Improved check [skip ci]

Co-authored-by: Arda Aytekin <arda.aytekin@microsoft.com>

.github/workflows/build.yml

@@ -115,6 +115,8 @@ jobs:
           sudo -u postgres make prove_installcheck
         env:
           PG_CFLAGS: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
+      - if: ${{ failure() }}
+        run: cat pgvector/regression.diffs
   valgrind:
     if: ${{ !startsWith(github.ref_name, 'mac') && !startsWith(github.ref_name, 'windows') }}
     runs-on: ubuntu-latest
@@ -123,6 +125,7 @@ jobs:
       - uses: ankane/setup-postgres-valgrind@v1
         with:
           postgres-version: 16
+          check-ub: yes
       - run: make OPTFLAGS=""
       - run: sudo --preserve-env=PG_CONFIG make install
       - run: make installcheck

CHANGELOG.md

@@ -2,11 +2,13 @@
 
 - Added `halfvec` type
 - Added `sparsevec` type
-- Added support for `bit` vectors to HNSW
+- Added support for indexing `bit` type
+- Added `binary_quantize` function
 - Added `hamming_distance` function
 - Added `jaccard_distance` function
-- Added `quantize_binary` function
+- Added `l2_normalize` function
 - Added `subvector` function
+- Added concatenate operator for vectors
 - Added CPU dispatching for distance functions on Linux x86-64
 - Updated comparison operators to support vectors with different dimensions
 

Makefile.win

@@ -4,7 +4,7 @@ EXTVERSION = 0.6.2
 OBJS = src\bitvector.obj src\halfutils.obj 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\sparsevec.obj src\vector.obj
 HEADERS = src\halfvec.h src\sparsevec.h src\vector.h
 
-REGRESS = bit_functions btree cast copy halfvec_functions halfvec_input hnsw_bit_hamming hnsw_bit_jaccard hnsw_halfvec_cosine hnsw_halfvec_ip hnsw_halfvec_l2 hnsw_options hnsw_sparsevec_cosine hnsw_sparsevec_ip hnsw_sparsevec_l2 hnsw_unlogged hnsw_vector_cosine hnsw_vector_ip hnsw_vector_l2 ivfflat_options ivfflat_unlogged ivfflat_vector_cosine ivfflat_vector_ip ivfflat_vector_l2 sparsevec_functions sparsevec_input vector_functions vector_input
+REGRESS = bit_functions btree_halfvec btree_sparsevec btree_vector cast copy halfvec_functions halfvec_input hnsw_bit_hamming hnsw_bit_jaccard hnsw_halfvec_cosine hnsw_halfvec_ip hnsw_halfvec_l2 hnsw_options hnsw_sparsevec_cosine hnsw_sparsevec_ip hnsw_sparsevec_l2 hnsw_unlogged hnsw_vector_cosine hnsw_vector_ip hnsw_vector_l2 ivfflat_halfvec_cosine ivfflat_halfvec_ip ivfflat_halfvec_l2 ivfflat_options ivfflat_unlogged ivfflat_vector_cosine ivfflat_vector_ip ivfflat_vector_l2 sparsevec_functions sparsevec_input vector_functions vector_input
 REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
 
 # For /arch flags

README.md

@@ -138,6 +138,12 @@ Get the nearest neighbors to a vector
 SELECT * FROM items ORDER BY embedding <-> '[3,1,2]' LIMIT 5;
 ```
 
+Supported distance functions are:
+
+- `<->` - L2 distance
+- `<#>` - (negative) inner product
+- `<=>` - cosine distance
+
 Get the nearest neighbors to a row
 
 ```sql
@@ -347,6 +353,7 @@ Supported types are:
 
 - `vector` - up to 2,000 dimensions
 - `halfvec` - up to 4,000 dimensions (unreleased)
+- `bit` - up to 64,000 dimensions (unreleased)
 
 ### Query Options
 
@@ -476,20 +483,20 @@ Also supports Jaccard distance (`<%>`)
 Use expression indexing for binary quantization
 
 ```sql
-CREATE INDEX ON items USING hnsw ((quantize_binary(embedding)::bit(3)) bit_hamming_ops);
+CREATE INDEX ON items USING hnsw ((binary_quantize(embedding)::bit(3)) bit_hamming_ops);
 ```
 
 Get the nearest neighbors by Hamming distance
 
 ```sql
-SELECT * FROM items ORDER BY quantize_binary(embedding)::bit(3) <~> quantize_binary('[1,-2,3]') LIMIT 5;
+SELECT * FROM items ORDER BY binary_quantize(embedding)::bit(3) <~> binary_quantize('[1,-2,3]') LIMIT 5;
 ```
 
 Re-rank by the original vectors for better recall
 
 ```sql
 SELECT * FROM (
-    SELECT * FROM items ORDER BY quantize_binary(embedding)::bit(3) <~> quantize_binary('[1,-2,3]') LIMIT 20
+    SELECT * FROM items ORDER BY binary_quantize(embedding)::bit(3) <~> binary_quantize('[1,-2,3]') LIMIT 20
 ) ORDER BY embedding <=> '[1,-2,3]' LIMIT 5;
 ```
 
@@ -509,7 +516,7 @@ Insert vectors
 INSERT INTO items (embedding) VALUES ('{1:1,3:2,5:3}/5'), ('{1:4,3:5,5:6}/5');
 ```
 
-Note: The format is `{index1:value1,index2:value2,...}/dimensions` and indices start at 1 like SQL arrays
+The format is `{index1:value1,index2:value2}/dimensions` and indices start at 1 like SQL arrays
 
 Get the nearest neighbors by L2 distance
 
@@ -844,6 +851,7 @@ Operator | Description | Added
 \+ | element-wise addition |
 \- | element-wise subtraction |
 \* | element-wise multiplication | 0.5.0
+\|\| | concatenate | unreleased
 <-> | Euclidean distance |
 <#> | negative inner product |
 <=> | cosine distance |
@@ -852,11 +860,12 @@ Operator | Description | Added
 
 Function | Description | Added
 --- | --- | ---
+binary_quantize(vector) → bit | binary quantize | unreleased
 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
+l2_distance(vector, vector) → double precision | Euclidean distance |
+l2_normalize(vector) → vector | Normalize with Euclidean norm | unreleased
 subvector(vector, integer, integer) → vector | subvector | unreleased
 vector_dims(vector) → integer | number of dimensions |
 vector_norm(vector) → double precision | Euclidean norm |
@@ -876,6 +885,10 @@ Each half vector takes `2 * dimensions + 8` bytes of storage. Each element is a
 
 Operator | Description | Added
 --- | --- | ---
+\+ | element-wise addition | unreleased
+\- | element-wise subtraction | unreleased
+\* | element-wise multiplication | unreleased
+\|\| | concatenate | unreleased
 <-> | Euclidean distance | unreleased
 <#> | negative inner product | unreleased
 <=> | cosine distance | unreleased
@@ -884,12 +897,22 @@ Operator | Description | Added
 
 Function | Description | Added
 --- | --- | ---
+binary_quantize(halfvec) → bit | binary quantize | unreleased
 cosine_distance(halfvec, halfvec) → double precision | cosine distance | unreleased
 inner_product(halfvec, halfvec) → double precision | inner product | unreleased
-l2_distance(halfvec, halfvec) → double precision | Euclidean distance | unreleased
 l1_distance(halfvec, halfvec) → double precision | taxicab distance | unreleased
-quantize_binary(halfvec) → bit | quantize | unreleased
+l2_distance(halfvec, halfvec) → double precision | Euclidean distance | unreleased
+l2_norm(halfvec) → double precision | Euclidean norm | unreleased
+l2_normalize(halfvec) → halfvec | Normalize with Euclidean norm | unreleased
 subvector(halfvec, integer, integer) → halfvec | subvector | unreleased
+vector_dims(halfvec) → integer | number of dimensions | unreleased
+
+### Halfvec Aggregate Functions
+
+Function | Description | Added
+--- | --- | ---
+avg(halfvec) → halfvec | average | unreleased
+sum(halfvec) → halfvec | sum | unreleased
 
 ### Bit Type
 
@@ -927,8 +950,10 @@ Function | Description | Added
 --- | --- | ---
 cosine_distance(sparsevec, sparsevec) → double precision | cosine distance | unreleased
 inner_product(sparsevec, sparsevec) → double precision | inner product | unreleased
-l2_distance(sparsevec, sparsevec) → double precision | Euclidean distance | unreleased
 l1_distance(sparsevec, sparsevec) → double precision | taxicab distance | unreleased
+l2_distance(sparsevec, sparsevec) → double precision | Euclidean distance | unreleased
+l2_norm(sparsevec) → double precision | Euclidean norm | unreleased
+l2_normalize(sparsevec) → sparsevec | Normalize with Euclidean norm | unreleased
 
 ## Installation Notes - Linux and Mac
 
@@ -1055,7 +1080,7 @@ Note: Replace `16` with your Postgres server version
 Install the FreeBSD package with:
 
 ```sh
-pkg install postgresql15-pg_vector
+pkg install postgresql15-pgvector
 ```
 
 or the port with:

sql/vector--0.6.2--0.7.0.sql

@@ -1,12 +1,22 @@
 -- 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 FUNCTION l2_normalize(vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION binary_quantize(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;
 
+CREATE FUNCTION vector_concat(vector, vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE OPERATOR || (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
+);
+
 CREATE FUNCTION hamming_distance(bit, bit) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
@@ -23,6 +33,18 @@ CREATE OPERATOR <%> (
 	COMMUTATOR = '<%>'
 );
 
+CREATE OPERATOR CLASS bit_hamming_ops
+	FOR TYPE bit USING ivfflat AS
+	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 hamming_distance(bit, bit),
+	FUNCTION 3 hamming_distance(bit, bit);
+
+CREATE OPERATOR CLASS bit_jaccard_ops
+	FOR TYPE bit USING ivfflat AS
+	OPERATOR 1 <%> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 jaccard_distance(bit, bit),
+	FUNCTION 3 jaccard_distance(bit, bit);
+
 CREATE OPERATOR CLASS bit_hamming_ops
 	FOR TYPE bit USING hnsw AS
 	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
@@ -71,15 +93,54 @@ CREATE FUNCTION cosine_distance(halfvec, halfvec) RETURNS float8
 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
+CREATE FUNCTION vector_dims(halfvec) RETURNS integer
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+	AS 'MODULE_PATHNAME', 'halfvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION quantize_binary(halfvec) RETURNS bit
+CREATE FUNCTION l2_norm(halfvec) RETURNS float8
-	AS 'MODULE_PATHNAME', 'halfvec_quantize_binary' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+	AS 'MODULE_PATHNAME', 'halfvec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_normalize(halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME', 'halfvec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION binary_quantize(halfvec) RETURNS bit
+	AS 'MODULE_PATHNAME', 'halfvec_binary_quantize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION subvector(halfvec, int, int) RETURNS halfvec
 	AS 'MODULE_PATHNAME', 'halfvec_subvector' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION halfvec_add(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_sub(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_mul(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_concat(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_lt(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_le(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_eq(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_ne(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_ge(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_gt(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_cmp(halfvec, halfvec) RETURNS int4
+	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;
 
@@ -89,9 +150,37 @@ CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
 CREATE FUNCTION halfvec_spherical_distance(halfvec, halfvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION halfvec_accum(double precision[], halfvec) RETURNS double precision[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_avg(double precision[]) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE AGGREGATE avg(halfvec) (
+	SFUNC = halfvec_accum,
+	STYPE = double precision[],
+	FINALFUNC = halfvec_avg,
+	COMBINEFUNC = vector_combine,
+	INITCOND = '{0}',
+	PARALLEL = SAFE
+);
+
+CREATE AGGREGATE sum(halfvec) (
+	SFUNC = halfvec_add,
+	STYPE = halfvec,
+	COMBINEFUNC = halfvec_add,
+	PARALLEL = SAFE
+);
+
 CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+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 FUNCTION array_to_halfvec(integer[], integer, boolean) RETURNS halfvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
@@ -110,8 +199,14 @@ CREATE FUNCTION halfvec_to_float4(halfvec, integer, boolean) RETURNS real[]
 CREATE CAST (halfvec AS halfvec)
 	WITH FUNCTION halfvec(halfvec, integer, boolean) AS IMPLICIT;
 
+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 IMPLICIT;
+
 CREATE CAST (halfvec AS real[])
-	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS IMPLICIT;
+	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS ASSIGNMENT;
 
 CREATE CAST (integer[] AS halfvec)
 	WITH FUNCTION array_to_halfvec(integer[], integer, boolean) AS ASSIGNMENT;
@@ -140,6 +235,69 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR + (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_add,
+	COMMUTATOR = +
+);
+
+CREATE OPERATOR - (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_sub
+);
+
+CREATE OPERATOR * (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_mul,
+	COMMUTATOR = *
+);
+
+CREATE OPERATOR || (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_concat
+);
+
+CREATE OPERATOR < (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+CREATE OPERATOR CLASS halfvec_ops
+	DEFAULT FOR TYPE halfvec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 halfvec_cmp(halfvec, halfvec);
+
 CREATE OPERATOR CLASS halfvec_l2_ops
 	FOR TYPE halfvec USING ivfflat AS
 	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
@@ -151,15 +309,15 @@ CREATE OPERATOR CLASS halfvec_ip_ops
 	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
 	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
 	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
-	FUNCTION 4 halfvec_norm(halfvec);
+	FUNCTION 4 l2_norm(halfvec);
 
 CREATE OPERATOR CLASS halfvec_cosine_ops
 	FOR TYPE halfvec USING ivfflat AS
 	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
 	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
-	FUNCTION 2 halfvec_norm(halfvec),
+	FUNCTION 2 l2_norm(halfvec),
 	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
-	FUNCTION 4 halfvec_norm(halfvec);
+	FUNCTION 4 l2_norm(halfvec);
 
 CREATE OPERATOR CLASS halfvec_l2_ops
 	FOR TYPE halfvec USING hnsw AS
@@ -175,19 +333,7 @@ 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);
+	FUNCTION 2 l2_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 IMPLICIT;
-
-CREATE CAST (vector AS halfvec)
-	WITH FUNCTION vector_to_halfvec(vector, integer, boolean) AS IMPLICIT;
 
 CREATE TYPE sparsevec;
 
@@ -224,7 +370,34 @@ CREATE FUNCTION inner_product(sparsevec, sparsevec) RETURNS float8
 CREATE FUNCTION cosine_distance(sparsevec, sparsevec) RETURNS float8
 	AS 'MODULE_PATHNAME', 'sparsevec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION sparsevec_norm(sparsevec) RETURNS float8
+CREATE FUNCTION l1_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_normalize(sparsevec) RETURNS sparsevec
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_lt(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_le(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_eq(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_ne(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_ge(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_gt(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_cmp(sparsevec, sparsevec) RETURNS int4
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION sparsevec_l2_squared_distance(sparsevec, sparsevec) RETURNS float8
@@ -246,7 +419,7 @@ CREATE CAST (sparsevec AS sparsevec)
 	WITH FUNCTION sparsevec(sparsevec, integer, boolean) AS IMPLICIT;
 
 CREATE CAST (sparsevec AS vector)
-	WITH FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) AS IMPLICIT;
+	WITH FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) AS ASSIGNMENT;
 
 CREATE CAST (vector AS sparsevec)
 	WITH FUNCTION vector_to_sparsevec(vector, integer, boolean) AS IMPLICIT;
@@ -266,6 +439,51 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR < (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+CREATE OPERATOR CLASS sparsevec_ops
+	DEFAULT FOR TYPE sparsevec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 sparsevec_cmp(sparsevec, sparsevec);
+
 CREATE OPERATOR CLASS sparsevec_l2_ops
 	FOR TYPE sparsevec USING hnsw AS
 	OPERATOR 1 <-> (sparsevec, sparsevec) FOR ORDER BY float_ops,
@@ -280,4 +498,4 @@ CREATE OPERATOR CLASS sparsevec_cosine_ops
 	FOR TYPE sparsevec USING hnsw AS
 	OPERATOR 1 <=> (sparsevec, sparsevec) FOR ORDER BY float_ops,
 	FUNCTION 1 sparsevec_negative_inner_product(sparsevec, sparsevec),
-	FUNCTION 2 sparsevec_norm(sparsevec);
+	FUNCTION 2 l2_norm(sparsevec);

sql/vector.sql

@@ -49,6 +49,17 @@ CREATE FUNCTION vector_dims(vector) RETURNS integer
 CREATE FUNCTION vector_norm(vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION l2_normalize(vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION binary_quantize(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
+
 CREATE FUNCTION vector_add(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
@@ -58,14 +69,9 @@ 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
+CREATE FUNCTION vector_concat(vector, vector) RETURNS vector
 	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
-
 CREATE FUNCTION vector_lt(vector, vector) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
@@ -194,6 +200,10 @@ CREATE OPERATOR * (
 	COMMUTATOR = *
 );
 
+CREATE OPERATOR || (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
+);
+
 CREATE OPERATOR < (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_lt,
 	COMMUTATOR = > , NEGATOR = >= ,
@@ -302,6 +312,8 @@ CREATE FUNCTION hamming_distance(bit, bit) RETURNS float8
 CREATE FUNCTION jaccard_distance(bit, bit) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+-- bit operators
+
 CREATE OPERATOR <~> (
 	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = hamming_distance,
 	COMMUTATOR = '<~>'
@@ -312,6 +324,20 @@ CREATE OPERATOR <%> (
 	COMMUTATOR = '<%>'
 );
 
+-- bit opclasses
+
+CREATE OPERATOR CLASS bit_hamming_ops
+	FOR TYPE bit USING ivfflat AS
+	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 hamming_distance(bit, bit),
+	FUNCTION 3 hamming_distance(bit, bit);
+
+CREATE OPERATOR CLASS bit_jaccard_ops
+	FOR TYPE bit USING ivfflat AS
+	OPERATOR 1 <%> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 jaccard_distance(bit, bit),
+	FUNCTION 3 jaccard_distance(bit, bit);
+
 CREATE OPERATOR CLASS bit_hamming_ops
 	FOR TYPE bit USING hnsw AS
 	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
@@ -364,17 +390,56 @@ CREATE FUNCTION cosine_distance(halfvec, halfvec) RETURNS float8
 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
+CREATE FUNCTION vector_dims(halfvec) RETURNS integer
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+	AS 'MODULE_PATHNAME', 'halfvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION quantize_binary(halfvec) RETURNS bit
+CREATE FUNCTION l2_norm(halfvec) RETURNS float8
-	AS 'MODULE_PATHNAME', 'halfvec_quantize_binary' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+	AS 'MODULE_PATHNAME', 'halfvec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_normalize(halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME', 'halfvec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION binary_quantize(halfvec) RETURNS bit
+	AS 'MODULE_PATHNAME', 'halfvec_binary_quantize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION subvector(halfvec, int, int) RETURNS halfvec
 	AS 'MODULE_PATHNAME', 'halfvec_subvector' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 -- halfvec private functions
 
+CREATE FUNCTION halfvec_add(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_sub(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_mul(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_concat(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_lt(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_le(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_eq(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_ne(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_ge(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_gt(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_cmp(halfvec, halfvec) RETURNS int4
+	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;
 
@@ -384,11 +449,41 @@ CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
 CREATE FUNCTION halfvec_spherical_distance(halfvec, halfvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION halfvec_accum(double precision[], halfvec) RETURNS double precision[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_avg(double precision[]) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- halfvec aggregates
+
+CREATE AGGREGATE avg(halfvec) (
+	SFUNC = halfvec_accum,
+	STYPE = double precision[],
+	FINALFUNC = halfvec_avg,
+	COMBINEFUNC = vector_combine,
+	INITCOND = '{0}',
+	PARALLEL = SAFE
+);
+
+CREATE AGGREGATE sum(halfvec) (
+	SFUNC = halfvec_add,
+	STYPE = halfvec,
+	COMBINEFUNC = halfvec_add,
+	PARALLEL = SAFE
+);
+
 -- halfvec cast functions
 
 CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+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 FUNCTION array_to_halfvec(integer[], integer, boolean) RETURNS halfvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
@@ -409,8 +504,14 @@ CREATE FUNCTION halfvec_to_float4(halfvec, integer, boolean) RETURNS real[]
 CREATE CAST (halfvec AS halfvec)
 	WITH FUNCTION halfvec(halfvec, integer, boolean) AS IMPLICIT;
 
+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 IMPLICIT;
+
 CREATE CAST (halfvec AS real[])
-	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS IMPLICIT;
+	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS ASSIGNMENT;
 
 CREATE CAST (integer[] AS halfvec)
 	WITH FUNCTION array_to_halfvec(integer[], integer, boolean) AS ASSIGNMENT;
@@ -441,8 +542,71 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR + (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_add,
+	COMMUTATOR = +
+);
+
+CREATE OPERATOR - (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_sub
+);
+
+CREATE OPERATOR * (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_mul,
+	COMMUTATOR = *
+);
+
+CREATE OPERATOR || (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_concat
+);
+
+CREATE OPERATOR < (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
 -- halfvec opclasses
 
+CREATE OPERATOR CLASS halfvec_ops
+	DEFAULT FOR TYPE halfvec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 halfvec_cmp(halfvec, halfvec);
+
 CREATE OPERATOR CLASS halfvec_l2_ops
 	FOR TYPE halfvec USING ivfflat AS
 	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
@@ -454,15 +618,15 @@ CREATE OPERATOR CLASS halfvec_ip_ops
 	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
 	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
 	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
-	FUNCTION 4 halfvec_norm(halfvec);
+	FUNCTION 4 l2_norm(halfvec);
 
 CREATE OPERATOR CLASS halfvec_cosine_ops
 	FOR TYPE halfvec USING ivfflat AS
 	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
 	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
-	FUNCTION 2 halfvec_norm(halfvec),
+	FUNCTION 2 l2_norm(halfvec),
 	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
-	FUNCTION 4 halfvec_norm(halfvec);
+	FUNCTION 4 l2_norm(halfvec);
 
 CREATE OPERATOR CLASS halfvec_l2_ops
 	FOR TYPE halfvec USING hnsw AS
@@ -478,21 +642,7 @@ 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);
+	FUNCTION 2 l2_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;
 
 --- sparsevec type
 
@@ -533,11 +683,38 @@ CREATE FUNCTION inner_product(sparsevec, sparsevec) RETURNS float8
 CREATE FUNCTION cosine_distance(sparsevec, sparsevec) RETURNS float8
 	AS 'MODULE_PATHNAME', 'sparsevec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION sparsevec_norm(sparsevec) RETURNS float8
+CREATE FUNCTION l1_distance(sparsevec, sparsevec) RETURNS float8
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+	AS 'MODULE_PATHNAME', 'sparsevec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_normalize(sparsevec) RETURNS sparsevec
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 -- sparsevec private functions
 
+CREATE FUNCTION sparsevec_lt(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_le(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_eq(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_ne(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_ge(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_gt(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_cmp(sparsevec, sparsevec) RETURNS int4
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE FUNCTION sparsevec_l2_squared_distance(sparsevec, sparsevec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
@@ -561,7 +738,7 @@ CREATE CAST (sparsevec AS sparsevec)
 	WITH FUNCTION sparsevec(sparsevec, integer, boolean) AS IMPLICIT;
 
 CREATE CAST (sparsevec AS vector)
-	WITH FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) AS IMPLICIT;
+	WITH FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) AS ASSIGNMENT;
 
 CREATE CAST (vector AS sparsevec)
 	WITH FUNCTION vector_to_sparsevec(vector, integer, boolean) AS IMPLICIT;
@@ -583,8 +760,53 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR < (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
 -- sparsevec opclasses
 
+CREATE OPERATOR CLASS sparsevec_ops
+	DEFAULT FOR TYPE sparsevec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 sparsevec_cmp(sparsevec, sparsevec);
+
 CREATE OPERATOR CLASS sparsevec_l2_ops
 	FOR TYPE sparsevec USING hnsw AS
 	OPERATOR 1 <-> (sparsevec, sparsevec) FOR ORDER BY float_ops,
@@ -599,4 +821,4 @@ CREATE OPERATOR CLASS sparsevec_cosine_ops
 	FOR TYPE sparsevec USING hnsw AS
 	OPERATOR 1 <=> (sparsevec, sparsevec) FOR ORDER BY float_ops,
 	FUNCTION 1 sparsevec_negative_inner_product(sparsevec, sparsevec),
-	FUNCTION 2 sparsevec_norm(sparsevec);
+	FUNCTION 2 l2_norm(sparsevec);

src/halfutils.c

@@ -19,8 +19,10 @@
 #endif
 #endif
 
+
 float		(*HalfvecL2SquaredDistance) (int dim, half * ax, half * bx);
 float		(*HalfvecInnerProduct) (int dim, half * ax, half * bx);
+double		(*HalfvecCosineSimilarity) (int dim, half * ax, half * bx);
 
 static float
 HalfvecL2SquaredDistanceDefault(int dim, half * ax, half * bx)
@@ -117,11 +119,92 @@ HalfvecInnerProductF16cFma(int dim, half * ax, half * bx)
 }
 #endif
 
-#ifdef HALFVEC_DISPATCH
+static double
-#define CPU_FEATURE_FMA  (1 << 12)
+HalfvecCosineSimilarityDefault(int dim, half * ax, half * bx)
-#define CPU_FEATURE_F16C (1 << 29)
+{
+	float		similarity = 0.0;
+	float		norma = 0.0;
+	float		normb = 0.0;
 
-static bool
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		axi = HalfToFloat4(ax[i]);
+		float		bxi = HalfToFloat4(bx[i]);
+
+		similarity += axi * bxi;
+		norma += axi * axi;
+		normb += bxi * bxi;
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	return (double) similarity / sqrt((double) norma * (double) normb);
+}
+
+#ifdef HALFVEC_DISPATCH
+TARGET_F16C_FMA static double
+HalfvecCosineSimilarityF16cFma(int dim, half * ax, half * bx)
+{
+	float		similarity;
+	float		norma;
+	float		normb;
+	int			i;
+	float		s[8];
+	int			count = (dim / 8) * 8;
+	__m256		sim = _mm256_setzero_ps();
+	__m256		na = _mm256_setzero_ps();
+	__m256		nb = _mm256_setzero_ps();
+
+	for (i = 0; i < count; i += 8)
+	{
+		__m128i		axi = _mm_loadu_si128((__m128i *) (ax + i));
+		__m128i		bxi = _mm_loadu_si128((__m128i *) (bx + i));
+		__m256		axs = _mm256_cvtph_ps(axi);
+		__m256		bxs = _mm256_cvtph_ps(bxi);
+
+		sim = _mm256_fmadd_ps(axs, bxs, sim);
+		na = _mm256_fmadd_ps(axs, axs, na);
+		nb = _mm256_fmadd_ps(bxs, bxs, nb);
+	}
+
+	_mm256_storeu_ps(s, sim);
+	similarity = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	_mm256_storeu_ps(s, na);
+	norma = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	_mm256_storeu_ps(s, nb);
+	normb = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	/* Auto-vectorized */
+	for (; i < dim; i++)
+	{
+		float		axi = HalfToFloat4(ax[i]);
+		float		bxi = HalfToFloat4(bx[i]);
+
+		similarity += axi * bxi;
+		norma += axi * axi;
+		normb += bxi * bxi;
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	return (double) similarity / sqrt((double) norma * (double) normb);
+}
+#endif
+
+#ifdef HALFVEC_DISPATCH
+#define CPU_FEATURE_FMA     (1 << 12)
+#define CPU_FEATURE_OSXSAVE (1 << 27)
+#define CPU_FEATURE_AVX     (1 << 28)
+#define CPU_FEATURE_F16C    (1 << 29)
+
+#ifdef _MSC_VER
+#define TARGET_XSAVE
+#else
+#define TARGET_XSAVE __attribute__((target("xsave")))
+#endif
+
+TARGET_XSAVE static bool
 SupportsCpuFeature(unsigned int feature)
 {
 	unsigned int exx[4] = {0, 0, 0, 0};
@@ -132,6 +215,12 @@ SupportsCpuFeature(unsigned int feature)
 	__cpuid(exx, 1);
 #endif
 
+	if ((exx[2] & CPU_FEATURE_OSXSAVE) != CPU_FEATURE_OSXSAVE)
+		return false;
+
+	if ((_xgetbv(0) & 6) != 6)
+		return false;
+
 	return (exx[2] & feature) == feature;
 }
 #endif
@@ -145,12 +234,14 @@ HalfvecInit(void)
 	 */
 	HalfvecL2SquaredDistance = HalfvecL2SquaredDistanceDefault;
 	HalfvecInnerProduct = HalfvecInnerProductDefault;
+	HalfvecCosineSimilarity = HalfvecCosineSimilarityDefault;
 
 #ifdef HALFVEC_DISPATCH
-	if (SupportsCpuFeature(CPU_FEATURE_FMA | CPU_FEATURE_F16C))
+	if (SupportsCpuFeature(CPU_FEATURE_AVX | CPU_FEATURE_FMA | CPU_FEATURE_F16C))
 	{
 		HalfvecL2SquaredDistance = HalfvecL2SquaredDistanceF16cFma;
 		HalfvecInnerProduct = HalfvecInnerProductF16cFma;
+		HalfvecCosineSimilarity = HalfvecCosineSimilarityF16cFma;
 	}
 #endif
 }

src/halfutils.h

@@ -12,6 +12,7 @@
 
 extern float (*HalfvecL2SquaredDistance) (int dim, half * ax, half * bx);
 extern float (*HalfvecInnerProduct) (int dim, half * ax, half * bx);
+extern double (*HalfvecCosineSimilarity) (int dim, half * ax, half * bx);
 
 void		HalfvecInit(void);
 
@@ -41,6 +42,19 @@ HalfIsInf(half num)
 #endif
 }
 
+/*
+ * Check if half is zero
+ */
+static inline bool
+HalfIsZero(half num)
+{
+#ifdef FLT16_SUPPORT
+	return num == 0;
+#else
+	return (num & 0x7FFF) == 0x0000;
+#endif
+}
+
 /*
  * Convert a half to a float4
  */

src/halfvec.c

@@ -23,6 +23,9 @@
 #define TYPALIGN_INT 'i'
 #endif
 
+#define STATE_DIMS(x) (ARR_DIMS(x)[0] - 1)
+#define CreateStateDatums(dim) palloc(sizeof(Datum) * (dim + 1))
+
 /*
  * Get a half from a message buffer
  */
@@ -146,6 +149,38 @@ halfvec_isspace(char ch)
 	return false;
 }
 
+/*
+ * Check state array
+ */
+static float8 *
+CheckStateArray(ArrayType *statearray, const char *caller)
+{
+	if (ARR_NDIM(statearray) != 1 ||
+		ARR_DIMS(statearray)[0] < 1 ||
+		ARR_HASNULL(statearray) ||
+		ARR_ELEMTYPE(statearray) != FLOAT8OID)
+		elog(ERROR, "%s: expected state array", caller);
+	return (float8 *) ARR_DATA_PTR(statearray);
+}
+
+#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
  */
@@ -591,28 +626,11 @@ 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 */
+	similarity = HalfvecCosineSimilarity(a->dim, a->x, b->x);
-	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 */
@@ -677,12 +695,24 @@ halfvec_l1_distance(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8((double) distance);
 }
 
+/*
+ * Get the dimensions of a half vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_vector_dims);
+Datum
+halfvec_vector_dims(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+
+	PG_RETURN_INT32(a->dim);
+}
+
 /*
  * Get the L2 norm of a half vector
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_norm);
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l2_norm);
 Datum
-halfvec_norm(PG_FUNCTION_ARGS)
+halfvec_l2_norm(PG_FUNCTION_ARGS)
 {
 	HalfVector *a = PG_GETARG_HALFVEC_P(0);
 	half	   *ax = a->x;
@@ -699,12 +729,195 @@ halfvec_norm(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(sqrt(norm));
 }
 
+/*
+ * Normalize a half vector with the L2 norm
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l2_normalize);
+Datum
+halfvec_l2_normalize(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	half	   *ax = a->x;
+	double		norm = 0;
+	HalfVector *result;
+	half	   *rx;
+
+	result = InitHalfVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		norm += (double) HalfToFloat4(ax[i]) * (double) HalfToFloat4(ax[i]);
+
+	norm = sqrt(norm);
+
+	/* Return zero vector for zero norm */
+	if (norm > 0)
+	{
+		for (int i = 0; i < a->dim; i++)
+			rx[i] = Float4ToHalfUnchecked(HalfToFloat4(ax[i]) / norm);
+
+		/* Check for overflow */
+		for (int i = 0; i < a->dim; i++)
+		{
+			if (HalfIsInf(rx[i]))
+				float_overflow_error();
+		}
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Add half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_add);
+Datum
+halfvec_add(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;
+	HalfVector *result;
+	half	   *rx;
+
+	CheckDims(a, b);
+
+	result = InitHalfVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+#ifdef FLT16_SUPPORT
+		rx[i] = ax[i] + bx[i];
+#else
+		rx[i] = Float4ToHalfUnchecked(HalfToFloat4(ax[i]) + HalfToFloat4(bx[i]));
+#endif
+	}
+
+	/* Check for overflow */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+		if (HalfIsInf(rx[i]))
+			float_overflow_error();
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Subtract half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_sub);
+Datum
+halfvec_sub(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;
+	HalfVector *result;
+	half	   *rx;
+
+	CheckDims(a, b);
+
+	result = InitHalfVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+#ifdef FLT16_SUPPORT
+		rx[i] = ax[i] - bx[i];
+#else
+		rx[i] = Float4ToHalfUnchecked(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+#endif
+	}
+
+	/* Check for overflow */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+		if (HalfIsInf(rx[i]))
+			float_overflow_error();
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Multiply half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_mul);
+Datum
+halfvec_mul(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;
+	HalfVector *result;
+	half	   *rx;
+
+	CheckDims(a, b);
+
+	result = InitHalfVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+#ifdef FLT16_SUPPORT
+		rx[i] = ax[i] * bx[i];
+#else
+		rx[i] = Float4ToHalfUnchecked(HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]));
+#endif
+	}
+
+	/* Check for overflow and underflow */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+		if (HalfIsInf(rx[i]))
+			float_overflow_error();
+
+		if (HalfIsZero(rx[i]) && !(HalfIsZero(ax[i]) || HalfIsZero(bx[i])))
+			float_underflow_error();
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Concatenate half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_concat);
+Datum
+halfvec_concat(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	HalfVector *result;
+	int			dim = a->dim + b->dim;
+
+	CheckDim(dim);
+	result = InitHalfVector(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);
+}
+
 /*
  * Quantize a half vector
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_quantize_binary);
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_binary_quantize);
 Datum
-halfvec_quantize_binary(PG_FUNCTION_ARGS)
+halfvec_binary_quantize(PG_FUNCTION_ARGS)
 {
 	HalfVector *a = PG_GETARG_HALFVEC_P(0);
 	half	   *ax = a->x;
@@ -775,3 +988,189 @@ halfvec_cmp_internal(HalfVector * a, HalfVector * b)
 
 	return 0;
 }
+
+/*
+ * Less than
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_lt);
+Datum
+halfvec_lt(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	PG_RETURN_BOOL(halfvec_cmp_internal(a, b) < 0);
+}
+
+/*
+ * Less than or equal
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_le);
+Datum
+halfvec_le(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	PG_RETURN_BOOL(halfvec_cmp_internal(a, b) <= 0);
+}
+
+/*
+ * Equal
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_eq);
+Datum
+halfvec_eq(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	PG_RETURN_BOOL(halfvec_cmp_internal(a, b) == 0);
+}
+
+/*
+ * Not equal
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_ne);
+Datum
+halfvec_ne(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	PG_RETURN_BOOL(halfvec_cmp_internal(a, b) != 0);
+}
+
+/*
+ * Greater than or equal
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_ge);
+Datum
+halfvec_ge(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	PG_RETURN_BOOL(halfvec_cmp_internal(a, b) >= 0);
+}
+
+/*
+ * Greater than
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_gt);
+Datum
+halfvec_gt(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	PG_RETURN_BOOL(halfvec_cmp_internal(a, b) > 0);
+}
+
+/*
+ * Compare half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_cmp);
+Datum
+halfvec_cmp(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	PG_RETURN_INT32(halfvec_cmp_internal(a, b));
+}
+
+/*
+ * Accumulate half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_accum);
+Datum
+halfvec_accum(PG_FUNCTION_ARGS)
+{
+	ArrayType  *statearray = PG_GETARG_ARRAYTYPE_P(0);
+	HalfVector *newval = PG_GETARG_HALFVEC_P(1);
+	float8	   *statevalues;
+	int16		dim;
+	bool		newarr;
+	float8		n;
+	Datum	   *statedatums;
+	half	   *x = newval->x;
+	ArrayType  *result;
+
+	/* Check array before using */
+	statevalues = CheckStateArray(statearray, "halfvec_accum");
+	dim = STATE_DIMS(statearray);
+	newarr = dim == 0;
+
+	if (newarr)
+		dim = newval->dim;
+	else
+		CheckExpectedDim(dim, newval->dim);
+
+	n = statevalues[0] + 1.0;
+
+	statedatums = CreateStateDatums(dim);
+	statedatums[0] = Float8GetDatum(n);
+
+	if (newarr)
+	{
+		for (int i = 0; i < dim; i++)
+			statedatums[i + 1] = Float8GetDatum((double) HalfToFloat4(x[i]));
+	}
+	else
+	{
+		for (int i = 0; i < dim; i++)
+		{
+			double		v = statevalues[i + 1] + (double) HalfToFloat4(x[i]);
+
+			/* Check for overflow */
+			if (isinf(v))
+				float_overflow_error();
+
+			statedatums[i + 1] = Float8GetDatum(v);
+		}
+	}
+
+	/* Use float8 array like float4_accum */
+	result = construct_array(statedatums, dim + 1,
+							 FLOAT8OID,
+							 sizeof(float8), FLOAT8PASSBYVAL, TYPALIGN_DOUBLE);
+
+	pfree(statedatums);
+
+	PG_RETURN_ARRAYTYPE_P(result);
+}
+
+/*
+ * Average half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_avg);
+Datum
+halfvec_avg(PG_FUNCTION_ARGS)
+{
+	ArrayType  *statearray = PG_GETARG_ARRAYTYPE_P(0);
+	float8	   *statevalues;
+	float8		n;
+	uint16		dim;
+	HalfVector *result;
+
+	/* Check array before using */
+	statevalues = CheckStateArray(statearray, "halfvec_avg");
+	n = statevalues[0];
+
+	/* SQL defines AVG of no values to be NULL */
+	if (n == 0.0)
+		PG_RETURN_NULL();
+
+	/* Create half vector */
+	dim = STATE_DIMS(statearray);
+	CheckDim(dim);
+	result = InitHalfVector(dim);
+	for (int i = 0; i < dim; i++)
+	{
+		result->x[i] = Float4ToHalf(statevalues[i + 1] / n);
+		CheckElement(result->x[i]);
+	}
+
+	PG_RETURN_POINTER(result);
+}

src/halfvec.h

@@ -5,6 +5,7 @@
 
 #include <float.h>
 
+#include "fmgr.h"
 #include "vector.h"
 
 #if defined(__x86_64__) || defined(_M_AMD64)
@@ -43,5 +44,6 @@ typedef struct HalfVector
 
 HalfVector *InitHalfVector(int dim);
 int			halfvec_cmp_internal(HalfVector * a, HalfVector * b);
+PGDLLEXPORT Datum halfvec_l2_normalize(PG_FUNCTION_ARGS);
 
 #endif

src/hnsw.h

@@ -377,7 +377,8 @@ 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);
+Datum		HnswNormValue(Datum value, HnswType type);
+bool		HnswCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value);
 void		HnswCheckValue(Datum value, HnswType type);
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);

src/hnswbuild.c

@@ -493,8 +493,10 @@ 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->type))
+		if (!HnswCheckNorm(buildstate->normprocinfo, buildstate->collation, value))
 			return false;
+
+		value = HnswNormValue(value, buildstate->type);
 	}
 
 	/* Get datum size */

src/hnswinsert.c

@@ -626,8 +626,10 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		if (!HnswNormValue(normprocinfo, collation, &value, type))
+		if (!HnswCheckNorm(normprocinfo, collation, value))
 			return;
+
+		value = HnswNormValue(value, type);
 	}
 
 	HnswInsertTupleOnDisk(index, value, values, isnull, heap_tid, false);

src/hnswscan.c

@@ -61,7 +61,7 @@ GetScanValue(IndexScanDesc scan)
 
 		/* Fine if normalization fails */
 		if (so->normprocinfo != NULL)
-			HnswNormValue(so->normprocinfo, so->collation, &value, HnswGetType(scan->indexRelation));
+			value = HnswNormValue(value, HnswGetType(scan->indexRelation));
 	}
 
 	return value;

src/hnswutils.c

@@ -5,6 +5,7 @@
 #include "access/generic_xlog.h"
 #include "catalog/pg_type.h"
 #include "catalog/pg_type_d.h"
+#include "fmgr.h"
 #include "halfutils.h"
 #include "halfvec.h"
 #include "hnsw.h"
@@ -192,63 +193,29 @@ HnswGetType(Relation index)
 }
 
 /*
- * Divide by the norm
+ * Normalize value
- *
+ */
- * Returns false if value should not be indexed
+Datum
- *
+HnswNormValue(Datum value, HnswType type)
- * The caller needs to free the pointer stored in value
+{
- * if it's different than the original value
+	/* TODO Remove type-specific code */
+	if (type == HNSW_TYPE_VECTOR)
+		return DirectFunctionCall1(l2_normalize, value);
+	else if (type == HNSW_TYPE_HALFVEC)
+		return DirectFunctionCall1(halfvec_l2_normalize, value);
+	else if (type == HNSW_TYPE_SPARSEVEC)
+		return DirectFunctionCall1(sparsevec_l2_normalize, value);
+	else
+		elog(ERROR, "Unsupported type");
+}
+
+/*
+ * Check if non-zero norm
  */
 bool
-HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, HnswType type)
+HnswCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value)
 {
-	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
+	return DatumGetFloat8(FunctionCall1Coll(procinfo, collation, value)) > 0;
-
-	if (norm > 0)
-	{
-		/* TODO Remove vector-specific code */
-		if (type == HNSW_TYPE_VECTOR)
-		{
-			Vector	   *v = DatumGetVector(*value);
-			Vector	   *result = InitVector(v->dim);
-
-			for (int i = 0; i < v->dim; i++)
-				result->x[i] = v->x[i] / norm;
-
-			*value = PointerGetDatum(result);
-		}
-		else if (type == HNSW_TYPE_HALFVEC)
-		{
-			HalfVector *v = DatumGetHalfVector(*value);
-			HalfVector *result = InitHalfVector(v->dim);
-
-			for (int i = 0; i < v->dim; i++)
-				result->x[i] = Float4ToHalfUnchecked(HalfToFloat4(v->x[i]) / norm);
-
-			*value = PointerGetDatum(result);
-		}
-		else if (type == HNSW_TYPE_SPARSEVEC)
-		{
-			SparseVector *v = DatumGetSparseVector(*value);
-			SparseVector *result = InitSparseVector(v->dim, v->nnz);
-			float	   *vx = SPARSEVEC_VALUES(v);
-			float	   *rx = SPARSEVEC_VALUES(result);
-
-			for (int i = 0; i < v->nnz; i++)
-			{
-				result->indices[i] = v->indices[i];
-				rx[i] = vx[i] / norm;
-			}
-
-			*value = PointerGetDatum(result);
-		}
-		else
-			elog(ERROR, "Unsupported type");
-
-		return true;
-	}
-
-	return false;
 }
 
 /*

src/ivfbuild.c

@@ -6,6 +6,7 @@
 #include "access/tableam.h"
 #include "access/parallel.h"
 #include "access/xact.h"
+#include "bitvector.h"
 #include "catalog/index.h"
 #include "catalog/pg_operator_d.h"
 #include "catalog/pg_type_d.h"
@@ -324,6 +325,8 @@ GetMaxDimensions(IvfflatType type)
 
 	if (type == IVFFLAT_TYPE_HALFVEC)
 		maxDimensions *= 2;
+	else if (type == IVFFLAT_TYPE_BIT)
+		maxDimensions *= 32;
 
 	return maxDimensions;
 }
@@ -338,6 +341,8 @@ GetItemSize(IvfflatType type, int dimensions)
 		return VECTOR_SIZE(dimensions);
 	else if (type == IVFFLAT_TYPE_HALFVEC)
 		return HALFVEC_SIZE(dimensions);
+	else if (type == IVFFLAT_TYPE_BIT)
+		return VARBITTOTALLEN(dimensions);
 	else
 		elog(ERROR, "Unsupported type");
 }

src/ivfflat.h

@@ -46,7 +46,8 @@
 typedef enum IvfflatType
 {
 	IVFFLAT_TYPE_VECTOR,
-	IVFFLAT_TYPE_HALFVEC
+	IVFFLAT_TYPE_HALFVEC,
+	IVFFLAT_TYPE_BIT
 }			IvfflatType;
 
 /* Build phases */
@@ -263,7 +264,7 @@ typedef struct IvfflatScanOpaqueData
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;
 
-#define VECTOR_ARRAY_SIZE(_length, _size) (sizeof(VectorArrayData) + (_length) * _size)
+#define VECTOR_ARRAY_SIZE(_length, _size) (sizeof(VectorArrayData) + (_length) * MAXALIGN(_size))
 #define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * (_arr)->itemsize)
 #define VectorArrayGet(_arr, _offset) VECTOR_ARRAY_OFFSET(_arr, _offset)
 #define VectorArraySet(_arr, _offset, _val) memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, (_arr)->itemsize)

src/ivfkmeans.c

@@ -3,10 +3,12 @@
 #include <float.h>
 #include <math.h>
 
+#include "bitvector.h"
 #include "halfutils.h"
 #include "halfvec.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
+#include "utils/builtins.h"
 #include "utils/datum.h"
 #include "utils/memutils.h"
 #include "vector.h"
@@ -134,6 +136,15 @@ CompareHalfVectors(const void *a, const void *b)
 	return halfvec_cmp_internal((HalfVector *) a, (HalfVector *) b);
 }
 
+/*
+ * Compare bit vectors
+ */
+static int
+CompareBitVectors(const void *a, const void *b)
+{
+	return DirectFunctionCall2(bitcmp, VarBitPGetDatum((VarBit *) a), VarBitPGetDatum((VarBit *) b));
+}
+
 /*
  * Quick approach if we have little data
  */
@@ -151,6 +162,8 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers, IvfflatTy
 			qsort(samples->items, samples->length, samples->itemsize, CompareVectors);
 		else if (type == IVFFLAT_TYPE_HALFVEC)
 			qsort(samples->items, samples->length, samples->itemsize, CompareHalfVectors);
+		else if (type == IVFFLAT_TYPE_BIT)
+			qsort(samples->items, samples->length, samples->itemsize, CompareBitVectors);
 		else
 			elog(ERROR, "Unsupported type");
 
@@ -191,6 +204,16 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers, IvfflatTy
 			for (int j = 0; j < dimensions; j++)
 				vec->x[j] = Float4ToHalfUnchecked((float) RandomDouble());
 		}
+		else if (type == IVFFLAT_TYPE_BIT)
+		{
+			VarBit	   *vec = DatumGetVarBitP(center);
+
+			SET_VARSIZE(vec, VARBITTOTALLEN(dimensions));
+			VARBITLEN(vec) = dimensions;
+
+			for (int j = 0; j < dimensions; j++)
+				VARBITS(vec)[j / dimensions] |= (RandomDouble() > 0.5 ? 1 : 0) << (7 - (j % 8));
+		}
 		else
 			elog(ERROR, "Unsupported type");
 
@@ -263,6 +286,17 @@ ComputeNewCenters(VectorArray samples, VectorArray aggCenters, VectorArray newCe
 				aggCenter->x[k] += HalfToFloat4(vec->x[k]);
 		}
 	}
+	else if (type == IVFFLAT_TYPE_BIT)
+	{
+		for (int j = 0; j < numSamples; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, closestCenters[j]);
+			VarBit	   *vec = (VarBit *) VectorArrayGet(samples, j);
+
+			for (int k = 0; k < dimensions; k++)
+				aggCenter->x[k] += (float) (((VARBITS(vec)[k / 8]) >> (7 - (k % 8))) & 0x01);
+		}
+	}
 	else
 		elog(ERROR, "Unsupported type");
 
@@ -308,6 +342,21 @@ ComputeNewCenters(VectorArray samples, VectorArray aggCenters, VectorArray newCe
 				newCenter->x[k] = Float4ToHalfUnchecked(aggCenter->x[k]);
 		}
 	}
+	else if (type == IVFFLAT_TYPE_BIT)
+	{
+		for (int j = 0; j < numCenters; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, j);
+			VarBit	   *newCenter = (VarBit *) VectorArrayGet(newCenters, j);
+			unsigned char *nx = VARBITS(newCenter);
+
+			for (uint32 k = 0; k < VARBITBYTES(newCenter); k++)
+				nx[k] = 0;
+
+			for (int k = 0; k < dimensions; k++)
+				nx[k / 8] |= (aggCenter->x[k] > 0.5) << (7 - (k % 8));
+		}
+	}
 
 	/* Normalize if needed */
 	if (normprocinfo != NULL)
@@ -425,6 +474,18 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatTyp
 			vec->dim = dimensions;
 		}
 	}
+	else if (type == IVFFLAT_TYPE_BIT)
+	{
+		newCenters = VectorArrayInit(numCenters, dimensions, centers->itemsize);
+
+		for (int j = 0; j < numCenters; j++)
+		{
+			VarBit	   *vec = (VarBit *) VectorArrayGet(newCenters, j);
+
+			SET_VARSIZE(vec, VARBITTOTALLEN(dimensions));
+			VARBITLEN(vec) = dimensions;
+		}
+	}
 	else
 		elog(ERROR, "Unsupported type");
 
@@ -642,23 +703,26 @@ CheckCenters(Relation index, VectorArray centers, IvfflatType type)
 					elog(ERROR, "Infinite value detected. Please report a bug.");
 			}
 		}
-		else
+		else if (type != IVFFLAT_TYPE_BIT)
 			elog(ERROR, "Unsupported type");
 	}
 
-	/* Ensure no duplicate centers */
+	if (type != IVFFLAT_TYPE_BIT)
-	/* Fine to sort in-place */
-	if (type == IVFFLAT_TYPE_VECTOR)
-		qsort(centers->items, centers->length, centers->itemsize, CompareVectors);
-	else if (type == IVFFLAT_TYPE_HALFVEC)
-		qsort(centers->items, centers->length, centers->itemsize, CompareHalfVectors);
-	else
-		elog(ERROR, "Unsupported type");
-
-	for (int i = 1; i < centers->length; i++)
 	{
-		if (datumIsEqual(PointerGetDatum(VectorArrayGet(centers, i)), PointerGetDatum(VectorArrayGet(centers, i - 1)), false, -1))
+		/* Ensure no duplicate centers */
-			elog(ERROR, "Duplicate centers detected. Please report a bug.");
+		/* Fine to sort in-place */
+		if (type == IVFFLAT_TYPE_VECTOR)
+			qsort(centers->items, centers->length, centers->itemsize, CompareVectors);
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+			qsort(centers->items, centers->length, centers->itemsize, CompareHalfVectors);
+		else
+			elog(ERROR, "Unsupported type");
+
+		for (int i = 1; i < centers->length; i++)
+		{
+			if (datumIsEqual(PointerGetDatum(VectorArrayGet(centers, i)), PointerGetDatum(VectorArrayGet(centers, i - 1)), false, -1))
+				elog(ERROR, "Duplicate centers detected. Please report a bug.");
+		}
 	}
 
 	/* Ensure no zero vectors for cosine distance */

src/ivfscan.c

@@ -3,6 +3,7 @@
 #include <float.h>
 
 #include "access/relscan.h"
+#include "bitvector.h"
 #include "catalog/pg_operator_d.h"
 #include "catalog/pg_type_d.h"
 #include "halfvec.h"
@@ -195,6 +196,8 @@ GetScanValue(IndexScanDesc scan)
 			value = PointerGetDatum(InitVector(so->dimensions));
 		else if (type == IVFFLAT_TYPE_HALFVEC)
 			value = PointerGetDatum(InitHalfVector(so->dimensions));
+		else if (type == IVFFLAT_TYPE_BIT)
+			value = PointerGetDatum(InitBitVector(so->dimensions));
 		else
 			elog(ERROR, "Unsupported type");
 	}

src/ivfutils.c

@@ -2,6 +2,7 @@
 
 #include "access/generic_xlog.h"
 #include "catalog/pg_type.h"
+#include "fmgr.h"
 #include "halfutils.h"
 #include "halfvec.h"
 #include "ivfflat.h"
@@ -17,6 +18,9 @@ VectorArrayInit(int maxlen, int dimensions, Size itemsize)
 {
 	VectorArray res = palloc(sizeof(VectorArrayData));
 
+	/* Ensure items are aligned to prevent UB */
+	itemsize = MAXALIGN(itemsize);
+
 	res->length = 0;
 	res->maxlen = maxlen;
 	res->dim = dimensions;
@@ -72,6 +76,9 @@ IvfflatGetType(Relation index)
 	Form_pg_type type;
 	IvfflatType result;
 
+	if (typid == BITOID)
+		return IVFFLAT_TYPE_BIT;
+
 	tuple = SearchSysCache1(TYPEOID, ObjectIdGetDatum(typid));
 	if (!HeapTupleIsValid(tuple))
 		elog(ERROR, "cache lookup failed for type %u", typid);
@@ -108,25 +115,9 @@ IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, IvfflatType ty
 	if (norm > 0)
 	{
 		if (type == IVFFLAT_TYPE_VECTOR)
-		{
+			*value = DirectFunctionCall1(l2_normalize, *value);
-			Vector	   *v = DatumGetVector(*value);
-			Vector	   *result = InitVector(v->dim);
-
-			for (int i = 0; i < v->dim; i++)
-				result->x[i] = v->x[i] / norm;
-
-			*value = PointerGetDatum(result);
-		}
 		else if (type == IVFFLAT_TYPE_HALFVEC)
-		{
+			*value = DirectFunctionCall1(halfvec_l2_normalize, *value);
-			HalfVector *v = DatumGetHalfVector(*value);
-			HalfVector *result = InitHalfVector(v->dim);
-
-			for (int i = 0; i < v->dim; i++)
-				result->x[i] = Float4ToHalfUnchecked(HalfToFloat4(v->x[i]) / norm);
-
-			*value = PointerGetDatum(result);
-		}
 		else
 			elog(ERROR, "Unsupported type");
 

src/sparsevec.c

@@ -579,7 +579,7 @@ vector_to_sparsevec(PG_FUNCTION_ARGS)
 		if (vec->x[i] != 0)
 		{
 			/* Safety check */
-			if (j == nnz)
+			if (j >= result->nnz)
 				elog(ERROR, "safety check failed");
 
 			result->indices[j] = i + 1;
@@ -594,12 +594,12 @@ vector_to_sparsevec(PG_FUNCTION_ARGS)
 /*
  * Get the L2 squared distance between sparse vectors
  */
-static double
+static float
 SparsevecL2SquaredDistance(SparseVector * a, SparseVector * b)
 {
 	float	   *ax = SPARSEVEC_VALUES(a);
 	float	   *bx = SPARSEVEC_VALUES(b);
-	double		distance = 0.0;
+	float		distance = 0.0;
 	int			bpos = 0;
 
 	for (int i = 0; i < a->nnz; i++)
@@ -673,12 +673,12 @@ sparsevec_l2_squared_distance(PG_FUNCTION_ARGS)
 /*
  * Get the inner product of two sparse vectors
  */
-static double
+static float
 SparsevecInnerProduct(SparseVector * a, SparseVector * b)
 {
 	float	   *ax = SPARSEVEC_VALUES(a);
 	float	   *bx = SPARSEVEC_VALUES(b);
-	double		distance = 0.0;
+	float		distance = 0.0;
 	int			bpos = 0;
 
 	for (int i = 0; i < a->nnz; i++)
@@ -781,12 +781,61 @@ sparsevec_cosine_distance(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(1.0 - similarity);
 }
 
+/*
+ * Get the L1 distance between two sparse vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_l1_distance);
+Datum
+sparsevec_l1_distance(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+	float	   *ax = SPARSEVEC_VALUES(a);
+	float	   *bx = SPARSEVEC_VALUES(b);
+	double		distance = 0.0;
+	int			bpos = 0;
+
+	CheckDims(a, b);
+
+	for (int i = 0; i < a->nnz; i++)
+	{
+		int			ai = a->indices[i];
+		int			bi = -1;
+
+		for (int j = bpos; j < b->nnz; j++)
+		{
+			bi = b->indices[j];
+
+			if (ai == bi)
+				distance += fabsf(ax[i] - bx[j]);
+			else if (ai > bi)
+				distance += fabsf(bx[j]);
+
+			/* Update start for next iteration */
+			if (ai >= bi)
+				bpos = j + 1;
+
+			/* Found or passed it */
+			if (bi >= ai)
+				break;
+		}
+
+		if (ai != bi)
+			distance += fabsf(ax[i]);
+	}
+
+	for (int j = bpos; j < b->nnz; j++)
+		distance += fabsf(bx[j]);
+
+	PG_RETURN_FLOAT8(distance);
+}
+
 /*
  * Get the L2 norm of a sparse vector
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_norm);
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_l2_norm);
 Datum
-sparsevec_norm(PG_FUNCTION_ARGS)
+sparsevec_l2_norm(PG_FUNCTION_ARGS)
 {
 	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
 	float	   *ax = SPARSEVEC_VALUES(a);
@@ -798,3 +847,205 @@ sparsevec_norm(PG_FUNCTION_ARGS)
 
 	PG_RETURN_FLOAT8(sqrt(norm));
 }
+
+/*
+ * Normalize a sparse vector with the L2 norm
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_l2_normalize);
+Datum
+sparsevec_l2_normalize(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	float	   *ax = SPARSEVEC_VALUES(a);
+	double		norm = 0;
+	SparseVector *result;
+	float	   *rx;
+
+	result = InitSparseVector(a->dim, a->nnz);
+	rx = SPARSEVEC_VALUES(result);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->nnz; i++)
+		norm += (double) ax[i] * (double) ax[i];
+
+	norm = sqrt(norm);
+
+	/* Return zero vector for zero norm */
+	if (norm > 0)
+	{
+		int			zeros = 0;
+
+		for (int i = 0; i < a->nnz; i++)
+		{
+			result->indices[i] = a->indices[i];
+			rx[i] = ax[i] / norm;
+
+			if (isinf(rx[i]))
+				float_overflow_error();
+
+			if (rx[i] == 0)
+				zeros++;
+		}
+
+		/* Allocate a new vector in the unlikely event there are zeros */
+		if (zeros > 0)
+		{
+			SparseVector *newResult = InitSparseVector(result->dim, result->nnz - zeros);
+			float	   *nx = SPARSEVEC_VALUES(newResult);
+			int			j = 0;
+
+			for (int i = 0; i < result->nnz; i++)
+			{
+				if (rx[i] == 0)
+					continue;
+
+				/* Safety check */
+				if (j >= newResult->nnz)
+					elog(ERROR, "safety check failed");
+
+				newResult->indices[j] = result->indices[i];
+				nx[j] = rx[i];
+				j++;
+			}
+
+			pfree(result);
+
+			PG_RETURN_POINTER(newResult);
+		}
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Internal helper to compare sparse vectors
+ */
+static int
+sparsevec_cmp_internal(SparseVector * a, SparseVector * b)
+{
+	float	   *ax = SPARSEVEC_VALUES(a);
+	float	   *bx = SPARSEVEC_VALUES(b);
+	int			nnz = Min(a->nnz, b->nnz);
+
+	/* Check values before dimensions to be consistent with Postgres arrays */
+	for (int i = 0; i < nnz; i++)
+	{
+		if (a->indices[i] < b->indices[i])
+			return ax[i] < 0 ? -1 : 1;
+
+		if (a->indices[i] > b->indices[i])
+			return bx[i] < 0 ? 1 : -1;
+
+		if (ax[i] < bx[i])
+			return -1;
+
+		if (ax[i] > bx[i])
+			return 1;
+	}
+
+	/* Check <= dim since indices start at 1 */
+	if (a->nnz < b->nnz && b->indices[nnz] <= a->dim)
+		return bx[nnz] < 0 ? 1 : -1;
+
+	if (a->nnz > b->nnz && a->indices[nnz] <= b->dim)
+		return ax[nnz] < 0 ? -1 : 1;
+
+	if (a->dim < b->dim)
+		return -1;
+
+	if (a->dim > b->dim)
+		return 1;
+
+	return 0;
+}
+
+/*
+ * Less than
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_lt);
+Datum
+sparsevec_lt(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	PG_RETURN_BOOL(sparsevec_cmp_internal(a, b) < 0);
+}
+
+/*
+ * Less than or equal
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_le);
+Datum
+sparsevec_le(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	PG_RETURN_BOOL(sparsevec_cmp_internal(a, b) <= 0);
+}
+
+/*
+ * Equal
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_eq);
+Datum
+sparsevec_eq(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	PG_RETURN_BOOL(sparsevec_cmp_internal(a, b) == 0);
+}
+
+/*
+ * Not equal
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_ne);
+Datum
+sparsevec_ne(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	PG_RETURN_BOOL(sparsevec_cmp_internal(a, b) != 0);
+}
+
+/*
+ * Greater than or equal
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_ge);
+Datum
+sparsevec_ge(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	PG_RETURN_BOOL(sparsevec_cmp_internal(a, b) >= 0);
+}
+
+/*
+ * Greater than
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_gt);
+Datum
+sparsevec_gt(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	PG_RETURN_BOOL(sparsevec_cmp_internal(a, b) > 0);
+}
+
+/*
+ * Compare sparse vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_cmp);
+Datum
+sparsevec_cmp(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	PG_RETURN_INT32(sparsevec_cmp_internal(a, b));
+}

src/sparsevec.h

@@ -1,6 +1,8 @@
 #ifndef SPARSEVEC_H
 #define SPARSEVEC_H
 
+#include "fmgr.h"
+
 #define SPARSEVEC_MAX_DIM 100000
 #define SPARSEVEC_MAX_NNZ 16000
 
@@ -21,5 +23,6 @@ typedef struct SparseVector
 }			SparseVector;
 
 SparseVector *InitSparseVector(int dim, int nnz);
+PGDLLEXPORT Datum sparsevec_l2_normalize(PG_FUNCTION_ARGS);
 
 #endif

src/vector.c

@@ -34,7 +34,14 @@
 #define CreateStateDatums(dim) palloc(sizeof(Datum) * (dim + 1))
 
 /* target_clones requires glibc */
-#if defined(__x86_64__) && defined(__gnu_linux__) && defined(__has_attribute) && __has_attribute(target_clones) && !defined(__FMA__)
+#if defined(__gnu_linux__) && defined(__has_attribute)
+/* Use separate line for portability */
+#if __has_attribute(target_clones)
+#define HAVE_TARGET_CLONES
+#endif
+#endif
+
+#if defined(__x86_64__) && defined(HAVE_TARGET_CLONES) && !defined(__FMA__)
 #define VECTOR_DISPATCH __attribute__((target_clones("default", "fma")))
 #else
 #define VECTOR_DISPATCH
@@ -653,6 +660,25 @@ vector_negative_inner_product(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8((double) -VectorInnerProduct(a->dim, a->x, b->x));
 }
 
+VECTOR_DISPATCH static double
+VectorCosineSimilarity(int dim, float *ax, float *bx)
+{
+	float		similarity = 0.0;
+	float		norma = 0.0;
+	float		normb = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		similarity += ax[i] * bx[i];
+		norma += ax[i] * ax[i];
+		normb += bx[i] * bx[i];
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	return (double) similarity / sqrt((double) norma * (double) normb);
+}
+
 /*
  * Get the cosine distance between two vectors
  */
@@ -662,25 +688,11 @@ cosine_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
-	float		norma = 0.0;
-	float		normb = 0.0;
 	double		similarity;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
+	similarity = VectorCosineSimilarity(a->dim, a->x, b->x);
-	for (int i = 0; i < a->dim; i++)
-	{
-		distance += ax[i] * bx[i];
-		norma += ax[i] * ax[i];
-		normb += bx[i] * bx[i];
-	}
-
-	/* 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 */
@@ -723,6 +735,18 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(acos(distance) / M_PI);
 }
 
+static float
+VectorL1Distance(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += fabsf(ax[i] - bx[i]);
+
+	return distance;
+}
+
 /*
  * Get the L1 distance between two vectors
  */
@@ -732,17 +756,10 @@ l1_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
+	PG_RETURN_FLOAT8((double) VectorL1Distance(a->dim, a->x, b->x));
-	for (int i = 0; i < a->dim; i++)
-		distance += fabsf(ax[i] - bx[i]);
-
-	PG_RETURN_FLOAT8((double) distance);
 }
 
 /*
@@ -775,6 +792,45 @@ vector_norm(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(sqrt(norm));
 }
 
+/*
+ * Normalize a vector with the L2 norm
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(l2_normalize);
+Datum
+l2_normalize(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	float	   *ax = a->x;
+	double		norm = 0;
+	Vector	   *result;
+	float	   *rx;
+
+	result = InitVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		norm += (double) ax[i] * (double) ax[i];
+
+	norm = sqrt(norm);
+
+	/* Return zero vector for zero norm */
+	if (norm > 0)
+	{
+		for (int i = 0; i < a->dim; i++)
+			rx[i] = ax[i] / norm;
+
+		/* Check for overflow */
+		for (int i = 0; i < a->dim; i++)
+		{
+			if (isinf(rx[i]))
+				float_overflow_error();
+		}
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
 /*
  * Add vectors
  */
@@ -877,12 +933,36 @@ vector_mul(PG_FUNCTION_ARGS)
 	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);
+}
+
 /*
  * Quantize a vector
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(quantize_binary);
+PGDLLEXPORT PG_FUNCTION_INFO_V1(binary_quantize);
 Datum
-quantize_binary(PG_FUNCTION_ARGS)
+binary_quantize(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	float	   *ax = a->x;
@@ -1107,7 +1187,7 @@ vector_accum(PG_FUNCTION_ARGS)
 }
 
 /*
- * Combine vectors
+ * Combine vectors or half vectors
  */
 PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_combine);
 Datum

src/vector.h

@@ -1,6 +1,8 @@
 #ifndef VECTOR_H
 #define VECTOR_H
 
+#include "fmgr.h"
+
 #define VECTOR_MAX_DIM 16000
 
 #define VECTOR_SIZE(_dim)		(offsetof(Vector, x) + sizeof(float)*(_dim))
@@ -19,5 +21,6 @@ typedef struct Vector
 Vector	   *InitVector(int dim);
 void		PrintVector(char *msg, Vector * vector);
 int			vector_cmp_internal(Vector * a, Vector * b);
+PGDLLEXPORT Datum l2_normalize(PG_FUNCTION_ARGS);
 
 #endif

test/expected/btree_halfvec.out

@@ -0,0 +1,20 @@
+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 (val);
+SELECT * FROM t WHERE val = '[1,2,3]';
+   val   
+---------
+ [1,2,3]
+(1 row)
+
+SELECT * FROM t ORDER BY val;
+   val   
+---------
+ [0,0,0]
+ [1,1,1]
+ [1,2,3]
+ 
+(4 rows)
+
+DROP TABLE t;

test/expected/btree_sparsevec.out

@@ -0,0 +1,20 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val sparsevec(3));
+INSERT INTO t (val) VALUES ('{}/3'), ('{1:1,2:2,3:3}/3'), ('{1:1,2:1,3:1}/3'), (NULL);
+CREATE INDEX ON t (val);
+SELECT * FROM t WHERE val = '{1:1,2:2,3:3}/3';
+       val       
+-----------------
+ {1:1,2:2,3:3}/3
+(1 row)
+
+SELECT * FROM t ORDER BY val;
+       val       
+-----------------
+ {}/3
+ {1:1,2:1,3:1}/3
+ {1:1,2:2,3:3}/3
+ 
+(4 rows)
+
+DROP TABLE t;

test/expected/btree_vector.out

@@ -8,10 +8,13 @@ SELECT * FROM t WHERE val = '[1,2,3]';
  [1,2,3]
 (1 row)
 
-SELECT * FROM t ORDER BY val LIMIT 1;
+SELECT * FROM t ORDER BY val;
    val   
 ---------
  [0,0,0]
-(1 row)
+ [1,1,1]
+ [1,2,3]
+ 
+(4 rows)
 
 DROP TABLE t;

test/expected/halfvec_functions.out

@@ -1,19 +1,179 @@
-SELECT round(halfvec_norm('[1,1]')::numeric, 5);
+SELECT '[1,2,3]'::halfvec + '[4,5,6]';
+ ?column? 
+----------
+ [5,7,9]
+(1 row)
+
+SELECT '[65519]'::halfvec + '[65519]';
+ERROR:  value out of range: overflow
+SELECT '[1,2]'::halfvec + '[3]';
+ERROR:  different halfvec dimensions 2 and 1
+SELECT '[1,2,3]'::halfvec - '[4,5,6]';
+  ?column?  
+------------
+ [-3,-3,-3]
+(1 row)
+
+SELECT '[-65519]'::halfvec - '[65519]';
+ERROR:  value out of range: overflow
+SELECT '[1,2]'::halfvec - '[3]';
+ERROR:  different halfvec dimensions 2 and 1
+SELECT '[1,2,3]'::halfvec * '[4,5,6]';
+ ?column?  
+-----------
+ [4,10,18]
+(1 row)
+
+SELECT '[65519]'::halfvec * '[65519]';
+ERROR:  value out of range: overflow
+SELECT '[1e-7]'::halfvec * '[1e-7]';
+ERROR:  value out of range: underflow
+SELECT '[1,2]'::halfvec * '[3]';
+ERROR:  different halfvec dimensions 2 and 1
+SELECT '[1,2,3]'::halfvec || '[4,5]';
+  ?column?   
+-------------
+ [1,2,3,4,5]
+(1 row)
+
+SELECT array_fill(0, ARRAY[16000])::halfvec || '[1]';
+ERROR:  halfvec cannot have more than 16000 dimensions
+SELECT '[1,2,3]'::halfvec < '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec < '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec <= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec <= '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec = '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec = '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec != '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec != '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec >= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec >= '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec > '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec > '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT halfvec_cmp('[1,2,3]', '[1,2,3]');
+ halfvec_cmp 
+-------------
+           0
+(1 row)
+
+SELECT halfvec_cmp('[1,2,3]', '[0,0,0]');
+ halfvec_cmp 
+-------------
+           1
+(1 row)
+
+SELECT halfvec_cmp('[0,0,0]', '[1,2,3]');
+ halfvec_cmp 
+-------------
+          -1
+(1 row)
+
+SELECT halfvec_cmp('[1,2]', '[1,2,3]');
+ halfvec_cmp 
+-------------
+          -1
+(1 row)
+
+SELECT halfvec_cmp('[1,2,3]', '[1,2]');
+ halfvec_cmp 
+-------------
+           1
+(1 row)
+
+SELECT halfvec_cmp('[1,2]', '[2,3,4]');
+ halfvec_cmp 
+-------------
+          -1
+(1 row)
+
+SELECT halfvec_cmp('[2,3]', '[1,2,3]');
+ halfvec_cmp 
+-------------
+           1
+(1 row)
+
+SELECT vector_dims('[1,2,3]'::halfvec);
+ vector_dims 
+-------------
+           3
+(1 row)
+
+SELECT round(l2_norm('[1,1]'::halfvec)::numeric, 5);
   round  
 ---------
  1.41421
 (1 row)
 
-SELECT halfvec_norm('[3,4]');
+SELECT l2_norm('[3,4]'::halfvec);
- halfvec_norm 
+ l2_norm 
---------------
+---------
-            5
+       5
 (1 row)
 
-SELECT halfvec_norm('[0,1]');
+SELECT l2_norm('[0,1]'::halfvec);
- halfvec_norm 
+ l2_norm 
---------------
+---------
-            1
+       1
 (1 row)
 
 SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
@@ -112,6 +272,18 @@ SELECT cosine_distance('[1,1]'::halfvec, '[-1.1,-1.1]');
                2
 (1 row)
 
+SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
 SELECT '[1,2]'::halfvec <=> '[2,4]';
  ?column? 
 ----------
@@ -132,14 +304,44 @@ SELECT l1_distance('[0,0]'::halfvec, '[0,1]');
 
 SELECT l1_distance('[1,2]'::halfvec, '[3]');
 ERROR:  different halfvec dimensions 2 and 1
-SELECT quantize_binary('[1,0,-1]'::halfvec);
+SELECT l2_normalize('[3,4]'::halfvec);
- quantize_binary 
+      l2_normalize      
+------------------------
+ [0.60009766,0.7998047]
+(1 row)
+
+SELECT l2_normalize('[3,0]'::halfvec);
+ l2_normalize 
+--------------
+ [1,0]
+(1 row)
+
+SELECT l2_normalize('[0,0.1]'::halfvec);
+ l2_normalize 
+--------------
+ [0,1]
+(1 row)
+
+SELECT l2_normalize('[0,0]'::halfvec);
+ l2_normalize 
+--------------
+ [0,0]
+(1 row)
+
+SELECT l2_normalize('[65504]'::halfvec);
+ l2_normalize 
+--------------
+ [1]
+(1 row)
+
+SELECT binary_quantize('[1,0,-1]'::halfvec);
+ binary_quantize 
 -----------------
  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]'::halfvec);
+SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::halfvec);
- quantize_binary 
+ binary_quantize 
 -----------------
  01001110101
 (1 row)
@@ -174,3 +376,53 @@ SELECT subvector('[1,2,3,4,5]'::halfvec, 3, -1);
 ERROR:  halfvec must have at least 1 dimension
 SELECT subvector('[1,2,3,4,5]'::halfvec, -1, 2);
 ERROR:  halfvec must have at least 1 dimension
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]']) v;
+    avg    
+-----------
+ [2,3.5,5]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]', NULL]) v;
+    avg    
+-----------
+ [2,3.5,5]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY[]::halfvec[]) v;
+ avg 
+-----
+ 
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2]'::halfvec, '[3]']) v;
+ERROR:  expected 2 dimensions, not 1
+SELECT avg(v) FROM unnest(ARRAY['[65504]'::halfvec, '[65504]']) v;
+   avg   
+---------
+ [65504]
+(1 row)
+
+SELECT halfvec_avg(array_agg(n)) FROM generate_series(1, 16002) n;
+ERROR:  halfvec cannot have more than 16000 dimensions
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]']) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]', NULL]) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY[]::halfvec[]) v;
+ sum 
+-----
+ 
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::halfvec, '[3]']) v;
+ERROR:  different halfvec dimensions 2 and 1
+SELECT sum(v) FROM unnest(ARRAY['[65504]'::halfvec, '[65504]']) v;
+ERROR:  value out of range: overflow

test/expected/ivfflat_bit_hamming.out

@@ -0,0 +1,36 @@
+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 ivfflat (val bit_hamming_ops) WITH (lists = 1);
+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;
+-- TODO move
+CREATE TABLE t (val varbit(3));
+CREATE INDEX ON t USING ivfflat (val bit_hamming_ops) WITH (lists = 1);
+ERROR:  type not supported for ivfflat index
+CREATE INDEX ON t USING ivfflat ((val::bit(3)) bit_hamming_ops) WITH (lists = 1);
+NOTICE:  ivfflat index created with little data
+DETAIL:  This will cause low recall.
+HINT:  Drop the index until the table has more data.
+CREATE INDEX ON t USING ivfflat ((val::bit(64001)) bit_hamming_ops) WITH (lists = 1);
+ERROR:  column cannot have more than 64000 dimensions for ivfflat index
+CREATE INDEX ON t USING ivfflat ((val::bit(2)) bit_hamming_ops) WITH (lists = 5);
+NOTICE:  ivfflat index created with little data
+DETAIL:  This will cause low recall.
+HINT:  Drop the index until the table has more data.
+DROP TABLE t;

test/expected/ivfflat_bit_jaccard.out

@@ -0,0 +1,21 @@
+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 ivfflat (val bit_jaccard_ops) WITH (lists = 1);
+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/sparsevec_functions.out

@@ -1,25 +1,139 @@
-SELECT round(sparsevec_norm('{1:1,2:1}/2')::numeric, 5);
+SELECT '{1:1,2:2,3:3}/3'::sparsevec < '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec < '{1:1,2:2}/2';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec <= '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec <= '{1:1,2:2}/2';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec = '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec = '{1:1,2:2}/2';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec != '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec != '{1:1,2:2}/2';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec >= '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec >= '{1:1,2:2}/2';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec > '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec > '{1:1,2:2}/2';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{1:1,2:2,3:3}/3');
+ sparsevec_cmp 
+---------------
+             0
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{}/3');
+ sparsevec_cmp 
+---------------
+             1
+(1 row)
+
+SELECT sparsevec_cmp('{}/3', '{1:1,2:2,3:3}/3');
+ sparsevec_cmp 
+---------------
+            -1
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2}/2', '{1:1,2:2,3:3}/3');
+ sparsevec_cmp 
+---------------
+            -1
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{1:1,2:2}/2');
+ sparsevec_cmp 
+---------------
+             1
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2}/2', '{1:2,2:3,3:4}/3');
+ sparsevec_cmp 
+---------------
+            -1
+(1 row)
+
+SELECT sparsevec_cmp('{1:2,2:3}/2', '{1:1,2:2,3:3}/3');
+ sparsevec_cmp 
+---------------
+             1
+(1 row)
+
+SELECT round(l2_norm('{1:1,2:1}/2'::sparsevec)::numeric, 5);
   round  
 ---------
  1.41421
 (1 row)
 
-SELECT sparsevec_norm('{1:3,2:4}/2');
+SELECT l2_norm('{1:3,2:4}/2'::sparsevec);
- sparsevec_norm 
+ l2_norm 
-----------------
+---------
-              5
+       5
 (1 row)
 
-SELECT sparsevec_norm('{2:1}/2');
+SELECT l2_norm('{2:1}/2'::sparsevec);
- sparsevec_norm 
+ l2_norm 
-----------------
+---------
-              1
+       1
 (1 row)
 
-SELECT sparsevec_norm('{1:3e37,2:4e37}/2')::real;
+SELECT l2_norm('{1:3e37,2:4e37}/2'::sparsevec)::real;
- sparsevec_norm 
+ l2_norm 
-----------------
+---------
-          5e+37
+   5e+37
 (1 row)
 
 SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
@@ -28,6 +142,18 @@ SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
            5
 (1 row)
 
+SELECT l2_distance('{1:3}/2'::sparsevec, '{2:4}/2');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('{2:4}/2'::sparsevec, '{1:3}/2');
+ l2_distance 
+-------------
+           5
+(1 row)
+
 SELECT l2_distance('{}/2'::sparsevec, '{2:1}/2');
  l2_distance 
 -------------
@@ -46,10 +172,24 @@ SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
             10
 (1 row)
 
-SELECT sparsevec_negative_inner_product('{1:1,2:2}/2', '{1:2,2:4}/2');
+SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
- sparsevec_negative_inner_product 
+ERROR:  different sparsevec dimensions 2 and 1
-----------------------------------
+SELECT inner_product('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
-                              -10
+ inner_product 
+---------------
+      Infinity
+(1 row)
+
+SELECT inner_product('{1:1,3:3,5:5}/5'::sparsevec, '{2:4,3:6,4:8}/5');
+ inner_product 
+---------------
+            18
+(1 row)
+
+SELECT '{1:1,2:2}/2'::sparsevec <#> '{1:3,2:4}/2';
+ ?column? 
+----------
+      -11
 (1 row)
 
 SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
@@ -64,6 +204,18 @@ SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{}/2');
              NaN
 (1 row)
 
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:1,2:1}/2');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('{1:1}/2'::sparsevec, '{2:2}/2');
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
 SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1,2:-1}/2');
  cosine_distance 
 -----------------
@@ -76,11 +228,109 @@ SELECT cosine_distance('{1:2}/2'::sparsevec, '{2:2}/2');
                1
 (1 row)
 
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+ERROR:  different sparsevec dimensions 2 and 1
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:1.1,2:1.1}/2');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1.1,2:-1.1}/2');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
 SELECT cosine_distance('{}/1'::sparsevec, '{}/1');
  cosine_distance 
 -----------------
              NaN
 (1 row)
 
-SELECT cosine_distance('{1:2}/2'::sparsevec, '{1:1}/3');
+SELECT '{1:1,2:2}/2'::sparsevec <=> '{1:2,2:4}/2';
-ERROR:  different sparsevec dimensions 2 and 3
+ ?column? 
+----------
+        0
+(1 row)
+
+SELECT l1_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('{}/2'::sparsevec, '{2:1}/2');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+ERROR:  different sparsevec dimensions 2 and 1
+SELECT l1_distance('{1:3e38}/1'::sparsevec, '{1:-3e38}/1');
+ l1_distance 
+-------------
+    Infinity
+(1 row)
+
+SELECT l1_distance('{1:1,3:3,5:5,7:7}/8'::sparsevec, '{2:2,4:4,6:6,8:8}/8');
+ l1_distance 
+-------------
+          36
+(1 row)
+
+SELECT l1_distance('{1:1,3:3,5:5,7:7,9:9}/9'::sparsevec, '{2:2,4:4,6:6,8:8}/9');
+ l1_distance 
+-------------
+          45
+(1 row)
+
+SELECT l2_normalize('{1:3,2:4}/2'::sparsevec);
+  l2_normalize   
+-----------------
+ {1:0.6,2:0.8}/2
+(1 row)
+
+SELECT l2_normalize('{1:3}/2'::sparsevec);
+ l2_normalize 
+--------------
+ {1:1}/2
+(1 row)
+
+SELECT l2_normalize('{2:0.1}/2'::sparsevec);
+ l2_normalize 
+--------------
+ {2:1}/2
+(1 row)
+
+SELECT l2_normalize('{}/2'::sparsevec);
+ l2_normalize 
+--------------
+ {}/2
+(1 row)
+
+SELECT l2_normalize('{1:3e38}/1'::sparsevec);
+ l2_normalize 
+--------------
+ {1:1}/1
+(1 row)
+
+SELECT l2_normalize('{1:3e38,2:1e-37}/2'::sparsevec);
+ l2_normalize 
+--------------
+ {1:1}/2
+(1 row)
+
+SELECT l2_normalize('{2:3e37,4:3e-37,6:4e37,8:4e-37}/9'::sparsevec);
+  l2_normalize   
+-----------------
+ {2:0.6,6:0.8}/9
+(1 row)
+

test/expected/vector_functions.out

@@ -6,6 +6,8 @@ SELECT '[1,2,3]'::vector + '[4,5,6]';
 
 SELECT '[3e38]'::vector + '[3e38]';
 ERROR:  value out of range: overflow
+SELECT '[1,2]'::vector + '[3]';
+ERROR:  different vector dimensions 2 and 1
 SELECT '[1,2,3]'::vector - '[4,5,6]';
   ?column?  
 ------------
@@ -14,6 +16,8 @@ SELECT '[1,2,3]'::vector - '[4,5,6]';
 
 SELECT '[-3e38]'::vector - '[3e38]';
 ERROR:  value out of range: overflow
+SELECT '[1,2]'::vector - '[3]';
+ERROR:  different vector dimensions 2 and 1
 SELECT '[1,2,3]'::vector * '[4,5,6]';
  ?column?  
 -----------
@@ -24,6 +28,16 @@ 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]'::vector * '[3]';
+ERROR:  different vector dimensions 2 and 1
+SELECT '[1,2,3]'::vector || '[4,5]';
+  ?column?   
+-------------
+ [1,2,3,4,5]
+(1 row)
+
+SELECT array_fill(0, ARRAY[16000])::vector || '[1]';
+ERROR:  vector cannot have more than 16000 dimensions
 SELECT '[1,2,3]'::vector < '[1,2,3]';
  ?column? 
 ----------
@@ -138,7 +152,7 @@ SELECT vector_cmp('[2,3]', '[1,2,3]');
           1
 (1 row)
 
-SELECT vector_dims('[1,2,3]');
+SELECT vector_dims('[1,2,3]'::vector);
  vector_dims 
 -------------
            3
@@ -188,6 +202,12 @@ SELECT l2_distance('[3e38]'::vector, '[-3e38]');
     Infinity
 (1 row)
 
+SELECT '[0,0]'::vector <-> '[3,4]';
+ ?column? 
+----------
+        5
+(1 row)
+
 SELECT inner_product('[1,2]'::vector, '[3,4]');
  inner_product 
 ---------------
@@ -202,6 +222,12 @@ SELECT inner_product('[3e38]'::vector, '[3e38]');
       Infinity
 (1 row)
 
+SELECT '[1,2]'::vector <#> '[3,4]';
+ ?column? 
+----------
+      -11
+(1 row)
+
 SELECT cosine_distance('[1,2]'::vector, '[2,4]');
  cosine_distance 
 -----------------
@@ -252,6 +278,12 @@ SELECT cosine_distance('[3e38]'::vector, '[3e38]');
              NaN
 (1 row)
 
+SELECT '[1,2]'::vector <=> '[2,4]';
+ ?column? 
+----------
+        0
+(1 row)
+
 SELECT l1_distance('[0,0]'::vector, '[3,4]');
  l1_distance 
 -------------
@@ -272,14 +304,44 @@ SELECT l1_distance('[3e38]'::vector, '[-3e38]');
     Infinity
 (1 row)
 
-SELECT quantize_binary('[1,0,-1]'::vector);
+SELECT l2_normalize('[3,4]'::vector);
- quantize_binary 
+ l2_normalize 
+--------------
+ [0.6,0.8]
+(1 row)
+
+SELECT l2_normalize('[3,0]'::vector);
+ l2_normalize 
+--------------
+ [1,0]
+(1 row)
+
+SELECT l2_normalize('[0,0.1]'::vector);
+ l2_normalize 
+--------------
+ [0,1]
+(1 row)
+
+SELECT l2_normalize('[0,0]'::vector);
+ l2_normalize 
+--------------
+ [0,0]
+(1 row)
+
+SELECT l2_normalize('[3e38]'::vector);
+ l2_normalize 
+--------------
+ [1]
+(1 row)
+
+SELECT binary_quantize('[1,0,-1]'::vector);
+ binary_quantize 
 -----------------
  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]'::vector);
+SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::vector);
- quantize_binary 
+ binary_quantize 
 -----------------
  01001110101
 (1 row)

test/sql/btree_halfvec.sql

@@ -0,0 +1,10 @@
+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 (val);
+
+SELECT * FROM t WHERE val = '[1,2,3]';
+SELECT * FROM t ORDER BY val;
+
+DROP TABLE t;

test/sql/btree_sparsevec.sql

@@ -0,0 +1,10 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val sparsevec(3));
+INSERT INTO t (val) VALUES ('{}/3'), ('{1:1,2:2,3:3}/3'), ('{1:1,2:1,3:1}/3'), (NULL);
+CREATE INDEX ON t (val);
+
+SELECT * FROM t WHERE val = '{1:1,2:2,3:3}/3';
+SELECT * FROM t ORDER BY val;
+
+DROP TABLE t;

test/sql/btree_vector.sql

@@ -5,6 +5,6 @@ INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
 CREATE INDEX ON t (val);
 
 SELECT * FROM t WHERE val = '[1,2,3]';
-SELECT * FROM t ORDER BY val LIMIT 1;
+SELECT * FROM t ORDER BY val;
 
 DROP TABLE t;

test/sql/halfvec_functions.sql

@@ -1,6 +1,45 @@
-SELECT round(halfvec_norm('[1,1]')::numeric, 5);
+SELECT '[1,2,3]'::halfvec + '[4,5,6]';
-SELECT halfvec_norm('[3,4]');
+SELECT '[65519]'::halfvec + '[65519]';
-SELECT halfvec_norm('[0,1]');
+SELECT '[1,2]'::halfvec + '[3]';
+
+SELECT '[1,2,3]'::halfvec - '[4,5,6]';
+SELECT '[-65519]'::halfvec - '[65519]';
+SELECT '[1,2]'::halfvec - '[3]';
+
+SELECT '[1,2,3]'::halfvec * '[4,5,6]';
+SELECT '[65519]'::halfvec * '[65519]';
+SELECT '[1e-7]'::halfvec * '[1e-7]';
+SELECT '[1,2]'::halfvec * '[3]';
+
+SELECT '[1,2,3]'::halfvec || '[4,5]';
+SELECT array_fill(0, ARRAY[16000])::halfvec || '[1]';
+
+SELECT '[1,2,3]'::halfvec < '[1,2,3]';
+SELECT '[1,2,3]'::halfvec < '[1,2]';
+SELECT '[1,2,3]'::halfvec <= '[1,2,3]';
+SELECT '[1,2,3]'::halfvec <= '[1,2]';
+SELECT '[1,2,3]'::halfvec = '[1,2,3]';
+SELECT '[1,2,3]'::halfvec = '[1,2]';
+SELECT '[1,2,3]'::halfvec != '[1,2,3]';
+SELECT '[1,2,3]'::halfvec != '[1,2]';
+SELECT '[1,2,3]'::halfvec >= '[1,2,3]';
+SELECT '[1,2,3]'::halfvec >= '[1,2]';
+SELECT '[1,2,3]'::halfvec > '[1,2,3]';
+SELECT '[1,2,3]'::halfvec > '[1,2]';
+
+SELECT halfvec_cmp('[1,2,3]', '[1,2,3]');
+SELECT halfvec_cmp('[1,2,3]', '[0,0,0]');
+SELECT halfvec_cmp('[0,0,0]', '[1,2,3]');
+SELECT halfvec_cmp('[1,2]', '[1,2,3]');
+SELECT halfvec_cmp('[1,2,3]', '[1,2]');
+SELECT halfvec_cmp('[1,2]', '[2,3,4]');
+SELECT halfvec_cmp('[2,3]', '[1,2,3]');
+
+SELECT vector_dims('[1,2,3]'::halfvec);
+
+SELECT round(l2_norm('[1,1]'::halfvec)::numeric, 5);
+SELECT l2_norm('[3,4]'::halfvec);
+SELECT l2_norm('[0,1]'::halfvec);
 
 SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
 SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
@@ -22,14 +61,22 @@ 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 cosine_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
 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]');
 
-SELECT quantize_binary('[1,0,-1]'::halfvec);
+SELECT l2_normalize('[3,4]'::halfvec);
-SELECT quantize_binary('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::halfvec);
+SELECT l2_normalize('[3,0]'::halfvec);
+SELECT l2_normalize('[0,0.1]'::halfvec);
+SELECT l2_normalize('[0,0]'::halfvec);
+SELECT l2_normalize('[65504]'::halfvec);
+
+SELECT binary_quantize('[1,0,-1]'::halfvec);
+SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::halfvec);
 
 SELECT subvector('[1,2,3,4,5]'::halfvec, 1, 3);
 SELECT subvector('[1,2,3,4,5]'::halfvec, 3, 2);
@@ -38,3 +85,16 @@ SELECT subvector('[1,2,3,4,5]'::halfvec, 3, 9);
 SELECT subvector('[1,2,3,4,5]'::halfvec, 1, 0);
 SELECT subvector('[1,2,3,4,5]'::halfvec, 3, -1);
 SELECT subvector('[1,2,3,4,5]'::halfvec, -1, 2);
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]']) v;
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]', NULL]) v;
+SELECT avg(v) FROM unnest(ARRAY[]::halfvec[]) v;
+SELECT avg(v) FROM unnest(ARRAY['[1,2]'::halfvec, '[3]']) v;
+SELECT avg(v) FROM unnest(ARRAY['[65504]'::halfvec, '[65504]']) v;
+SELECT halfvec_avg(array_agg(n)) FROM generate_series(1, 16002) n;
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]']) v;
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]', NULL]) v;
+SELECT sum(v) FROM unnest(ARRAY[]::halfvec[]) v;
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::halfvec, '[3]']) v;
+SELECT sum(v) FROM unnest(ARRAY['[65504]'::halfvec, '[65504]']) v;

test/sql/ivfflat_bit_hamming.sql

@@ -0,0 +1,20 @@
+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 ivfflat (val bit_hamming_ops) WITH (lists = 1);
+
+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;
+
+-- TODO move
+CREATE TABLE t (val varbit(3));
+CREATE INDEX ON t USING ivfflat (val bit_hamming_ops) WITH (lists = 1);
+CREATE INDEX ON t USING ivfflat ((val::bit(3)) bit_hamming_ops) WITH (lists = 1);
+CREATE INDEX ON t USING ivfflat ((val::bit(64001)) bit_hamming_ops) WITH (lists = 1);
+CREATE INDEX ON t USING ivfflat ((val::bit(2)) bit_hamming_ops) WITH (lists = 5);
+DROP TABLE t;

test/sql/ivfflat_bit_jaccard.sql

@@ -0,0 +1,12 @@
+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 ivfflat (val bit_jaccard_ops) WITH (lists = 1);
+
+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/sparsevec_functions.sql

@@ -1,18 +1,65 @@
-SELECT round(sparsevec_norm('{1:1,2:1}/2')::numeric, 5);
+SELECT '{1:1,2:2,3:3}/3'::sparsevec < '{1:1,2:2,3:3}/3';
-SELECT sparsevec_norm('{1:3,2:4}/2');
+SELECT '{1:1,2:2,3:3}/3'::sparsevec < '{1:1,2:2}/2';
-SELECT sparsevec_norm('{2:1}/2');
+SELECT '{1:1,2:2,3:3}/3'::sparsevec <= '{1:1,2:2,3:3}/3';
-SELECT sparsevec_norm('{1:3e37,2:4e37}/2')::real;
+SELECT '{1:1,2:2,3:3}/3'::sparsevec <= '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec = '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec = '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec != '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec != '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec >= '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec >= '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec > '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec > '{1:1,2:2}/2';
+
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{1:1,2:2,3:3}/3');
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{}/3');
+SELECT sparsevec_cmp('{}/3', '{1:1,2:2,3:3}/3');
+SELECT sparsevec_cmp('{1:1,2:2}/2', '{1:1,2:2,3:3}/3');
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{1:1,2:2}/2');
+SELECT sparsevec_cmp('{1:1,2:2}/2', '{1:2,2:3,3:4}/3');
+SELECT sparsevec_cmp('{1:2,2:3}/2', '{1:1,2:2,3:3}/3');
+
+SELECT round(l2_norm('{1:1,2:1}/2'::sparsevec)::numeric, 5);
+SELECT l2_norm('{1:3,2:4}/2'::sparsevec);
+SELECT l2_norm('{2:1}/2'::sparsevec);
+SELECT l2_norm('{1:3e37,2:4e37}/2'::sparsevec)::real;
 
 SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+SELECT l2_distance('{1:3}/2'::sparsevec, '{2:4}/2');
+SELECT l2_distance('{2:4}/2'::sparsevec, '{1:3}/2');
 SELECT l2_distance('{}/2'::sparsevec, '{2:1}/2');
 SELECT '{}/2'::sparsevec <-> '{1:3,2:4}/2';
 
 SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
-SELECT sparsevec_negative_inner_product('{1:1,2:2}/2', '{1:2,2:4}/2');
+SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+SELECT inner_product('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
+SELECT inner_product('{1:1,3:3,5:5}/5'::sparsevec, '{2:4,3:6,4:8}/5');
+SELECT '{1:1,2:2}/2'::sparsevec <#> '{1:3,2:4}/2';
 
 SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
 SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{}/2');
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:1,2:1}/2');
+SELECT cosine_distance('{1:1}/2'::sparsevec, '{2:2}/2');
 SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1,2:-1}/2');
 SELECT cosine_distance('{1:2}/2'::sparsevec, '{2:2}/2');
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:1.1,2:1.1}/2');
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1.1,2:-1.1}/2');
+SELECT cosine_distance('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
 SELECT cosine_distance('{}/1'::sparsevec, '{}/1');
-SELECT cosine_distance('{1:2}/2'::sparsevec, '{1:1}/3');
+SELECT '{1:1,2:2}/2'::sparsevec <=> '{1:2,2:4}/2';
+
+SELECT l1_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+SELECT l1_distance('{}/2'::sparsevec, '{2:1}/2');
+SELECT l1_distance('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+SELECT l1_distance('{1:3e38}/1'::sparsevec, '{1:-3e38}/1');
+SELECT l1_distance('{1:1,3:3,5:5,7:7}/8'::sparsevec, '{2:2,4:4,6:6,8:8}/8');
+SELECT l1_distance('{1:1,3:3,5:5,7:7,9:9}/9'::sparsevec, '{2:2,4:4,6:6,8:8}/9');
+
+SELECT l2_normalize('{1:3,2:4}/2'::sparsevec);
+SELECT l2_normalize('{1:3}/2'::sparsevec);
+SELECT l2_normalize('{2:0.1}/2'::sparsevec);
+SELECT l2_normalize('{}/2'::sparsevec);
+SELECT l2_normalize('{1:3e38}/1'::sparsevec);
+SELECT l2_normalize('{1:3e38,2:1e-37}/2'::sparsevec);
+SELECT l2_normalize('{2:3e37,4:3e-37,6:4e37,8:4e-37}/9'::sparsevec);

test/sql/vector_functions.sql

@@ -1,10 +1,18 @@
 SELECT '[1,2,3]'::vector + '[4,5,6]';
 SELECT '[3e38]'::vector + '[3e38]';
+SELECT '[1,2]'::vector + '[3]';
+
 SELECT '[1,2,3]'::vector - '[4,5,6]';
 SELECT '[-3e38]'::vector - '[3e38]';
+SELECT '[1,2]'::vector - '[3]';
+
 SELECT '[1,2,3]'::vector * '[4,5,6]';
 SELECT '[1e37]'::vector * '[1e37]';
 SELECT '[1e-37]'::vector * '[1e-37]';
+SELECT '[1,2]'::vector * '[3]';
+
+SELECT '[1,2,3]'::vector || '[4,5]';
+SELECT array_fill(0, ARRAY[16000])::vector || '[1]';
 
 SELECT '[1,2,3]'::vector < '[1,2,3]';
 SELECT '[1,2,3]'::vector < '[1,2]';
@@ -27,7 +35,7 @@ SELECT vector_cmp('[1,2,3]', '[1,2]');
 SELECT vector_cmp('[1,2]', '[2,3,4]');
 SELECT vector_cmp('[2,3]', '[1,2,3]');
 
-SELECT vector_dims('[1,2,3]');
+SELECT vector_dims('[1,2,3]'::vector);
 
 SELECT round(vector_norm('[1,1]')::numeric, 5);
 SELECT vector_norm('[3,4]');
@@ -38,10 +46,12 @@ SELECT l2_distance('[0,0]'::vector, '[3,4]');
 SELECT l2_distance('[0,0]'::vector, '[0,1]');
 SELECT l2_distance('[1,2]'::vector, '[3]');
 SELECT l2_distance('[3e38]'::vector, '[-3e38]');
+SELECT '[0,0]'::vector <-> '[3,4]';
 
 SELECT inner_product('[1,2]'::vector, '[3,4]');
 SELECT inner_product('[1,2]'::vector, '[3]');
 SELECT inner_product('[3e38]'::vector, '[3e38]');
+SELECT '[1,2]'::vector <#> '[3,4]';
 
 SELECT cosine_distance('[1,2]'::vector, '[2,4]');
 SELECT cosine_distance('[1,2]'::vector, '[0,0]');
@@ -52,14 +62,21 @@ SELECT cosine_distance('[1,2]'::vector, '[3]');
 SELECT cosine_distance('[1,1]'::vector, '[1.1,1.1]');
 SELECT cosine_distance('[1,1]'::vector, '[-1.1,-1.1]');
 SELECT cosine_distance('[3e38]'::vector, '[3e38]');
+SELECT '[1,2]'::vector <=> '[2,4]';
 
 SELECT l1_distance('[0,0]'::vector, '[3,4]');
 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]'::vector);
+SELECT l2_normalize('[3,4]'::vector);
-SELECT quantize_binary('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::vector);
+SELECT l2_normalize('[3,0]'::vector);
+SELECT l2_normalize('[0,0.1]'::vector);
+SELECT l2_normalize('[0,0]'::vector);
+SELECT l2_normalize('[3e38]'::vector);
+
+SELECT binary_quantize('[1,0,-1]'::vector);
+SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::vector);
 
 SELECT subvector('[1,2,3,4,5]'::vector, 1, 3);
 SELECT subvector('[1,2,3,4,5]'::vector, 3, 2);

test/t/025_hnsw_sparsevec_insert_recall.pl

@@ -99,7 +99,7 @@ for my $i (0 .. $#operators)
 	}
 
 	# Test approximate results
-	my $min = $operator eq "<#>" ? 0.80 : 0.99;
+	my $min = $operator eq "<#>" ? 0.79 : 0.99;
 	test_recall($min, $operator);
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");

test/t/032_ivfflat_halfvec_build_recall.pl

@@ -105,8 +105,8 @@ for my $i (0 .. $#operators)
 	if ($operator ne "<#>")
 	{
 		# TODO Fix test (uniform random vectors all have similar inner product)
-		test_recall(1, 0.35, $operator);
+		test_recall(1, 0.34, $operator);
-		test_recall(10, 0.95, $operator);
+		test_recall(10, 0.93, $operator);
 	}
 
 	# Test probes equals lists
@@ -134,8 +134,8 @@ for my $i (0 .. $#operators)
 	if ($operator ne "<#>")
 	{
 		# TODO Fix test (uniform random vectors all have similar inner product)
-		test_recall(1, 0.35, $operator);
+		test_recall(1, 0.34, $operator);
-		test_recall(10, 0.95, $operator);
+		test_recall(10, 0.93, $operator);
 	}
 
 	# Test probes equals lists

test/t/033_comparison.pl

@@ -0,0 +1,48 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my $array_sql = join(",", ('floor(random() * 2)::int - 1') x 3);
+
+# Initialize node
+$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 (v real[]);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
+);
+
+for (1 .. 50)
+{
+	# Generate query
+	my @r = ();
+	for (1 .. (int(rand() * 3) + 2))
+	{
+		push(@r, int(rand() * 2) - 1);
+	}
+	my $query = "{" . join(",", @r) . "}";
+
+	# Get expected result
+	my $expected = $node->safe_psql("postgres", "SELECT btarraycmp(v, '$query') FROM tst");
+
+	# Test vector
+	my $actual = $node->safe_psql("postgres", "SELECT vector_cmp(v::vector, '$query'::real[]::vector) FROM tst");
+	is($expected, $actual);
+
+	# Test halfvec
+	$actual = $node->safe_psql("postgres", "SELECT halfvec_cmp(v::halfvec, '$query'::real[]::halfvec) FROM tst");
+	is($expected, $actual);
+
+	# Test sparsevec
+	$actual = $node->safe_psql("postgres", "SELECT sparsevec_cmp(v::vector::sparsevec, '$query'::real[]::vector::sparsevec) FROM tst");
+	is($expected, $actual);
+}
+
+done_testing();

test/t/034_distance_functions.pl

@@ -0,0 +1,54 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my $dim = 5;
+my $array_sql = join(",", ('floor(random() * 4)::int - 2') x $dim);
+
+# Initialize node
+$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 (v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, int(rand() * 4) - 2);
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each distance function
+my @functions = ("l2_distance", "inner_product", "cosine_distance", "l1_distance");
+
+for my $function (@functions)
+{
+	for my $query (@queries)
+	{
+		my $expected = $node->safe_psql("postgres", "SELECT $function(v, '$query') FROM tst");
+
+		# Test halfvec
+		my $actual = $node->safe_psql("postgres", "SELECT $function(v::halfvec, '$query'::vector::halfvec) FROM tst");
+		is($expected, $actual, "halfvec $function");
+
+		# Test sparsevec
+		$actual = $node->safe_psql("postgres", "SELECT $function(v::sparsevec, '$query'::vector::sparsevec) FROM tst");
+		is($expected, $actual, "sparsevec $function");
+	}
+}
+
+done_testing();

test/t/035_ivfflat_bit_build_recall.pl

@@ -0,0 +1,128 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 52;
+my $max = 2**$dim;
+
+sub test_recall
+{
+	my ($probes, $min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET ivfflat.probes = $probes;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator $queries[0] LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx on tst/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET ivfflat.probes = $probes;
+			SELECT i FROM tst ORDER BY v $operator $queries[$i] LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+
+		my @expected_ids = split("\n", $expected[$i]);
+		my %expected_set = map { $_ => 1 } @expected_ids;
+
+		foreach (@actual_ids)
+		{
+			if (exists($expected_set{$_}))
+			{
+				$correct++;
+			}
+		}
+
+		$total += $limit;
+	}
+
+	cmp_ok($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 bit($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, (random() * $max)::bigint::bit($dim) FROM generate_series(1, 100000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r = int(rand() * $max);
+	push(@queries, "${r}::bigint::bit($dim)");
+}
+
+# Check each index type
+my @operators = ("<~>", "<\%>");
+my @opclasses = ("bit_hamming_ops", "bit_jaccard_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", qq(
+			WITH top AS (
+				SELECT v $operator $_ AS distance FROM tst ORDER BY distance LIMIT $limit
+			)
+			SELECT i FROM tst WHERE (v $operator $_) <= (SELECT MAX(distance) FROM top)
+		));
+		push(@expected, $res);
+	}
+
+	# Build index serially
+	$node->safe_psql("postgres", qq(
+		SET max_parallel_maintenance_workers = 0;
+		CREATE INDEX idx ON tst USING ivfflat (v $opclass);
+	));
+
+	# Test approximate results
+	test_recall(1, 0.08, $operator);
+	test_recall(10, 0.50, $operator);
+
+	# Test probes equals lists
+	test_recall(100, 1.00, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel
+	my ($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 ivfflat (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	test_recall(1, 0.08, $operator);
+	test_recall(10, 0.50, $operator);
+
+	# Test probes equals lists
+	test_recall(100, 1.00, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();