Test sparsevec vacuum recall

Co-authored-by: Heikki Linnakangas <heikki.linnakangas@iki.fi>

.github/workflows/build.yml

@@ -1,14 +1,31 @@
 name: build
 on: [push, pull_request]
 jobs:
-  valgrind:
+  ubuntu:
+    runs-on: ${{ matrix.os }}
     if: ${{ !startsWith(github.ref_name, 'mac') && !startsWith(github.ref_name, 'windows') }}
-    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - postgres: 14
+            os: ubuntu-22.04
     steps:
       - uses: actions/checkout@v4
-      - uses: ankane/setup-postgres-valgrind@v1
+      - uses: ankane/setup-postgres@v1
         with:
-          postgres-version: 16
-      - run: make OPTFLAGS=""
-      - run: sudo --preserve-env=PG_CONFIG make install
+          postgres-version: ${{ matrix.postgres }}
+          dev-files: true
+      - run: make
+        env:
+          PG_CFLAGS: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
+      - run: |
+          export PG_CONFIG=`which pg_config`
+          sudo --preserve-env=PG_CONFIG make install
       - run: make installcheck
+      - if: ${{ failure() }}
+        run: cat regression.diffs
+      - run: |
+          sudo apt-get update
+          sudo apt-get install libipc-run-perl
+      - run: for run in {1..100}; do make prove_installcheck PROVE_TESTS=test/t/031_hnsw_sparsevec_vacuum_recall.pl || break; done

CHANGELOG.md

@@ -2,11 +2,15 @@
 
 - Added `halfvec` type
 - Added `sparsevec` type
-- Added support for `bit` vectors to HNSW
+- Added support for indexing `bit` type
+- Added support for indexing L1 distance with HNSW
+- 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
 
 ## 0.6.2 (2024-03-18)

Makefile

@@ -3,7 +3,7 @@ EXTVERSION = 0.6.2
 
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
-OBJS = src/bitvector.o src/halfvec.o src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/sparsevec.o src/vector.o
+OBJS = src/bitutils.o src/bitvec.o src/halfutils.o src/halfvec.o src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/sparsevec.o src/vector.o
 HEADERS = src/halfvec.h src/sparsevec.h src/vector.h
 
 TESTS = $(wildcard test/sql/*.sql)

Makefile.win

@@ -1,10 +1,10 @@
 EXTENSION = vector
 EXTVERSION = 0.6.2
 
-OBJS = src\bitvector.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
+OBJS = src\bitutils.obj src\bitvec.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

@@ -81,7 +81,7 @@ Get the nearest neighbors by L2 distance
 SELECT * FROM items ORDER BY embedding <-> '[3,1,2]' LIMIT 5;
 ```
 
-Also supports inner product (`<#>`) and cosine distance (`<=>`)
+Also supports inner product (`<#>`), cosine distance (`<=>`), and L1 distance (`<+>`, unreleased)
 
 Note: `<#>` returns the negative inner product since Postgres only supports `ASC` order index scans on operators
 
@@ -138,6 +138,13 @@ 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
+- `<+>` - L1 distance (unreleased)
+
 Get the nearest neighbors to a row
 
 ```sql
@@ -221,6 +228,12 @@ Cosine distance
 CREATE INDEX ON items USING hnsw (embedding vector_cosine_ops);
 ```
 
+L1 distance - unreleased
+
+```sql
+CREATE INDEX ON items USING hnsw (embedding vector_l1_ops);
+```
+
 Hamming distance - unreleased
 
 ```sql
@@ -343,9 +356,17 @@ Cosine distance
 CREATE INDEX ON items USING ivfflat (embedding vector_cosine_ops) WITH (lists = 100);
 ```
 
+Hamming distance - unreleased
+
+```sql
+CREATE INDEX ON items USING ivfflat (embedding bit_hamming_ops) WITH (lists = 100);
+```
+
 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
 
@@ -475,20 +496,20 @@ 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;
 ```
 
@@ -508,7 +529,7 @@ 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
 
@@ -527,6 +548,30 @@ SELECT id, content FROM items, plainto_tsquery('hello search') query
 
 You can use [Reciprocal Rank Fusion](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search_rrf.py) or a [cross-encoder](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search.py) to combine results.
 
+## Indexing Subvectors
+
+*Unreleased*
+
+Use expression indexing to index subvectors
+
+```sql
+CREATE INDEX ON items USING hnsw ((subvector(embedding, 1, 3)::vector(3)) vector_cosine_ops);
+```
+
+Get the nearest neighbors by cosine distance
+
+```sql
+SELECT * FROM items ORDER BY subvector(embedding, 1, 3)::vector(3) <=> subvector('[1,2,3,4,5]'::vector, 1, 3) LIMIT 5;
+```
+
+Re-rank by the full vectors for better recall
+
+```sql
+SELECT * FROM (
+    SELECT * FROM items ORDER BY subvector(embedding, 1, 3)::vector(3) <=> subvector('[1,2,3,4,5]'::vector, 1, 3) LIMIT 20
+) ORDER BY embedding <=> '[1,2,3,4,5]' LIMIT 5;
+```
+
 ## Performance
 
 ### Tuning
@@ -819,19 +864,22 @@ Operator | Description | Added
 \+ | element-wise addition |
 \- | element-wise subtraction |
 \* | element-wise multiplication | 0.5.0
+\|\| | concatenate | unreleased
 <-> | Euclidean distance |
 <#> | negative inner product |
 <=> | cosine distance |
+<+> | taxicab distance | unreleased
 
 ### Vector Functions
 
 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 |
@@ -851,20 +899,35 @@ 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
+<+> | taxicab distance | unreleased
 
 ### Halfvec Functions
 
 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
 
@@ -895,6 +958,7 @@ Operator | Description | Added
 <-> | Euclidean distance | unreleased
 <#> | negative inner product | unreleased
 <=> | cosine distance | unreleased
+<+> | taxicab distance | unreleased
 
 ### Sparsevec Functions
 
@@ -902,8 +966,10 @@ 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
 
@@ -1030,7 +1096,7 @@ 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

@@ -1,18 +1,44 @@
 -- 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 = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR || (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
+);
+
+CREATE OPERATOR CLASS vector_l1_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <+> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(vector, vector);
+
 CREATE FUNCTION hamming_distance(bit, bit) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION jaccard_distance(bit, bit) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION bit_ivfflat_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION bit_hnsw_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE OPERATOR <~> (
 	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = hamming_distance,
 	COMMUTATOR = '<~>'
@@ -23,15 +49,24 @@ 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),
+	FUNCTION 6 bit_ivfflat_support(internal);
+
 CREATE OPERATOR CLASS bit_hamming_ops
 	FOR TYPE bit USING hnsw AS
 	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
-	FUNCTION 1 hamming_distance(bit, bit);
+	FUNCTION 1 hamming_distance(bit, bit),
+	FUNCTION 4 bit_hnsw_support(internal);
 
 CREATE OPERATOR CLASS bit_jaccard_ops
 	FOR TYPE bit USING hnsw AS
 	OPERATOR 1 <%> (bit, bit) FOR ORDER BY float_ops,
-	FUNCTION 1 jaccard_distance(bit, bit);
+	FUNCTION 1 jaccard_distance(bit, bit),
+	FUNCTION 4 bit_hnsw_support(internal);
 
 CREATE TYPE halfvec;
 
@@ -71,24 +106,100 @@ 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
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION vector_dims(halfvec) RETURNS integer
+	AS 'MODULE_PATHNAME', 'halfvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION quantize_binary(halfvec) RETURNS bit
-	AS 'MODULE_PATHNAME', 'halfvec_quantize_binary' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION l2_norm(halfvec) RETURNS float8
+	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;
 
 CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+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 FUNCTION halfvec_ivfflat_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_hnsw_support(internal) RETURNS internal
+	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;
 
@@ -107,8 +218,14 @@ 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;
@@ -137,33 +254,125 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR <+> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = l1_distance,
+	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,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec),
+	FUNCTION 3 l2_distance(halfvec, halfvec),
+	FUNCTION 6 halfvec_ivfflat_support(internal);
+
+CREATE OPERATOR CLASS halfvec_ip_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 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 l2_norm(halfvec),
+	FUNCTION 5 l2_normalize(halfvec),
+	FUNCTION 6 halfvec_ivfflat_support(internal);
+
+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 l2_norm(halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 l2_norm(halfvec),
+	FUNCTION 5 l2_normalize(halfvec),
+	FUNCTION 6 halfvec_ivfflat_support(internal);
+
 CREATE OPERATOR CLASS halfvec_l2_ops
 	FOR TYPE halfvec USING hnsw AS
 	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
-	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec);
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_hnsw_support(internal);
 
 CREATE OPERATOR CLASS halfvec_ip_ops
 	FOR TYPE halfvec USING hnsw AS
 	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
-	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec);
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 4 halfvec_hnsw_support(internal);
 
 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),
+	FUNCTION 3 l2_normalize(halfvec),
+	FUNCTION 4 halfvec_hnsw_support(internal);
 
-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 OPERATOR CLASS halfvec_l1_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <+> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_hnsw_support(internal);
 
 CREATE TYPE sparsevec;
 
@@ -200,7 +409,34 @@ 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
@@ -218,15 +454,30 @@ CREATE FUNCTION vector_to_sparsevec(vector, integer, boolean) RETURNS sparsevec
 CREATE FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION halfvec_to_sparsevec(halfvec, integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_to_halfvec(sparsevec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_hnsw_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 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;
 
+CREATE CAST (sparsevec AS halfvec)
+	WITH FUNCTION sparsevec_to_halfvec(sparsevec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (halfvec AS sparsevec)
+	WITH FUNCTION halfvec_to_sparsevec(halfvec, integer, boolean) AS IMPLICIT;
+
 CREATE OPERATOR <-> (
 	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = l2_distance,
 	COMMUTATOR = '<->'
@@ -242,18 +493,78 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR <+> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = l1_distance,
+	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,
-	FUNCTION 1 sparsevec_l2_squared_distance(sparsevec, sparsevec);
+	FUNCTION 1 sparsevec_l2_squared_distance(sparsevec, sparsevec),
+	FUNCTION 4 sparsevec_hnsw_support(internal);
 
 CREATE OPERATOR CLASS sparsevec_ip_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 1 sparsevec_negative_inner_product(sparsevec, sparsevec),
+	FUNCTION 4 sparsevec_hnsw_support(internal);
 
 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),
+	FUNCTION 3 l2_normalize(sparsevec),
+	FUNCTION 4 sparsevec_hnsw_support(internal);
+
+CREATE OPERATOR CLASS sparsevec_l1_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <+> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(sparsevec, sparsevec),
+	FUNCTION 4 sparsevec_hnsw_support(internal);

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;
 
@@ -180,6 +186,11 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR <+> (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
 CREATE OPERATOR + (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_add,
 	COMMUTATOR = +
@@ -194,6 +205,10 @@ CREATE OPERATOR * (
 	COMMUTATOR = *
 );
 
+CREATE OPERATOR || (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
+);
+
 CREATE OPERATOR < (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_lt,
 	COMMUTATOR = > , NEGATOR = >= ,
@@ -294,6 +309,11 @@ CREATE OPERATOR CLASS vector_cosine_ops
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
 	FUNCTION 2 vector_norm(vector);
 
+CREATE OPERATOR CLASS vector_l1_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <+> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(vector, vector);
+
 -- bit functions
 
 CREATE FUNCTION hamming_distance(bit, bit) RETURNS float8
@@ -302,6 +322,16 @@ 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 private functions
+
+CREATE FUNCTION bit_ivfflat_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION bit_hnsw_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- bit operators
+
 CREATE OPERATOR <~> (
 	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = hamming_distance,
 	COMMUTATOR = '<~>'
@@ -312,15 +342,26 @@ 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),
+	FUNCTION 6 bit_ivfflat_support(internal);
+
 CREATE OPERATOR CLASS bit_hamming_ops
 	FOR TYPE bit USING hnsw AS
 	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
-	FUNCTION 1 hamming_distance(bit, bit);
+	FUNCTION 1 hamming_distance(bit, bit),
+	FUNCTION 4 bit_hnsw_support(internal);
 
 CREATE OPERATOR CLASS bit_jaccard_ops
 	FOR TYPE bit USING hnsw AS
 	OPERATOR 1 <%> (bit, bit) FOR ORDER BY float_ops,
-	FUNCTION 1 jaccard_distance(bit, bit);
+	FUNCTION 1 jaccard_distance(bit, bit),
+	FUNCTION 4 bit_hnsw_support(internal);
 
 -- halfvec type
 
@@ -364,28 +405,106 @@ 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
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION vector_dims(halfvec) RETURNS integer
+	AS 'MODULE_PATHNAME', 'halfvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION quantize_binary(halfvec) RETURNS bit
-	AS 'MODULE_PATHNAME', 'halfvec_quantize_binary' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION l2_norm(halfvec) RETURNS float8
+	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;
 
 CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+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 FUNCTION halfvec_ivfflat_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_hnsw_support(internal) RETURNS internal
+	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;
 
@@ -406,8 +525,14 @@ 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;
@@ -438,37 +563,127 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR <+> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = l1_distance,
+	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,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec),
+	FUNCTION 3 l2_distance(halfvec, halfvec),
+	FUNCTION 6 halfvec_ivfflat_support(internal);
+
+CREATE OPERATOR CLASS halfvec_ip_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 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 l2_norm(halfvec),
+	FUNCTION 5 l2_normalize(halfvec),
+	FUNCTION 6 halfvec_ivfflat_support(internal);
+
+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 l2_norm(halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 l2_norm(halfvec),
+	FUNCTION 5 l2_normalize(halfvec),
+	FUNCTION 6 halfvec_ivfflat_support(internal);
+
 CREATE OPERATOR CLASS halfvec_l2_ops
 	FOR TYPE halfvec USING hnsw AS
 	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
-	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec);
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_hnsw_support(internal);
 
 CREATE OPERATOR CLASS halfvec_ip_ops
 	FOR TYPE halfvec USING hnsw AS
 	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
-	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec);
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 4 halfvec_hnsw_support(internal);
 
 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),
+	FUNCTION 3 l2_normalize(halfvec),
+	FUNCTION 4 halfvec_hnsw_support(internal);
 
--- 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;
+CREATE OPERATOR CLASS halfvec_l1_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <+> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_hnsw_support(internal);
 
 --- sparsevec type
 
@@ -509,11 +724,38 @@ 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
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+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;
 
 -- 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;
 
@@ -531,17 +773,32 @@ CREATE FUNCTION vector_to_sparsevec(vector, integer, boolean) RETURNS sparsevec
 CREATE FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION halfvec_to_sparsevec(halfvec, integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_to_halfvec(sparsevec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_hnsw_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 -- sparsevec casts
 
 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;
 
+CREATE CAST (sparsevec AS halfvec)
+	WITH FUNCTION sparsevec_to_halfvec(sparsevec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (halfvec AS sparsevec)
+	WITH FUNCTION halfvec_to_sparsevec(halfvec, integer, boolean) AS IMPLICIT;
+
 -- sparsevec operators
 
 CREATE OPERATOR <-> (
@@ -559,20 +816,80 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR <+> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = l1_distance,
+	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,
-	FUNCTION 1 sparsevec_l2_squared_distance(sparsevec, sparsevec);
+	FUNCTION 1 sparsevec_l2_squared_distance(sparsevec, sparsevec),
+	FUNCTION 4 sparsevec_hnsw_support(internal);
 
 CREATE OPERATOR CLASS sparsevec_ip_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 1 sparsevec_negative_inner_product(sparsevec, sparsevec),
+	FUNCTION 4 sparsevec_hnsw_support(internal);
 
 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),
+	FUNCTION 3 l2_normalize(sparsevec),
+	FUNCTION 4 sparsevec_hnsw_support(internal);
+
+CREATE OPERATOR CLASS sparsevec_l1_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <+> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(sparsevec, sparsevec),
+	FUNCTION 4 sparsevec_hnsw_support(internal);

src/bitutils.c

@@ -0,0 +1,217 @@
+#include "postgres.h"
+
+#include "bitutils.h"
+#include "port/pg_bitutils.h"
+
+#ifdef BIT_DISPATCH
+#include <immintrin.h>
+
+#if defined(HAVE__GET_CPUID)
+#include <cpuid.h>
+#else
+#include <intrin.h>
+#endif
+
+#ifdef _MSC_VER
+#define TARGET_AVX512_POPCOUNT
+#else
+#define TARGET_AVX512_POPCOUNT __attribute__((target("avx512f,avx512vpopcntdq")))
+#endif
+#endif
+
+/* Disable for LLVM due to crash with bitcode generation */
+#if defined(USE_TARGET_CLONES) && !defined(__POPCNT__) && !defined(__llvm__)
+#define BIT_TARGET_CLONES __attribute__((target_clones("default", "popcnt")))
+#else
+#define BIT_TARGET_CLONES
+#endif
+
+/* Use built-ins when possible for inlining */
+#if defined(HAVE__BUILTIN_POPCOUNT) && defined(HAVE_LONG_INT_64)
+#define popcount64(x) __builtin_popcountl(x)
+#elif defined(HAVE__BUILTIN_POPCOUNT) && defined(HAVE_LONG_LONG_INT_64)
+#define popcount64(x) __builtin_popcountll(x)
+#elif !defined(_MSC_VER)
+/* Fails to resolve with MSVC */
+#define popcount64(x) pg_popcount64(x)
+#endif
+
+uint64		(*BitHammingDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance);
+double		(*BitJaccardDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb);
+
+BIT_TARGET_CLONES static uint64
+BitHammingDistanceDefault(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance)
+{
+#ifdef popcount64
+	for (; bytes >= sizeof(uint64); bytes -= sizeof(uint64))
+	{
+		uint64		axs;
+		uint64		bxs;
+
+		/* Ensure aligned */
+		memcpy(&axs, ax, sizeof(uint64));
+		memcpy(&bxs, bx, sizeof(uint64));
+
+		distance += popcount64(axs ^ bxs);
+
+		ax += sizeof(uint64);
+		bx += sizeof(uint64);
+	}
+#endif
+
+	for (uint32 i = 0; i < bytes; i++)
+		distance += pg_number_of_ones[ax[i] ^ bx[i]];
+
+	return distance;
+}
+
+#ifdef BIT_DISPATCH
+TARGET_AVX512_POPCOUNT static uint64
+BitHammingDistanceAvx512Popcount(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance)
+{
+	__m512i		dist = _mm512_setzero_si512();
+
+	for (; bytes >= sizeof(__m512i); bytes -= sizeof(__m512i))
+	{
+		__m512i		axs = _mm512_loadu_si512((const __m512i *) ax);
+		__m512i		bxs = _mm512_loadu_si512((const __m512i *) bx);
+
+		dist = _mm512_add_epi64(dist, _mm512_popcnt_epi64(_mm512_xor_si512(axs, bxs)));
+
+		ax += sizeof(__m512i);
+		bx += sizeof(__m512i);
+	}
+
+	distance += _mm512_reduce_add_epi64(dist);
+
+	return BitHammingDistanceDefault(bytes, ax, bx, distance);
+}
+#endif
+
+BIT_TARGET_CLONES static double
+BitJaccardDistanceDefault(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb)
+{
+#ifdef popcount64
+	for (; bytes >= sizeof(uint64); bytes -= sizeof(uint64))
+	{
+		uint64		axs;
+		uint64		bxs;
+
+		/* Ensure aligned */
+		memcpy(&axs, ax, sizeof(uint64));
+		memcpy(&bxs, bx, sizeof(uint64));
+
+		ab += popcount64(axs & bxs);
+		aa += popcount64(axs);
+		bb += popcount64(bxs);
+
+		ax += sizeof(uint64);
+		bx += sizeof(uint64);
+	}
+#endif
+
+	for (uint32 i = 0; i < bytes; i++)
+	{
+		ab += pg_number_of_ones[ax[i] & bx[i]];
+		aa += pg_number_of_ones[ax[i]];
+		bb += pg_number_of_ones[bx[i]];
+	}
+
+	if (ab == 0)
+		return 1;
+	else
+		return 1 - (ab / ((double) (aa + bb - ab)));
+}
+
+#ifdef BIT_DISPATCH
+TARGET_AVX512_POPCOUNT static double
+BitJaccardDistanceAvx512Popcount(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb)
+{
+	__m512i		abx = _mm512_setzero_si512();
+	__m512i		aax = _mm512_setzero_si512();
+	__m512i		bbx = _mm512_setzero_si512();
+
+	for (; bytes >= sizeof(__m512i); bytes -= sizeof(__m512i))
+	{
+		__m512i		axs = _mm512_loadu_si512((const __m512i *) ax);
+		__m512i		bxs = _mm512_loadu_si512((const __m512i *) bx);
+
+		abx = _mm512_add_epi64(abx, _mm512_popcnt_epi64(_mm512_and_si512(axs, bxs)));
+		aax = _mm512_add_epi64(aax, _mm512_popcnt_epi64(axs));
+		bbx = _mm512_add_epi64(bbx, _mm512_popcnt_epi64(bxs));
+
+		ax += sizeof(__m512i);
+		bx += sizeof(__m512i);
+	}
+
+	ab += _mm512_reduce_add_epi64(abx);
+	aa += _mm512_reduce_add_epi64(aax);
+	bb += _mm512_reduce_add_epi64(bbx);
+
+	return BitJaccardDistanceDefault(bytes, ax, bx, ab, aa, bb);
+}
+#endif
+
+#ifdef BIT_DISPATCH
+#define CPU_FEATURE_OSXSAVE         (1 << 27)	/* F1 ECX */
+#define CPU_FEATURE_AVX512F         (1 << 16)	/* F7,0 EBX */
+#define CPU_FEATURE_AVX512VPOPCNTDQ (1 << 14)	/* F7,0 ECX */
+
+#ifdef _MSC_VER
+#define TARGET_XSAVE
+#else
+#define TARGET_XSAVE __attribute__((target("xsave")))
+#endif
+
+TARGET_XSAVE static bool
+SupportsAvx512Popcount()
+{
+	unsigned int exx[4] = {0, 0, 0, 0};
+
+#if defined(HAVE__GET_CPUID)
+	__get_cpuid(1, &exx[0], &exx[1], &exx[2], &exx[3]);
+#else
+	__cpuid(exx, 1);
+#endif
+
+	/* Check OS supports XSAVE */
+	if ((exx[2] & CPU_FEATURE_OSXSAVE) != CPU_FEATURE_OSXSAVE)
+		return false;
+
+	/* Check XMM, YMM, and ZMM registers are enabled */
+	if ((_xgetbv(0) & 0xe6) != 0xe6)
+		return false;
+
+#if defined(HAVE__GET_CPUID)
+	__get_cpuid_count(7, 0, &exx[0], &exx[1], &exx[2], &exx[3]);
+#else
+	__cpuidex(exx, 7, 0);
+#endif
+
+	/* Check AVX512F */
+	if ((exx[1] & CPU_FEATURE_AVX512F) != CPU_FEATURE_AVX512F)
+		return false;
+
+	/* Check AVX512VPOPCNTDQ */
+	return (exx[2] & CPU_FEATURE_AVX512VPOPCNTDQ) == CPU_FEATURE_AVX512VPOPCNTDQ;
+}
+#endif
+
+void
+BitvecInit(void)
+{
+	/*
+	 * Could skip pointer when single function, but no difference in
+	 * performance
+	 */
+	BitHammingDistance = BitHammingDistanceDefault;
+	BitJaccardDistance = BitJaccardDistanceDefault;
+
+#ifdef BIT_DISPATCH
+	if (SupportsAvx512Popcount())
+	{
+		BitHammingDistance = BitHammingDistanceAvx512Popcount;
+		BitJaccardDistance = BitJaccardDistanceAvx512Popcount;
+	}
+#endif
+}

src/bitutils.h

@@ -0,0 +1,31 @@
+#ifndef BITUTILS_H
+#define BITUTILS_H
+
+/* We use two types of dispatching: intrinsics and target_clones */
+/* TODO Move to better place */
+#ifndef DISABLE_DISPATCH
+/* Only enable for more recent compilers to keep build process simple */
+#if defined(__x86_64__) && defined(__GNUC__) && __GNUC__ >= 8
+#define USE_DISPATCH
+#elif defined(__x86_64__) && defined(__clang_major__) && __clang_major__ >= 7
+#define USE_DISPATCH
+#elif defined(_M_AMD64) && defined(_MSC_VER) && _MSC_VER >= 1920
+#define USE_DISPATCH
+#endif
+#endif
+
+/* target_clones requires glibc */
+#if defined(USE_DISPATCH) && defined(__gnu_linux__)
+#define USE_TARGET_CLONES
+#endif
+
+#if defined(USE_DISPATCH)
+#define BIT_DISPATCH
+#endif
+
+extern uint64 (*BitHammingDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance);
+extern double (*BitJaccardDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb);
+
+void		BitvecInit(void);
+
+#endif

src/bitvec.c

@@ -1,7 +1,7 @@
 #include "postgres.h"
 
-#include "bitvector.h"
-#include "port/pg_bitutils.h"
+#include "bitutils.h"
+#include "bitvec.h"
 #include "utils/varbit.h"
 
 #if PG_VERSION_NUM >= 160000
@@ -46,17 +46,10 @@ hamming_distance(PG_FUNCTION_ARGS)
 {
 	VarBit	   *a = PG_GETARG_VARBIT_P(0);
 	VarBit	   *b = PG_GETARG_VARBIT_P(1);
-	unsigned char *ax = VARBITS(a);
-	unsigned char *bx = VARBITS(b);
-	uint64		distance = 0;
 
 	CheckDims(a, b);
 
-	/* TODO Improve performance */
-	for (uint32 i = 0; i < VARBITBYTES(a); i++)
-		distance += pg_number_of_ones[ax[i] ^ bx[i]];
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) BitHammingDistance(VARBITBYTES(a), VARBITS(a), VARBITS(b), 0));
 }
 
 /*
@@ -68,23 +61,8 @@ jaccard_distance(PG_FUNCTION_ARGS)
 {
 	VarBit	   *a = PG_GETARG_VARBIT_P(0);
 	VarBit	   *b = PG_GETARG_VARBIT_P(1);
-	unsigned char *ax = VARBITS(a);
-	unsigned char *bx = VARBITS(b);
-	uint64		ab = 0;
-	uint64		aa;
-	uint64		bb;
 
 	CheckDims(a, b);
 
-	/* TODO Improve performance */
-	for (uint32 i = 0; i < VARBITBYTES(a); i++)
-		ab += pg_number_of_ones[ax[i] & bx[i]];
-
-	if (ab == 0)
-		PG_RETURN_FLOAT8(1);
-
-	aa = pg_popcount((char *) ax, VARBITBYTES(a));
-	bb = pg_popcount((char *) bx, VARBITBYTES(b));
-
-	PG_RETURN_FLOAT8(1 - (ab / ((double) (aa + bb - ab))));
+	PG_RETURN_FLOAT8(BitJaccardDistance(VARBITBYTES(a), VARBITS(a), VARBITS(b), 0, 0, 0));
 }

src/halfutils.c

@@ -0,0 +1,298 @@
+#include "postgres.h"
+
+#include "halfutils.h"
+#include "halfvec.h"
+
+#ifdef HALFVEC_DISPATCH
+#include <immintrin.h>
+
+#if defined(HAVE__GET_CPUID)
+#include <cpuid.h>
+#else
+#include <intrin.h>
+#endif
+
+#ifdef _MSC_VER
+#define TARGET_F16C
+#else
+#define TARGET_F16C __attribute__((target("avx,f16c,fma")))
+#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);
+float		(*HalfvecL1Distance) (int dim, half * ax, half * bx);
+
+static float
+HalfvecL2SquaredDistanceDefault(int dim, half * ax, half * bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+
+#ifdef HALFVEC_DISPATCH
+TARGET_F16C static float
+HalfvecL2SquaredDistanceF16c(int dim, half * ax, half * bx)
+{
+	float		distance;
+	int			i;
+	float		s[8];
+	int			count = (dim / 8) * 8;
+	__m256		dist = _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);
+		__m256		diff = _mm256_sub_ps(axs, bxs);
+
+		dist = _mm256_fmadd_ps(diff, diff, dist);
+	}
+
+	_mm256_storeu_ps(s, dist);
+
+	distance = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	for (; i < dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+#endif
+
+static float
+HalfvecInnerProductDefault(int dim, half * ax, half * bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	return distance;
+}
+
+#ifdef HALFVEC_DISPATCH
+TARGET_F16C static float
+HalfvecInnerProductF16c(int dim, half * ax, half * bx)
+{
+	float		distance;
+	int			i;
+	float		s[8];
+	int			count = (dim / 8) * 8;
+	__m256		dist = _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);
+
+		dist = _mm256_fmadd_ps(axs, bxs, dist);
+	}
+
+	_mm256_storeu_ps(s, dist);
+
+	distance = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	for (; i < dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	return distance;
+}
+#endif
+
+static double
+HalfvecCosineSimilarityDefault(int dim, half * ax, half * bx)
+{
+	float		similarity = 0.0;
+	float		norma = 0.0;
+	float		normb = 0.0;
+
+	/* 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 static double
+HalfvecCosineSimilarityF16c(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
+
+static float
+HalfvecL1DistanceDefault(int dim, half * ax, half * bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += fabsf(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+
+	return distance;
+}
+
+#ifdef HALFVEC_DISPATCH
+/* Does not require FMA, but keep logic simple */
+TARGET_F16C static float
+HalfvecL1DistanceF16c(int dim, half * ax, half * bx)
+{
+	float		distance;
+	int			i;
+	float		s[8];
+	int			count = (dim / 8) * 8;
+	__m256		dist = _mm256_setzero_ps();
+	__m256		sign = _mm256_set1_ps(-0.0);
+
+	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);
+
+		dist = _mm256_add_ps(dist, _mm256_andnot_ps(sign, _mm256_sub_ps(axs, bxs)));
+	}
+
+	_mm256_storeu_ps(s, dist);
+
+	distance = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	for (; i < dim; i++)
+		distance += fabsf(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+
+	return distance;
+}
+#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};
+
+#if defined(HAVE__GET_CPUID)
+	__get_cpuid(1, &exx[0], &exx[1], &exx[2], &exx[3]);
+#else
+	__cpuid(exx, 1);
+#endif
+
+	/* Check OS supports XSAVE */
+	if ((exx[2] & CPU_FEATURE_OSXSAVE) != CPU_FEATURE_OSXSAVE)
+		return false;
+
+	/* Check XMM and YMM registers are enabled */
+	if ((_xgetbv(0) & 6) != 6)
+		return false;
+
+	/* Now check features */
+	return (exx[2] & feature) == feature;
+}
+#endif
+
+void
+HalfvecInit(void)
+{
+	/*
+	 * Could skip pointer when single function, but no difference in
+	 * performance
+	 */
+	HalfvecL2SquaredDistance = HalfvecL2SquaredDistanceDefault;
+	HalfvecInnerProduct = HalfvecInnerProductDefault;
+	HalfvecCosineSimilarity = HalfvecCosineSimilarityDefault;
+	HalfvecL1Distance = HalfvecL1DistanceDefault;
+
+#ifdef HALFVEC_DISPATCH
+	if (SupportsCpuFeature(CPU_FEATURE_AVX | CPU_FEATURE_F16C | CPU_FEATURE_FMA))
+	{
+		HalfvecL2SquaredDistance = HalfvecL2SquaredDistanceF16c;
+		HalfvecInnerProduct = HalfvecInnerProductF16c;
+		HalfvecCosineSimilarity = HalfvecCosineSimilarityF16c;
+		/* Does not require FMA, but keep logic simple */
+		HalfvecL1Distance = HalfvecL1DistanceF16c;
+	}
+#endif
+}

src/halfutils.h

@@ -0,0 +1,269 @@
+#ifndef HALFUTILS_H
+#define HALFUTILS_H
+
+#include <math.h>
+
+#include "common/shortest_dec.h"
+#include "halfvec.h"
+
+#ifdef F16C_SUPPORT
+#include <immintrin.h>
+#endif
+
+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);
+extern float (*HalfvecL1Distance) (int dim, half * ax, half * bx);
+
+void		HalfvecInit(void);
+
+/*
+ * Check if half is NaN
+ */
+static inline bool
+HalfIsNan(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isnan(num);
+#else
+	return (num & 0x7C00) == 0x7C00 && (num & 0x7FFF) != 0x7C00;
+#endif
+}
+
+/*
+ * Check if half is infinite
+ */
+static inline bool
+HalfIsInf(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isinf(num);
+#else
+	return (num & 0x7FFF) == 0x7C00;
+#endif
+}
+
+/*
+ * Check if half is zero
+ */
+static inline bool
+HalfIsZero(half num)
+{
+#ifdef FLT16_SUPPORT
+	return num == 0;
+#else
+	return (num & 0x7FFF) == 0x0000;
+#endif
+}
+
+/*
+ * Convert a half to a float4
+ */
+static inline float
+HalfToFloat4(half num)
+{
+#if defined(F16C_SUPPORT)
+	return _cvtsh_ss(num);
+#elif defined(FLT16_SUPPORT)
+	return (float) num;
+#else
+	/* TODO Improve performance */
+
+	/* Assumes same endianness for floats and integers */
+	union
+	{
+		float		f;
+		uint32		i;
+	}			swapfloat;
+
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swaphalf;
+
+	uint16		bin;
+	uint32		exponent;
+	uint32		mantissa;
+	uint32		result;
+
+	swaphalf.h = num;
+	bin = swaphalf.i;
+	exponent = (bin & 0x7C00) >> 10;
+	mantissa = bin & 0x03FF;
+
+	/* Sign */
+	result = (bin & 0x8000) << 16;
+
+	if (unlikely(exponent == 31))
+	{
+		if (mantissa == 0)
+		{
+			/* Infinite */
+			result |= 0x7F800000;
+		}
+		else
+		{
+			/* NaN */
+			result |= 0x7FC00000;
+		}
+	}
+	else if (unlikely(exponent == 0))
+	{
+		/* Subnormal */
+		if (mantissa != 0)
+		{
+			exponent = -14;
+
+			for (int i = 0; i < 10; i++)
+			{
+				mantissa <<= 1;
+				exponent -= 1;
+
+				if ((mantissa >> 10) % 2 == 1)
+				{
+					mantissa &= 0x03ff;
+					break;
+				}
+			}
+
+			result |= (exponent + 127) << 23;
+		}
+	}
+	else
+	{
+		/* Normal */
+		result |= (exponent - 15 + 127) << 23;
+	}
+
+	result |= mantissa << 13;
+
+	swapfloat.i = result;
+	return swapfloat.f;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+static inline half
+Float4ToHalfUnchecked(float num)
+{
+#if defined(F16C_SUPPORT)
+	return _cvtss_sh(num, 0);
+#elif defined(FLT16_SUPPORT)
+	return (_Float16) num;
+#else
+	/* TODO Improve performance */
+
+	/* Assumes same endianness for floats and integers */
+	union
+	{
+		float		f;
+		uint32		i;
+	}			swapfloat;
+
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swaphalf;
+
+	uint32		bin;
+	int			exponent;
+	int			mantissa;
+	uint16		result;
+
+	swapfloat.f = num;
+	bin = swapfloat.i;
+	exponent = (bin & 0x7F800000) >> 23;
+	mantissa = bin & 0x007FFFFF;
+
+	/* Sign */
+	result = (bin & 0x80000000) >> 16;
+
+	if (isinf(num))
+	{
+		/* Infinite */
+		result |= 0x7C00;
+	}
+	else if (isnan(num))
+	{
+		/* NaN */
+		result |= 0x7E00;
+		result |= mantissa >> 13;
+	}
+	else if (exponent > 98)
+	{
+		int			m;
+		int			gr;
+		int			s;
+
+		exponent -= 127;
+		s = mantissa & 0x00000FFF;
+
+		/* Subnormal */
+		if (exponent < -14)
+		{
+			int			diff = -exponent - 14;
+
+			mantissa >>= diff;
+			mantissa += 1 << (23 - diff);
+			s |= mantissa & 0x00000FFF;
+		}
+
+		m = mantissa >> 13;
+
+		/* Round */
+		gr = (mantissa >> 12) % 4;
+		if (gr == 3 || (gr == 1 && s != 0))
+			m += 1;
+
+		if (m == 1024)
+		{
+			m = 0;
+			exponent += 1;
+		}
+
+		if (exponent > 15)
+		{
+			/* Infinite */
+			result |= 0x7C00;
+		}
+		else
+		{
+			if (exponent >= -14)
+				result |= (exponent + 15) << 10;
+
+			result |= m;
+		}
+	}
+
+	swaphalf.i = result;
+	return swaphalf.h;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+static inline half
+Float4ToHalf(float num)
+{
+	half		result = Float4ToHalfUnchecked(num);
+
+	if (unlikely(HalfIsInf(result)) && !isinf(num))
+	{
+		char	   *buf = palloc(FLOAT_SHORTEST_DECIMAL_LEN);
+
+		float_to_shortest_decimal_buf(num, buf);
+
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("\"%s\" is out of range for type halfvec", buf)));
+	}
+
+	return result;
+}
+
+#endif

src/halfvec.h

@@ -5,11 +5,18 @@
 
 #include <float.h>
 
+#include "bitutils.h"
+#include "fmgr.h"
 #include "vector.h"
 
+#if defined(USE_DISPATCH)
+#define HALFVEC_DISPATCH
+#endif
+
+/* F16C has better performance than _Float16 (on x86-64) */
 #if defined(__F16C__)
 #define F16C_SUPPORT
-#elif defined(__FLT16_MAX__)
+#elif defined(__FLT16_MAX__) && !defined(HALFVEC_DISPATCH)
 #define FLT16_SUPPORT
 #endif
 
@@ -17,7 +24,6 @@
 #define half _Float16
 #define HALF_MAX FLT16_MAX
 #else
-/* TODO #pragma message("")? */
 #define half uint16
 #define HALF_MAX 65504
 #endif
@@ -38,8 +44,6 @@ typedef struct HalfVector
 }			HalfVector;
 
 HalfVector *InitHalfVector(int dim);
-float		HalfToFloat4(half num);
-half		Float4ToHalf(float num);
-half		Float4ToHalfUnchecked(float num);
+int			halfvec_cmp_internal(HalfVector * a, HalfVector * b);
 
 #endif

src/hnsw.c

@@ -194,7 +194,7 @@ hnswhandler(PG_FUNCTION_ARGS)
 	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);
 
 	amroutine->amstrategies = 0;
-	amroutine->amsupport = 2;
+	amroutine->amsupport = 4;
 #if PG_VERSION_NUM >= 130000
 	amroutine->amoptsprocnum = 0;
 #endif

src/hnsw.h

@@ -22,6 +22,8 @@
 /* Support functions */
 #define HNSW_DISTANCE_PROC 1
 #define HNSW_NORM_PROC 2
+#define HNSW_NORMALIZE_PROC 3
+#define HNSW_TYPE_SUPPORT_PROC 4
 
 #define HNSW_VERSION	1
 #define HNSW_MAGIC_NUMBER 0xA953A953
@@ -61,7 +63,8 @@ typedef enum HnswType
 	HNSW_TYPE_VECTOR,
 	HNSW_TYPE_HALFVEC,
 	HNSW_TYPE_BIT,
-	HNSW_TYPE_SPARSEVEC
+	HNSW_TYPE_SPARSEVEC,
+	HNSW_TYPE_UNSUPPORTED
 }			HnswType;
 
 /* Build phases */
@@ -265,6 +268,7 @@ typedef struct HnswBuildState
 	/* Support functions */
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;
 
 	/* Variables */
@@ -341,6 +345,7 @@ typedef struct HnswScanOpaqueData
 	/* Support functions */
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;
 }			HnswScanOpaqueData;
 
@@ -377,7 +382,8 @@ 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(FmgrInfo *procinfo, Oid collation, Datum value);
+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(buildstate->normalizeprocinfo, buildstate->collation, value);
 	}
 
 	/* Get datum size */
@@ -723,6 +725,7 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	/* Get support functions */
 	buildstate->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
 	buildstate->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	buildstate->normalizeprocinfo = HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC);
 	buildstate->collation = index->rd_indcollation[0];
 
 	InitGraph(&buildstate->graphData, NULL, maintenance_work_mem * 1024L);

src/hnswinsert.c

@@ -614,20 +614,21 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	Datum		value;
 	FmgrInfo   *normprocinfo;
 	Oid			collation = index->rd_indcollation[0];
-	HnswType	type = HnswGetType(index);
 
 	/* Detoast once for all calls */
 	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
 
 	/* Check value */
-	HnswCheckValue(value, type);
+	HnswCheckValue(value, HnswGetType(index));
 
 	/* Normalize if needed */
 	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		if (!HnswNormValue(normprocinfo, collation, &value, type))
+		if (!HnswCheckNorm(normprocinfo, collation, value))
 			return;
+
+		value = HnswNormValue(HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC), collation, value);
 	}
 
 	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(so->normalizeprocinfo, so->collation, value);
 	}
 
 	return value;
@@ -87,6 +87,7 @@ hnswbeginscan(Relation index, int nkeys, int norderbys)
 	/* Set support functions */
 	so->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
 	so->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	so->normalizeprocinfo = HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC);
 	so->collation = index->rd_indcollation[0];
 
 	scan->opaque = so;

src/hnswutils.c

@@ -5,7 +5,7 @@
 #include "access/generic_xlog.h"
 #include "catalog/pg_type.h"
 #include "catalog/pg_type_d.h"
-#include "halfvec.h"
+#include "fmgr.h"
 #include "hnsw.h"
 #include "lib/pairingheap.h"
 #include "sparsevec.h"
@@ -13,8 +13,6 @@
 #include "utils/datum.h"
 #include "utils/memdebug.h"
 #include "utils/rel.h"
-#include "utils/syscache.h"
-#include "vector.h"
 
 #if PG_VERSION_NUM >= 130000
 #include "common/hashfn.h"
@@ -160,97 +158,40 @@ HnswOptionalProcInfo(Relation index, uint16 procnum)
 HnswType
 HnswGetType(Relation index)
 {
+	FmgrInfo   *procinfo = HnswOptionalProcInfo(index, HNSW_TYPE_SUPPORT_PROC);
 	Oid			typid = TupleDescAttr(index->rd_att, 0)->atttypid;
-	HeapTuple	tuple;
-	Form_pg_type type;
 	HnswType	result;
 
-	if (typid == BITOID)
-		return HNSW_TYPE_BIT;
+	if (procinfo == NULL)
+		return HNSW_TYPE_VECTOR;
 
-	tuple = SearchSysCache1(TYPEOID, ObjectIdGetDatum(typid));
-	if (!HeapTupleIsValid(tuple))
-		elog(ERROR, "cache lookup failed for type %u", typid);
+	result = (HnswType) DatumGetInt32(FunctionCall1(procinfo, ObjectIdGetDatum(typid)));
 
-	type = (Form_pg_type) GETSTRUCT(tuple);
-	if (strcmp(NameStr(type->typname), "vector") == 0)
-		result = HNSW_TYPE_VECTOR;
-	else if (strcmp(NameStr(type->typname), "halfvec") == 0)
-		result = HNSW_TYPE_HALFVEC;
-	else if (strcmp(NameStr(type->typname), "sparsevec") == 0)
-		result = HNSW_TYPE_SPARSEVEC;
-	else
-	{
-		ReleaseSysCache(tuple);
+	if (result == HNSW_TYPE_UNSUPPORTED)
 		elog(ERROR, "type not supported for hnsw index");
-	}
-
-	ReleaseSysCache(tuple);
 
 	return result;
 }
 
 /*
- * Divide by the norm
- *
- * Returns false if value should not be indexed
- *
- * The caller needs to free the pointer stored in value
- * if it's different than the original value
+ * Normalize value
+ */
+Datum
+HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum value)
+{
+	if (procinfo == NULL)
+		return DirectFunctionCall1(l2_normalize, value);
+
+	return FunctionCall1Coll(procinfo, collation, value);
+}
+
+/*
+ * 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));
-
-	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++)
-			{
-				/* TODO Fix */
-				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;
+	return DatumGetFloat8(FunctionCall1Coll(procinfo, collation, value)) > 0;
 }
 
 /*
@@ -1361,3 +1302,29 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 		ep = w;
 	}
 }
+
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_hnsw_support);
+Datum
+halfvec_hnsw_support(PG_FUNCTION_ARGS)
+{
+	PG_RETURN_INT32(HNSW_TYPE_HALFVEC);
+};
+
+PGDLLEXPORT PG_FUNCTION_INFO_V1(bit_hnsw_support);
+Datum
+bit_hnsw_support(PG_FUNCTION_ARGS)
+{
+	Oid			typid = PG_GETARG_OID(0);
+
+	if (typid == BITOID)
+		PG_RETURN_INT32(HNSW_TYPE_BIT);
+	else
+		PG_RETURN_INT32(HNSW_TYPE_UNSUPPORTED);
+};
+
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_hnsw_support);
+Datum
+sparsevec_hnsw_support(PG_FUNCTION_ARGS)
+{
+	PG_RETURN_INT32(HNSW_TYPE_SPARSEVEC);
+};

src/ivfbuild.c

@@ -6,16 +6,19 @@
 #include "access/tableam.h"
 #include "access/parallel.h"
 #include "access/xact.h"
+#include "bitvec.h"
 #include "catalog/index.h"
 #include "catalog/pg_operator_d.h"
 #include "catalog/pg_type_d.h"
 #include "commands/progress.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
 #include "optimizer/optimizer.h"
 #include "storage/bufmgr.h"
 #include "tcop/tcopprot.h"
 #include "utils/memutils.h"
+#include "vector.h"
 
 #if PG_VERSION_NUM >= 140000
 #include "utils/backend_progress.h"
@@ -57,13 +60,15 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 	 */
 	if (buildstate->kmeansnormprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->type))
+		if (!IvfflatCheckNorm(buildstate->kmeansnormprocinfo, buildstate->collation, value))
 			return;
+
+		value = IvfflatNormValue(buildstate->normalizeprocinfo, buildstate->collation, value);
 	}
 
 	if (samples->length < targsamples)
 	{
-		VectorArraySet(samples, samples->length, DatumGetVector(value));
+		VectorArraySet(samples, samples->length, DatumGetPointer(value));
 		samples->length++;
 	}
 	else
@@ -80,7 +85,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 #endif
 
 			Assert(k >= 0 && k < targsamples);
-			VectorArraySet(samples, k, DatumGetVector(value));
+			VectorArraySet(samples, k, DatumGetPointer(value));
 		}
 
 		buildstate->rowstoskip -= 1;
@@ -153,8 +158,10 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState
 	/* Normalize if needed */
 	if (buildstate->normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->type))
+		if (!IvfflatCheckNorm(buildstate->normprocinfo, buildstate->collation, value))
 			return;
+
+		value = IvfflatNormValue(buildstate->normalizeprocinfo, buildstate->collation, value);
 	}
 
 	/* Find the list that minimizes the distance */
@@ -318,7 +325,30 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 static int
 GetMaxDimensions(IvfflatType type)
 {
-	return IVFFLAT_MAX_DIM;
+	int			maxDimensions = IVFFLAT_MAX_DIM;
+
+	if (type == IVFFLAT_TYPE_HALFVEC)
+		maxDimensions *= 2;
+	else if (type == IVFFLAT_TYPE_BIT)
+		maxDimensions *= 32;
+
+	return maxDimensions;
+}
+
+/*
+ * Get item size
+ */
+static Size
+GetItemSize(IvfflatType type, int dimensions)
+{
+	if (type == IVFFLAT_TYPE_VECTOR)
+		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");
 }
 
 /*
@@ -353,6 +383,7 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
 	buildstate->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	buildstate->kmeansnormprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
+	buildstate->normalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC);
 	buildstate->collation = index->rd_indcollation[0];
 
 	/* Require more than one dimension for spherical k-means */
@@ -367,7 +398,7 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 
 	buildstate->slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsVirtual);
 
-	buildstate->centers = VectorArrayInit(buildstate->lists, buildstate->dimensions);
+	buildstate->centers = VectorArrayInit(buildstate->lists, buildstate->dimensions, GetItemSize(buildstate->type, buildstate->dimensions));
 	buildstate->listInfo = palloc(sizeof(ListInfo) * buildstate->lists);
 
 	buildstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
@@ -422,7 +453,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 
 	/* Sample rows */
 	/* TODO Ensure within maintenance_work_mem */
-	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions);
+	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions, buildstate->centers->itemsize);
 	if (buildstate->heap != NULL)
 	{
 		SampleRows(buildstate);
@@ -437,7 +468,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 	}
 
 	/* Calculate centers */
-	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers));
+	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers, buildstate->type));
 
 	/* Free samples before we allocate more memory */
 	VectorArrayFree(buildstate->samples);
@@ -482,7 +513,7 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	Size		listSize;
 	IvfflatList list;
 
-	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(dimensions));
+	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(centers->itemsize));
 	list = palloc0(listSize);
 
 	buf = IvfflatNewBuffer(index, forkNum);
@@ -495,7 +526,7 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 		/* Load list */
 		list->startPage = InvalidBlockNumber;
 		list->insertPage = InvalidBlockNumber;
-		memcpy(&list->center, VectorArrayGet(centers, i), VECTOR_SIZE(dimensions));
+		memcpy(&list->center, VectorArrayGet(centers, i), centers->itemsize);
 
 		/* Ensure free space */
 		if (PageGetFreeSpace(page) < listSize)
@@ -600,7 +631,7 @@ ParallelHeapScan(IvfflatBuildState * buildstate)
  * Perform a worker's portion of a parallel sort
  */
 static void
-IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, Sharedsort *sharedsort, Vector * ivfcenters, int sortmem, bool progress)
+IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, Sharedsort *sharedsort, char *ivfcenters, int sortmem, bool progress)
 {
 	SortCoordinate coordinate;
 	IvfflatBuildState buildstate;
@@ -624,7 +655,7 @@ IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, S
 	indexInfo = BuildIndexInfo(ivfspool->index);
 	indexInfo->ii_Concurrent = ivfshared->isconcurrent;
 	InitBuildState(&buildstate, ivfspool->heap, ivfspool->index, indexInfo);
-	memcpy(buildstate.centers->items, ivfcenters, VECTOR_SIZE(buildstate.centers->dim) * buildstate.centers->maxlen);
+	memcpy(buildstate.centers->items, ivfcenters, buildstate.centers->itemsize * buildstate.centers->maxlen);
 	buildstate.centers->length = buildstate.centers->maxlen;
 	ivfspool->sortstate = tuplesort_begin_heap(buildstate.tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, sortmem, coordinate, false);
 	buildstate.sortstate = ivfspool->sortstate;
@@ -672,7 +703,7 @@ IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc)
 	IvfflatSpool *ivfspool;
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 	Relation	heapRel;
 	Relation	indexRel;
 	LOCKMODE	heapLockmode;
@@ -786,7 +817,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	Size		estcenters;
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 	IvfflatLeader *ivfleader = (IvfflatLeader *) palloc0(sizeof(IvfflatLeader));
 	bool		leaderparticipates = true;
 	int			querylen;
@@ -813,7 +844,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	shm_toc_estimate_chunk(&pcxt->estimator, estivfshared);
 	estsort = tuplesort_estimate_shared(scantuplesortstates);
 	shm_toc_estimate_chunk(&pcxt->estimator, estsort);
-	estcenters = VECTOR_SIZE(buildstate->dimensions) * buildstate->lists;
+	estcenters = buildstate->centers->itemsize * buildstate->centers->maxlen;
 	shm_toc_estimate_chunk(&pcxt->estimator, estcenters);
 	shm_toc_estimate_keys(&pcxt->estimator, 3);
 
@@ -865,7 +896,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	tuplesort_initialize_shared(sharedsort, scantuplesortstates,
 								pcxt->seg);
 
-	ivfcenters = (Vector *) shm_toc_allocate(pcxt->toc, estcenters);
+	ivfcenters = shm_toc_allocate(pcxt->toc, estcenters);
 	memcpy(ivfcenters, buildstate->centers->items, estcenters);
 
 	shm_toc_insert(pcxt->toc, PARALLEL_KEY_IVFFLAT_SHARED, ivfshared);

src/ivfflat.c

@@ -188,7 +188,7 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);
 
 	amroutine->amstrategies = 0;
-	amroutine->amsupport = 4;
+	amroutine->amsupport = 6;
 #if PG_VERSION_NUM >= 130000
 	amroutine->amoptsprocnum = 0;
 #endif

src/ivfflat.h

@@ -28,6 +28,8 @@
 #define IVFFLAT_NORM_PROC 2
 #define IVFFLAT_KMEANS_DISTANCE_PROC 3
 #define IVFFLAT_KMEANS_NORM_PROC 4
+#define IVFFLAT_NORMALIZE_PROC 5
+#define IVFFLAT_TYPE_SUPPORT_PROC 6
 
 #define IVFFLAT_VERSION	1
 #define IVFFLAT_MAGIC_NUMBER 0x14FF1A7
@@ -45,7 +47,10 @@
 
 typedef enum IvfflatType
 {
-	IVFFLAT_TYPE_VECTOR
+	IVFFLAT_TYPE_VECTOR,
+	IVFFLAT_TYPE_HALFVEC,
+	IVFFLAT_TYPE_BIT,
+	IVFFLAT_TYPE_UNSUPPORTED
 }			IvfflatType;
 
 /* Build phases */
@@ -54,7 +59,7 @@ typedef enum IvfflatType
 #define PROGRESS_IVFFLAT_PHASE_ASSIGN	3
 #define PROGRESS_IVFFLAT_PHASE_LOAD		4
 
-#define IVFFLAT_LIST_SIZE(_dim)	(offsetof(IvfflatListData, center) + VECTOR_SIZE(_dim))
+#define IVFFLAT_LIST_SIZE(size)	(offsetof(IvfflatListData, center) + size)
 
 #define IvfflatPageGetOpaque(page)	((IvfflatPageOpaque) PageGetSpecialPointer(page))
 #define IvfflatPageGetMeta(page)	((IvfflatMetaPageData *) PageGetContents(page))
@@ -90,7 +95,8 @@ typedef struct VectorArrayData
 	int			length;
 	int			maxlen;
 	int			dim;
-	Vector	   *items;
+	Size		itemsize;
+	char	   *items;
 }			VectorArrayData;
 
 typedef VectorArrayData * VectorArray;
@@ -149,7 +155,7 @@ typedef struct IvfflatLeader
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
 	Snapshot	snapshot;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 }			IvfflatLeader;
 
 typedef struct IvfflatBuildState
@@ -172,6 +178,7 @@ typedef struct IvfflatBuildState
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
 	FmgrInfo   *kmeansnormprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;
 
 	/* Variables */
@@ -252,7 +259,9 @@ typedef struct IvfflatScanOpaqueData
 	/* Support functions */
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;
+	Datum		(*distfunc) (FmgrInfo *flinfo, Oid collation, Datum arg1, Datum arg2);
 
 	/* Lists */
 	pairingheap *listQueue;
@@ -261,19 +270,19 @@ typedef struct IvfflatScanOpaqueData
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;
 
-#define VECTOR_ARRAY_SIZE(_length, _dim) (sizeof(VectorArrayData) + (_length) * VECTOR_SIZE(_dim))
-#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * VECTOR_SIZE((_arr)->dim))
-#define VectorArrayGet(_arr, _offset) ((Vector *) VECTOR_ARRAY_OFFSET(_arr, _offset))
-#define VectorArraySet(_arr, _offset, _val) memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, VECTOR_SIZE((_arr)->dim))
+#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)
 
 /* Methods */
-VectorArray VectorArrayInit(int maxlen, int dimensions);
+VectorArray VectorArrayInit(int maxlen, int dimensions, Size itemsize);
 void		VectorArrayFree(VectorArray arr);
-void		PrintVectorArray(char *msg, VectorArray arr);
-void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
+void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatType type);
 FmgrInfo   *IvfflatOptionalProcInfo(Relation index, uint16 procnum);
 IvfflatType IvfflatGetType(Relation index);
-bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, IvfflatType type);
+Datum		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum value);
+bool		IvfflatCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value);
 int			IvfflatGetLists(Relation index);
 void		IvfflatGetMetaPageInfo(Relation index, int *lists, int *dimensions);
 void		IvfflatUpdateList(Relation index, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);

src/ivfinsert.c

@@ -85,8 +85,12 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(normprocinfo, index->rd_indcollation[0], &value, IvfflatGetType(index)))
+		Oid			collation = index->rd_indcollation[0];
+
+		if (!IvfflatCheckNorm(normprocinfo, collation, value))
 			return;
+
+		value = IvfflatNormValue(IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC), collation, value);
 	}
 
 	/* Find the insert page - sets the page and list info */

src/ivfkmeans.c

@@ -3,12 +3,15 @@
 #include <float.h>
 #include <math.h>
 
+#include "bitvec.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
-
-#ifdef IVFFLAT_MEMORY
+#include "utils/builtins.h"
+#include "utils/datum.h"
 #include "utils/memutils.h"
-#endif
+#include "vector.h"
 
 /*
  * Initialize with kmeans++
@@ -46,12 +49,12 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 
 		for (j = 0; j < numSamples; j++)
 		{
-			Vector	   *vec = VectorArrayGet(samples, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, j));
 			double		distance;
 
 			/* Only need to compute distance for new center */
 			/* TODO Use triangle inequality to reduce distance calculations */
-			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, i))));
+			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, i))));
 
 			/* Set lower bound */
 			lowerBound[j * numCenters + i] = distance;
@@ -86,19 +89,31 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 }
 
 /*
- * Apply norm to vector
+ * Norm centers
  */
-static inline void
-ApplyNorm(FmgrInfo *normprocinfo, Oid collation, Vector * vec)
+static void
+NormCenters(FmgrInfo *normalizeprocinfo, Oid collation, VectorArray centers)
 {
-	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(vec)));
+	MemoryContext normCtx = AllocSetContextCreate(CurrentMemoryContext,
+												  "Ivfflat norm temporary context",
+												  ALLOCSET_DEFAULT_SIZES);
+	MemoryContext oldCtx = MemoryContextSwitchTo(normCtx);
 
-	/* TODO Handle zero norm */
-	if (norm > 0)
+	for (int j = 0; j < centers->length; j++)
 	{
-		for (int i = 0; i < vec->dim; i++)
-			vec->x[i] /= norm;
+		Datum		center = PointerGetDatum(VectorArrayGet(centers, j));
+		Datum		newCenter = IvfflatNormValue(normalizeprocinfo, collation, center);
+		Size		size = VARSIZE_ANY(DatumGetPointer(newCenter));
+
+		if (size > centers->itemsize)
+			elog(ERROR, "safety check failed");
+
+		memcpy(DatumGetPointer(center), DatumGetPointer(newCenter), size);
+		MemoryContextReset(normCtx);
 	}
+
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(normCtx);
 }
 
 /*
@@ -110,27 +125,63 @@ CompareVectors(const void *a, const void *b)
 	return vector_cmp_internal((Vector *) a, (Vector *) b);
 }
 
+/*
+ * Compare half vectors
+ */
+static int
+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));
+}
+
+/*
+ * Sort vector array
+ */
+static void
+SortVectorArray(VectorArray arr, IvfflatType type)
+{
+	if (type == IVFFLAT_TYPE_VECTOR)
+		qsort(arr->items, arr->length, arr->itemsize, CompareVectors);
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+		qsort(arr->items, arr->length, arr->itemsize, CompareHalfVectors);
+	else if (type == IVFFLAT_TYPE_BIT)
+		qsort(arr->items, arr->length, arr->itemsize, CompareBitVectors);
+	else
+		elog(ERROR, "Unsupported type");
+}
+
 /*
  * Quick approach if we have little data
  */
 static void
-QuickCenters(Relation index, VectorArray samples, VectorArray centers)
+QuickCenters(Relation index, VectorArray samples, VectorArray centers, IvfflatType type)
 {
 	int			dimensions = centers->dim;
 	Oid			collation = index->rd_indcollation[0];
 	FmgrInfo   *normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
+	FmgrInfo   *normalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC);
 
 	/* Copy existing vectors while avoiding duplicates */
 	if (samples->length > 0)
 	{
-		qsort(samples->items, samples->length, VECTOR_SIZE(samples->dim), CompareVectors);
+		SortVectorArray(samples, type);
+
 		for (int i = 0; i < samples->length; i++)
 		{
-			Vector	   *vec = VectorArrayGet(samples, i);
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, i));
 
-			if (i == 0 || CompareVectors(vec, VectorArrayGet(samples, i - 1)) != 0)
+			if (i == 0 || !datumIsEqual(vec, PointerGetDatum(VectorArrayGet(samples, i - 1)), false, -1))
 			{
-				VectorArraySet(centers, centers->length, vec);
+				VectorArraySet(centers, centers->length, DatumGetPointer(vec));
 				centers->length++;
 			}
 		}
@@ -139,20 +190,47 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	/* Fill remaining with random data */
 	while (centers->length < centers->maxlen)
 	{
-		Vector	   *vec = VectorArrayGet(centers, centers->length);
+		Datum		center = PointerGetDatum(VectorArrayGet(centers, centers->length));
+
+		if (type == IVFFLAT_TYPE_VECTOR)
+		{
+			Vector	   *vec = DatumGetVector(center);
 
 			SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
 			vec->dim = dimensions;
 
 			for (int j = 0; j < dimensions; j++)
 				vec->x[j] = RandomDouble();
+		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *vec = DatumGetHalfVector(center);
 
-		/* Normalize if needed (only needed for random centers) */
-		if (normprocinfo != NULL)
-			ApplyNorm(normprocinfo, collation, vec);
+			SET_VARSIZE(vec, HALFVEC_SIZE(dimensions));
+			vec->dim = dimensions;
+
+			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");
 
 		centers->length++;
 	}
+
+	/* Fine if existing vectors are normalized twice */
+	if (normprocinfo != NULL)
+		NormCenters(normalizeprocinfo, collation, centers);
 }
 
 #ifdef IVFFLAT_MEMORY
@@ -160,18 +238,163 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
  * Show memory usage
  */
 static void
-ShowMemoryUsage(Size estimatedSize)
+ShowMemoryUsage(MemoryContext context, Size estimatedSize)
 {
 #if PG_VERSION_NUM >= 130000
 	elog(INFO, "total memory: %zu MB",
-		 MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
+		 MemoryContextMemAllocated(context, true) / (1024 * 1024));
 #else
-	MemoryContextStats(CurrentMemoryContext);
+	MemoryContextStats(context);
 #endif
 	elog(INFO, "estimated memory: %zu MB", estimatedSize / (1024 * 1024));
 }
 #endif
 
+/*
+ * Sum centers
+ */
+static void
+SumCenters(VectorArray samples, VectorArray aggCenters, int *closestCenters, IvfflatType type)
+{
+	int			dimensions = aggCenters->dim;
+	int			numSamples = samples->length;
+
+	if (type == IVFFLAT_TYPE_VECTOR)
+	{
+		for (int j = 0; j < numSamples; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, closestCenters[j]);
+			Vector	   *vec = (Vector *) VectorArrayGet(samples, j);
+
+			for (int k = 0; k < dimensions; k++)
+				aggCenter->x[k] += vec->x[k];
+		}
+	}
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		for (int j = 0; j < numSamples; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, closestCenters[j]);
+			HalfVector *vec = (HalfVector *) VectorArrayGet(samples, j);
+
+			for (int k = 0; k < dimensions; k++)
+				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");
+}
+
+/*
+ * Set new centers
+ */
+static void
+SetNewCenters(VectorArray aggCenters, VectorArray newCenters, IvfflatType type)
+{
+	int			dimensions = aggCenters->dim;
+	int			numCenters = aggCenters->maxlen;
+
+	if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		for (int j = 0; j < numCenters; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, j);
+			HalfVector *newCenter = (HalfVector *) VectorArrayGet(newCenters, j);
+
+			for (int k = 0; k < dimensions; k++)
+				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));
+		}
+	}
+}
+
+/*
+ * Compute new centers
+ */
+static void
+ComputeNewCenters(VectorArray samples, VectorArray aggCenters, VectorArray newCenters, int *centerCounts, int *closestCenters, FmgrInfo *normprocinfo, FmgrInfo *normalizeprocinfo, Oid collation, IvfflatType type)
+{
+	int			dimensions = aggCenters->dim;
+	int			numCenters = aggCenters->maxlen;
+	int			numSamples = samples->length;
+
+	/* Reset sum and count */
+	for (int j = 0; j < numCenters; j++)
+	{
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
+		for (int k = 0; k < dimensions; k++)
+			vec->x[k] = 0.0;
+
+		centerCounts[j] = 0;
+	}
+
+	/* Increment sum of closest center */
+	SumCenters(samples, aggCenters, closestCenters, type);
+
+	/* Increment count of closest center */
+	for (int j = 0; j < numSamples; j++)
+		centerCounts[closestCenters[j]] += 1;
+
+	/* Divide sum by count */
+	for (int j = 0; j < numCenters; j++)
+	{
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
+		if (centerCounts[j] > 0)
+		{
+			/* Double avoids overflow, but requires more memory */
+			/* TODO Update bounds */
+			for (int k = 0; k < dimensions; k++)
+			{
+				if (isinf(vec->x[k]))
+					vec->x[k] = vec->x[k] > 0 ? FLT_MAX : -FLT_MAX;
+			}
+
+			for (int k = 0; k < dimensions; k++)
+				vec->x[k] /= centerCounts[j];
+		}
+		else
+		{
+			/* TODO Handle empty centers properly */
+			for (int k = 0; k < dimensions; k++)
+				vec->x[k] = RandomDouble();
+		}
+	}
+
+	/* Set new centers if different from agg centers */
+	SetNewCenters(aggCenters, newCenters, type);
+
+	/* Normalize if needed */
+	if (normprocinfo != NULL)
+		NormCenters(normalizeprocinfo, collation, newCenters);
+}
+
 /*
  * Use Elkan for performance. This requires distance function to satisfy triangle inequality.
  *
@@ -181,19 +404,17 @@ ShowMemoryUsage(Size estimatedSize)
  * https://www.aaai.org/Papers/ICML/2003/ICML03-022.pdf
  */
 static void
-ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
+ElkanKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatType type)
 {
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;
-	Vector	   *vec;
-	Vector	   *newCenter;
-	int64		j;
-	int64		k;
 	int			dimensions = centers->dim;
 	int			numCenters = centers->maxlen;
 	int			numSamples = samples->length;
 	VectorArray newCenters;
+	VectorArray aggCenters;
 	int		   *centerCounts;
 	int		   *closestCenters;
 	float	   *lowerBound;
@@ -201,11 +422,14 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	float	   *s;
 	float	   *halfcdist;
 	float	   *newcdist;
+	MemoryContext kmeansCtx;
+	MemoryContext oldCtx;
 
 	/* Calculate allocation sizes */
-	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->dim);
-	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->dim);
-	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, dimensions);
+	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->itemsize);
+	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->itemsize);
+	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, centers->itemsize);
+	Size		aggCentersSize = type == IVFFLAT_TYPE_VECTOR ? 0 : VECTOR_ARRAY_SIZE(numCenters, VECTOR_SIZE(dimensions));
 	Size		centerCountsSize = sizeof(int) * numCenters;
 	Size		closestCentersSize = sizeof(int) * numSamples;
 	Size		lowerBoundSize = sizeof(float) * numSamples * numCenters;
@@ -215,7 +439,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	Size		newcdistSize = sizeof(float) * numCenters;
 
 	/* Calculate total size */
-	Size		totalSize = samplesSize + centersSize + newCentersSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
+	Size		totalSize = samplesSize + centersSize + newCentersSize + aggCentersSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
 
 	/* Check memory requirements */
 	/* Add one to error message to ceil */
@@ -232,8 +456,15 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	/* Set support functions */
 	procinfo = index_getprocinfo(index, 1, IVFFLAT_KMEANS_DISTANCE_PROC);
 	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
+	normalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC);
 	collation = index->rd_indcollation[0];
 
+	/* Use memory context */
+	kmeansCtx = AllocSetContextCreate(CurrentMemoryContext,
+									  "Ivfflat kmeans temporary context",
+									  ALLOCSET_DEFAULT_SIZES);
+	oldCtx = MemoryContextSwitchTo(kmeansCtx);
+
 	/* Allocate space */
 	/* Use float instead of double to save memory */
 	centerCounts = palloc(centerCountsSize);
@@ -244,29 +475,66 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	halfcdist = palloc_extended(halfcdistSize, MCXT_ALLOC_HUGE);
 	newcdist = palloc(newcdistSize);
 
-	newCenters = VectorArrayInit(numCenters, dimensions);
-	for (j = 0; j < numCenters; j++)
+	aggCenters = VectorArrayInit(numCenters, dimensions, VECTOR_SIZE(dimensions));
+	aggCenters->length = numCenters;
+
+	for (int j = 0; j < numCenters; j++)
 	{
-		vec = VectorArrayGet(newCenters, j);
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
 		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
 		vec->dim = dimensions;
 	}
 
+	if (type == IVFFLAT_TYPE_VECTOR)
+	{
+		/* Use same centers to save memory */
+		newCenters = aggCenters;
+	}
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		newCenters = VectorArrayInit(numCenters, dimensions, centers->itemsize);
+		newCenters->length = numCenters;
+
+		for (int j = 0; j < numCenters; j++)
+		{
+			HalfVector *vec = (HalfVector *) VectorArrayGet(newCenters, j);
+
+			SET_VARSIZE(vec, HALFVEC_SIZE(dimensions));
+			vec->dim = dimensions;
+		}
+	}
+	else if (type == IVFFLAT_TYPE_BIT)
+	{
+		newCenters = VectorArrayInit(numCenters, dimensions, centers->itemsize);
+		newCenters->length = numCenters;
+
+		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");
+
 #ifdef IVFFLAT_MEMORY
-	ShowMemoryUsage(totalSize);
+	ShowMemoryUsage(oldCtx, totalSize);
 #endif
 
 	/* Pick initial centers */
 	InitCenters(index, samples, centers, lowerBound);
 
 	/* Assign each x to its closest initial center c(x) = argmin d(x,c) */
-	for (j = 0; j < numSamples; j++)
+	for (int64 j = 0; j < numSamples; j++)
 	{
 		float		minDistance = FLT_MAX;
 		int			closestCenter = 0;
 
 		/* Find closest center */
-		for (k = 0; k < numCenters; k++)
+		for (int64 k = 0; k < numCenters; k++)
 		{
 			/* TODO Use Lemma 1 in k-means++ initialization */
 			float		distance = lowerBound[j * numCenters + k];
@@ -292,13 +560,13 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		CHECK_FOR_INTERRUPTS();
 
 		/* Step 1: For all centers, compute distance */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
-			vec = VectorArrayGet(centers, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(centers, j));
 
-			for (k = j + 1; k < numCenters; k++)
+			for (int64 k = j + 1; k < numCenters; k++)
 			{
-				float		distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
+				float		distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, k))));
 
 				halfcdist[j * numCenters + k] = distance;
 				halfcdist[k * numCenters + j] = distance;
@@ -306,11 +574,11 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		}
 
 		/* For all centers c, compute s(c) */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
 			float		minDistance = FLT_MAX;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
 				float		distance;
 
@@ -327,7 +595,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 		rjreset = iteration != 0;
 
-		for (j = 0; j < numSamples; j++)
+		for (int64 j = 0; j < numSamples; j++)
 		{
 			bool		rj;
 
@@ -337,8 +605,9 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 			rj = rjreset;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
+				Datum		vec;
 				float		dxcx;
 
 				/* Step 3: For all remaining points x and centers c */
@@ -351,12 +620,12 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 				if (upperBound[j] <= halfcdist[closestCenters[j] * numCenters + k])
 					continue;
 
-				vec = VectorArrayGet(samples, j);
+				vec = PointerGetDatum(VectorArrayGet(samples, j));
 
 				/* Step 3a */
 				if (rj)
 				{
-					dxcx = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, closestCenters[j]))));
+					dxcx = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, closestCenters[j]))));
 
 					/* d(x,c(x)) computed, which is a form of d(x,c) */
 					lowerBound[j * numCenters + closestCenters[j]] = dxcx;
@@ -370,7 +639,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 				/* Step 3b */
 				if (dxcx > lowerBound[j * numCenters + k] || dxcx > halfcdist[closestCenters[j] * numCenters + k])
 				{
-					float		dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
+					float		dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, k))));
 
 					/* d(x,c) calculated */
 					lowerBound[j * numCenters + k] = dxc;
@@ -389,66 +658,15 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		}
 
 		/* Step 4: For each center c, let m(c) be mean of all points assigned */
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-			for (k = 0; k < dimensions; k++)
-				vec->x[k] = 0.0;
-
-			centerCounts[j] = 0;
-		}
-
-		for (j = 0; j < numSamples; j++)
-		{
-			int			closestCenter;
-
-			vec = VectorArrayGet(samples, j);
-			closestCenter = closestCenters[j];
-
-			/* Increment sum and count of closest center */
-			newCenter = VectorArrayGet(newCenters, closestCenter);
-			for (k = 0; k < dimensions; k++)
-				newCenter->x[k] += vec->x[k];
-
-			centerCounts[closestCenter] += 1;
-		}
-
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-
-			if (centerCounts[j] > 0)
-			{
-				/* Double avoids overflow, but requires more memory */
-				/* TODO Update bounds */
-				for (k = 0; k < dimensions; k++)
-				{
-					if (isinf(vec->x[k]))
-						vec->x[k] = vec->x[k] > 0 ? FLT_MAX : -FLT_MAX;
-				}
-
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] /= centerCounts[j];
-			}
-			else
-			{
-				/* TODO Handle empty centers properly */
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] = RandomDouble();
-			}
-
-			/* Normalize if needed */
-			if (normprocinfo != NULL)
-				ApplyNorm(normprocinfo, collation, vec);
-		}
+		ComputeNewCenters(samples, aggCenters, newCenters, centerCounts, closestCenters, normprocinfo, normalizeprocinfo, collation, type);
 
 		/* Step 5 */
-		for (j = 0; j < numCenters; j++)
+		for (int j = 0; j < numCenters; j++)
 			newcdist[j] = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(VectorArrayGet(centers, j)), PointerGetDatum(VectorArrayGet(newCenters, j))));
 
-		for (j = 0; j < numSamples; j++)
+		for (int64 j = 0; j < numSamples; j++)
 		{
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
 				float		distance = lowerBound[j * numCenters + k] - newcdist[k];
 
@@ -461,32 +679,26 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 		/* Step 6 */
 		/* We reset r(x) before Step 3 in the next iteration */
-		for (j = 0; j < numSamples; j++)
+		for (int j = 0; j < numSamples; j++)
 			upperBound[j] += newcdist[closestCenters[j]];
 
 		/* Step 7 */
-		for (j = 0; j < numCenters; j++)
+		for (int j = 0; j < numCenters; j++)
 			VectorArraySet(centers, j, VectorArrayGet(newCenters, j));
 
 		if (changes == 0 && iteration != 0)
 			break;
 	}
 
-	VectorArrayFree(newCenters);
-	pfree(centerCounts);
-	pfree(closestCenters);
-	pfree(lowerBound);
-	pfree(upperBound);
-	pfree(s);
-	pfree(halfcdist);
-	pfree(newcdist);
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(kmeansCtx);
 }
 
 /*
  * Detect issues with centers
  */
 static void
-CheckCenters(Relation index, VectorArray centers)
+CheckCenters(Relation index, VectorArray centers, IvfflatType type)
 {
 	FmgrInfo   *normprocinfo;
 
@@ -496,7 +708,9 @@ CheckCenters(Relation index, VectorArray centers)
 	/* Ensure no NaN or infinite values */
 	for (int i = 0; i < centers->length; i++)
 	{
-		Vector	   *vec = VectorArrayGet(centers, i);
+		if (type == IVFFLAT_TYPE_VECTOR)
+		{
+			Vector	   *vec = (Vector *) VectorArrayGet(centers, i);
 
 			for (int j = 0; j < vec->dim; j++)
 			{
@@ -507,15 +721,34 @@ CheckCenters(Relation index, VectorArray centers)
 					elog(ERROR, "Infinite value detected. Please report a bug.");
 			}
 		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *vec = (HalfVector *) VectorArrayGet(centers, i);
 
+			for (int j = 0; j < vec->dim; j++)
+			{
+				if (HalfIsNan(vec->x[j]))
+					elog(ERROR, "NaN detected. Please report a bug.");
+
+				if (HalfIsInf(vec->x[j]))
+					elog(ERROR, "Infinite value detected. Please report a bug.");
+			}
+		}
+		else if (type != IVFFLAT_TYPE_BIT)
+			elog(ERROR, "Unsupported type");
+	}
+
+	if (type != IVFFLAT_TYPE_BIT)
+	{
 		/* Ensure no duplicate centers */
-	/* Fine to sort in-place */
-	qsort(centers->items, centers->length, VECTOR_SIZE(centers->dim), CompareVectors);
+		SortVectorArray(centers, type);
+
 		for (int i = 1; i < centers->length; i++)
 		{
-		if (CompareVectors(VectorArrayGet(centers, i), VectorArrayGet(centers, i - 1)) == 0)
+			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 */
 	/* Check NORM_PROC instead of KMEANS_NORM_PROC */
@@ -539,12 +772,12 @@ CheckCenters(Relation index, VectorArray centers)
  * We use spherical k-means for inner product and cosine
  */
 void
-IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers)
+IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatType type)
 {
 	if (samples->length <= centers->maxlen)
-		QuickCenters(index, samples, centers);
+		QuickCenters(index, samples, centers, type);
 	else
-		ElkanKmeans(index, samples, centers);
+		ElkanKmeans(index, samples, centers, type);
 
-	CheckCenters(index, centers);
+	CheckCenters(index, centers, type);
 }

src/ivfscan.c

@@ -56,7 +56,7 @@ GetScanLists(IndexScanDesc scan, Datum value)
 			double		distance;
 
 			/* Use procinfo from the index instead of scan key for performance */
-			distance = DatumGetFloat8(FunctionCall2Coll(so->procinfo, so->collation, PointerGetDatum(&list->center), value));
+			distance = DatumGetFloat8(so->distfunc(so->procinfo, so->collation, PointerGetDatum(&list->center), value));
 
 			if (listCount < so->probes)
 			{
@@ -149,7 +149,7 @@ GetScanItems(IndexScanDesc scan, Datum value)
 				 * performance
 				 */
 				ExecClearTuple(slot);
-				slot->tts_values[0] = FunctionCall2Coll(so->procinfo, so->collation, datum, value);
+				slot->tts_values[0] = so->distfunc(so->procinfo, so->collation, datum, value);
 				slot->tts_isnull[0] = false;
 				slot->tts_values[1] = PointerGetDatum(&itup->t_tid);
 				slot->tts_isnull[1] = false;
@@ -177,6 +177,46 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	tuplesort_performsort(so->sortstate);
 }
 
+/*
+ * Zero distance
+ */
+static Datum
+ZeroDistance(FmgrInfo *flinfo, Oid collation, Datum arg1, Datum arg2)
+{
+	return Float8GetDatum(0.0);
+}
+
+/*
+ * Get scan value
+ */
+static Datum
+GetScanValue(IndexScanDesc scan)
+{
+	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
+	Datum		value;
+
+	if (scan->orderByData->sk_flags & SK_ISNULL)
+	{
+		value = PointerGetDatum(NULL);
+		so->distfunc = ZeroDistance;
+	}
+	else
+	{
+		value = scan->orderByData->sk_argument;
+		so->distfunc = FunctionCall2Coll;
+
+		/* Value should not be compressed or toasted */
+		Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
+		Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
+
+		/* Check normprocinfo since normalizeprocinfo not set for vector */
+		if (so->normprocinfo != NULL)
+			value = IvfflatNormValue(so->normalizeprocinfo, so->collation, value);
+	}
+
+	return value;
+}
+
 /*
  * Prepare for an index scan
  */
@@ -209,6 +249,7 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	/* Set support functions */
 	so->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
 	so->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
+	so->normalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC);
 	so->collation = index->rd_indcollation[0];
 
 	/* Create tuple description for sorting */
@@ -268,7 +309,6 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 	if (so->first)
 	{
 		Datum		value;
-		IvfflatType type = IvfflatGetType(scan->indexRelation);
 
 		/* Count index scan for stats */
 		pgstat_count_index_scan(scan->indexRelation);
@@ -282,26 +322,7 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (!IsMVCCSnapshot(scan->xs_snapshot))
 			elog(ERROR, "non-MVCC snapshots are not supported with ivfflat");
 
-		if (scan->orderByData->sk_flags & SK_ISNULL)
-		{
-			if (type == IVFFLAT_TYPE_VECTOR)
-				value = PointerGetDatum(InitVector(so->dimensions));
-			else
-				elog(ERROR, "Unsupported type");
-		}
-		else
-		{
-			value = scan->orderByData->sk_argument;
-
-			/* Value should not be compressed or toasted */
-			Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
-			Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
-
-			/* Fine if normalization fails */
-			if (so->normprocinfo != NULL)
-				IvfflatNormValue(so->normprocinfo, so->collation, &value, type);
-		}
-
+		value = GetScanValue(scan);
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
 		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;

src/ivfutils.c

@@ -1,22 +1,27 @@
 #include "postgres.h"
 
 #include "access/generic_xlog.h"
+#include "catalog/pg_type.h"
+#include "fmgr.h"
 #include "ivfflat.h"
 #include "storage/bufmgr.h"
-#include "vector.h"
 
 /*
  * Allocate a vector array
  */
 VectorArray
-VectorArrayInit(int maxlen, int dimensions)
+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;
-	res->items = palloc_extended(maxlen * VECTOR_SIZE(dimensions), MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
+	res->itemsize = itemsize;
+	res->items = palloc_extended(maxlen * itemsize, MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
 	return res;
 }
 
@@ -30,16 +35,6 @@ VectorArrayFree(VectorArray arr)
 	pfree(arr);
 }
 
-/*
- * Print vector array - useful for debugging
- */
-void
-PrintVectorArray(char *msg, VectorArray arr)
-{
-	for (int i = 0; i < arr->length; i++)
-		PrintVector(msg, VectorArrayGet(arr, i));
-}
-
 /*
  * Get the number of lists in the index
  */
@@ -72,41 +67,40 @@ IvfflatOptionalProcInfo(Relation index, uint16 procnum)
 IvfflatType
 IvfflatGetType(Relation index)
 {
+	FmgrInfo   *procinfo = IvfflatOptionalProcInfo(index, IVFFLAT_TYPE_SUPPORT_PROC);
+	Oid			typid = TupleDescAttr(index->rd_att, 0)->atttypid;
+	IvfflatType result;
+
+	if (procinfo == NULL)
 		return IVFFLAT_TYPE_VECTOR;
+
+	result = (IvfflatType) DatumGetInt32(FunctionCall1(procinfo, ObjectIdGetDatum(typid)));
+
+	if (result == IVFFLAT_TYPE_UNSUPPORTED)
+		elog(ERROR, "type not supported for ivfflat index");
+
+	return result;
 }
 
 /*
- * Divide by the norm
- *
- * Returns false if value should not be indexed
- *
- * The caller needs to free the pointer stored in value
- * if it's different than the original value
+ * Normalize value
+ */
+Datum
+IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum value)
+{
+	if (procinfo == NULL)
+		return DirectFunctionCall1(l2_normalize, value);
+
+	return FunctionCall1Coll(procinfo, collation, value);
+}
+
+/*
+ * Check if non-zero norm
  */
 bool
-IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, IvfflatType type)
+IvfflatCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value)
 {
-	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
-
-	if (norm > 0)
-	{
-		if (type == IVFFLAT_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
-			elog(ERROR, "Unsupported type");
-
-		return true;
-	}
-
-	return false;
+	return DatumGetFloat8(FunctionCall1Coll(procinfo, collation, value)) > 0;
 }
 
 /*
@@ -251,3 +245,22 @@ IvfflatUpdateList(Relation index, ListInfo listInfo,
 		UnlockReleaseBuffer(buf);
 	}
 }
+
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_ivfflat_support);
+Datum
+halfvec_ivfflat_support(PG_FUNCTION_ARGS)
+{
+	PG_RETURN_INT32(IVFFLAT_TYPE_HALFVEC);
+};
+
+PGDLLEXPORT PG_FUNCTION_INFO_V1(bit_ivfflat_support);
+Datum
+bit_ivfflat_support(PG_FUNCTION_ARGS)
+{
+	Oid			typid = PG_GETARG_OID(0);
+
+	if (typid == BITOID)
+		PG_RETURN_INT32(IVFFLAT_TYPE_BIT);
+	else
+		PG_RETURN_INT32(IVFFLAT_TYPE_UNSUPPORTED);
+};

src/sparsevec.c

@@ -4,6 +4,8 @@
 #include <math.h>
 
 #include "fmgr.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "libpq/pqformat.h"
 #include "sparsevec.h"
 #include "utils/array.h"
@@ -18,6 +20,12 @@
 #include "utils/builtins.h"
 #endif
 
+typedef struct SparseInputElement
+{
+	int32		index;
+	float		value;
+}			SparseInputElement;
+
 /*
  * Ensure same dimensions
  */
@@ -164,6 +172,21 @@ sparsevec_isspace(char ch)
 	return false;
 }
 
+/*
+ * Compare indices
+ */
+static int
+CompareIndices(const void *a, const void *b)
+{
+	if (((SparseInputElement *) a)->index < ((SparseInputElement *) b)->index)
+		return -1;
+
+	if (((SparseInputElement *) a)->index > ((SparseInputElement *) b)->index)
+		return 1;
+
+	return 0;
+}
+
 /*
  * Convert textual representation to internal representation
  */
@@ -174,19 +197,15 @@ sparsevec_in(PG_FUNCTION_ARGS)
 	char	   *lit = PG_GETARG_CSTRING(0);
 	int32		typmod = PG_GETARG_INT32(2);
 	int			dim;
-	char	   *pt;
+	char	   *pt = lit;
 	char	   *stringEnd;
 	SparseVector *result;
 	float	   *rvalues;
-	char	   *litcopy = pstrdup(lit);
-	char	   *str = litcopy;
-	int32	   *indices;
-	float	   *values;
+	SparseInputElement *elements;
 	int			maxNnz;
 	int			nnz = 0;
 
 	maxNnz = 1;
-	pt = str;
 	while (*pt != '\0')
 	{
 		if (*pt == ',')
@@ -200,23 +219,29 @@ sparsevec_in(PG_FUNCTION_ARGS)
 				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
 				 errmsg("sparsevec cannot have more than %d non-zero elements", SPARSEVEC_MAX_NNZ)));
 
-	indices = palloc(maxNnz * sizeof(int32));
-	values = palloc(maxNnz * sizeof(float));
+	elements = palloc(maxNnz * sizeof(SparseInputElement));
 
-	while (sparsevec_isspace(*str))
-		str++;
+	pt = lit;
 
-	if (*str != '{')
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '{')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed sparsevec literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
 				 errdetail("Vector contents must start with \"{\".")));
 
-	str++;
-	pt = strtok(str, ",");
-	stringEnd = pt;
+	pt++;
 
-	while (pt != NULL && *stringEnd != '}')
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt == '}')
+		pt++;
+	else
+	{
+		for (;;)
 		{
 			long		index;
 			float		value;
@@ -250,26 +275,25 @@ sparsevec_in(PG_FUNCTION_ARGS)
 						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
 						 errmsg("index \"%ld\" is out of range for type sparsevec", index)));
 
-		if (stringEnd == pt)
+			pt = stringEnd;
+
+			while (sparsevec_isspace(*pt))
+				pt++;
+
+			if (*pt != ':')
 				ereport(ERROR,
 						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
 
-		while (sparsevec_isspace(*stringEnd))
-			stringEnd++;
+			pt++;
 
-		if (*stringEnd != ':')
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
-
-		stringEnd++;
-
-		while (sparsevec_isspace(*stringEnd))
-			stringEnd++;
+			while (sparsevec_isspace(*pt))
+				pt++;
 
 			errno = 0;
-		pt = stringEnd;
+
+			/* Use strtof like float4in to avoid a double-rounding problem */
+			/* Postgres sets LC_NUMERIC to C on startup */
 			value = strtof(pt, &stringEnd);
 
 			if (stringEnd == pt)
@@ -281,43 +305,53 @@ sparsevec_in(PG_FUNCTION_ARGS)
 			if (errno == ERANGE && (value == 0 || isinf(value)))
 				ereport(ERROR,
 						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-					 errmsg("\"%s\" is out of range for type sparsevec", pt)));
+						 errmsg("\"%s\" is out of range for type sparsevec", pnstrdup(pt, stringEnd - pt))));
 
-		/* TODO Decide whether to store zero values */
+			CheckElement(value);
+
+			/* Do not store zero values */
 			if (value != 0)
 			{
-			indices[nnz] = index;
-			values[nnz] = value;
+				elements[nnz].index = index;
+				elements[nnz].value = value;
 				nnz++;
 			}
 
-		if (*stringEnd != '\0' && *stringEnd != '}')
+			pt = stringEnd;
+
+			while (sparsevec_isspace(*pt))
+				pt++;
+
+			if (*pt == ',')
+				pt++;
+			else if (*pt == '}')
+			{
+				pt++;
+				break;
+			}
+			else
 				ereport(ERROR,
 						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
-
-		pt = strtok(NULL, ",");
+		}
 	}
 
-	if (stringEnd == NULL || *stringEnd != '}')
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '/')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed sparsevec literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
 				 errdetail("Unexpected end of input.")));
 
-	stringEnd++;
+	pt++;
 
-	if (*stringEnd != '/')
-		ereport(ERROR,
-				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed sparsevec literal: \"%s\"", lit),
-				 errdetail("Unexpected end of input.")));
-
-	stringEnd++;
+	while (sparsevec_isspace(*pt))
+		pt++;
 
 	/* Use similar logic as int2vectorin */
 	errno = 0;
-	pt = stringEnd;
 	dim = strtol(pt, &stringEnd, 10);
 
 	if (stringEnd == pt)
@@ -325,30 +359,31 @@ sparsevec_in(PG_FUNCTION_ARGS)
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
 
-	/* Only whitespace is allowed after the closing brace */
-	while (sparsevec_isspace(*stringEnd))
-		stringEnd++;
+	pt = stringEnd;
 
-	if (*stringEnd != '\0')
+	/* Only whitespace is allowed after the closing brace */
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '\0')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed sparsevec literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
 				 errdetail("Junk after closing.")));
 
-	pfree(litcopy);
-
 	CheckDim(dim);
 	CheckExpectedDim(typmod, dim);
 
+	qsort(elements, nnz, sizeof(SparseInputElement), CompareIndices);
+
 	result = InitSparseVector(dim, nnz);
 	rvalues = SPARSEVEC_VALUES(result);
 	for (int i = 0; i < nnz; i++)
 	{
-		result->indices[i] = indices[i];
-		rvalues[i] = values[i];
+		result->indices[i] = elements[i].index;
+		rvalues[i] = elements[i].value;
 
 		CheckIndex(result->indices, i, dim);
-		CheckElement(rvalues[i]);
 	}
 
 	PG_RETURN_POINTER(result);
@@ -492,6 +527,10 @@ sparsevec_recv(PG_FUNCTION_ARGS)
 	{
 		values[i] = pq_getmsgfloat4(buf);
 		CheckElement(values[i]);
+		if (values[i] == 0)
+			ereport(ERROR,
+					(errcode(ERRCODE_DATA_EXCEPTION),
+					 errmsg("binary representation of sparsevec cannot contain zero values")));
 	}
 
 	PG_RETURN_POINTER(result);
@@ -567,7 +606,7 @@ 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;
@@ -579,15 +618,58 @@ vector_to_sparsevec(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+/*
+ * Convert half vector to sparse vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_to_sparsevec);
+Datum
+halfvec_to_sparsevec(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	SparseVector *result;
+	int			dim = vec->dim;
+	int			nnz = 0;
+	float	   *values;
+	int			j = 0;
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	for (int i = 0; i < dim; i++)
+	{
+		if (!HalfIsZero(vec->x[i]))
+			nnz++;
+	}
+
+	result = InitSparseVector(dim, nnz);
+	values = SPARSEVEC_VALUES(result);
+	for (int i = 0; i < dim; i++)
+	{
+		if (!HalfIsZero(vec->x[i]))
+		{
+			/* Safety check */
+			if (j >= result->nnz)
+				elog(ERROR, "safety check failed");
+
+			result->indices[j] = i + 1;
+			values[j] = HalfToFloat4(vec->x[i]);
+			j++;
+		}
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
 /*
  * Get the L2 squared distance between sparse vectors
  */
-static double
-l2_distance_squared_internal(SparseVector * a, SparseVector * b)
+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++)
@@ -601,7 +683,7 @@ l2_distance_squared_internal(SparseVector * a, SparseVector * b)
 
 			if (ai == bi)
 			{
-				double		diff = ax[i] - bx[j];
+				float		diff = ax[i] - bx[j];
 
 				distance += diff * diff;
 			}
@@ -639,7 +721,7 @@ sparsevec_l2_distance(PG_FUNCTION_ARGS)
 
 	CheckDims(a, b);
 
-	PG_RETURN_FLOAT8(sqrt(l2_distance_squared_internal(a, b)));
+	PG_RETURN_FLOAT8(sqrt((double) SparsevecL2SquaredDistance(a, b)));
 }
 
 /*
@@ -655,18 +737,18 @@ sparsevec_l2_squared_distance(PG_FUNCTION_ARGS)
 
 	CheckDims(a, b);
 
-	PG_RETURN_FLOAT8(l2_distance_squared_internal(a, b));
+	PG_RETURN_FLOAT8((double) SparsevecL2SquaredDistance(a, b));
 }
 
 /*
  * Get the inner product of two sparse vectors
  */
-static double
-inner_product_internal(SparseVector * a, SparseVector * b)
+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++)
@@ -706,7 +788,7 @@ sparsevec_inner_product(PG_FUNCTION_ARGS)
 
 	CheckDims(a, b);
 
-	PG_RETURN_FLOAT8(inner_product_internal(a, b));
+	PG_RETURN_FLOAT8((double) SparsevecInnerProduct(a, b));
 }
 
 /*
@@ -721,7 +803,7 @@ sparsevec_negative_inner_product(PG_FUNCTION_ARGS)
 
 	CheckDims(a, b);
 
-	PG_RETURN_FLOAT8(-inner_product_internal(a, b));
+	PG_RETURN_FLOAT8((double) -SparsevecInnerProduct(a, b));
 }
 
 /*
@@ -741,7 +823,7 @@ sparsevec_cosine_distance(PG_FUNCTION_ARGS)
 
 	CheckDims(a, b);
 
-	similarity = inner_product_internal(a, b);
+	similarity = SparsevecInnerProduct(a, b);
 
 	/* Auto-vectorized */
 	for (int i = 0; i < a->nnz; i++)
@@ -769,12 +851,61 @@ 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);
+	float		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((double) 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);
@@ -786,3 +917,205 @@ 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

@@ -1,25 +1,40 @@
 #ifndef SPARSEVEC_H
 #define SPARSEVEC_H
 
-#define SPARSEVEC_MAX_DIM 100000
+#include "fmgr.h"
+
+#define SPARSEVEC_MAX_DIM 1000000
 #define SPARSEVEC_MAX_NNZ 16000
 
-/* Ensure values are aligned */
-#define SPARSEVEC_SIZE(_nnz)		(offsetof(SparseVector, indices) + MAXALIGN((_nnz) * sizeof(int32)) + (_nnz * sizeof(float)))
-#define SPARSEVEC_VALUES(x)		((float *) (((char *) (x)) + offsetof(SparseVector, indices) + MAXALIGN((x)->nnz * sizeof(int32))))
 #define DatumGetSparseVector(x)		((SparseVector *) PG_DETOAST_DATUM(x))
 #define PG_GETARG_SPARSEVEC_P(x)	DatumGetSparseVector(PG_GETARG_DATUM(x))
 #define PG_RETURN_SPARSEVEC_P(x)	PG_RETURN_POINTER(x)
 
+/* Indices are always sorted */
+/* Values come after indices */
 typedef struct SparseVector
 {
 	int32		vl_len_;		/* varlena header (do not touch directly!) */
 	int32		dim;			/* number of dimensions */
-	int32		nnz;
+	int32		nnz;			/* number of non-zero elements */
 	int32		unused;
 	int32		indices[FLEXIBLE_ARRAY_MEMBER];
 }			SparseVector;
 
+/* Use functions instead of macros to avoid double evaluation */
+
+static inline Size
+SPARSEVEC_SIZE(int nnz)
+{
+	return offsetof(SparseVector, indices) + (nnz * sizeof(int32)) + (nnz * sizeof(float));
+}
+
+static inline float *
+SPARSEVEC_VALUES(SparseVector * x)
+{
+	return (float *) (((char *) x) + offsetof(SparseVector, indices) + (x->nnz * sizeof(int32)));
+}
+
 SparseVector *InitSparseVector(int dim, int nnz);
 
 #endif

src/vector.c

@@ -2,10 +2,12 @@
 
 #include <math.h>
 
-#include "bitvector.h"
+#include "bitutils.h"
+#include "bitvec.h"
 #include "catalog/pg_type.h"
 #include "common/shortest_dec.h"
 #include "fmgr.h"
+#include "halfutils.h"
 #include "halfvec.h"
 #include "hnsw.h"
 #include "ivfflat.h"
@@ -32,6 +34,12 @@
 #define STATE_DIMS(x) (ARR_DIMS(x)[0] - 1)
 #define CreateStateDatums(dim) palloc(sizeof(Datum) * (dim + 1))
 
+#if defined(USE_TARGET_CLONES) && !defined(__FMA__)
+#define VECTOR_TARGET_CLONES __attribute__((target_clones("default", "fma")))
+#else
+#define VECTOR_TARGET_CLONES
+#endif
+
 PG_MODULE_MAGIC;
 
 /*
@@ -41,6 +49,8 @@ PGDLLEXPORT void _PG_init(void);
 void
 _PG_init(void)
 {
+	BitvecInit();
+	HalfvecInit();
 	HnswInit();
 	IvfflatInit();
 }
@@ -179,28 +189,32 @@ vector_in(PG_FUNCTION_ARGS)
 	int32		typmod = PG_GETARG_INT32(2);
 	float		x[VECTOR_MAX_DIM];
 	int			dim = 0;
-	char	   *pt;
-	char	   *stringEnd;
+	char	   *pt = lit;
 	Vector	   *result;
-	char	   *litcopy = pstrdup(lit);
-	char	   *str = litcopy;
 
-	while (vector_isspace(*str))
-		str++;
+	while (vector_isspace(*pt))
+		pt++;
 
-	if (*str != '[')
+	if (*pt != '[')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type vector: \"%s\"", lit),
 				 errdetail("Vector contents must start with \"[\".")));
 
-	str++;
-	pt = strtok(str, ",");
-	stringEnd = pt;
+	pt++;
 
-	while (pt != NULL && *stringEnd != ']')
+	while (vector_isspace(*pt))
+		pt++;
+
+	if (*pt == ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("vector must have at least 1 dimension")));
+
+	for (;;)
 	{
 		float		val;
+		char	   *stringEnd;
 
 		if (dim == VECTOR_MAX_DIM)
 			ereport(ERROR,
@@ -216,8 +230,10 @@ vector_in(PG_FUNCTION_ARGS)
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
 
-		/* Use strtof like float4in to avoid a double-rounding problem */
 		errno = 0;
+
+		/* Use strtof like float4in to avoid a double-rounding problem */
+		/* Postgres sets LC_NUMERIC to C on startup */
 		val = strtof(pt, &stringEnd);
 
 		if (stringEnd == pt)
@@ -229,56 +245,40 @@ vector_in(PG_FUNCTION_ARGS)
 		if (errno == ERANGE && isinf(val))
 			ereport(ERROR,
 					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-					 errmsg("\"%s\" is out of range for type vector", pt)));
+					 errmsg("\"%s\" is out of range for type vector", pnstrdup(pt, stringEnd - pt))));
 
 		CheckElement(val);
 		x[dim++] = val;
 
-		while (vector_isspace(*stringEnd))
-			stringEnd++;
+		pt = stringEnd;
 
-		if (*stringEnd != '\0' && *stringEnd != ']')
+		while (vector_isspace(*pt))
+			pt++;
+
+		if (*pt == ',')
+			pt++;
+		else if (*pt == ']')
+		{
+			pt++;
+			break;
+		}
+		else
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
-
-		pt = strtok(NULL, ",");
 	}
 
-	if (stringEnd == NULL || *stringEnd != ']')
-		ereport(ERROR,
-				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
-				 errdetail("Unexpected end of input.")));
-
-	stringEnd++;
-
 	/* Only whitespace is allowed after the closing brace */
-	while (vector_isspace(*stringEnd))
-		stringEnd++;
+	while (vector_isspace(*pt))
+		pt++;
 
-	if (*stringEnd != '\0')
+	if (*pt != '\0')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type vector: \"%s\"", lit),
 				 errdetail("Junk after closing right brace.")));
 
-	/* Ensure no consecutive delimiters since strtok skips */
-	for (pt = lit + 1; *pt != '\0'; pt++)
-	{
-		if (pt[-1] == ',' && *pt == ',')
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("malformed vector literal: \"%s\"", lit)));
-	}
-
-	if (dim < 1)
-		ereport(ERROR,
-				(errcode(ERRCODE_DATA_EXCEPTION),
-				 errmsg("vector must have at least 1 dimension")));
-
-	pfree(litcopy);
-
+	CheckDim(dim);
 	CheckExpectedDim(typmod, dim);
 
 	result = InitVector(dim);
@@ -565,6 +565,22 @@ halfvec_to_vector(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+VECTOR_TARGET_CLONES static float
+VectorL2SquaredDistance(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		diff = ax[i] - bx[i];
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+
 /*
  * Get the L2 distance between vectors
  */
@@ -574,21 +590,10 @@ l2_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		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
-
-	PG_RETURN_FLOAT8(sqrt((double) distance));
+	PG_RETURN_FLOAT8(sqrt((double) VectorL2SquaredDistance(a->dim, a->x, b->x)));
 }
 
 /*
@@ -601,21 +606,22 @@ vector_l2_squared_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		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
+	PG_RETURN_FLOAT8((double) VectorL2SquaredDistance(a->dim, a->x, b->x));
 }
 
-	PG_RETURN_FLOAT8((double) distance);
+VECTOR_TARGET_CLONES static float
+VectorInnerProduct(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += ax[i] * bx[i];
+
+	return distance;
 }
 
 /*
@@ -627,17 +633,10 @@ inner_product(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 */
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) VectorInnerProduct(a->dim, a->x, b->x));
 }
 
 /*
@@ -649,17 +648,29 @@ vector_negative_inner_product(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 */
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
+	PG_RETURN_FLOAT8((double) -VectorInnerProduct(a->dim, a->x, b->x));
+}
 
-	PG_RETURN_FLOAT8((double) distance * -1);
+VECTOR_TARGET_CLONES 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);
 }
 
 /*
@@ -671,25 +682,11 @@ 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 */
-	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);
+	similarity = VectorCosineSimilarity(a->dim, a->x, b->x);
 
 #ifdef _MSC_VER
 	/* /fp:fast may not propagate NaN */
@@ -717,18 +714,11 @@ vector_spherical_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		dp = 0.0;
 	double		distance;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		dp += ax[i] * bx[i];
-
-	distance = (double) dp;
+	distance = (double) VectorInnerProduct(a->dim, a->x, b->x);
 
 	/* Prevent NaN with acos with loss of precision */
 	if (distance > 1)
@@ -739,6 +729,19 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(acos(distance) / M_PI);
 }
 
+/* Does not require FMA, but keep logic simple */
+VECTOR_TARGET_CLONES 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
  */
@@ -748,17 +751,10 @@ 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 */
-	for (int i = 0; i < a->dim; i++)
-		distance += fabsf(ax[i] - bx[i]);
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) VectorL1Distance(a->dim, a->x, b->x));
 }
 
 /*
@@ -791,6 +787,45 @@ 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
  */
@@ -893,12 +928,36 @@ 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;
@@ -1123,7 +1182,7 @@ 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/bit_functions.out

@@ -28,6 +28,24 @@ SELECT hamming_distance('10101010101010101010', '01010101010101010101');
                20
 (1 row)
 
+SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
+ hamming_distance 
+------------------
+                0
+(1 row)
+
+SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
+ hamming_distance 
+------------------
+              513
+(1 row)
+
+SELECT hamming_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
+ hamming_distance 
+------------------
+                2
+(1 row)
+
 SELECT hamming_distance('', '');
  hamming_distance 
 ------------------
@@ -86,6 +104,24 @@ SELECT jaccard_distance('10101010101010101010', '01010101010101010101');
                 1
 (1 row)
 
+SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
+ jaccard_distance 
+------------------
+                0
+(1 row)
+
+SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
+ jaccard_distance 
+------------------
+              0.5
+(1 row)
+
 SELECT jaccard_distance('', '');
  jaccard_distance 
 ------------------

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/cast.out

@@ -28,6 +28,26 @@ SELECT ARRAY[1,2,3]::numeric[]::vector;
  [1,2,3]
 (1 row)
 
+SELECT '[1,2,3]'::vector::real[];
+ float4  
+---------
+ {1,2,3}
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector(2);
+ERROR:  expected 2 dimensions, not 3
 SELECT '{NULL}'::real[]::vector;
 ERROR:  array must not contain nulls
 SELECT '{NaN}'::real[]::vector;
@@ -40,10 +60,26 @@ SELECT '{}'::real[]::vector;
 ERROR:  vector must have at least 1 dimension
 SELECT '{{1}}'::real[]::vector;
 ERROR:  array must be 1-D
-SELECT '[1,2,3]'::vector::real[];
- float4  
+SELECT '{1,2,3}'::double precision[]::vector;
+ vector  
 ---------
- {1,2,3}
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::double precision[]::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::double precision[]::vector(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{4e38,-4e38}'::double precision[]::vector;
+ERROR:  infinite value not allowed in vector
+SELECT '{1e-46,-1e-46}'::double precision[]::vector;
+ vector 
+--------
+ [0,-0]
 (1 row)
 
 SELECT '[1,2,3]'::vector::halfvec;
@@ -52,19 +88,121 @@ SELECT '[1,2,3]'::vector::halfvec;
  [1,2,3]
 (1 row)
 
-SELECT '[1,2,3]'::halfvec::vector;
- vector  
+SELECT '[1,2,3]'::vector::halfvec(3);
+ halfvec 
 ---------
  [1,2,3]
 (1 row)
 
 SELECT '[1,2,3]'::vector::halfvec(2);
 ERROR:  expected 2 dimensions, not 3
+SELECT '[65520]'::vector::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '[1e-8]'::vector::halfvec;
+ halfvec 
+---------
+ [0]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
 SELECT '[1,2,3]'::halfvec::vector(2);
 ERROR:  expected 2 dimensions, not 3
-SELECT '[65520]'::vector::halfvec;
-ERROR:  infinite value not allowed in halfvec
-SELECT '[1e-8]'::vector::halfvec;
+SELECT '{1,2,3}'::real[]::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::halfvec(3);
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{65520,-65520}'::real[]::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '{1e-8,-1e-8}'::real[]::halfvec;
+ halfvec 
+---------
+ [0,-0]
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(5);
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector;
+     vector      
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(5);
+     vector      
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{}/16001'::sparsevec::vector;
+ERROR:  vector cannot have more than 16000 dimensions
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec;
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec(5);
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec;
+     halfvec     
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec(5);
+     halfvec     
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{}/16001'::sparsevec::halfvec;
+ERROR:  halfvec cannot have more than 16000 dimensions
+SELECT '{1:65520}/1'::sparsevec::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '{1:1e-8}/1'::sparsevec::halfvec;
  halfvec 
 ---------
  [0]

test/expected/copy.out

@@ -1,15 +1,15 @@
-CREATE TABLE t (val vector(3), val2 halfvec(3));
-INSERT INTO t (val, val2) VALUES ('[0,0,0]', '[0,0,0]'), ('[1,2,3]', '[1,2,3]'), ('[1,1,1]', '[1,1,1]'), (NULL, NULL);
-CREATE TABLE t2 (val vector(3), val2 halfvec(3));
+CREATE TABLE t (val vector(3), val2 halfvec(3), val3 sparsevec(3));
+INSERT INTO t (val, val2, val3) VALUES ('[0,0,0]', '[0,0,0]', '{}/3'), ('[1,2,3]', '[1,2,3]', '{1:1,2:2,3:3}/3'), ('[1,1,1]', '[1,1,1]', '{1:1,2:1,3:1}/3'), (NULL, NULL, NULL);
+CREATE TABLE t2 (val vector(3), val2 halfvec(3), val3 sparsevec(3));
 \copy t TO 'results/data.bin' WITH (FORMAT binary)
 \copy t2 FROM 'results/data.bin' WITH (FORMAT binary)
 SELECT * FROM t2 ORDER BY val;
-   val   |  val2   
----------+---------
- [0,0,0] | [0,0,0]
- [1,1,1] | [1,1,1]
- [1,2,3] | [1,2,3]
-         | 
+   val   |  val2   |      val3       
+---------+---------+-----------------
+ [0,0,0] | [0,0,0] | {}/3
+ [1,1,1] | [1,1,1] | {1:1,2:1,3:1}/3
+ [1,2,3] | [1,2,3] | {1:1,2:2,3:3}/3
+         |         | 
 (4 rows)
 
 DROP TABLE t;

test/expected/halfvec_functions.out

@@ -1,3 +1,193 @@
+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 l2_norm('[3,4]'::halfvec);
+ l2_norm 
+---------
+       5
+(1 row)
+
+SELECT l2_norm('[0,1]'::halfvec);
+ l2_norm 
+---------
+       1
+(1 row)
+
+SELECT l2_norm('[0,0]'::halfvec);
+ l2_norm 
+---------
+       0
+(1 row)
+
+SELECT l2_norm('[2]'::halfvec);
+ l2_norm 
+---------
+       2
+(1 row)
+
 SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
  l2_distance 
 -------------
@@ -12,6 +202,12 @@ SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
 
 SELECT l2_distance('[1,2]'::halfvec, '[3]');
 ERROR:  different halfvec dimensions 2 and 1
+SELECT l2_distance('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,1,1,1,1,1,1,4,5]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
 SELECT '[0,0]'::halfvec <-> '[3,4]';
  ?column? 
 ----------
@@ -32,6 +228,12 @@ SELECT inner_product('[65504]'::halfvec, '[65504]');
     4290774016
 (1 row)
 
+SELECT inner_product('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+ inner_product 
+---------------
+            45
+(1 row)
+
 SELECT '[1,2]'::halfvec <#> '[3,4]';
  ?column? 
 ----------
@@ -82,6 +284,18 @@ 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? 
 ----------
@@ -102,14 +316,62 @@ 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);
- quantize_binary 
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+ l1_distance 
+-------------
+           0
+(1 row)
+
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[0,3,2,5,4,7,6,9,8]');
+ l1_distance 
+-------------
+           9
+(1 row)
+
+SELECT '[0,0]'::halfvec <+> '[3,4]';
+ ?column? 
+----------
+        7
+(1 row)
+
+SELECT l2_normalize('[3,4]'::halfvec);
+      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);
- quantize_binary 
+SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::halfvec);
+ binary_quantize 
 -----------------
  01001110101
 (1 row)
@@ -144,3 +406,53 @@ 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/halfvec_input.out

@@ -55,51 +55,64 @@ ERROR:  "65520" is out of range for type halfvec
 LINE 1: SELECT '[65520,-65520]'::halfvec;
                ^
 SELECT '[1e-8,-1e-8]'::halfvec;
-ERROR:  "1e-8" is out of range for type halfvec
-LINE 1: SELECT '[1e-8,-1e-8]'::halfvec;
-               ^
+ halfvec 
+---------
+ [0,-0]
+(1 row)
+
 SELECT '[4e38,1]'::halfvec;
 ERROR:  "4e38" is out of range for type halfvec
 LINE 1: SELECT '[4e38,1]'::halfvec;
                ^
 SELECT '[1e-46,1]'::halfvec;
-ERROR:  "1e-46" is out of range for type halfvec
-LINE 1: SELECT '[1e-46,1]'::halfvec;
-               ^
+ halfvec 
+---------
+ [0,1]
+(1 row)
+
 SELECT '[1,2,3'::halfvec;
-ERROR:  malformed halfvec literal: "[1,2,3"
+ERROR:  invalid input syntax for type halfvec: "[1,2,3"
 LINE 1: SELECT '[1,2,3'::halfvec;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[1,2,3]9'::halfvec;
-ERROR:  malformed halfvec literal: "[1,2,3]9"
+ERROR:  invalid input syntax for type halfvec: "[1,2,3]9"
 LINE 1: SELECT '[1,2,3]9'::halfvec;
                ^
 DETAIL:  Junk after closing right brace.
 SELECT '1,2,3'::halfvec;
-ERROR:  malformed halfvec literal: "1,2,3"
+ERROR:  invalid input syntax for type halfvec: "1,2,3"
 LINE 1: SELECT '1,2,3'::halfvec;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT ''::halfvec;
-ERROR:  malformed halfvec literal: ""
+ERROR:  invalid input syntax for type halfvec: ""
 LINE 1: SELECT ''::halfvec;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT '['::halfvec;
-ERROR:  malformed halfvec literal: "["
+ERROR:  invalid input syntax for type halfvec: "["
+LINE 1: SELECT '['::halfvec;
+               ^
+SELECT '[ '::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[ "
 LINE 1: SELECT '[ '::halfvec;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[,'::halfvec;
-ERROR:  malformed halfvec literal: "[,"
+ERROR:  invalid input syntax for type halfvec: "[,"
 LINE 1: SELECT '[,'::halfvec;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[]'::halfvec;
 ERROR:  halfvec must have at least 1 dimension
 LINE 1: SELECT '[]'::halfvec;
                ^
+SELECT '[ ]'::halfvec;
+ERROR:  halfvec must have at least 1 dimension
+LINE 1: SELECT '[ ]'::halfvec;
+               ^
+SELECT '[,]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[,]"
+LINE 1: SELECT '[,]'::halfvec;
+               ^
 SELECT '[1,]'::halfvec;
 ERROR:  invalid input syntax for type halfvec: "[1,]"
 LINE 1: SELECT '[1,]'::halfvec;
@@ -109,7 +122,7 @@ ERROR:  invalid input syntax for type halfvec: "[1a]"
 LINE 1: SELECT '[1a]'::halfvec;
                ^
 SELECT '[1,,3]'::halfvec;
-ERROR:  malformed halfvec literal: "[1,,3]"
+ERROR:  invalid input syntax for type halfvec: "[1,,3]"
 LINE 1: SELECT '[1,,3]'::halfvec;
                ^
 SELECT '[1, ,3]'::halfvec;

test/expected/hnsw_bit_hamming.out

@@ -24,4 +24,6 @@ CREATE TABLE t (val varbit(3));
 CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
 ERROR:  type not supported for hnsw index
 CREATE INDEX ON t USING hnsw ((val::bit(3)) bit_hamming_ops);
+CREATE INDEX ON t USING hnsw ((val::bit(64001)) bit_hamming_ops);
+ERROR:  column cannot have more than 64000 dimensions for hnsw index
 DROP TABLE t;

test/expected/hnsw_halfvec_l1.out

@@ -0,0 +1,21 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_l1_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <+> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::halfvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_sparsevec_l1.out

@@ -0,0 +1,21 @@
+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 USING hnsw (val sparsevec_l1_ops);
+INSERT INTO t (val) VALUES ('{1:1,2:2,3:4}/3');
+SELECT * FROM t ORDER BY val <+> '{1:3,2:3,3:3}/3';
+       val       
+-----------------
+ {1:1,2:2,3:3}/3
+ {1:1,2:2,3:4}/3
+ {1:1,2:1,3:1}/3
+ {}/3
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::sparsevec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_vector_l1.out

@@ -0,0 +1,21 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l1_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <+> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::vector)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

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_halfvec_cosine.out

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

test/expected/ivfflat_halfvec_ip.out

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

test/expected/ivfflat_halfvec_l2.out

@@ -0,0 +1,36 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING ivfflat (val halfvec_l2_ops) WITH (lists = 1);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::halfvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+SELECT COUNT(*) FROM t;
+ count 
+-------
+     5
+(1 row)
+
+TRUNCATE t;
+NOTICE:  ivfflat index created with little data
+DETAIL:  This will cause low recall.
+HINT:  Drop the index until the table has more data.
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+ val 
+-----
+(0 rows)
+
+DROP TABLE t;

test/expected/ivfflat_vector_l2.out

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

test/expected/sparsevec_functions.out

@@ -1,9 +1,177 @@
+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 l2_norm('{1:3,2:4}/2'::sparsevec);
+ l2_norm 
+---------
+       5
+(1 row)
+
+SELECT l2_norm('{2:1}/2'::sparsevec);
+ l2_norm 
+---------
+       1
+(1 row)
+
+SELECT l2_norm('{1:3e37,2:4e37}/2'::sparsevec)::real;
+ l2_norm 
+---------
+   5e+37
+(1 row)
+
+SELECT l2_norm('{}/2'::sparsevec);
+ l2_norm 
+---------
+       0
+(1 row)
+
+SELECT l2_norm('{1:2}/1'::sparsevec);
+ l2_norm 
+---------
+       2
+(1 row)
+
 SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
  l2_distance 
 -------------
            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('{1:3,2:4}/2'::sparsevec, '{}/2');
+ l2_distance 
+-------------
+           5
+(1 row)
+
 SELECT l2_distance('{}/2'::sparsevec, '{2:1}/2');
  l2_distance 
 -------------
@@ -22,10 +190,54 @@ 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');
- sparsevec_negative_inner_product 
-----------------------------------
-                              -10
+SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+ERROR:  different sparsevec dimensions 2 and 1
+SELECT inner_product('{1:1,3:3}/4'::sparsevec, '{2:2,4:4}/4');
+ inner_product 
+---------------
+             0
+(1 row)
+
+SELECT inner_product('{2:2,4:4}/4'::sparsevec, '{1:1,3:3}/4');
+ inner_product 
+---------------
+             0
+(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 inner_product('{1:1}/2'::sparsevec, '{}/2');
+ inner_product 
+---------------
+             0
+(1 row)
+
+SELECT inner_product('{}/2'::sparsevec, '{1:1}/2');
+ inner_product 
+---------------
+             0
+(1 row)
+
+SELECT inner_product('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
+ 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');
@@ -40,6 +252,18 @@ 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 
 -----------------
@@ -52,11 +276,121 @@ SELECT cosine_distance('{1:2}/2'::sparsevec, '{2:2}/2');
                1
 (1 row)
 
+SELECT cosine_distance('{2:2}/2'::sparsevec, '{1:2}/2');
+ cosine_distance 
+-----------------
+               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');
-ERROR:  different sparsevec dimensions 2 and 3
+SELECT '{1:1,2:2}/2'::sparsevec <=> '{1:2,2:4}/2';
+ ?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 '{}/2'::sparsevec <+> '{1:3,2:4}/2';
+ ?column? 
+----------
+        7
+(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/sparsevec_input.out

@@ -4,26 +4,159 @@ SELECT '{1:1.5,3:3.5}/5'::sparsevec;
  {1:1.5,3:3.5}/5
 (1 row)
 
-SELECT '{1:1.5,3:3.5}/5'::sparsevec::vector;
-     vector      
------------------
- [1.5,0,3.5,0,0]
+SELECT '{1:-2,3:-4}/5'::sparsevec;
+   sparsevec   
+---------------
+ {1:-2,3:-4}/5
 (1 row)
 
-SELECT '{1:1.5,3:3.5}/5'::sparsevec::vector(5);
-     vector      
------------------
- [1.5,0,3.5,0,0]
+SELECT '{1:2.,3:4.}/5'::sparsevec;
+  sparsevec  
+-------------
+ {1:2,3:4}/5
 (1 row)
 
-SELECT '{1:1.5,3:3.5}/5'::sparsevec::vector(4);
-ERROR:  expected 4 dimensions, not 5
-SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
+SELECT ' { 1 : 1.5 ,  3  :  3.5  } / 5 '::sparsevec;
     sparsevec    
 -----------------
- {2:1.5,4:3.5}/5
+ {1:1.5,3:3.5}/5
 (1 row)
 
+SELECT '{1:1.23456}/1'::sparsevec;
+   sparsevec   
+---------------
+ {1:1.23456}/1
+(1 row)
+
+SELECT '{1:hello,2:1}/2'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:hello,2:1}/2"
+LINE 1: SELECT '{1:hello,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:NaN,2:1}/2'::sparsevec;
+ERROR:  NaN not allowed in sparsevec
+LINE 1: SELECT '{1:NaN,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:Infinity,2:1}/2'::sparsevec;
+ERROR:  infinite value not allowed in sparsevec
+LINE 1: SELECT '{1:Infinity,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:-Infinity,2:1}/2'::sparsevec;
+ERROR:  infinite value not allowed in sparsevec
+LINE 1: SELECT '{1:-Infinity,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:1.5e38,2:-1.5e38}/2'::sparsevec;
+        sparsevec         
+--------------------------
+ {1:1.5e+38,2:-1.5e+38}/2
+(1 row)
+
+SELECT '{1:1.5e+38,2:-1.5e+38}/2'::sparsevec;
+        sparsevec         
+--------------------------
+ {1:1.5e+38,2:-1.5e+38}/2
+(1 row)
+
+SELECT '{1:1.5e-38,2:-1.5e-38}/2'::sparsevec;
+        sparsevec         
+--------------------------
+ {1:1.5e-38,2:-1.5e-38}/2
+(1 row)
+
+SELECT '{1:4e38,2:1}/2'::sparsevec;
+ERROR:  "4e38" is out of range for type sparsevec
+LINE 1: SELECT '{1:4e38,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:-4e38,2:1}/2'::sparsevec;
+ERROR:  "-4e38" is out of range for type sparsevec
+LINE 1: SELECT '{1:-4e38,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:1e-46,2:1}/2'::sparsevec;
+ERROR:  "1e-46" is out of range for type sparsevec
+LINE 1: SELECT '{1:1e-46,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:-1e-46,2:1}/2'::sparsevec;
+ERROR:  "-1e-46" is out of range for type sparsevec
+LINE 1: SELECT '{1:-1e-46,2:1}/2'::sparsevec;
+               ^
+SELECT ''::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: ""
+LINE 1: SELECT ''::sparsevec;
+               ^
+DETAIL:  Vector contents must start with "{".
+SELECT '{'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{"
+LINE 1: SELECT '{'::sparsevec;
+               ^
+SELECT '{ '::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{ "
+LINE 1: SELECT '{ '::sparsevec;
+               ^
+SELECT '{:'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{:"
+LINE 1: SELECT '{:'::sparsevec;
+               ^
+SELECT '{,'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{,"
+LINE 1: SELECT '{,'::sparsevec;
+               ^
+SELECT '{}'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{}"
+LINE 1: SELECT '{}'::sparsevec;
+               ^
+DETAIL:  Unexpected end of input.
+SELECT '{}/'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{}/"
+LINE 1: SELECT '{}/'::sparsevec;
+               ^
+SELECT '{}/1'::sparsevec;
+ sparsevec 
+-----------
+ {}/1
+(1 row)
+
+SELECT '{}/1a'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{}/1a"
+LINE 1: SELECT '{}/1a'::sparsevec;
+               ^
+DETAIL:  Junk after closing.
+SELECT '{ }/1'::sparsevec;
+ sparsevec 
+-----------
+ {}/1
+(1 row)
+
+SELECT '{:}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{:}/1"
+LINE 1: SELECT '{:}/1'::sparsevec;
+               ^
+SELECT '{,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{,}/1"
+LINE 1: SELECT '{,}/1'::sparsevec;
+               ^
+SELECT '{1,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1,}/1"
+LINE 1: SELECT '{1,}/1'::sparsevec;
+               ^
+SELECT '{:1}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{:1}/1"
+LINE 1: SELECT '{:1}/1'::sparsevec;
+               ^
+SELECT '{1:}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:}/1"
+LINE 1: SELECT '{1:}/1'::sparsevec;
+               ^
+SELECT '{1a:1}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1a:1}/1"
+LINE 1: SELECT '{1a:1}/1'::sparsevec;
+               ^
+SELECT '{1:1a}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:1a}/1"
+LINE 1: SELECT '{1:1a}/1'::sparsevec;
+               ^
+SELECT '{1:1,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:1,}/1"
+LINE 1: SELECT '{1:1,}/1'::sparsevec;
+               ^
 SELECT '{1:0,2:1,3:0}/3'::sparsevec;
  sparsevec 
 -----------
@@ -31,8 +164,18 @@ SELECT '{1:0,2:1,3:0}/3'::sparsevec;
 (1 row)
 
 SELECT '{2:1,1:1}/2'::sparsevec;
-ERROR:  indexes must be in ascending order
-LINE 1: SELECT '{2:1,1:1}/2'::sparsevec;
+  sparsevec  
+-------------
+ {1:1,2:1}/2
+(1 row)
+
+SELECT '{1:1,1:1}/2'::sparsevec;
+ERROR:  indexes must not contain duplicates
+LINE 1: SELECT '{1:1,1:1}/2'::sparsevec;
+               ^
+SELECT '{1:1,2:1,1:1}/2'::sparsevec;
+ERROR:  indexes must not contain duplicates
+LINE 1: SELECT '{1:1,2:1,1:1}/2'::sparsevec;
                ^
 SELECT '{}/5'::sparsevec;
  sparsevec 
@@ -44,12 +187,10 @@ SELECT '{}/-1'::sparsevec;
 ERROR:  sparsevec must have at least 1 dimension
 LINE 1: SELECT '{}/-1'::sparsevec;
                ^
-SELECT '{}/100001'::sparsevec;
-ERROR:  sparsevec cannot have more than 100000 dimensions
-LINE 1: SELECT '{}/100001'::sparsevec;
+SELECT '{}/1000001'::sparsevec;
+ERROR:  sparsevec cannot have more than 1000000 dimensions
+LINE 1: SELECT '{}/1000001'::sparsevec;
                ^
-SELECT '{}/16001'::sparsevec::vector;
-ERROR:  vector cannot have more than 16000 dimensions
 SELECT '{0:1}/1'::sparsevec;
 ERROR:  index "0" is out of range for type sparsevec
 LINE 1: SELECT '{0:1}/1'::sparsevec;
@@ -58,5 +199,27 @@ SELECT '{2:1}/1'::sparsevec;
 ERROR:  index must be less than or equal to dimensions
 LINE 1: SELECT '{2:1}/1'::sparsevec;
                ^
-SELECT '{}/1'::sparsevec(2);
-ERROR:  expected 2 dimensions, not 1
+SELECT '{}/3'::sparsevec(3);
+ sparsevec 
+-----------
+ {}/3
+(1 row)
+
+SELECT '{}/3'::sparsevec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{}/3'::sparsevec(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '{}/3'::sparsevec(3, 2);
+                       ^
+SELECT '{}/3'::sparsevec('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '{}/3'::sparsevec('a');
+                       ^
+SELECT '{}/3'::sparsevec(0);
+ERROR:  dimensions for type sparsevec must be at least 1
+LINE 1: SELECT '{}/3'::sparsevec(0);
+                       ^
+SELECT '{}/3'::sparsevec(1000001);
+ERROR:  dimensions for type sparsevec cannot exceed 1000000
+LINE 1: SELECT '{}/3'::sparsevec(1000001);
+                       ^

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
@@ -168,6 +182,18 @@ SELECT vector_norm('[3e37,4e37]')::real;
        5e+37
 (1 row)
 
+SELECT vector_norm('[0,0]');
+ vector_norm 
+-------------
+           0
+(1 row)
+
+SELECT vector_norm('[2]');
+ vector_norm 
+-------------
+           2
+(1 row)
+
 SELECT l2_distance('[0,0]'::vector, '[3,4]');
  l2_distance 
 -------------
@@ -188,6 +214,18 @@ SELECT l2_distance('[3e38]'::vector, '[-3e38]');
     Infinity
 (1 row)
 
+SELECT l2_distance('[1,1,1,1,1,1,1,1,1]'::vector, '[1,1,1,1,1,1,1,4,5]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT '[0,0]'::vector <-> '[3,4]';
+ ?column? 
+----------
+        5
+(1 row)
+
 SELECT inner_product('[1,2]'::vector, '[3,4]');
  inner_product 
 ---------------
@@ -202,6 +240,18 @@ SELECT inner_product('[3e38]'::vector, '[3e38]');
       Infinity
 (1 row)
 
+SELECT inner_product('[1,1,1,1,1,1,1,1,1]'::vector, '[1,2,3,4,5,6,7,8,9]');
+ inner_product 
+---------------
+            45
+(1 row)
+
+SELECT '[1,2]'::vector <#> '[3,4]';
+ ?column? 
+----------
+      -11
+(1 row)
+
 SELECT cosine_distance('[1,2]'::vector, '[2,4]');
  cosine_distance 
 -----------------
@@ -252,6 +302,24 @@ SELECT cosine_distance('[3e38]'::vector, '[3e38]');
              NaN
 (1 row)
 
+SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[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]'::vector, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT '[1,2]'::vector <=> '[2,4]';
+ ?column? 
+----------
+        0
+(1 row)
+
 SELECT l1_distance('[0,0]'::vector, '[3,4]');
  l1_distance 
 -------------
@@ -272,14 +340,62 @@ SELECT l1_distance('[3e38]'::vector, '[-3e38]');
     Infinity
 (1 row)
 
-SELECT quantize_binary('[1,0,-1]'::vector);
- quantize_binary 
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[1,2,3,4,5,6,7,8,9]');
+ l1_distance 
+-------------
+           0
+(1 row)
+
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[0,3,2,5,4,7,6,9,8]');
+ l1_distance 
+-------------
+           9
+(1 row)
+
+SELECT '[0,0]'::vector <+> '[3,4]';
+ ?column? 
+----------
+        7
+(1 row)
+
+SELECT l2_normalize('[3,4]'::vector);
+ 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);
- quantize_binary 
+SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::vector);
+ binary_quantize 
 -----------------
  01001110101
 (1 row)

test/expected/vector_input.out

@@ -83,39 +83,48 @@ SELECT '[-1e-46,1]'::vector;
 (1 row)
 
 SELECT '[1,2,3'::vector;
-ERROR:  malformed vector literal: "[1,2,3"
+ERROR:  invalid input syntax for type vector: "[1,2,3"
 LINE 1: SELECT '[1,2,3'::vector;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[1,2,3]9'::vector;
-ERROR:  malformed vector literal: "[1,2,3]9"
+ERROR:  invalid input syntax for type vector: "[1,2,3]9"
 LINE 1: SELECT '[1,2,3]9'::vector;
                ^
 DETAIL:  Junk after closing right brace.
 SELECT '1,2,3'::vector;
-ERROR:  malformed vector literal: "1,2,3"
+ERROR:  invalid input syntax for type vector: "1,2,3"
 LINE 1: SELECT '1,2,3'::vector;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT ''::vector;
-ERROR:  malformed vector literal: ""
+ERROR:  invalid input syntax for type vector: ""
 LINE 1: SELECT ''::vector;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT '['::vector;
-ERROR:  malformed vector literal: "["
+ERROR:  invalid input syntax for type vector: "["
+LINE 1: SELECT '['::vector;
+               ^
+SELECT '[ '::vector;
+ERROR:  invalid input syntax for type vector: "[ "
 LINE 1: SELECT '[ '::vector;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[,'::vector;
-ERROR:  malformed vector literal: "[,"
+ERROR:  invalid input syntax for type vector: "[,"
 LINE 1: SELECT '[,'::vector;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[]'::vector;
 ERROR:  vector must have at least 1 dimension
 LINE 1: SELECT '[]'::vector;
                ^
+SELECT '[ ]'::vector;
+ERROR:  vector must have at least 1 dimension
+LINE 1: SELECT '[ ]'::vector;
+               ^
+SELECT '[,]'::vector;
+ERROR:  invalid input syntax for type vector: "[,]"
+LINE 1: SELECT '[,]'::vector;
+               ^
 SELECT '[1,]'::vector;
 ERROR:  invalid input syntax for type vector: "[1,]"
 LINE 1: SELECT '[1,]'::vector;
@@ -125,7 +134,7 @@ ERROR:  invalid input syntax for type vector: "[1a]"
 LINE 1: SELECT '[1a]'::vector;
                ^
 SELECT '[1,,3]'::vector;
-ERROR:  malformed vector literal: "[1,,3]"
+ERROR:  invalid input syntax for type vector: "[1,,3]"
 LINE 1: SELECT '[1,,3]'::vector;
                ^
 SELECT '[1, ,3]'::vector;

test/sql/bit_functions.sql

@@ -3,6 +3,9 @@ SELECT hamming_distance('111', '110');
 SELECT hamming_distance('111', '100');
 SELECT hamming_distance('111', '000');
 SELECT hamming_distance('10101010101010101010', '01010101010101010101');
+SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
+SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
+SELECT hamming_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
 SELECT hamming_distance('', '');
 SELECT hamming_distance('111', '00');
 SELECT hamming_distance('111', '000'::varbit(4));
@@ -15,6 +18,9 @@ SELECT jaccard_distance('1111', '1000');
 SELECT jaccard_distance('1111', '0000');
 SELECT jaccard_distance('1100', '1000');
 SELECT jaccard_distance('10101010101010101010', '01010101010101010101');
+SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
+SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
+SELECT jaccard_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
 SELECT jaccard_distance('', '');
 SELECT jaccard_distance('1111', '000');
 SELECT jaccard_distance('1111', '0000'::varbit(5));

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/cast.sql

@@ -3,19 +3,61 @@ SELECT ARRAY[1.0,2.0,3.0]::vector;
 SELECT ARRAY[1,2,3]::float4[]::vector;
 SELECT ARRAY[1,2,3]::float8[]::vector;
 SELECT ARRAY[1,2,3]::numeric[]::vector;
+
+SELECT '[1,2,3]'::vector::real[];
+
+SELECT '{1,2,3}'::real[]::vector;
+SELECT '{1,2,3}'::real[]::vector(3);
+SELECT '{1,2,3}'::real[]::vector(2);
 SELECT '{NULL}'::real[]::vector;
 SELECT '{NaN}'::real[]::vector;
 SELECT '{Infinity}'::real[]::vector;
 SELECT '{-Infinity}'::real[]::vector;
 SELECT '{}'::real[]::vector;
 SELECT '{{1}}'::real[]::vector;
-SELECT '[1,2,3]'::vector::real[];
+
+SELECT '{1,2,3}'::double precision[]::vector;
+SELECT '{1,2,3}'::double precision[]::vector(3);
+SELECT '{1,2,3}'::double precision[]::vector(2);
+SELECT '{4e38,-4e38}'::double precision[]::vector;
+SELECT '{1e-46,-1e-46}'::double precision[]::vector;
+
 SELECT '[1,2,3]'::vector::halfvec;
-SELECT '[1,2,3]'::halfvec::vector;
+SELECT '[1,2,3]'::vector::halfvec(3);
 SELECT '[1,2,3]'::vector::halfvec(2);
-SELECT '[1,2,3]'::halfvec::vector(2);
 SELECT '[65520]'::vector::halfvec;
 SELECT '[1e-8]'::vector::halfvec;
+
+SELECT '[1,2,3]'::halfvec::vector;
+SELECT '[1,2,3]'::halfvec::vector(3);
+SELECT '[1,2,3]'::halfvec::vector(2);
+
+SELECT '{1,2,3}'::real[]::halfvec;
+SELECT '{1,2,3}'::real[]::halfvec(3);
+SELECT '{1,2,3}'::real[]::halfvec(2);
+SELECT '{65520,-65520}'::real[]::halfvec;
+SELECT '{1e-8,-1e-8}'::real[]::halfvec;
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(5);
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(4);
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector;
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(5);
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(4);
+SELECT '{}/16001'::sparsevec::vector;
+
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec;
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec(5);
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec(4);
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec;
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec(5);
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec(4);
+SELECT '{}/16001'::sparsevec::halfvec;
+SELECT '{1:65520}/1'::sparsevec::halfvec;
+SELECT '{1:1e-8}/1'::sparsevec::halfvec;
+
 SELECT array_agg(n)::vector FROM generate_series(1, 16001) n;
 SELECT array_to_vector(array_agg(n), 16001, false) FROM generate_series(1, 16001) n;
 

test/sql/copy.sql

@@ -1,7 +1,7 @@
-CREATE TABLE t (val vector(3), val2 halfvec(3));
-INSERT INTO t (val, val2) VALUES ('[0,0,0]', '[0,0,0]'), ('[1,2,3]', '[1,2,3]'), ('[1,1,1]', '[1,1,1]'), (NULL, NULL);
+CREATE TABLE t (val vector(3), val2 halfvec(3), val3 sparsevec(3));
+INSERT INTO t (val, val2, val3) VALUES ('[0,0,0]', '[0,0,0]', '{}/3'), ('[1,2,3]', '[1,2,3]', '{1:1,2:2,3:3}/3'), ('[1,1,1]', '[1,1,1]', '{1:1,2:1,3:1}/3'), (NULL, NULL, NULL);
 
-CREATE TABLE t2 (val vector(3), val2 halfvec(3));
+CREATE TABLE t2 (val vector(3), val2 halfvec(3), val3 sparsevec(3));
 
 \copy t TO 'results/data.bin' WITH (FORMAT binary)
 \copy t2 FROM 'results/data.bin' WITH (FORMAT binary)

test/sql/halfvec_functions.sql

@@ -1,11 +1,58 @@
+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 '[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_norm('[0,0]'::halfvec);
+SELECT l2_norm('[2]'::halfvec);
+
 SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
 SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
 SELECT l2_distance('[1,2]'::halfvec, '[3]');
+SELECT l2_distance('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,1,1,1,1,1,1,4,5]');
 SELECT '[0,0]'::halfvec <-> '[3,4]';
 
 SELECT inner_product('[1,2]'::halfvec, '[3,4]');
 SELECT inner_product('[1,2]'::halfvec, '[3]');
 SELECT inner_product('[65504]'::halfvec, '[65504]');
+SELECT inner_product('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
 SELECT '[1,2]'::halfvec <#> '[3,4]';
 
 SELECT cosine_distance('[1,2]'::halfvec, '[2,4]');
@@ -16,14 +63,25 @@ 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 l1_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[0,3,2,5,4,7,6,9,8]');
+SELECT '[0,0]'::halfvec <+> '[3,4]';
 
-SELECT quantize_binary('[1,0,-1]'::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('[3,4]'::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);
@@ -32,3 +90,16 @@ 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/halfvec_input.sql

@@ -17,8 +17,11 @@ SELECT '[1,2,3]9'::halfvec;
 SELECT '1,2,3'::halfvec;
 SELECT ''::halfvec;
 SELECT '['::halfvec;
+SELECT '[ '::halfvec;
 SELECT '[,'::halfvec;
 SELECT '[]'::halfvec;
+SELECT '[ ]'::halfvec;
+SELECT '[,]'::halfvec;
 SELECT '[1,]'::halfvec;
 SELECT '[1a]'::halfvec;
 SELECT '[1,,3]'::halfvec;

test/sql/hnsw_bit_hamming.sql

@@ -15,4 +15,5 @@ DROP TABLE t;
 CREATE TABLE t (val varbit(3));
 CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
 CREATE INDEX ON t USING hnsw ((val::bit(3)) bit_hamming_ops);
+CREATE INDEX ON t USING hnsw ((val::bit(64001)) bit_hamming_ops);
 DROP TABLE t;

test/sql/hnsw_halfvec_l1.sql

@@ -0,0 +1,12 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_l1_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <+> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::halfvec)) t2;
+
+DROP TABLE t;

test/sql/hnsw_sparsevec_l1.sql

@@ -0,0 +1,12 @@
+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 USING hnsw (val sparsevec_l1_ops);
+
+INSERT INTO t (val) VALUES ('{1:1,2:2,3:4}/3');
+
+SELECT * FROM t ORDER BY val <+> '{1:3,2:3,3:3}/3';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::sparsevec)) t2;
+
+DROP TABLE t;

test/sql/hnsw_vector_l1.sql

@@ -0,0 +1,12 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l1_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <+> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::vector)) t2;
+
+DROP TABLE t;

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_halfvec_cosine.sql

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

test/sql/ivfflat_halfvec_ip.sql

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

test/sql/ivfflat_halfvec_l2.sql

@@ -0,0 +1,16 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING ivfflat (val halfvec_l2_ops) WITH (lists = 1);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::halfvec)) t2;
+SELECT COUNT(*) FROM t;
+
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+DROP TABLE t;

test/sql/ivfflat_vector_l2.sql

@@ -7,7 +7,7 @@ CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 1);
 INSERT INTO t (val) VALUES ('[1,2,4]');
 
 SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector)) t2;
 SELECT COUNT(*) FROM t;
 
 TRUNCATE t;

test/sql/sparsevec_functions.sql

@@ -1,13 +1,75 @@
+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 '{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_norm('{}/2'::sparsevec);
+SELECT l2_norm('{1:2}/1'::sparsevec);
+
 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('{1:3,2:4}/2'::sparsevec, '{}/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('{1:1,3:3}/4'::sparsevec, '{2:2,4:4}/4');
+SELECT inner_product('{2:2,4:4}/4'::sparsevec, '{1:1,3:3}/4');
+SELECT inner_product('{1:1,3:3,5:5}/5'::sparsevec, '{2:4,3:6,4:8}/5');
+SELECT inner_product('{1:1}/2'::sparsevec, '{}/2');
+SELECT inner_product('{}/2'::sparsevec, '{1:1}/2');
+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('{2:2}/2'::sparsevec, '{1:2}/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 '{}/2'::sparsevec <+> '{1:3,2:4}/2';
+
+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/sparsevec_input.sql

@@ -1,19 +1,50 @@
 SELECT '{1:1.5,3:3.5}/5'::sparsevec;
-SELECT '{1:1.5,3:3.5}/5'::sparsevec::vector;
-SELECT '{1:1.5,3:3.5}/5'::sparsevec::vector(5);
-SELECT '{1:1.5,3:3.5}/5'::sparsevec::vector(4);
-SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
-
+SELECT '{1:-2,3:-4}/5'::sparsevec;
+SELECT '{1:2.,3:4.}/5'::sparsevec;
+SELECT ' { 1 : 1.5 ,  3  :  3.5  } / 5 '::sparsevec;
+SELECT '{1:1.23456}/1'::sparsevec;
+SELECT '{1:hello,2:1}/2'::sparsevec;
+SELECT '{1:NaN,2:1}/2'::sparsevec;
+SELECT '{1:Infinity,2:1}/2'::sparsevec;
+SELECT '{1:-Infinity,2:1}/2'::sparsevec;
+SELECT '{1:1.5e38,2:-1.5e38}/2'::sparsevec;
+SELECT '{1:1.5e+38,2:-1.5e+38}/2'::sparsevec;
+SELECT '{1:1.5e-38,2:-1.5e-38}/2'::sparsevec;
+SELECT '{1:4e38,2:1}/2'::sparsevec;
+SELECT '{1:-4e38,2:1}/2'::sparsevec;
+SELECT '{1:1e-46,2:1}/2'::sparsevec;
+SELECT '{1:-1e-46,2:1}/2'::sparsevec;
+SELECT ''::sparsevec;
+SELECT '{'::sparsevec;
+SELECT '{ '::sparsevec;
+SELECT '{:'::sparsevec;
+SELECT '{,'::sparsevec;
+SELECT '{}'::sparsevec;
+SELECT '{}/'::sparsevec;
+SELECT '{}/1'::sparsevec;
+SELECT '{}/1a'::sparsevec;
+SELECT '{ }/1'::sparsevec;
+SELECT '{:}/1'::sparsevec;
+SELECT '{,}/1'::sparsevec;
+SELECT '{1,}/1'::sparsevec;
+SELECT '{:1}/1'::sparsevec;
+SELECT '{1:}/1'::sparsevec;
+SELECT '{1a:1}/1'::sparsevec;
+SELECT '{1:1a}/1'::sparsevec;
+SELECT '{1:1,}/1'::sparsevec;
 SELECT '{1:0,2:1,3:0}/3'::sparsevec;
-
 SELECT '{2:1,1:1}/2'::sparsevec;
-
+SELECT '{1:1,1:1}/2'::sparsevec;
+SELECT '{1:1,2:1,1:1}/2'::sparsevec;
 SELECT '{}/5'::sparsevec;
 SELECT '{}/-1'::sparsevec;
-SELECT '{}/100001'::sparsevec;
-SELECT '{}/16001'::sparsevec::vector;
-
+SELECT '{}/1000001'::sparsevec;
 SELECT '{0:1}/1'::sparsevec;
 SELECT '{2:1}/1'::sparsevec;
 
-SELECT '{}/1'::sparsevec(2);
+SELECT '{}/3'::sparsevec(3);
+SELECT '{}/3'::sparsevec(2);
+SELECT '{}/3'::sparsevec(3, 2);
+SELECT '{}/3'::sparsevec('a');
+SELECT '{}/3'::sparsevec(0);
+SELECT '{}/3'::sparsevec(1000001);

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]';
@@ -27,21 +35,27 @@ 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]');
 SELECT vector_norm('[0,1]');
 SELECT vector_norm('[3e37,4e37]')::real;
+SELECT vector_norm('[0,0]');
+SELECT vector_norm('[2]');
 
 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 l2_distance('[1,1,1,1,1,1,1,1,1]'::vector, '[1,1,1,1,1,1,1,4,5]');
+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 inner_product('[1,1,1,1,1,1,1,1,1]'::vector, '[1,2,3,4,5,6,7,8,9]');
+SELECT '[1,2]'::vector <#> '[3,4]';
 
 SELECT cosine_distance('[1,2]'::vector, '[2,4]');
 SELECT cosine_distance('[1,2]'::vector, '[0,0]');
@@ -52,14 +66,26 @@ 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 cosine_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[1,2,3,4,5,6,7,8,9]');
+SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
+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 l1_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[1,2,3,4,5,6,7,8,9]');
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[0,3,2,5,4,7,6,9,8]');
+SELECT '[0,0]'::vector <+> '[3,4]';
 
-SELECT quantize_binary('[1,0,-1]'::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('[3,4]'::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/sql/vector_input.sql

@@ -19,8 +19,11 @@ SELECT '[1,2,3]9'::vector;
 SELECT '1,2,3'::vector;
 SELECT ''::vector;
 SELECT '['::vector;
+SELECT '[ '::vector;
 SELECT '[,'::vector;
 SELECT '[]'::vector;
+SELECT '[ ]'::vector;
+SELECT '[,]'::vector;
 SELECT '[1,]'::vector;
 SELECT '[1a]'::vector;
 SELECT '[1,,3]'::vector;

test/t/003_ivfflat_build_recall.pl

@@ -30,18 +30,19 @@ sub test_recall
 			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
 		));
 		my @actual_ids = split("\n", $actual);
-		my %actual_set = map { $_ => 1 } @actual_ids;
 
 		my @expected_ids = split("\n", $expected[$i]);
+		my %expected_set = map { $_ => 1 } @expected_ids;
 
-		foreach (@expected_ids)
+		foreach (@actual_ids)
 		{
-			if (exists($actual_set{$_}))
+			if (exists($expected_set{$_}))
 			{
 				$correct++;
 			}
-			$total++;
 		}
+
+		$total += $limit;
 	}
 
 	cmp_ok($correct / $total, ">=", $min, $operator);
@@ -81,7 +82,12 @@ for my $i (0 .. $#operators)
 	@expected = ();
 	foreach (@queries)
 	{
-		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
+		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);
 	}
 
@@ -98,8 +104,16 @@ for my $i (0 .. $#operators)
 		test_recall(1, 0.71, $operator);
 		test_recall(10, 0.95, $operator);
 	}
-	# Account for equal distances
+
+	# Test probes equals lists
+	if ($operator eq "<=>")
+	{
 		test_recall(100, 0.9925, $operator);
+	}
+	else
+	{
+		test_recall(100, 1.00, $operator);
+	}
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");
 
@@ -119,8 +133,16 @@ for my $i (0 .. $#operators)
 		test_recall(1, 0.71, $operator);
 		test_recall(10, 0.95, $operator);
 	}
-	# Account for equal distances
+
+	# Test probes equals lists
+	if ($operator eq "<=>")
+	{
 		test_recall(100, 0.9925, $operator);
+	}
+	else
+	{
+		test_recall(100, 1.00, $operator);
+	}
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");
 }

test/t/012_hnsw_build_recall.pl

@@ -67,8 +67,8 @@ for (1 .. 20)
 }
 
 # Check each index type
-my @operators = ("<->", "<#>", "<=>");
-my @opclasses = ("vector_l2_ops", "vector_ip_ops", "vector_cosine_ops");
+my @operators = ("<->", "<#>", "<=>", "<+>");
+my @opclasses = ("vector_l2_ops", "vector_ip_ops", "vector_cosine_ops", "vector_l1_ops");
 
 for my $i (0 .. $#operators)
 {

test/t/013_hnsw_insert_recall.pl

@@ -64,8 +64,8 @@ for (1 .. 20)
 }
 
 # Check each index type
-my @operators = ("<->", "<#>", "<=>");
-my @opclasses = ("vector_l2_ops", "vector_ip_ops", "vector_cosine_ops");
+my @operators = ("<->", "<#>", "<=>", "<+>");
+my @opclasses = ("vector_l2_ops", "vector_ip_ops", "vector_cosine_ops", "vector_l1_ops");
 
 for my $i (0 .. $#operators)
 {
@@ -98,6 +98,7 @@ for my $i (0 .. $#operators)
 		push(@expected, $res);
 	}
 
+	# Test approximate results
 	my $min = $operator eq "<#>" ? 0.80 : 0.99;
 	test_recall($min, $operator);
 

test/t/020_hnsw_bit_build_recall.pl

@@ -85,7 +85,7 @@ for my $i (0 .. $#operators)
 		# Handle ties
 		my $res = $node->safe_psql("postgres", qq(
 			WITH top AS (
-				SELECT v $operator $_ AS distance FROM tst ORDER BY v $operator $_ LIMIT $limit
+				SELECT v $operator $_ AS distance FROM tst ORDER BY distance LIMIT $limit
 			)
 			SELECT i FROM tst WHERE (v $operator $_) <= (SELECT MAX(distance) FROM top)
 		));

test/t/021_hnsw_halfvec_build_recall.pl

@@ -71,8 +71,8 @@ for (1 .. 20)
 }
 
 # Check each index type
-my @operators = ("<->", "<#>", "<=>");
-my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops");
+my @operators = ("<->", "<#>", "<=>", "<+>");
+my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops", "halfvec_l1_ops");
 
 for my $i (0 .. $#operators)
 {
@@ -94,7 +94,7 @@ for my $i (0 .. $#operators)
 	));
 
 	# Test approximate results
-	my $min = $operator eq "<#>" ? 0.95 : 0.98;
+	my $min = $operator eq "<#>" ? 0.93 : 0.98;
 	test_recall($min, $operator);
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");

test/t/022_hnsw_sparsevec_build_recall.pl

@@ -67,8 +67,8 @@ for (1 .. 20)
 }
 
 # Check each index type
-my @operators = ("<->", "<#>", "<=>");
-my @opclasses = ("sparsevec_l2_ops", "sparsevec_ip_ops", "sparsevec_cosine_ops");
+my @operators = ("<->", "<#>", "<=>", "<+>");
+my @opclasses = ("sparsevec_l2_ops", "sparsevec_ip_ops", "sparsevec_cosine_ops", "sparsevec_l1_ops");
 
 for my $i (0 .. $#operators)
 {

test/t/023_hnsw_bit_insert_recall.pl

@@ -0,0 +1,116 @@
+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 ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 100;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator $queries[0] LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = 100;
+			SELECT i FROM tst ORDER BY v $operator $queries[$i] LIMIT $limit;
+		));
+		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 serial, v bit($dim));");
+
+# 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];
+
+	# Add index
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v $opclass);");
+
+	# Use concurrent inserts
+	$node->pgbench(
+		"--no-vacuum --client=10 --transactions=1000",
+		0,
+		[qr{actually processed}],
+		[qr{^$}],
+		"concurrent INSERTs",
+		{
+			"023_hnsw_bit_insert_recall_$opclass" => "INSERT INTO tst (v) VALUES ((random() * $max)::bigint::bit($dim));"
+		}
+	);
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		# Handle ties
+		my $res = $node->safe_psql("postgres", qq(
+			SET enable_indexscan = off;
+			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);
+	}
+
+	# Test approximate results
+	my $min = $operator eq "<\%>" ? 0.95 : 0.98;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres", "TRUNCATE tst;");
+}
+
+done_testing();

test/t/024_hnsw_halfvec_insert_recall.pl

@@ -0,0 +1,113 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 10;
+my $array_sql = join(",", ('random()') x $dim);
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i serial, v halfvec($dim));");
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>", "<+>");
+my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops", "halfvec_l1_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Add index
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v $opclass);");
+
+	# Use concurrent inserts
+	$node->pgbench(
+		"--no-vacuum --client=10 --transactions=1000",
+		0,
+		[qr{actually processed}],
+		[qr{^$}],
+		"concurrent INSERTs",
+		{
+			"024_hnsw_halfvec_insert_recall_$opclass" => "INSERT INTO tst (v) VALUES (ARRAY[$array_sql]);"
+		}
+	);
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", qq(
+			SET enable_indexscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;
+		));
+		push(@expected, $res);
+	}
+
+	# Test approximate results
+	my $min = $operator eq "<#>" ? 0.94 : 0.98;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres", "TRUNCATE tst;");
+}
+
+done_testing();

test/t/025_hnsw_sparsevec_insert_recall.pl

@@ -0,0 +1,109 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i serial, v sparsevec(3));");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "{1:$r1,2:$r2,3:$r3}/3");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>", "<+>");
+my @opclasses = ("sparsevec_l2_ops", "sparsevec_ip_ops", "sparsevec_cosine_ops", "sparsevec_l1_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Add index
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v $opclass);");
+
+	# Use concurrent inserts
+	$node->pgbench(
+		"--no-vacuum --client=10 --transactions=1000",
+		0,
+		[qr{actually processed}],
+		[qr{^$}],
+		"concurrent INSERTs",
+		{
+			"025_hnsw_sparsevec_insert_recall_$opclass" => "INSERT INTO tst (v) VALUES (ARRAY[random(), random(), random()]::vector::sparsevec);"
+		}
+	);
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", qq(
+			SET enable_indexscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;
+		));
+		push(@expected, $res);
+	}
+
+	# Test approximate results
+	my $min = $operator eq "<#>" ? 0.79 : 0.99;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres", "TRUNCATE tst;");
+}
+
+done_testing();

test/t/026_hnsw_bit_duplicates.pl

@@ -0,0 +1,58 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (v bit(3));");
+
+sub insert_vectors
+{
+	for my $i (1 .. 20)
+	{
+		$node->safe_psql("postgres", "INSERT INTO tst VALUES ('111');");
+	}
+}
+
+sub test_duplicates
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 1;
+		SELECT COUNT(*) FROM (SELECT * FROM tst ORDER BY v <~> '111') t;
+	));
+	is($res, 10);
+}
+
+# Test duplicates with build
+insert_vectors();
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v bit_hamming_ops);");
+test_duplicates();
+
+# Reset
+$node->safe_psql("postgres", "TRUNCATE tst;");
+
+# Test duplicates with inserts
+insert_vectors();
+test_duplicates();
+
+# Test fallback path for inserts
+$node->pgbench(
+	"--no-vacuum --client=5 --transactions=100",
+	0,
+	[qr{actually processed}],
+	[qr{^$}],
+	"concurrent INSERTs",
+	{
+		"026_hnsw_bit_duplicates" => "INSERT INTO tst VALUES ('111');"
+	}
+);
+
+done_testing();

test/t/027_hnsw_halfvec_duplicates.pl

@@ -0,0 +1,58 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (v halfvec(3));");
+
+sub insert_vectors
+{
+	for my $i (1 .. 20)
+	{
+		$node->safe_psql("postgres", "INSERT INTO tst VALUES ('[1,1,1]');");
+	}
+}
+
+sub test_duplicates
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 1;
+		SELECT COUNT(*) FROM (SELECT * FROM tst ORDER BY v <-> '[1,1,1]') t;
+	));
+	is($res, 10);
+}
+
+# Test duplicates with build
+insert_vectors();
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v halfvec_l2_ops);");
+test_duplicates();
+
+# Reset
+$node->safe_psql("postgres", "TRUNCATE tst;");
+
+# Test duplicates with inserts
+insert_vectors();
+test_duplicates();
+
+# Test fallback path for inserts
+$node->pgbench(
+	"--no-vacuum --client=5 --transactions=100",
+	0,
+	[qr{actually processed}],
+	[qr{^$}],
+	"concurrent INSERTs",
+	{
+		"027_hnsw_halfvec_duplicates" => "INSERT INTO tst VALUES ('[1,1,1]');"
+	}
+);
+
+done_testing();

test/t/028_hnsw_sparsevec_duplicates.pl

@@ -0,0 +1,58 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (v sparsevec(3));");
+
+sub insert_vectors
+{
+	for my $i (1 .. 20)
+	{
+		$node->safe_psql("postgres", "INSERT INTO tst VALUES ('{1:1,2:1,3:1}/3');");
+	}
+}
+
+sub test_duplicates
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 1;
+		SELECT COUNT(*) FROM (SELECT * FROM tst ORDER BY v <-> '{1:1,2:1,3:1}/3') t;
+	));
+	is($res, 10);
+}
+
+# Test duplicates with build
+insert_vectors();
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v sparsevec_l2_ops);");
+test_duplicates();
+
+# Reset
+$node->safe_psql("postgres", "TRUNCATE tst;");
+
+# Test duplicates with inserts
+insert_vectors();
+test_duplicates();
+
+# Test fallback path for inserts
+$node->pgbench(
+	"--no-vacuum --client=5 --transactions=100",
+	0,
+	[qr{actually processed}],
+	[qr{^$}],
+	"concurrent INSERTs",
+	{
+		"028_hnsw_sparsevec_duplicates" => "INSERT INTO tst VALUES ('{1:1,2:1,3:1}/3');"
+	}
+);
+
+done_testing();

test/t/029_hnsw_bit_vacuum_recall.pl

@@ -0,0 +1,100 @@
+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 ($min, $ef_search, $test_name) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = $ef_search;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <~> $queries[0] LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = $ef_search;
+			SELECT i FROM tst ORDER BY v <~> $queries[$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, $test_name);
+}
+
+# Initialize node
+$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", "ALTER TABLE tst SET (autovacuum_enabled = false);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, (random() * $max)::bigint::bit($dim) FROM generate_series(1, 10000) i;"
+);
+
+# Add index
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v bit_hamming_ops) WITH (m = 4, ef_construction = 8);");
+
+# Delete data
+$node->safe_psql("postgres", "DELETE FROM tst WHERE i > 2500;");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r = int(rand() * $max);
+	push(@queries, "${r}::bigint::bit($dim)");
+}
+
+# Get exact results
+@expected = ();
+foreach (@queries)
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_indexscan = off;
+		WITH top AS (
+			SELECT v <~> $_ AS distance FROM tst ORDER BY distance LIMIT $limit
+		)
+		SELECT i FROM tst WHERE (v <~> $_) <= (SELECT MAX(distance) FROM top)
+	));
+	push(@expected, $res);
+}
+
+test_recall(0.35, 100, "before vacuum");
+
+# TODO Test concurrent inserts with vacuum
+$node->safe_psql("postgres", "VACUUM tst;");
+
+test_recall(0.80, 100, "after vacuum");
+
+done_testing();

test/t/030_hnsw_halfvec_vacuum_recall.pl

@@ -0,0 +1,97 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($min, $ef_search, $test_name) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = $ef_search;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = $ef_search;
+			SELECT i FROM tst ORDER BY v <-> '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $test_name);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v halfvec(3));");
+$node->safe_psql("postgres", "ALTER TABLE tst SET (autovacuum_enabled = false);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 10000) i;"
+);
+
+# Add index
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v halfvec_l2_ops) WITH (m = 4, ef_construction = 8);");
+
+# Delete data
+$node->safe_psql("postgres", "DELETE FROM tst WHERE i > 2500;");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "[$r1,$r2,$r3]");
+}
+
+# Get exact results
+@expected = ();
+foreach (@queries)
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_indexscan = off;
+		SELECT i FROM tst ORDER BY v <-> '$_' LIMIT $limit;
+	));
+	push(@expected, $res);
+}
+
+test_recall(0.18, $limit, "before vacuum");
+test_recall(0.95, 100, "before vacuum");
+
+# TODO Test concurrent inserts with vacuum
+$node->safe_psql("postgres", "VACUUM tst;");
+
+test_recall(0.95, $limit, "after vacuum");
+
+done_testing();

test/t/031_hnsw_sparsevec_vacuum_recall.pl

@@ -0,0 +1,97 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($min, $ef_search, $test_name) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = $ef_search;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = $ef_search;
+			SELECT i FROM tst ORDER BY v <-> '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $test_name);
+}
+
+# Initialize node
+$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 sparsevec(3));");
+$node->safe_psql("postgres", "ALTER TABLE tst SET (autovacuum_enabled = false);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()]::vector::sparsevec(3) FROM generate_series(1, 10000) i;"
+);
+
+# Add index
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v sparsevec_l2_ops) WITH (m = 4, ef_construction = 8);");
+
+# Delete data
+$node->safe_psql("postgres", "DELETE FROM tst WHERE i > 2500;");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "{1:$r1,2:$r2,3:$r3}/3");
+}
+
+# Get exact results
+@expected = ();
+foreach (@queries)
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_indexscan = off;
+		SELECT i FROM tst ORDER BY v <-> '$_' LIMIT $limit;
+	));
+	push(@expected, $res);
+}
+
+test_recall(0.18, $limit, "before vacuum");
+test_recall(0.95, 100, "before vacuum");
+
+# TODO Test concurrent inserts with vacuum
+$node->safe_psql("postgres", "VACUUM tst;");
+
+test_recall(0.95, $limit, "after vacuum");
+
+done_testing();

test/t/032_ivfflat_halfvec_build_recall.pl

@@ -0,0 +1,154 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 10;
+my $array_sql = join(",", ('random()') x $dim);
+
+sub test_recall
+{
+	my ($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 halfvec($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", 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 $opclass);
+	));
+
+	# Test approximate results
+	if ($operator ne "<#>")
+	{
+		# TODO Fix test (uniform random vectors all have similar inner product)
+		test_recall(1, 0.34, $operator);
+		test_recall(10, 0.93, $operator);
+	}
+
+	# Test probes equals lists
+	if ($operator eq "<=>")
+	{
+		test_recall(100, 0.98, $operator);
+	}
+	else
+	{
+		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
+	if ($operator ne "<#>")
+	{
+		# TODO Fix test (uniform random vectors all have similar inner product)
+		test_recall(1, 0.34, $operator);
+		test_recall(10, 0.93, $operator);
+	}
+
+	# Test probes equals lists
+	if ($operator eq "<=>")
+	{
+		test_recall(100, 0.98, $operator);
+	}
+	else
+	{
+		test_recall(100, 1.00, $operator);
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();

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");
+
+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();