg("halfvec cannot have more than %d dimensions", HALFVEC_MAX_DIM)));
+
+		while (halfvec_isspace(*pt))
+			pt++;
+
+		/* Check for empty string like float4in */
+		if (*pt == '\0')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+
+		/* Use strtof like float4in to avoid a double-rounding problem */
+		x[dim] = Float4ToHalf(strtof(pt, &stringEnd));
+		CheckElement(x[dim]);
+		dim++;
+
+		if (stringEnd == pt)
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+
+		while (halfvec_isspace(*stringEnd))
+			stringEnd++;
+
+		if (*stringEnd != '\0' && *stringEnd != ']')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+
+		pt = strtok(NULL, ",");
+	}
+
+	if (stringEnd == NULL || *stringEnd != ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("malformed halfvec literal: \"%s\"", lit),
+				 errdetail("Unexpected end of input.")));
+
+	stringEnd++;
+
+	/* Only whitespace is allowed after the closing brace */
+	while (halfvec_isspace(*stringEnd))
+		stringEnd++;
+
+	if (*stringEnd != '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("malformed halfvec literal: \"%s\"", lit),
+				 errdetail("Junk after closing right brace.")));
+
+	/* Ensure no consecutive delimiters since strtok skips */
+	for (pt = lit + 1; *pt != '\0'; pt++)
+	{
+		if (pt[-1] == ',' && *pt == ',')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("malformed halfvec literal: \"%s\"", lit)));
+	}
+
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("halfvec must have at least 1 dimension")));
+
+	pfree(litcopy);
+
+	CheckExpectedDim(typmod, dim);
+
+	result = InitHalfVector(dim);
+	for (int i = 0; i < dim; i++)
+		result->x[i] = x[i];
+
+	PG_RETURN_POINTER(result);
+}
+
+#define AppendChar(ptr, c) (*(ptr)++ = (c))
+#define AppendFloat(ptr, f) ((ptr) += float_to_shortest_decimal_bufn((f), (ptr)))
+
+/*
+ * Convert internal representation to textual representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_out);
+Datum
+halfvec_out(PG_FUNCTION_ARGS)
+{
+	HalfVector *vector = PG_GETARG_HALFVEC_P(0);
+	int			dim = vector->dim;
+	char	   *buf;
+	char	   *ptr;
+
+	/*
+	 * Need:
+	 *
+	 * dim * (FLOAT_SHORTEST_DECIMAL_LEN - 1) bytes for
+	 * float_to_shortest_decimal_bufn
+	 *
+	 * dim - 1 bytes for separator
+	 *
+	 * 3 bytes for [, ], and \0
+	 */
+	buf = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN * dim + 2);
+	ptr = buf;
+
+	AppendChar(ptr, '[');
+
+	for (int i = 0; i < dim; i++)
+	{
+		if (i > 0)
+			AppendChar(ptr, ',');
+
+		AppendFloat(ptr, HalfToFloat4(vector->x[i]));
+	}
+
+	AppendChar(ptr, ']');
+	*ptr = '\0';
+
+	PG_FREE_IF_COPY(vector, 0);
+	PG_RETURN_CSTRING(buf);
+}
+
+/*
+ * Convert type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_typmod_in);
+Datum
+halfvec_typmod_in(PG_FUNCTION_ARGS)
+{
+	ArrayType  *ta = PG_GETARG_ARRAYTYPE_P(0);
+	int32	   *tl;
+	int			n;
+
+	tl = ArrayGetIntegerTypmods(ta, &n);
+
+	if (n != 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("invalid type modifier")));
+
+	if (*tl < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type halfvec must be at least 1")));
+
+	if (*tl > HALFVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type halfvec cannot exceed %d", HALFVEC_MAX_DIM)));
+
+	PG_RETURN_INT32(*tl);
+}
+
+/*
+ * Convert external binary representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_recv);
+Datum
+halfvec_recv(PG_FUNCTION_ARGS)
+{
+	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	HalfVector *result;
+	int16		dim;
+	int16		unused;
+
+	dim = pq_getmsgint(buf, sizeof(int16));
+	unused = pq_getmsgint(buf, sizeof(int16));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	if (unused != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected unused to be 0, not %d", unused)));
+
+	result = InitHalfVector(dim);
+	for (int i = 0; i < dim; i++)
+	{
+		result->x[i] = pq_getmsghalf(buf);
+		CheckElement(result->x[i]);
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert internal representation to the external binary representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_send);
+Datum
+halfvec_send(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	StringInfoData buf;
+
+	pq_begintypsend(&buf);
+	pq_sendint(&buf, vec->dim, sizeof(int16));
+	pq_sendint(&buf, vec->unused, sizeof(int16));
+	for (int i = 0; i < vec->dim; i++)
+		pq_sendhalf(&buf, vec->x[i]);
+
+	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
+}
+
+/*
+ * Convert half vector to half vector
+ * This is needed to check the type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec);
+Datum
+halfvec(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+
+	CheckExpectedDim(typmod, vec->dim);
+
+	PG_RETURN_POINTER(vec);
+}
+
+/*
+ * Convert array to half vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(array_to_halfvec);
+Datum
+array_to_halfvec(PG_FUNCTION_ARGS)
+{
+	ArrayType  *array = PG_GETARG_ARRAYTYPE_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	HalfVector *result;
+	int16		typlen;
+	bool		typbyval;
+	char		typalign;
+	Datum	   *elemsp;
+	int			nelemsp;
+
+	if (ARR_NDIM(array) > 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("array must be 1-D")));
+
+	if (ARR_HASNULL(array) && array_contains_nulls(array))
+		ereport(ERROR,
+				(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
+				 errmsg("array must not contain nulls")));
+
+	get_typlenbyvalalign(ARR_ELEMTYPE(array), &typlen, &typbyval, &typalign);
+	deconstruct_array(array, ARR_ELEMTYPE(array), typlen, typbyval, typalign, &elemsp, NULL, &nelemsp);
+
+	CheckDim(nelemsp);
+	CheckExpectedDim(typmod, nelemsp);
+
+	result = InitHalfVector(nelemsp);
+
+	if (ARR_ELEMTYPE(array) == INT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetInt32(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == FLOAT8OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat8(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == FLOAT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat4(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == NUMERICOID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat4(DirectFunctionCall1(numeric_float4, elemsp[i])));
+	}
+	else
+	{
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("unsupported array type")));
+	}
+
+	/*
+	 * Free allocation from deconstruct_array. Do not free individual elements
+	 * when pass-by-reference since they point to original array.
+	 */
+	pfree(elemsp);
+
+	/* Check elements */
+	for (int i = 0; i < result->dim; i++)
+		CheckElement(result->x[i]);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert half vector to float4[]
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_to_float4);
+Datum
+halfvec_to_float4(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	Datum	   *datums;
+	ArrayType  *result;
+
+	datums = (Datum *) palloc(sizeof(Datum) * vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		datums[i] = Float4GetDatum(HalfToFloat4(vec->x[i]));
+
+	/* Use TYPALIGN_INT for float4 */
+	result = construct_array(datums, vec->dim, FLOAT4OID, sizeof(float4), true, TYPALIGN_INT);
+
+	pfree(datums);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert vector to half vec
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_to_halfvec);
+Datum
+vector_to_halfvec(PG_FUNCTION_ARGS)
+{
+	Vector	   *vec = PG_GETARG_VECTOR_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	HalfVector *result;
+
+	CheckDim(vec->dim);
+	CheckExpectedDim(typmod, vec->dim);
+
+	result = InitHalfVector(vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+	{
+		result->x[i] = Float4ToHalfUnchecked(vec->x[i]);
+		/* TODO Better error for overflow */
+		CheckElement(result->x[i]);
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Get the L2 distance between half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l2_distance);
+Datum
+halfvec_l2_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	PG_RETURN_FLOAT8(sqrt((double) distance));
+}
+
+/*
+ * Get the L2 squared distance between half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l2_squared_distance);
+Datum
+halfvec_l2_squared_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the inner product of two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_inner_product);
+Datum
+halfvec_inner_product(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the negative inner product of two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_negative_inner_product);
+Datum
+halfvec_negative_inner_product(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	PG_RETURN_FLOAT8((double) distance * -1);
+}
+
+/*
+ * Get the cosine distance between two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_cosine_distance);
+Datum
+halfvec_cosine_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+	float		norma = 0.0;
+	float		normb = 0.0;
+	double		similarity;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		float		axi = HalfToFloat4(ax[i]);
+		float		bxi = HalfToFloat4(bx[i]);
+
+		distance += axi * bxi;
+		norma += axi * axi;
+		normb += bxi * bxi;
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	similarity = (double) distance / sqrt((double) norma * (double) normb);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	if (isnan(similarity))
+		PG_RETURN_FLOAT8(NAN);
+#endif
+
+	/* Keep in range */
+	if (similarity > 1)
+		similarity = 1;
+	else if (similarity < -1)
+		similarity = -1;
+
+	PG_RETURN_FLOAT8(1 - similarity);
+}
+
+/*
+ * Get the L1 distance between two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l1_distance);
+Datum
+halfvec_l1_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += fabsf(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the L2 norm of a half vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_norm);
+Datum
+halfvec_norm(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	half	   *ax = a->x;
+	double		norm = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		double		axi = (double) HalfToFloat4(ax[i]);
+
+		norm += axi * axi;
+	}
+
+	PG_RETURN_FLOAT8(sqrt(norm));
+}

src/halfvec.h

@@ -0,0 +1,41 @@
+#ifndef HALFVEC_H
+#define HALFVEC_H
+
+#define __STDC_WANT_IEC_60559_TYPES_EXT__
+
+#include <float.h>
+
+#ifdef __FLT16_MAX__
+#define FLT16_SUPPORT
+#endif
+
+#ifdef FLT16_SUPPORT
+#define half _Float16
+#define HALF_MAX FLT16_MAX
+#else
+/* TODO #pragma message("")? */
+#define half uint16
+#define HALF_MAX 65504
+#endif
+
+#define HALFVEC_MAX_DIM 16000
+
+#define HALFVEC_SIZE(_dim)		(offsetof(HalfVector, x) + sizeof(half)*(_dim))
+#define DatumGetHalfVector(x)	((HalfVector *) PG_DETOAST_DATUM(x))
+#define PG_GETARG_HALFVEC_P(x)	DatumGetHalfVector(PG_GETARG_DATUM(x))
+#define PG_RETURN_HALFVEC_P(x)	PG_RETURN_POINTER(x)
+
+typedef struct HalfVector
+{
+	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int16		dim;			/* number of dimensions */
+	int16		unused;
+	half		x[FLEXIBLE_ARRAY_MEMBER];
+}			HalfVector;
+
+HalfVector *InitHalfVector(int dim);
+float		HalfToFloat4(half num);
+half		Float4ToHalf(float num);
+half		Float4ToHalfUnchecked(float num);
+
+#endif

src/hnsw.h

@@ -55,6 +55,10 @@
 #define HNSW_UPDATE_ENTRY_GREATER 1
 #define HNSW_UPDATE_ENTRY_ALWAYS 2
 
+/* Data types */
+#define HNSW_TYPE_VECTOR 1
+#define HNSW_TYPE_HALFVEC 2
+
 /* Build phases */
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
 #define PROGRESS_HNSW_PHASE_LOAD		2
@@ -242,6 +246,7 @@ typedef struct HnswBuildState
 	Relation	index;
 	IndexInfo  *indexInfo;
 	ForkNumber	forkNum;
+	int			type;
 
 	/* Settings */
 	int			dimensions;
@@ -262,7 +267,6 @@ typedef struct HnswBuildState
 	HnswGraph  *graph;
 	double		ml;
 	int			maxLevel;
-	Vector	   *normvec;
 
 	/* Memory */
 	MemoryContext graphCtx;
@@ -367,7 +371,8 @@ typedef struct HnswVacuumState
 int			HnswGetM(Relation index);
 int			HnswGetEfConstruction(Relation index);
 FmgrInfo   *HnswOptionalProcInfo(Relation index, uint16 procnum);
-bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+int			HnswGetType(Relation index);
+bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, int type);
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);
 void		HnswInit(void);

src/hnswbuild.c

@@ -489,7 +489,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, Hn
 	/* Normalize if needed */
 	if (buildstate->normprocinfo != NULL)
 	{
-		if (!HnswNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->normvec))
+		if (!HnswNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->type))
 			return false;
 	}
 
@@ -671,21 +671,27 @@ HnswSharedMemoryAlloc(Size size, void *state)
 static void
 InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, IndexInfo *indexInfo, ForkNumber forkNum)
 {
+	int			maxDimensions = HNSW_MAX_DIM;
+
 	buildstate->heap = heap;
 	buildstate->index = index;
 	buildstate->indexInfo = indexInfo;
 	buildstate->forkNum = forkNum;
+	buildstate->type = HnswGetType(index);
 
 	buildstate->m = HnswGetM(index);
 	buildstate->efConstruction = HnswGetEfConstruction(index);
 	buildstate->dimensions = TupleDescAttr(index->rd_att, 0)->atttypmod;
 
+	if (buildstate->type == HNSW_TYPE_HALFVEC)
+		maxDimensions *= 2;
+
 	/* Require column to have dimensions to be indexed */
 	if (buildstate->dimensions < 0)
 		elog(ERROR, "column does not have dimensions");
 
-	if (buildstate->dimensions > HNSW_MAX_DIM)
+	if (buildstate->dimensions > maxDimensions)
-		elog(ERROR, "column cannot have more than %d dimensions for hnsw index", HNSW_MAX_DIM);
+		elog(ERROR, "column cannot have more than %d dimensions for hnsw index", maxDimensions);
 
 	if (buildstate->efConstruction < 2 * buildstate->m)
 		elog(ERROR, "ef_construction must be greater than or equal to 2 * m");
@@ -703,9 +709,6 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	buildstate->ml = HnswGetMl(buildstate->m);
 	buildstate->maxLevel = HnswGetMaxLevel(buildstate->m);
 
-	/* Reuse for each tuple */
-	buildstate->normvec = InitVector(buildstate->dimensions);
-
 	buildstate->graphCtx = GenerationContextCreate(CurrentMemoryContext,
 												   "Hnsw build graph context",
 #if PG_VERSION_NUM >= 150000
@@ -729,7 +732,6 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 static void
 FreeBuildState(HnswBuildState * buildstate)
 {
-	pfree(buildstate->normvec);
 	MemoryContextDelete(buildstate->graphCtx);
 	MemoryContextDelete(buildstate->tmpCtx);
 }

src/hnswinsert.c

@@ -622,7 +622,7 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		if (!HnswNormValue(normprocinfo, collation, &value, NULL))
+		if (!HnswNormValue(normprocinfo, collation, &value, HnswGetType(index)))
 			return;
 	}
 

src/hnswscan.c

@@ -1,6 +1,7 @@
 #include "postgres.h"
 
 #include "access/relscan.h"
+#include "halfvec.h"
 #include "hnsw.h"
 #include "pgstat.h"
 #include "storage/bufmgr.h"
@@ -73,7 +74,14 @@ GetScanValue(IndexScanDesc scan)
 	Datum		value;
 
 	if (scan->orderByData->sk_flags & SK_ISNULL)
-		value = PointerGetDatum(InitVector(GetDimensions(scan->indexRelation)));
+	{
+		int			dimensions = GetDimensions(scan->indexRelation);
+
+		if (HnswGetType(scan->indexRelation) == HNSW_TYPE_HALFVEC)
+			value = PointerGetDatum(InitHalfVector(dimensions));
+		else
+			value = PointerGetDatum(InitVector(dimensions));
+	}
 	else
 	{
 		value = scan->orderByData->sk_argument;
@@ -84,7 +92,7 @@ GetScanValue(IndexScanDesc scan)
 
 		/* Fine if normalization fails */
 		if (so->normprocinfo != NULL)
-			HnswNormValue(so->normprocinfo, so->collation, &value, NULL);
+			HnswNormValue(so->normprocinfo, so->collation, &value, HnswGetType(scan->indexRelation));
 	}
 
 	return value;

src/hnswutils.c

@@ -3,12 +3,15 @@
 #include <math.h>
 
 #include "access/generic_xlog.h"
+#include "catalog/pg_type.h"
+#include "halfvec.h"
 #include "hnsw.h"
 #include "lib/pairingheap.h"
 #include "storage/bufmgr.h"
 #include "utils/datum.h"
 #include "utils/memdebug.h"
 #include "utils/rel.h"
+#include "utils/syscache.h"
 #include "vector.h"
 
 #if PG_VERSION_NUM >= 130000
@@ -149,6 +152,32 @@ HnswOptionalProcInfo(Relation index, uint16 procnum)
 	return index_getprocinfo(index, 1, procnum);
 }
 
+/*
+ * Get type
+ */
+int
+HnswGetType(Relation index)
+{
+	Oid			typeOid = TupleDescAttr(index->rd_att, 0)->atttypid;
+	HeapTuple	tuple;
+	Form_pg_type type;
+	int			result;
+
+	tuple = SearchSysCache1(TYPEOID, ObjectIdGetDatum(typeOid));
+	if (!HeapTupleIsValid(tuple))
+		elog(ERROR, "cache lookup failed for type %u", typeOid);
+
+	type = (Form_pg_type) GETSTRUCT(tuple);
+	if (strcmp(NameStr(type->typname), "halfvec") == 0)
+		result = HNSW_TYPE_HALFVEC;
+	else
+		result = HNSW_TYPE_VECTOR;
+
+	ReleaseSysCache(tuple);
+
+	return result;
+}
+
 /*
  * Divide by the norm
  *
@@ -158,21 +187,37 @@ HnswOptionalProcInfo(Relation index, uint16 procnum)
  * if it's different than the original value
  */
 bool
-HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result)
+HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, int type)
 {
 	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
 
 	if (norm > 0)
 	{
-		Vector	   *v = DatumGetVector(*value);
+		if (type == HNSW_TYPE_HALFVEC)
+		{
+			HalfVector *v = DatumGetHalfVector(*value);
+			HalfVector *result = InitHalfVector(v->dim);
 
-		if (result == NULL)
+			for (int i = 0; i < v->dim; i++)
-			result = InitVector(v->dim);
+			{
+				/* TODO Fix */
+				result->x[i] = Float4ToHalfUnchecked(HalfToFloat4(v->x[i]) / norm);
+			}
 
-		for (int i = 0; i < v->dim; i++)
+			*value = PointerGetDatum(result);
-			result->x[i] = v->x[i] / norm;
+		}
+		else if (type == HNSW_TYPE_VECTOR)
+		{
+			Vector	   *v = DatumGetVector(*value);
+			Vector	   *result = InitVector(v->dim);
 
-		*value = PointerGetDatum(result);
+			for (int i = 0; i < v->dim; i++)
+				result->x[i] = v->x[i] / norm;
+
+			*value = PointerGetDatum(result);
+		}
+		else
+			elog(ERROR, "Unsupported type");
 
 		return true;
 	}

src/vector.c

@@ -5,6 +5,7 @@
 #include "catalog/pg_type.h"
 #include "common/shortest_dec.h"
 #include "fmgr.h"
+#include "halfvec.h"
 #include "hnsw.h"
 #include "ivfflat.h"
 #include "lib/stringinfo.h"
@@ -532,6 +533,28 @@ vector_to_float4(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+/*
+ * Convert half vector to vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_to_vector);
+Datum
+halfvec_to_vector(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	Vector	   *result;
+
+	CheckDim(vec->dim);
+	CheckExpectedDim(typmod, vec->dim);
+
+	result = InitVector(vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		result->x[i] = HalfToFloat4(vec->x[i]);
+
+	PG_RETURN_POINTER(result);
+}
+
 /*
  * Get the L2 distance between vectors
  */
@@ -1160,28 +1183,3 @@ vector_avg(PG_FUNCTION_ARGS)
 
 	PG_RETURN_POINTER(result);
 }
-
-/*
- * Concat vectors
- */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_concat);
-Datum
-vector_concat(PG_FUNCTION_ARGS)
-{
-	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	Vector	   *result;
-	int			dim = a->dim + b->dim;
-
-	CheckDim(dim);
-
-	result = InitVector(dim);
-
-	for (int i = 0; i < a->dim; i++)
-		result->x[i] = a->x[i];
-
-	for (int i = 0; i < b->dim; i++)
-		result->x[i + a->dim] = b->x[i];
-
-	PG_RETURN_POINTER(result);
-}

test/expected/cast.out

@@ -46,6 +46,30 @@ SELECT '[1,2,3]'::vector::real[];
  {1,2,3}
 (1 row)
 
+SELECT '[1,2,3]'::vector::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::vector::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::halfvec::vector(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '[65520]'::vector::halfvec;
+ERROR:  infinite value not allowed in halfvec
+SELECT '[1e-8]'::vector::halfvec;
+ halfvec 
+---------
+ [0]
+(1 row)
+
 SELECT array_agg(n)::vector FROM generate_series(1, 16001) n;
 ERROR:  vector cannot have more than 16000 dimensions
 SELECT array_to_vector(array_agg(n), 16001, false) FROM generate_series(1, 16001) n;

test/expected/copy.out

@@ -1,15 +1,15 @@
-CREATE TABLE t (val vector(3));
+CREATE TABLE t (val vector(3), val2 halfvec(3));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+INSERT INTO t (val, val2) VALUES ('[0,0,0]', '[0,0,0]'), ('[1,2,3]', '[1,2,3]'), ('[1,1,1]', '[1,1,1]'), (NULL, NULL);
-CREATE TABLE t2 (val vector(3));
+CREATE TABLE t2 (val vector(3), val2 halfvec(3));
 \copy t TO 'results/data.bin' WITH (FORMAT binary)
 \copy t2 FROM 'results/data.bin' WITH (FORMAT binary)
 SELECT * FROM t2 ORDER BY val;
-   val   
+   val   |  val2   
----------
+---------+---------
- [0,0,0]
+ [0,0,0] | [0,0,0]
- [1,1,1]
+ [1,1,1] | [1,1,1]
- [1,2,3]
+ [1,2,3] | [1,2,3]
- 
+         | 
 (4 rows)
 
 DROP TABLE t;

test/expected/functions.out

@@ -24,14 +24,6 @@ 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 || '[4,5]'::vector;
-  ?column?   
--------------
- [1,2,3,4,5]
-(1 row)
-
-SELECT array_fill(0, ARRAY[16000])::vector || '[1]'::vector;
-ERROR:  vector cannot have more than 16000 dimensions
 SELECT '[1,2,3]'::vector = '[1,2,3]';
  ?column? 
 ----------
@@ -112,105 +104,105 @@ SELECT vector_norm('[3e37,4e37]')::real;
        5e+37
 (1 row)
 
-SELECT l2_distance('[0,0]', '[3,4]');
+SELECT l2_distance('[0,0]'::vector, '[3,4]');
  l2_distance 
 -------------
            5
 (1 row)
 
-SELECT l2_distance('[0,0]', '[0,1]');
+SELECT l2_distance('[0,0]'::vector, '[0,1]');
  l2_distance 
 -------------
            1
 (1 row)
 
-SELECT l2_distance('[1,2]', '[3]');
+SELECT l2_distance('[1,2]'::vector, '[3]');
 ERROR:  different vector dimensions 2 and 1
-SELECT l2_distance('[3e38]', '[-3e38]');
+SELECT l2_distance('[3e38]'::vector, '[-3e38]');
  l2_distance 
 -------------
     Infinity
 (1 row)
 
-SELECT inner_product('[1,2]', '[3,4]');
+SELECT inner_product('[1,2]'::vector, '[3,4]');
  inner_product 
 ---------------
             11
 (1 row)
 
-SELECT inner_product('[1,2]', '[3]');
+SELECT inner_product('[1,2]'::vector, '[3]');
 ERROR:  different vector dimensions 2 and 1
-SELECT inner_product('[3e38]', '[3e38]');
+SELECT inner_product('[3e38]'::vector, '[3e38]');
  inner_product 
 ---------------
       Infinity
 (1 row)
 
-SELECT cosine_distance('[1,2]', '[2,4]');
+SELECT cosine_distance('[1,2]'::vector, '[2,4]');
  cosine_distance 
 -----------------
                0
 (1 row)
 
-SELECT cosine_distance('[1,2]', '[0,0]');
+SELECT cosine_distance('[1,2]'::vector, '[0,0]');
  cosine_distance 
 -----------------
              NaN
 (1 row)
 
-SELECT cosine_distance('[1,1]', '[1,1]');
+SELECT cosine_distance('[1,1]'::vector, '[1,1]');
  cosine_distance 
 -----------------
                0
 (1 row)
 
-SELECT cosine_distance('[1,0]', '[0,2]');
+SELECT cosine_distance('[1,0]'::vector, '[0,2]');
  cosine_distance 
 -----------------
                1
 (1 row)
 
-SELECT cosine_distance('[1,1]', '[-1,-1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1,-1]');
  cosine_distance 
 -----------------
                2
 (1 row)
 
-SELECT cosine_distance('[1,2]', '[3]');
+SELECT cosine_distance('[1,2]'::vector, '[3]');
 ERROR:  different vector dimensions 2 and 1
-SELECT cosine_distance('[1,1]', '[1.1,1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[1.1,1.1]');
  cosine_distance 
 -----------------
                0
 (1 row)
 
-SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1.1,-1.1]');
  cosine_distance 
 -----------------
                2
 (1 row)
 
-SELECT cosine_distance('[3e38]', '[3e38]');
+SELECT cosine_distance('[3e38]'::vector, '[3e38]');
  cosine_distance 
 -----------------
              NaN
 (1 row)
 
-SELECT l1_distance('[0,0]', '[3,4]');
+SELECT l1_distance('[0,0]'::vector, '[3,4]');
  l1_distance 
 -------------
            7
 (1 row)
 
-SELECT l1_distance('[0,0]', '[0,1]');
+SELECT l1_distance('[0,0]'::vector, '[0,1]');
  l1_distance 
 -------------
            1
 (1 row)
 
-SELECT l1_distance('[1,2]', '[3]');
+SELECT l1_distance('[1,2]'::vector, '[3]');
 ERROR:  different vector dimensions 2 and 1
-SELECT l1_distance('[3e38]', '[-3e38]');
+SELECT l1_distance('[3e38]'::vector, '[-3e38]');
  l1_distance 
 -------------
     Infinity

test/expected/halfvec_functions.out

@@ -0,0 +1,104 @@
+SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
+ l2_distance 
+-------------
+           1
+(1 row)
+
+SELECT l2_distance('[1,2]'::halfvec, '[3]');
+ERROR:  different halfvec dimensions 2 and 1
+SELECT '[0,0]'::halfvec <-> '[3,4]';
+ ?column? 
+----------
+        5
+(1 row)
+
+SELECT inner_product('[1,2]'::halfvec, '[3,4]');
+ inner_product 
+---------------
+            11
+(1 row)
+
+SELECT inner_product('[1,2]'::halfvec, '[3]');
+ERROR:  different halfvec dimensions 2 and 1
+SELECT inner_product('[65504]'::halfvec, '[65504]');
+ inner_product 
+---------------
+    4290774016
+(1 row)
+
+SELECT '[1,2]'::halfvec <#> '[3,4]';
+ ?column? 
+----------
+      -11
+(1 row)
+
+SELECT cosine_distance('[1,2]'::halfvec, '[2,4]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,2]'::halfvec, '[0,0]');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('[1,1]'::halfvec, '[1,1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,0]'::halfvec, '[0,2]');
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
+SELECT cosine_distance('[1,1]'::halfvec, '[-1,-1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('[1,2]'::halfvec, '[3]');
+ERROR:  different halfvec dimensions 2 and 1
+SELECT cosine_distance('[1,1]'::halfvec, '[1.1,1.1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,1]'::halfvec, '[-1.1,-1.1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT '[1,2]'::halfvec <=> '[2,4]';
+ ?column? 
+----------
+        0
+(1 row)
+
+SELECT l1_distance('[0,0]'::halfvec, '[3,4]');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('[0,0]'::halfvec, '[0,1]');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('[1,2]'::halfvec, '[3]');
+ERROR:  different halfvec dimensions 2 and 1

test/expected/halfvec_input.out

@@ -0,0 +1,147 @@
+SELECT '[1,2,3]'::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[-1,-2,-3]'::halfvec;
+  halfvec   
+------------
+ [-1,-2,-3]
+(1 row)
+
+SELECT '[1.,2.,3.]'::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT ' [ 1,  2 ,    3  ] '::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1.23456]'::halfvec;
+  halfvec   
+------------
+ [1.234375]
+(1 row)
+
+SELECT '[hello,1]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[hello,1]"
+LINE 1: SELECT '[hello,1]'::halfvec;
+               ^
+SELECT '[NaN,1]'::halfvec;
+ERROR:  NaN not allowed in halfvec
+LINE 1: SELECT '[NaN,1]'::halfvec;
+               ^
+SELECT '[Infinity,1]'::halfvec;
+ERROR:  infinite value not allowed in halfvec
+LINE 1: SELECT '[Infinity,1]'::halfvec;
+               ^
+SELECT '[-Infinity,1]'::halfvec;
+ERROR:  infinite value not allowed in halfvec
+LINE 1: SELECT '[-Infinity,1]'::halfvec;
+               ^
+SELECT '[65519,-65519]'::halfvec;
+    halfvec     
+----------------
+ [65504,-65504]
+(1 row)
+
+SELECT '[65520,-65520]'::halfvec;
+ERROR:  value out of range: overflow
+LINE 1: SELECT '[65520,-65520]'::halfvec;
+               ^
+SELECT '[1e-8,-1e-8]'::halfvec;
+ERROR:  value out of range: underflow
+LINE 1: SELECT '[1e-8,-1e-8]'::halfvec;
+               ^
+SELECT '[4e38,1]'::halfvec;
+ERROR:  infinite value not allowed in halfvec
+LINE 1: SELECT '[4e38,1]'::halfvec;
+               ^
+SELECT '[1,2,3'::halfvec;
+ERROR:  malformed halfvec literal: "[1,2,3"
+LINE 1: SELECT '[1,2,3'::halfvec;
+               ^
+DETAIL:  Unexpected end of input.
+SELECT '[1,2,3]9'::halfvec;
+ERROR:  malformed halfvec literal: "[1,2,3]9"
+LINE 1: SELECT '[1,2,3]9'::halfvec;
+               ^
+DETAIL:  Junk after closing right brace.
+SELECT '1,2,3'::halfvec;
+ERROR:  malformed halfvec literal: "1,2,3"
+LINE 1: SELECT '1,2,3'::halfvec;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT ''::halfvec;
+ERROR:  malformed halfvec literal: ""
+LINE 1: SELECT ''::halfvec;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT '['::halfvec;
+ERROR:  malformed halfvec literal: "["
+LINE 1: SELECT '['::halfvec;
+               ^
+DETAIL:  Unexpected end of input.
+SELECT '[,'::halfvec;
+ERROR:  malformed halfvec literal: "[,"
+LINE 1: SELECT '[,'::halfvec;
+               ^
+DETAIL:  Unexpected end of input.
+SELECT '[]'::halfvec;
+ERROR:  halfvec must have at least 1 dimension
+LINE 1: SELECT '[]'::halfvec;
+               ^
+SELECT '[1,]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1,]"
+LINE 1: SELECT '[1,]'::halfvec;
+               ^
+SELECT '[1a]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1a]"
+LINE 1: SELECT '[1a]'::halfvec;
+               ^
+SELECT '[1,,3]'::halfvec;
+ERROR:  malformed halfvec literal: "[1,,3]"
+LINE 1: SELECT '[1,,3]'::halfvec;
+               ^
+SELECT '[1, ,3]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1, ,3]"
+LINE 1: SELECT '[1, ,3]'::halfvec;
+               ^
+SELECT '[1,2,3]'::halfvec(3);
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::halfvec(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '[1,2,3]'::halfvec(3, 2);
+                          ^
+SELECT '[1,2,3]'::halfvec('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '[1,2,3]'::halfvec('a');
+                          ^
+SELECT '[1,2,3]'::halfvec(0);
+ERROR:  dimensions for type halfvec must be at least 1
+LINE 1: SELECT '[1,2,3]'::halfvec(0);
+                          ^
+SELECT '[1,2,3]'::halfvec(16001);
+ERROR:  dimensions for type halfvec cannot exceed 16000
+LINE 1: SELECT '[1,2,3]'::halfvec(16001);
+                          ^
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::halfvec[]);
+ unnest  
+---------
+ [1,2,3]
+ [4,5,6]
+(2 rows)
+
+SELECT '{"[1,2,3]"}'::halfvec(2)[];
+ERROR:  expected 2 dimensions, not 3

test/expected/hnsw_halfvec_cosine.out

@@ -0,0 +1,26 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_cosine_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <=> '[3,3,3]';
+   val   
+---------
+ [1,1,1]
+ [1,2,3]
+ [1,2,4]
+(3 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
+ count 
+-------
+     3
+(1 row)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::halfvec)) t2;
+ count 
+-------
+     3
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_halfvec_ip.out

@@ -0,0 +1,21 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_ip_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <#> '[3,3,3]';
+   val   
+---------
+ [1,2,4]
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <#> (SELECT NULL::halfvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_halfvec_l2.out

@@ -0,0 +1,36 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_l2_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT * FROM t ORDER BY val <-> (SELECT NULL::halfvec);
+   val   
+---------
+ [0,0,0]
+ [1,1,1]
+ [1,2,3]
+ [1,2,4]
+(4 rows)
+
+SELECT COUNT(*) FROM t;
+ count 
+-------
+     5
+(1 row)
+
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+ val 
+-----
+(0 rows)
+
+DROP TABLE t;

test/expected/input.out

@@ -116,8 +116,30 @@ SELECT '[1, ,3]'::vector;
 ERROR:  invalid input syntax for type vector: "[1, ,3]"
 LINE 1: SELECT '[1, ,3]'::vector;
                ^
+SELECT '[1,2,3]'::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
 SELECT '[1,2,3]'::vector(2);
 ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::vector(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '[1,2,3]'::vector(3, 2);
+                          ^
+SELECT '[1,2,3]'::vector('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '[1,2,3]'::vector('a');
+                          ^
+SELECT '[1,2,3]'::vector(0);
+ERROR:  dimensions for type vector must be at least 1
+LINE 1: SELECT '[1,2,3]'::vector(0);
+                          ^
+SELECT '[1,2,3]'::vector(16001);
+ERROR:  dimensions for type vector cannot exceed 16000
+LINE 1: SELECT '[1,2,3]'::vector(16001);
+                          ^
 SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
  unnest  
 ---------

test/sql/cast.sql

@@ -10,6 +10,12 @@ SELECT '{-Infinity}'::real[]::vector;
 SELECT '{}'::real[]::vector;
 SELECT '{{1}}'::real[]::vector;
 SELECT '[1,2,3]'::vector::real[];
+SELECT '[1,2,3]'::vector::halfvec;
+SELECT '[1,2,3]'::halfvec::vector;
+SELECT '[1,2,3]'::vector::halfvec(2);
+SELECT '[1,2,3]'::halfvec::vector(2);
+SELECT '[65520]'::vector::halfvec;
+SELECT '[1e-8]'::vector::halfvec;
 SELECT array_agg(n)::vector FROM generate_series(1, 16001) n;
 SELECT array_to_vector(array_agg(n), 16001, false) FROM generate_series(1, 16001) n;
 

test/sql/copy.sql

@@ -1,7 +1,7 @@
-CREATE TABLE t (val vector(3));
+CREATE TABLE t (val vector(3), val2 halfvec(3));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+INSERT INTO t (val, val2) VALUES ('[0,0,0]', '[0,0,0]'), ('[1,2,3]', '[1,2,3]'), ('[1,1,1]', '[1,1,1]'), (NULL, NULL);
 
-CREATE TABLE t2 (val vector(3));
+CREATE TABLE t2 (val vector(3), val2 halfvec(3));
 
 \copy t TO 'results/data.bin' WITH (FORMAT binary)
 \copy t2 FROM 'results/data.bin' WITH (FORMAT binary)

test/sql/functions.sql

@@ -6,9 +6,6 @@ SELECT '[1,2,3]'::vector * '[4,5,6]';
 SELECT '[1e37]'::vector * '[1e37]';
 SELECT '[1e-37]'::vector * '[1e-37]';
 
-SELECT '[1,2,3]'::vector || '[4,5]'::vector;
-SELECT array_fill(0, ARRAY[16000])::vector || '[1]'::vector;
-
 SELECT '[1,2,3]'::vector = '[1,2,3]';
 SELECT '[1,2,3]'::vector = '[1,2]';
 
@@ -27,29 +24,29 @@ SELECT vector_norm('[3,4]');
 SELECT vector_norm('[0,1]');
 SELECT vector_norm('[3e37,4e37]')::real;
 
-SELECT l2_distance('[0,0]', '[3,4]');
+SELECT l2_distance('[0,0]'::vector, '[3,4]');
-SELECT l2_distance('[0,0]', '[0,1]');
+SELECT l2_distance('[0,0]'::vector, '[0,1]');
-SELECT l2_distance('[1,2]', '[3]');
+SELECT l2_distance('[1,2]'::vector, '[3]');
-SELECT l2_distance('[3e38]', '[-3e38]');
+SELECT l2_distance('[3e38]'::vector, '[-3e38]');
 
-SELECT inner_product('[1,2]', '[3,4]');
+SELECT inner_product('[1,2]'::vector, '[3,4]');
-SELECT inner_product('[1,2]', '[3]');
+SELECT inner_product('[1,2]'::vector, '[3]');
-SELECT inner_product('[3e38]', '[3e38]');
+SELECT inner_product('[3e38]'::vector, '[3e38]');
 
-SELECT cosine_distance('[1,2]', '[2,4]');
+SELECT cosine_distance('[1,2]'::vector, '[2,4]');
-SELECT cosine_distance('[1,2]', '[0,0]');
+SELECT cosine_distance('[1,2]'::vector, '[0,0]');
-SELECT cosine_distance('[1,1]', '[1,1]');
+SELECT cosine_distance('[1,1]'::vector, '[1,1]');
-SELECT cosine_distance('[1,0]', '[0,2]');
+SELECT cosine_distance('[1,0]'::vector, '[0,2]');
-SELECT cosine_distance('[1,1]', '[-1,-1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1,-1]');
-SELECT cosine_distance('[1,2]', '[3]');
+SELECT cosine_distance('[1,2]'::vector, '[3]');
-SELECT cosine_distance('[1,1]', '[1.1,1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[1.1,1.1]');
-SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1.1,-1.1]');
-SELECT cosine_distance('[3e38]', '[3e38]');
+SELECT cosine_distance('[3e38]'::vector, '[3e38]');
 
-SELECT l1_distance('[0,0]', '[3,4]');
+SELECT l1_distance('[0,0]'::vector, '[3,4]');
-SELECT l1_distance('[0,0]', '[0,1]');
+SELECT l1_distance('[0,0]'::vector, '[0,1]');
-SELECT l1_distance('[1,2]', '[3]');
+SELECT l1_distance('[1,2]'::vector, '[3]');
-SELECT l1_distance('[3e38]', '[-3e38]');
+SELECT l1_distance('[3e38]'::vector, '[-3e38]');
 
 SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
 SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;

test/sql/halfvec_functions.sql

@@ -0,0 +1,23 @@
+SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
+SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
+SELECT l2_distance('[1,2]'::halfvec, '[3]');
+SELECT '[0,0]'::halfvec <-> '[3,4]';
+
+SELECT inner_product('[1,2]'::halfvec, '[3,4]');
+SELECT inner_product('[1,2]'::halfvec, '[3]');
+SELECT inner_product('[65504]'::halfvec, '[65504]');
+SELECT '[1,2]'::halfvec <#> '[3,4]';
+
+SELECT cosine_distance('[1,2]'::halfvec, '[2,4]');
+SELECT cosine_distance('[1,2]'::halfvec, '[0,0]');
+SELECT cosine_distance('[1,1]'::halfvec, '[1,1]');
+SELECT cosine_distance('[1,0]'::halfvec, '[0,2]');
+SELECT cosine_distance('[1,1]'::halfvec, '[-1,-1]');
+SELECT cosine_distance('[1,2]'::halfvec, '[3]');
+SELECT cosine_distance('[1,1]'::halfvec, '[1.1,1.1]');
+SELECT cosine_distance('[1,1]'::halfvec, '[-1.1,-1.1]');
+SELECT '[1,2]'::halfvec <=> '[2,4]';
+
+SELECT l1_distance('[0,0]'::halfvec, '[3,4]');
+SELECT l1_distance('[0,0]'::halfvec, '[0,1]');
+SELECT l1_distance('[1,2]'::halfvec, '[3]');

test/sql/halfvec_input.sql

@@ -0,0 +1,34 @@
+SELECT '[1,2,3]'::halfvec;
+SELECT '[-1,-2,-3]'::halfvec;
+SELECT '[1.,2.,3.]'::halfvec;
+SELECT ' [ 1,  2 ,    3  ] '::halfvec;
+SELECT '[1.23456]'::halfvec;
+SELECT '[hello,1]'::halfvec;
+SELECT '[NaN,1]'::halfvec;
+SELECT '[Infinity,1]'::halfvec;
+SELECT '[-Infinity,1]'::halfvec;
+SELECT '[65519,-65519]'::halfvec;
+SELECT '[65520,-65520]'::halfvec;
+SELECT '[1e-8,-1e-8]'::halfvec;
+SELECT '[4e38,1]'::halfvec;
+SELECT '[1,2,3'::halfvec;
+SELECT '[1,2,3]9'::halfvec;
+SELECT '1,2,3'::halfvec;
+SELECT ''::halfvec;
+SELECT '['::halfvec;
+SELECT '[,'::halfvec;
+SELECT '[]'::halfvec;
+SELECT '[1,]'::halfvec;
+SELECT '[1a]'::halfvec;
+SELECT '[1,,3]'::halfvec;
+SELECT '[1, ,3]'::halfvec;
+
+SELECT '[1,2,3]'::halfvec(3);
+SELECT '[1,2,3]'::halfvec(2);
+SELECT '[1,2,3]'::halfvec(3, 2);
+SELECT '[1,2,3]'::halfvec('a');
+SELECT '[1,2,3]'::halfvec(0);
+SELECT '[1,2,3]'::halfvec(16001);
+
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::halfvec[]);
+SELECT '{"[1,2,3]"}'::halfvec(2)[];

test/sql/hnsw_halfvec_cosine.sql

@@ -0,0 +1,13 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_cosine_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <=> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::halfvec)) t2;
+
+DROP TABLE t;

test/sql/hnsw_halfvec_ip.sql

@@ -0,0 +1,12 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_ip_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <#> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <#> (SELECT NULL::halfvec)) t2;
+
+DROP TABLE t;

test/sql/hnsw_halfvec_l2.sql

@@ -0,0 +1,16 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_l2_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+SELECT * FROM t ORDER BY val <-> (SELECT NULL::halfvec);
+SELECT COUNT(*) FROM t;
+
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+DROP TABLE t;

test/sql/input.sql

@@ -22,7 +22,13 @@ SELECT '[1,]'::vector;
 SELECT '[1a]'::vector;
 SELECT '[1,,3]'::vector;
 SELECT '[1, ,3]'::vector;
+
+SELECT '[1,2,3]'::vector(3);
 SELECT '[1,2,3]'::vector(2);
+SELECT '[1,2,3]'::vector(3, 2);
+SELECT '[1,2,3]'::vector('a');
+SELECT '[1,2,3]'::vector(0);
+SELECT '[1,2,3]'::vector(16001);
 
 SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
 SELECT '{"[1,2,3]"}'::vector(2)[];

test/t/020_hnsw_halfvec_build_recall.pl

@@ -0,0 +1,132 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 10;
+my $array_sql = join(",", ('random()') x $dim);
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v halfvec($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
+		push(@expected, $res);
+	}
+
+	# Build index serially
+	$node->safe_psql("postgres", qq(
+		SET max_parallel_maintenance_workers = 0;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+
+	# Test approximate results
+	my $min = $operator eq "<#>" ? 0.95 : 0.99;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel in memory
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		SET client_min_messages = DEBUG;
+		SET min_parallel_table_scan_size = 1;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	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();

vector.control

@@ -1,4 +1,4 @@
 comment = 'vector data type and ivfflat and hnsw access methods'
-default_version = '0.6.1'
+default_version = '0.6.2'
 module_pathname = '$libdir/vector'
 relocatable = true