Updated readme [skip ci]

.github/workflows/build.yml

@@ -40,21 +40,13 @@ jobs:
           sudo apt-get install libipc-run-perl
       - run: make prove_installcheck
   mac:
-    runs-on: ${{ matrix.os }}
+    runs-on: macos-latest
     if: ${{ !startsWith(github.ref_name, 'windows') }}
-    strategy:
-      fail-fast: false
-      matrix:
-        include:
-          - postgres: 16
-            os: macos-14
-          - postgres: 14
-            os: macos-12
     steps:
       - uses: actions/checkout@v4
       - uses: ankane/setup-postgres@v1
         with:
-          postgres-version: ${{ matrix.postgres }}
+          postgres-version: 14
       - run: make
         env:
           PG_CFLAGS: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter
@@ -62,19 +54,13 @@ jobs:
       - run: make installcheck
       - if: ${{ failure() }}
         run: cat regression.diffs
-      # Homebrew Postgres does not enable TAP tests, so need to download
       - run: |
           brew install cpanm
           cpanm --notest IPC::Run
-          wget -q https://github.com/postgres/postgres/archive/refs/tags/$TAG.tar.gz
-          tar xf $TAG.tar.gz
-          mv postgres-$TAG postgres
-        env:
-          TAG: ${{ matrix.postgres == 16 && 'REL_16_2' || 'REL_14_11' }}
-      - run: make prove_installcheck PROVE_FLAGS="-I ./postgres/src/test/perl -I ./test/perl"
-        env:
-          PERL5LIB: /Users/runner/perl5/lib/perl5
-      - run: make clean && $(brew --prefix llvm@15)/bin/scan-build --status-bugs make
+          wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_14_10.tar.gz
+          tar xf REL_14_10.tar.gz
+      - run: make prove_installcheck PROVE_FLAGS="-I ./postgres-REL_14_10/src/test/perl" PERL5LIB="/Users/runner/perl5/lib/perl5"
+      - run: make clean && /usr/local/opt/llvm@15/bin/scan-build --status-bugs make
         env:
           PG_CFLAGS: -DUSE_ASSERT_CHECKING
   windows:

CHANGELOG.md

@@ -1,12 +1,6 @@
 ## 0.7.0 (unreleased)
 
-- Added support for bit vectors to HNSW
-- Added `hamming_distance` function
-- Added `jaccard_distance` function
-- Added `quantize_binary` function
-- Added `subvector` function
-- Added concatenate operator for vectors
-- Updated comparison operators to support vectors with different dimensions
+- Added `halfvec` type
 
 ## 0.6.2 (2024-03-18)
 

Makefile

@@ -3,8 +3,8 @@ EXTVERSION = 0.6.2
 
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
-OBJS = src/bitvector.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
+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/halfvec.h src/vector.h
 
 TESTS = $(wildcard test/sql/*.sql)
 REGRESS = $(patsubst test/sql/%.sql,%,$(TESTS))
@@ -12,7 +12,7 @@ REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
 
 OPTFLAGS = -march=native
 
-# Mac ARM doesn't always support -march=native
+# Mac ARM doesn't support -march=native
 ifeq ($(shell uname -s), Darwin)
 	ifeq ($(shell uname -p), arm)
 		# no difference with -march=armv8.5-a

Makefile.win

@@ -1,10 +1,10 @@
 EXTENSION = vector
 EXTVERSION = 0.6.2
 
-OBJS = src\bitvector.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
+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\halfvec.h src\vector.h
 
-REGRESS = bit_functions btree cast copy hnsw_cosine hnsw_hamming hnsw_ip hnsw_jaccard hnsw_l2 hnsw_options hnsw_unlogged ivfflat_cosine ivfflat_ip ivfflat_l2 ivfflat_options ivfflat_unlogged vector_functions vector_input
+REGRESS = btree cast copy functions input ivfflat_cosine ivfflat_ip ivfflat_l2 ivfflat_options ivfflat_unlogged
 REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
 
 # For /arch flags

README.md

@@ -221,19 +221,7 @@ Cosine distance
 CREATE INDEX ON items USING hnsw (embedding vector_cosine_ops);
 ```
 
-Hamming distance - unreleased
-
-```sql
-CREATE INDEX ON items USING hnsw (embedding bit_hamming_ops);
-```
-
-Jaccard distance - unreleased
-
-```sql
-CREATE INDEX ON items USING hnsw (embedding bit_jaccard_ops);
-```
-
-Vectors with up to 2,000 dimensions can be indexed, or bit vectors with up to 64,000 dimensions.
+Vectors with up to 2,000 dimensions can be indexed.
 
 ### Index Options
 
@@ -412,6 +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.
@@ -427,19 +438,7 @@ You can use [Reciprocal Rank Fusion](https://github.com/pgvector/pgvector-python
 
 ### Tuning
 
-Use a tool like [PgTune](https://pgtune.leopard.in.ua/) to set initial values for Postgres server parameters. For instance, `shared_buffers` should typically be 25% of the server’s memory. You can find the config file with:
-
-```sql
-SHOW config_file;
-```
-
-And check individual settings with:
-
-```sql
-SHOW shared_buffers;
-```
-
-Be sure to restart Postgres for changes to take effect.
+Use a tool like [PgTune](https://pgtune.leopard.in.ua/) to set initial values for Postgres server parameters.
 
 ### Loading
 
@@ -711,12 +710,9 @@ Also, note that `NULL` vectors are not indexed (as well as zero vectors for cosi
 
 ## Reference
 
-- [Vector](#vector-type)
-- [Bit](#bit-type)
-
 ### Vector Type
 
-Each vector takes `4 * dimensions + 8` bytes of storage. Each element is a single-precision floating-point number (like the `real` type in Postgres), and all elements must be finite (no `NaN`, `Infinity` or `-Infinity`). Vectors can have up to 16,000 dimensions.
+Each vector takes `4 * dimensions + 8` bytes of storage. Each element is a single precision floating-point number (like the `real` type in Postgres), and all elements must be finite (no `NaN`, `Infinity` or `-Infinity`). Vectors can have up to 16,000 dimensions.
 
 ### Vector Operators
 
@@ -725,7 +721,6 @@ Operator | Description | Added
 \+ | element-wise addition |
 \- | element-wise subtraction |
 \* | element-wise multiplication | 0.5.0
-\|\| | concatenate | unreleased
 <-> | Euclidean distance |
 <#> | negative inner product |
 <=> | cosine distance |
@@ -738,35 +733,36 @@ cosine_distance(vector, vector) → double precision | cosine distance |
 inner_product(vector, vector) → double precision | inner product |
 l2_distance(vector, vector) → double precision | Euclidean distance |
 l1_distance(vector, vector) → double precision | taxicab distance | 0.5.0
-quantize_binary(vector) → bit | quantize | unreleased
-subvector(vector, integer, integer) → vector | subvector | unreleased
 vector_dims(vector) → integer | number of dimensions |
 vector_norm(vector) → double precision | Euclidean norm |
 
-### Vector Aggregate Functions
+### Aggregate Functions
 
 Function | Description | Added
 --- | --- | ---
 avg(vector) → vector | average |
 sum(vector) → vector | sum | 0.5.0
 
-### Bit Type
+### Halfvec Type
 
-Each bit vector takes `dimensions / 8 + (5 or 8)` bytes of storage. See the [Postgres docs](https://www.postgresql.org/docs/current/datatype-bit.html) for more info.
+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.
 
-### Bit Operators
+### Halfvec Operators
 
 Operator | Description | Added
 --- | --- | ---
-<~> | Hamming distance | unreleased
-<%> | Jaccard distance | unreleased
+<-> | Euclidean distance | 0.7.0
+<#> | negative inner product | 0.7.0
+<=> | cosine distance | 0.7.0
 
-### Bit Functions
+### Halfvec Functions
 
 Function | Description | Added
 --- | --- | ---
-hamming_distance(bit, bit) → double precision | Hamming distance | unreleased
-jaccard_distance(bit, bit) → double precision | Jaccard distance | unreleased
+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
 

sql/vector--0.6.2--0.7.0.sql

@@ -1,41 +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 quantize_binary(vector) RETURNS bit
+CREATE TYPE halfvec;
+
+CREATE FUNCTION halfvec_in(cstring, oid, integer) RETURNS halfvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION subvector(vector, int, int) RETURNS vector
+CREATE FUNCTION halfvec_out(halfvec) RETURNS cstring
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION vector_concat(vector, vector) RETURNS vector
+CREATE FUNCTION halfvec_typmod_in(cstring[]) RETURNS integer
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE OPERATOR || (
-	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
+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 hamming_distance(bit, bit) RETURNS float8
+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 jaccard_distance(bit, bit) RETURNS float8
+CREATE FUNCTION halfvec_l2_squared_distance(halfvec, halfvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE OPERATOR <~> (
-	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = hamming_distance,
-	COMMUTATOR = '<~>'
+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 = bit, RIGHTARG = bit, PROCEDURE = jaccard_distance,
-	COMMUTATOR = '<%>'
+CREATE OPERATOR <#> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_negative_inner_product,
+	COMMUTATOR = '<#>'
 );
 
-CREATE OPERATOR CLASS bit_hamming_ops
-	FOR TYPE bit USING hnsw AS
-	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
-	FUNCTION 1 hamming_distance(bit, bit);
+CREATE OPERATOR <=> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
 
-CREATE OPERATOR CLASS bit_jaccard_ops
-	FOR TYPE bit USING hnsw AS
-	OPERATOR 1 <%> (bit, bit) FOR ORDER BY float_ops,
-	FUNCTION 1 jaccard_distance(bit, bit);
+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

@@ -1,7 +1,7 @@
 -- complain if script is sourced in psql, rather than via CREATE EXTENSION
 \echo Use "CREATE EXTENSION vector" to load this file. \quit
 
--- vector type
+-- type
 
 CREATE TYPE vector;
 
@@ -29,7 +29,7 @@ CREATE TYPE vector (
 	STORAGE   = external
 );
 
--- vector functions
+-- functions
 
 CREATE FUNCTION l2_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -58,13 +58,7 @@ CREATE FUNCTION vector_sub(vector, vector) RETURNS vector
 CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION quantize_binary(vector) RETURNS bit
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
-CREATE FUNCTION subvector(vector, int, int) RETURNS vector
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
--- vector private functions
+-- private functions
 
 CREATE FUNCTION vector_lt(vector, vector) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -105,10 +99,7 @@ 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;
-
--- vector aggregates
+-- aggregates
 
 CREATE AGGREGATE avg(vector) (
 	SFUNC = vector_accum,
@@ -126,7 +117,7 @@ CREATE AGGREGATE sum(vector) (
 	PARALLEL = SAFE
 );
 
--- vector cast functions
+-- cast functions
 
 CREATE FUNCTION vector(vector, integer, boolean) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -146,7 +137,7 @@ CREATE FUNCTION array_to_vector(numeric[], integer, boolean) RETURNS vector
 CREATE FUNCTION vector_to_float4(vector, integer, boolean) RETURNS real[]
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- vector casts
+-- casts
 
 CREATE CAST (vector AS vector)
 	WITH FUNCTION vector(vector, integer, boolean) AS IMPLICIT;
@@ -166,7 +157,7 @@ CREATE CAST (double precision[] AS vector)
 CREATE CAST (numeric[] AS vector)
 	WITH FUNCTION array_to_vector(numeric[], integer, boolean) AS ASSIGNMENT;
 
--- vector operators
+-- operators
 
 CREATE OPERATOR <-> (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = l2_distance,
@@ -197,10 +188,6 @@ CREATE OPERATOR * (
 	COMMUTATOR = *
 );
 
-CREATE OPERATOR || (
-	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
-);
-
 CREATE OPERATOR < (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_lt,
 	COMMUTATOR = > , NEGATOR = >= ,
@@ -253,7 +240,7 @@ CREATE ACCESS METHOD hnsw TYPE INDEX HANDLER hnswhandler;
 
 COMMENT ON ACCESS METHOD hnsw IS 'hnsw index access method';
 
--- vector opclasses
+-- opclasses
 
 CREATE OPERATOR CLASS vector_ops
 	DEFAULT FOR TYPE vector USING btree AS
@@ -301,30 +288,144 @@ CREATE OPERATOR CLASS vector_cosine_ops
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
 	FUNCTION 2 vector_norm(vector);
 
--- bit functions
+-- halfvec type
 
-CREATE FUNCTION hamming_distance(bit, bit) RETURNS float8
+CREATE TYPE halfvec;
+
+CREATE FUNCTION halfvec_in(cstring, oid, integer) RETURNS halfvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION jaccard_distance(bit, bit) RETURNS float8
+CREATE FUNCTION halfvec_out(halfvec) RETURNS cstring
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE OPERATOR <~> (
-	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = hamming_distance,
-	COMMUTATOR = '<~>'
+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 OPERATOR <%> (
-	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = jaccard_distance,
-	COMMUTATOR = '<%>'
+-- 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 CLASS bit_hamming_ops
-	FOR TYPE bit USING hnsw AS
-	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
-	FUNCTION 1 hamming_distance(bit, bit);
+CREATE OPERATOR <#> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
 
-CREATE OPERATOR CLASS bit_jaccard_ops
-	FOR TYPE bit USING hnsw AS
-	OPERATOR 1 <%> (bit, bit) FOR ORDER BY float_ops,
-	FUNCTION 1 jaccard_distance(bit, bit);
+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/bitvector.c

@@ -1,90 +0,0 @@
-#include "postgres.h"
-
-#include "bitvector.h"
-#include "port/pg_bitutils.h"
-#include "utils/varbit.h"
-
-#if PG_VERSION_NUM >= 160000
-#include "varatt.h"
-#endif
-
-/*
- * Allocate and initialize a new bit vector
- */
-VarBit *
-InitBitVector(int dim)
-{
-	VarBit	   *result;
-	int			size;
-
-	size = VARBITTOTALLEN(dim);
-	result = (VarBit *) palloc0(size);
-	SET_VARSIZE(result, size);
-	VARBITLEN(result) = dim;
-
-	return result;
-}
-
-/*
- * Ensure same dimensions
- */
-static inline void
-CheckDims(VarBit *a, VarBit *b)
-{
-	if (VARBITLEN(a) != VARBITLEN(b))
-		ereport(ERROR,
-				(errcode(ERRCODE_DATA_EXCEPTION),
-				 errmsg("different bit lengths %u and %u", VARBITLEN(a), VARBITLEN(b))));
-}
-
-/*
- * Get the Hamming distance between two bit vectors
- */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(hamming_distance);
-Datum
-hamming_distance(PG_FUNCTION_ARGS)
-{
-	VarBit	   *a = PG_GETARG_VARBIT_P(0);
-	VarBit	   *b = PG_GETARG_VARBIT_P(1);
-	unsigned char *ax = VARBITS(a);
-	unsigned char *bx = VARBITS(b);
-	uint64		distance = 0;
-
-	CheckDims(a, b);
-
-	/* TODO Improve performance */
-	for (uint32 i = 0; i < VARBITBYTES(a); i++)
-		distance += pg_number_of_ones[ax[i] ^ bx[i]];
-
-	PG_RETURN_FLOAT8((double) distance);
-}
-
-/*
- * Get the Jaccard distance between two bit vectors
- */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(jaccard_distance);
-Datum
-jaccard_distance(PG_FUNCTION_ARGS)
-{
-	VarBit	   *a = PG_GETARG_VARBIT_P(0);
-	VarBit	   *b = PG_GETARG_VARBIT_P(1);
-	unsigned char *ax = VARBITS(a);
-	unsigned char *bx = VARBITS(b);
-	uint64		ab = 0;
-	uint64		aa;
-	uint64		bb;
-
-	CheckDims(a, b);
-
-	/* TODO Improve performance */
-	for (uint32 i = 0; i < VARBITBYTES(a); i++)
-		ab += pg_number_of_ones[ax[i] & bx[i]];
-
-	if (ab == 0)
-		PG_RETURN_FLOAT8(1);
-
-	aa = pg_popcount((char *) ax, VARBITBYTES(a));
-	bb = pg_popcount((char *) bx, VARBITBYTES(b));
-
-	PG_RETURN_FLOAT8(1 - (ab / ((double) (aa + bb - ab))));
-}

src/bitvector.h

@@ -1,8 +0,0 @@
-#ifndef BITVECTOR_H
-#define BITVECTOR_H
-
-#include "utils/varbit.h"
-
-VarBit	   *InitBitVector(int dim);
-
-#endif

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

@@ -55,11 +55,9 @@
 #define HNSW_UPDATE_ENTRY_GREATER 1
 #define HNSW_UPDATE_ENTRY_ALWAYS 2
 
-typedef enum HnswType
-{
-	HNSW_TYPE_VECTOR,
-	HNSW_TYPE_BIT
-}			HnswType;
+/* Data types */
+#define HNSW_TYPE_VECTOR 1
+#define HNSW_TYPE_HALFVEC 2
 
 /* Build phases */
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
@@ -248,7 +246,7 @@ typedef struct HnswBuildState
 	Relation	index;
 	IndexInfo  *indexInfo;
 	ForkNumber	forkNum;
-	HnswType	type;
+	int			type;
 
 	/* Settings */
 	int			dimensions;
@@ -373,8 +371,8 @@ typedef struct HnswVacuumState
 int			HnswGetM(Relation index);
 int			HnswGetEfConstruction(Relation index);
 FmgrInfo   *HnswOptionalProcInfo(Relation index, uint16 procnum);
-HnswType	HnswGetType(Relation index);
-bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, HnswType type);
+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

@@ -44,7 +44,6 @@
 #include "access/xact.h"
 #include "access/xloginsert.h"
 #include "catalog/index.h"
-#include "catalog/pg_type_d.h"
 #include "commands/progress.h"
 #include "hnsw.h"
 #include "miscadmin.h"
@@ -666,27 +665,13 @@ HnswSharedMemoryAlloc(Size size, void *state)
 	return chunk;
 }
 
-/*
- * Get max dimensions
- */
-static int
-GetMaxDimensions(HnswType type)
-{
-	int			maxDimensions = HNSW_MAX_DIM;
-
-	if (type == HNSW_TYPE_BIT)
-		maxDimensions *= 32;
-
-	return maxDimensions;
-}
-
 /*
  * Initialize the build state
  */
 static void
 InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, IndexInfo *indexInfo, ForkNumber forkNum)
 {
-	int			maxDimensions;
+	int			maxDimensions = HNSW_MAX_DIM;
 
 	buildstate->heap = heap;
 	buildstate->index = index;
@@ -698,7 +683,8 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	buildstate->efConstruction = HnswGetEfConstruction(index);
 	buildstate->dimensions = TupleDescAttr(index->rd_att, 0)->atttypmod;
 
-	maxDimensions = GetMaxDimensions(buildstate->type);
+	if (buildstate->type == HNSW_TYPE_HALFVEC)
+		maxDimensions *= 2;
 
 	/* Require column to have dimensions to be indexed */
 	if (buildstate->dimensions < 0)

src/hnswscan.c

@@ -1,8 +1,7 @@
 #include "postgres.h"
 
 #include "access/relscan.h"
-#include "bitvector.h"
-#include "catalog/pg_type_d.h"
+#include "halfvec.h"
 #include "hnsw.h"
 #include "pgstat.h"
 #include "storage/bufmgr.h"
@@ -42,6 +41,29 @@ GetScanItems(IndexScanDesc scan, Datum q)
 	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
 }
 
+/*
+ * Get dimensions from metapage
+ */
+static int
+GetDimensions(Relation index)
+{
+	Buffer		buf;
+	Page		page;
+	HnswMetaPage metap;
+	int			dimensions;
+
+	buf = ReadBuffer(index, HNSW_METAPAGE_BLKNO);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	metap = HnswPageGetMeta(page);
+
+	dimensions = metap->dimensions;
+
+	UnlockReleaseBuffer(buf);
+
+	return dimensions;
+}
+
 /*
  * Get scan value
  */
@@ -52,7 +74,14 @@ GetScanValue(IndexScanDesc scan)
 	Datum		value;
 
 	if (scan->orderByData->sk_flags & SK_ISNULL)
-		value = PointerGetDatum(NULL);
+	{
+		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;

src/hnswutils.c

@@ -3,13 +3,15 @@
 #include <math.h>
 
 #include "access/generic_xlog.h"
-#include "catalog/pg_type_d.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
@@ -153,15 +155,27 @@ HnswOptionalProcInfo(Relation index, uint16 procnum)
 /*
  * Get type
  */
-HnswType
+int
 HnswGetType(Relation index)
 {
-	Oid			typid = TupleDescAttr(index->rd_att, 0)->atttypid;
+	Oid			typeOid = TupleDescAttr(index->rd_att, 0)->atttypid;
+	HeapTuple	tuple;
+	Form_pg_type type;
+	int			result;
 
-	if (typid == BITOID || typid == VARBITOID)
-		return HNSW_TYPE_BIT;
+	tuple = SearchSysCache1(TYPEOID, ObjectIdGetDatum(typeOid));
+	if (!HeapTupleIsValid(tuple))
+		elog(ERROR, "cache lookup failed for type %u", typeOid);
 
-	return HNSW_TYPE_VECTOR;
+	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;
 }
 
 /*
@@ -173,14 +187,26 @@ HnswGetType(Relation index)
  * if it's different than the original value
  */
 bool
-HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, HnswType type)
+HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, int type)
 {
 	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
 
 	if (norm > 0)
 	{
-		/* TODO Remove vector-specific code */
-		if (type == HNSW_TYPE_VECTOR)
+		if (type == HNSW_TYPE_HALFVEC)
+		{
+			HalfVector *v = DatumGetHalfVector(*value);
+			HalfVector *result = InitHalfVector(v->dim);
+
+			for (int i = 0; i < v->dim; i++)
+			{
+				/* TODO Fix */
+				result->x[i] = Float4ToHalfUnchecked(HalfToFloat4(v->x[i]) / norm);
+			}
+
+			*value = PointerGetDatum(result);
+		}
+		else if (type == HNSW_TYPE_VECTOR)
 		{
 			Vector	   *v = DatumGetVector(*value);
 			Vector	   *result = InitVector(v->dim);
@@ -594,12 +620,7 @@ HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index,
 
 	/* Calculate distance */
 	if (distance != NULL)
-	{
-		if (DatumGetPointer(*q) == NULL)
-			*distance = 0;
-		else
-			*distance = (float) DatumGetFloat8(FunctionCall2Coll(procinfo, collation, *q, PointerGetDatum(&etup->data)));
-	}
+		*distance = (float) DatumGetFloat8(FunctionCall2Coll(procinfo, collation, *q, PointerGetDatum(&etup->data)));
 
 	UnlockReleaseBuffer(buf);
 }

src/ivfbuild.c

@@ -57,7 +57,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 	 */
 	if (buildstate->kmeansnormprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value))
+		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->normvec))
 			return;
 	}
 
@@ -105,7 +105,7 @@ SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
 
 	/* Add sample */
-	AddSample(values, buildstate);
+	AddSample(values, state);
 
 	/* Reset memory context */
 	MemoryContextSwitchTo(oldCtx);
@@ -153,7 +153,7 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState
 	/* Normalize if needed */
 	if (buildstate->normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value))
+		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->normvec))
 			return;
 	}
 
@@ -356,6 +356,9 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->centers = VectorArrayInit(buildstate->lists, buildstate->dimensions);
 	buildstate->listInfo = palloc(sizeof(ListInfo) * buildstate->lists);
 
+	/* Reuse for each tuple */
+	buildstate->normvec = InitVector(buildstate->dimensions);
+
 	buildstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 											   "Ivfflat build temporary context",
 											   ALLOCSET_DEFAULT_SIZES);
@@ -377,6 +380,7 @@ FreeBuildState(IvfflatBuildState * buildstate)
 {
 	VectorArrayFree(buildstate->centers);
 	pfree(buildstate->listInfo);
+	pfree(buildstate->normvec);
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	pfree(buildstate->listSums);

src/ivfflat.h

@@ -172,6 +172,7 @@ typedef struct IvfflatBuildState
 	VectorArray samples;
 	VectorArray centers;
 	ListInfo   *listInfo;
+	Vector	   *normvec;
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	double		inertia;
@@ -266,7 +267,7 @@ void		VectorArrayFree(VectorArray arr);
 void		PrintVectorArray(char *msg, VectorArray arr);
 void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
 FmgrInfo   *IvfflatOptionalProcInfo(Relation index, uint16 procnum);
-bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value);
+bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
 int			IvfflatGetLists(Relation index);
 void		IvfflatGetMetaPageInfo(Relation index, int *lists, int *dimensions);
 void		IvfflatUpdateList(Relation index, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);

src/ivfinsert.c

@@ -85,7 +85,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(normprocinfo, index->rd_indcollation[0], &value))
+		if (!IvfflatNormValue(normprocinfo, index->rd_indcollation[0], &value, NULL))
 			return;
 	}
 

src/ivfscan.c

@@ -293,7 +293,7 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 
 			/* Fine if normalization fails */
 			if (so->normprocinfo != NULL)
-				IvfflatNormValue(so->normprocinfo, so->collation, &value);
+				IvfflatNormValue(so->normprocinfo, so->collation, &value, NULL);
 		}
 
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));

src/ivfutils.c

@@ -75,14 +75,16 @@ IvfflatOptionalProcInfo(Relation index, uint16 procnum)
  * if it's different than the original value
  */
 bool
-IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value)
+IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result)
 {
 	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
 
 	if (norm > 0)
 	{
 		Vector	   *v = DatumGetVector(*value);
-		Vector	   *result = InitVector(v->dim);
+
+		if (result == NULL)
+			result = InitVector(v->dim);
 
 		for (int i = 0; i < v->dim; i++)
 			result->x[i] = v->x[i] / norm;

src/vector.c

@@ -2,10 +2,10 @@
 
 #include <math.h>
 
-#include "bitvector.h"
 #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"
@@ -276,9 +276,6 @@ vector_in(PG_FUNCTION_ARGS)
 	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
  */
@@ -290,6 +287,7 @@ vector_out(PG_FUNCTION_ARGS)
 	int			dim = vector->dim;
 	char	   *buf;
 	char	   *ptr;
+	int			n;
 
 	/*
 	 * Need:
@@ -304,17 +302,21 @@ vector_out(PG_FUNCTION_ARGS)
 	buf = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN * dim + 2);
 	ptr = buf;
 
-	AppendChar(ptr, '[');
-
+	*ptr = '[';
+	ptr++;
 	for (int i = 0; i < dim; i++)
 	{
 		if (i > 0)
-			AppendChar(ptr, ',');
+		{
+			*ptr = ',';
+			ptr++;
+		}
 
-		AppendFloat(ptr, vector->x[i]);
+		n = float_to_shortest_decimal_bufn(vector->x[i], ptr);
+		ptr += n;
 	}
-
-	AppendChar(ptr, ']');
+	*ptr = ']';
+	ptr++;
 	*ptr = '\0';
 
 	PG_FREE_IF_COPY(vector, 0);
@@ -531,6 +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
  */
@@ -859,80 +883,6 @@ vector_mul(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
-/*
- * Quantize a vector
- */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(quantize_binary);
-Datum
-quantize_binary(PG_FUNCTION_ARGS)
-{
-	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	float	   *ax = a->x;
-	VarBit	   *result = InitBitVector(a->dim);
-	unsigned char *rx = VARBITS(result);
-
-	for (int i = 0; i < a->dim; i++)
-		rx[i / 8] |= (ax[i] > 0) << (7 - (i % 8));
-
-	PG_RETURN_VARBIT_P(result);
-}
-
-/*
- * Get a subvector
- */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(subvector);
-Datum
-subvector(PG_FUNCTION_ARGS)
-{
-	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	int32		start = PG_GETARG_INT32(1);
-	int32		count = PG_GETARG_INT32(2);
-	int32		end = start + count;
-	float	   *ax = a->x;
-	Vector	   *result;
-	int			dim;
-
-	/* Indexing starts at 1, like substring */
-	if (start < 1)
-		start = 1;
-
-	if (end > a->dim)
-		end = a->dim + 1;
-
-	dim = end - start;
-	CheckDim(dim);
-	result = InitVector(dim);
-
-	for (int i = 0; i < dim; i++)
-		result->x[i] = ax[start - 1 + i];
-
-	PG_RETURN_POINTER(result);
-}
-
-/*
- * Concatenate 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);
-}
-
 /*
  * Internal helper to compare vectors
  */
@@ -970,6 +920,9 @@ vector_lt(PG_FUNCTION_ARGS)
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
+	/* TODO Remove in 0.7.0 */
+	CheckDims(a, b);
+
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) < 0);
 }
 
@@ -983,6 +936,9 @@ vector_le(PG_FUNCTION_ARGS)
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
+	/* TODO Remove in 0.7.0 */
+	CheckDims(a, b);
+
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) <= 0);
 }
 
@@ -996,6 +952,9 @@ vector_eq(PG_FUNCTION_ARGS)
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
+	/* TODO Remove in 0.7.0 */
+	CheckDims(a, b);
+
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) == 0);
 }
 
@@ -1009,6 +968,9 @@ vector_ne(PG_FUNCTION_ARGS)
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
+	/* TODO Remove in 0.7.0 */
+	CheckDims(a, b);
+
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) != 0);
 }
 
@@ -1022,6 +984,9 @@ vector_ge(PG_FUNCTION_ARGS)
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
+	/* TODO Remove in 0.7.0 */
+	CheckDims(a, b);
+
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) >= 0);
 }
 
@@ -1035,6 +1000,9 @@ vector_gt(PG_FUNCTION_ARGS)
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
+	/* TODO Remove in 0.7.0 */
+	CheckDims(a, b);
+
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) > 0);
 }
 

test/expected/bit_functions.out

@@ -1,64 +0,0 @@
-SELECT hamming_distance(B'111', B'111');
- hamming_distance 
-------------------
-                0
-(1 row)
-
-SELECT hamming_distance(B'111', B'110');
- hamming_distance 
-------------------
-                1
-(1 row)
-
-SELECT hamming_distance(B'111', B'100');
- hamming_distance 
-------------------
-                2
-(1 row)
-
-SELECT hamming_distance(B'111', B'000');
- hamming_distance 
-------------------
-                3
-(1 row)
-
-SELECT hamming_distance(B'111', B'00');
-ERROR:  different bit lengths 3 and 2
-SELECT jaccard_distance(B'1111', B'1111');
- jaccard_distance 
-------------------
-                0
-(1 row)
-
-SELECT jaccard_distance(B'1111', B'1110');
- jaccard_distance 
-------------------
-             0.25
-(1 row)
-
-SELECT jaccard_distance(B'1111', B'1100');
- jaccard_distance 
-------------------
-              0.5
-(1 row)
-
-SELECT jaccard_distance(B'1111', B'1000');
- jaccard_distance 
-------------------
-             0.75
-(1 row)
-
-SELECT jaccard_distance(B'1111', B'0000');
- jaccard_distance 
-------------------
-                1
-(1 row)
-
-SELECT jaccard_distance(B'1100', B'1000');
- jaccard_distance 
-------------------
-              0.5
-(1 row)
-
-SELECT jaccard_distance(B'1111', B'000');
-ERROR:  different bit lengths 4 and 3

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));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE TABLE t2 (val vector(3));
+CREATE TABLE t (val vector(3), val2 halfvec(3));
+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), 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   
----------
- [0,0,0]
- [1,1,1]
- [1,2,3]
- 
+   val   |  val2   
+---------+---------
+ [0,0,0] | [0,0,0]
+ [1,1,1] | [1,1,1]
+ [1,2,3] | [1,2,3]
+         | 
 (4 rows)
 
 DROP TABLE t;

test/expected/functions.out

@@ -24,38 +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? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::vector < '[1,2]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::vector <= '[1,2,3]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::vector <= '[1,2]';
- ?column? 
-----------
- f
-(1 row)
-
 SELECT '[1,2,3]'::vector = '[1,2,3]';
  ?column? 
 ----------
@@ -63,47 +31,7 @@ SELECT '[1,2,3]'::vector = '[1,2,3]';
 (1 row)
 
 SELECT '[1,2,3]'::vector = '[1,2]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::vector != '[1,2,3]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::vector != '[1,2]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::vector >= '[1,2,3]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::vector >= '[1,2]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::vector > '[1,2,3]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::vector > '[1,2]';
- ?column? 
-----------
- t
-(1 row)
-
+ERROR:  different vector dimensions 3 and 2
 SELECT vector_cmp('[1,2,3]', '[1,2,3]');
  vector_cmp 
 ------------
@@ -280,48 +208,6 @@ SELECT l1_distance('[3e38]'::vector, '[-3e38]');
     Infinity
 (1 row)
 
-SELECT quantize_binary('[1,0,-1]');
- quantize_binary 
------------------
- 100
-(1 row)
-
-SELECT quantize_binary('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]');
- quantize_binary 
------------------
- 01001110101
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]', 1, 3);
- subvector 
------------
- [1,2,3]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]', 3, 2);
- subvector 
------------
- [3,4]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]', -1, 3);
- subvector 
------------
- [1]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]', 3, 9);
- subvector 
------------
- [3,4,5]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]', 1, 0);
-ERROR:  vector must have at least 1 dimension
-SELECT subvector('[1,2,3,4,5]', 3, -1);
-ERROR:  vector must have at least 1 dimension
-SELECT subvector('[1,2,3,4,5]', -1, 2);
-ERROR:  vector must have at least 1 dimension
 SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
     avg    
 -----------

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/hnsw_hamming.out

@@ -1,21 +0,0 @@
-SET enable_seqscan = off;
-CREATE TABLE t (val bit(3));
-INSERT INTO t (val) VALUES (B'000'), (B'100'), (B'111'), (NULL);
-CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
-INSERT INTO t (val) VALUES (B'110');
-SELECT * FROM t ORDER BY val <~> B'111';
- val 
------
- 111
- 110
- 100
- 000
-(4 rows)
-
-SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <~> (SELECT NULL::bit)) t2;
- count 
--------
-     4
-(1 row)
-
-DROP TABLE t;

test/expected/hnsw_jaccard.out

@@ -1,21 +0,0 @@
-SET enable_seqscan = off;
-CREATE TABLE t (val bit(4));
-INSERT INTO t (val) VALUES (B'0000'), (B'1100'), (B'1111'), (NULL);
-CREATE INDEX ON t USING hnsw (val bit_jaccard_ops);
-INSERT INTO t (val) VALUES (B'1110');
-SELECT * FROM t ORDER BY val <%> B'1111';
- val  
-------
- 1111
- 1110
- 1100
- 0000
-(4 rows)
-
-SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <%> (SELECT NULL::bit)) t2;
- count 
--------
-     4
-(1 row)
-
-DROP TABLE t;

test/expected/hnsw_l2.out

@@ -12,11 +12,14 @@ SELECT * FROM t ORDER BY val <-> '[3,3,3]';
  [0,0,0]
 (4 rows)
 
-SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector)) t2;
- count 
--------
-     4
-(1 row)
+SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
+   val   
+---------
+ [0,0,0]
+ [1,1,1]
+ [1,2,3]
+ [1,2,4]
+(4 rows)
 
 SELECT COUNT(*) FROM t;
  count 

test/expected/input.out

@@ -66,22 +66,6 @@ SELECT '[4e38,1]'::vector;
 ERROR:  infinite value not allowed in vector
 LINE 1: SELECT '[4e38,1]'::vector;
                ^
-SELECT '[-4e38,1]'::vector;
-ERROR:  infinite value not allowed in vector
-LINE 1: SELECT '[-4e38,1]'::vector;
-               ^
-SELECT '[1e-46,1]'::vector;
- vector 
---------
- [0,1]
-(1 row)
-
-SELECT '[-1e-46,1]'::vector;
- vector 
---------
- [-0,1]
-(1 row)
-
 SELECT '[1,2,3'::vector;
 ERROR:  malformed vector literal: "[1,2,3"
 LINE 1: SELECT '[1,2,3'::vector;

test/sql/bit_functions.sql

@@ -1,13 +0,0 @@
-SELECT hamming_distance(B'111', B'111');
-SELECT hamming_distance(B'111', B'110');
-SELECT hamming_distance(B'111', B'100');
-SELECT hamming_distance(B'111', B'000');
-SELECT hamming_distance(B'111', B'00');
-
-SELECT jaccard_distance(B'1111', B'1111');
-SELECT jaccard_distance(B'1111', B'1110');
-SELECT jaccard_distance(B'1111', B'1100');
-SELECT jaccard_distance(B'1111', B'1000');
-SELECT jaccard_distance(B'1111', B'0000');
-SELECT jaccard_distance(B'1100', B'1000');
-SELECT jaccard_distance(B'1111', B'000');

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));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE TABLE t (val vector(3), val2 halfvec(3));
+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

@@ -6,21 +6,8 @@ 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]';
-SELECT '[1,2,3]'::vector <= '[1,2,3]';
-SELECT '[1,2,3]'::vector <= '[1,2]';
 SELECT '[1,2,3]'::vector = '[1,2,3]';
 SELECT '[1,2,3]'::vector = '[1,2]';
-SELECT '[1,2,3]'::vector != '[1,2,3]';
-SELECT '[1,2,3]'::vector != '[1,2]';
-SELECT '[1,2,3]'::vector >= '[1,2,3]';
-SELECT '[1,2,3]'::vector >= '[1,2]';
-SELECT '[1,2,3]'::vector > '[1,2,3]';
-SELECT '[1,2,3]'::vector > '[1,2]';
 
 SELECT vector_cmp('[1,2,3]', '[1,2,3]');
 SELECT vector_cmp('[1,2,3]', '[0,0,0]');
@@ -61,17 +48,6 @@ SELECT l1_distance('[0,0]'::vector, '[0,1]');
 SELECT l1_distance('[1,2]'::vector, '[3]');
 SELECT l1_distance('[3e38]'::vector, '[-3e38]');
 
-SELECT quantize_binary('[1,0,-1]');
-SELECT quantize_binary('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]');
-
-SELECT subvector('[1,2,3,4,5]', 1, 3);
-SELECT subvector('[1,2,3,4,5]', 3, 2);
-SELECT subvector('[1,2,3,4,5]', -1, 3);
-SELECT subvector('[1,2,3,4,5]', 3, 9);
-SELECT subvector('[1,2,3,4,5]', 1, 0);
-SELECT subvector('[1,2,3,4,5]', 3, -1);
-SELECT subvector('[1,2,3,4,5]', -1, 2);
-
 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;
 SELECT avg(v) FROM unnest(ARRAY[]::vector[]) 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/hnsw_hamming.sql

@@ -1,12 +0,0 @@
-SET enable_seqscan = off;
-
-CREATE TABLE t (val bit(3));
-INSERT INTO t (val) VALUES (B'000'), (B'100'), (B'111'), (NULL);
-CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
-
-INSERT INTO t (val) VALUES (B'110');
-
-SELECT * FROM t ORDER BY val <~> B'111';
-SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <~> (SELECT NULL::bit)) t2;
-
-DROP TABLE t;

test/sql/hnsw_jaccard.sql

@@ -1,12 +0,0 @@
-SET enable_seqscan = off;
-
-CREATE TABLE t (val bit(4));
-INSERT INTO t (val) VALUES (B'0000'), (B'1100'), (B'1111'), (NULL);
-CREATE INDEX ON t USING hnsw (val bit_jaccard_ops);
-
-INSERT INTO t (val) VALUES (B'1110');
-
-SELECT * FROM t ORDER BY val <%> B'1111';
-SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <%> (SELECT NULL::bit)) t2;
-
-DROP TABLE t;

test/sql/hnsw_l2.sql

@@ -7,7 +7,7 @@ CREATE INDEX ON t USING hnsw (val vector_l2_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::vector)) t2;
+SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
 SELECT COUNT(*) FROM t;
 
 TRUNCATE t;

test/sql/input.sql

@@ -11,9 +11,6 @@ SELECT '[1.5e38,-1.5e38]'::vector;
 SELECT '[1.5e+38,-1.5e+38]'::vector;
 SELECT '[1.5e-38,-1.5e-38]'::vector;
 SELECT '[4e38,1]'::vector;
-SELECT '[-4e38,1]'::vector;
-SELECT '[1e-46,1]'::vector;
-SELECT '[-1e-46,1]'::vector;
 SELECT '[1,2,3'::vector;
 SELECT '[1,2,3]9'::vector;
 SELECT '1,2,3'::vector;

test/t/016_hnsw_vacuum_recall.pl

@@ -86,7 +86,7 @@ foreach (@queries)
 	push(@expected, $res);
 }
 
-test_recall(0.19, $limit, "before vacuum");
+test_recall(0.20, $limit, "before vacuum");
 test_recall(0.95, 100, "before vacuum");
 
 # TODO Test concurrent inserts with vacuum

test/t/020_hnsw_halfvec_build_recall.pl

@@ -8,8 +8,8 @@ my $node;
 my @queries = ();
 my @expected;
 my $limit = 20;
-my $dim = 52;
-my $max = 2**$dim;
+my $dim = 10;
+my $array_sql = join(",", ('random()') x $dim);
 
 sub test_recall
 {
@@ -19,8 +19,7 @@ sub test_recall
 
 	my $explain = $node->safe_psql("postgres", qq(
 		SET enable_seqscan = off;
-		SET hnsw.ef_search = 100;
-		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator $queries[0] LIMIT $limit;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
 	));
 	like($explain, qr/Index Scan/);
 
@@ -28,23 +27,21 @@ sub test_recall
 	{
 		my $actual = $node->safe_psql("postgres", qq(
 			SET enable_seqscan = off;
-			SET hnsw.ef_search = 100;
-			SELECT i FROM tst ORDER BY v $operator $queries[$i] LIMIT $limit;
+			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]);
-		my %expected_set = map { $_ => 1 } @expected_ids;
 
-		foreach (@actual_ids)
+		foreach (@expected_ids)
 		{
-			if (exists($expected_set{$_}))
+			if (exists($actual_set{$_}))
 			{
 				$correct++;
 			}
+			$total++;
 		}
-
-		$total += $limit;
 	}
 
 	cmp_ok($correct / $total, ">=", $min, $operator);
@@ -57,21 +54,25 @@ $node->start;
 
 # Create table
 $node->safe_psql("postgres", "CREATE EXTENSION vector;");
-$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v bit($dim));");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v halfvec($dim));");
 $node->safe_psql("postgres",
-	"INSERT INTO tst SELECT i, (random() * $max)::bigint::bit($dim) FROM generate_series(1, 10000) i;"
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
 );
 
 # Generate queries
 for (1 .. 20)
 {
-	my $r = int(rand() * $max);
-	push(@queries, "${r}::bigint::bit($dim)");
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	push(@queries, "[" . join(",", @r) . "]");
 }
 
 # Check each index type
-my @operators = ("<~>", "<\%>");
-my @opclasses = ("bit_hamming_ops", "bit_jaccard_ops");
+my @operators = ("<->", "<#>", "<=>");
+my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops");
 
 for my $i (0 .. $#operators)
 {
@@ -82,13 +83,7 @@ for my $i (0 .. $#operators)
 	@expected = ();
 	foreach (@queries)
 	{
-		# Handle ties
-		my $res = $node->safe_psql("postgres", qq(
-			WITH top AS (
-				SELECT v $operator $_ AS distance FROM tst ORDER BY v $operator $_ LIMIT $limit
-			)
-			SELECT i FROM tst WHERE (v $operator $_) <= (SELECT MAX(distance) FROM top)
-		));
+		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
 		push(@expected, $res);
 	}
 
@@ -99,7 +94,7 @@ for my $i (0 .. $#operators)
 	));
 
 	# Test approximate results
-	my $min = $operator eq "<\%>" ? 0.96 : 0.98;
+	my $min = $operator eq "<#>" ? 0.95 : 0.99;
 	test_recall($min, $operator);
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");