Use integer[] for consistency [skip ci]

This reverts commit 772ab69de6.

.github/workflows/build.yml

@@ -49,7 +49,7 @@ jobs:
           - postgres: 16
             os: macos-14
           - postgres: 14
-            os: macos-12
+            os: macos-13
     steps:
       - uses: actions/checkout@v4
       - uses: ankane/setup-postgres@v1

CHANGELOG.md

@@ -1,6 +1,10 @@
 ## 0.8.0 (unreleased)
 
+- Added support for iterative index scans
+- Added `intvec` type
 - Added casts for arrays to `sparsevec`
+- Improved cost estimation
+- Improved performance of HNSW inserts and on-disk index builds
 - Reduced memory usage for HNSW index scans
 - Dropped support for Postgres 12
 

Dockerfile

@@ -1,4 +1,4 @@
-ARG PG_MAJOR=16
+ARG PG_MAJOR=17
 FROM postgres:$PG_MAJOR
 ARG PG_MAJOR
 

Makefile

@@ -4,8 +4,8 @@ EXTVERSION = 0.7.4
 MODULE_big = vector
 DATA = $(wildcard sql/*--*--*.sql)
 DATA_built = sql/$(EXTENSION)--$(EXTVERSION).sql
-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/minivec.o src/ivfvacuum.o src/sparsevec.o src/vector.o
-HEADERS = src/halfvec.h src/minivec.h src/sparsevec.h src/vector.h
+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/intvec.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/intvec.h src/sparsevec.h src/vector.h
 
 TESTS = $(wildcard test/sql/*.sql)
 REGRESS = $(patsubst test/sql/%.sql,%,$(TESTS))
@@ -66,7 +66,7 @@ dist:
 	git archive --format zip --prefix=$(EXTENSION)-$(EXTVERSION)/ --output dist/$(EXTENSION)-$(EXTVERSION).zip master
 
 # for Docker
-PG_MAJOR ?= 16
+PG_MAJOR ?= 17
 
 .PHONY: docker
 

Makefile.win

@@ -2,10 +2,10 @@ EXTENSION = vector
 EXTVERSION = 0.7.4
 
 DATA_built = sql\$(EXTENSION)--$(EXTVERSION).sql
-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\minivec.obj src\sparsevec.obj src\vector.obj
-HEADERS = src\halfvec.h src\minivec.h src\sparsevec.h src\vector.h
+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\intvec.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\intvec.h src\sparsevec.h src\vector.h
 
-REGRESS = bit btree cast copy halfvec hnsw_bit hnsw_halfvec hnsw_sparsevec hnsw_vector ivfflat_bit ivfflat_halfvec ivfflat_vector minivec sparsevec vector_type
+REGRESS = bit btree cast copy halfvec hnsw_bit hnsw_halfvec hnsw_sparsevec hnsw_vector ivfflat_bit ivfflat_halfvec ivfflat_vector sparsevec vector_type
 REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
 
 # For /arch flags

README.md

@@ -52,6 +52,8 @@ nmake /F Makefile.win
 nmake /F Makefile.win install
 ```
 
+Note: Postgres 17 is not supported yet due to an upstream issue
+
 See the [installation notes](#installation-notes---windows) if you run into issues
 
 You can also install it with [Docker](#docker) or [conda-forge](#conda-forge).
@@ -100,6 +102,8 @@ Or add a vector column to an existing table
 ALTER TABLE items ADD COLUMN embedding vector(3);
 ```
 
+Also supports [half-precision](#half-precision-vectors), [binary](#binary-vectors), and [sparse](#sparse-vectors) vectors
+
 Insert vectors
 
 ```sql
@@ -145,6 +149,8 @@ Supported distance functions are:
 - `<#>` - (negative) inner product
 - `<=>` - cosine distance
 - `<+>` - L1 distance (added in 0.7.0)
+- `<~>` - Hamming distance (binary vectors, added in 0.7.0)
+- `<%>` - Jaccard distance (binary vectors, added in 0.7.0)
 
 Get the nearest neighbors to a row
 
@@ -217,7 +223,7 @@ L2 distance
 CREATE INDEX ON items USING hnsw (embedding vector_l2_ops);
 ```
 
-Note: Use `halfvec_l2_ops` for `halfvec` and `sparsevec_l2_ops` for `sparsevec` (and similar with the other distance functions)
+Note: Use `halfvec_l2_ops` for `halfvec`, `intvec_l2_ops` for `intvec`, and `sparsevec_l2_ops` for `sparsevec` (and similar with the other distance functions)
 
 Inner product
 
@@ -253,6 +259,7 @@ Supported types are:
 
 - `vector` - up to 2,000 dimensions
 - `halfvec` - up to 4,000 dimensions (added in 0.7.0)
+- `intvec` - up to 8,000 dimensions (added in 0.8.0)
 - `bit` - up to 64,000 dimensions (added in 0.7.0)
 - `sparsevec` - up to 1,000 non-zero elements (added in 0.7.0)
 
@@ -471,6 +478,16 @@ Get the nearest neighbors
 SELECT * FROM items ORDER BY embedding::halfvec(3) <-> '[1,2,3]' LIMIT 5;
 ```
 
+## Integer Vectors
+
+*Added in 0.8.0*
+
+Use the `intvec` type to store 8-bit integer vectors
+
+```sql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding intvec(3));
+```
+
 ## Binary Vectors
 
 Use the `bit` type to store binary vectors ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/imagehash/example.py))
@@ -934,36 +951,29 @@ Function | Description | Added
 avg(halfvec) → halfvec | average | 0.7.0
 sum(halfvec) → halfvec | sum | 0.7.0
 
-### Minivec Type
+### Intvec Type
 
-Each mini vector takes `dimensions + 8` bytes of storage. Each element is a E4M3 8-bit floating-point number, and all elements must be finite (no `NaN`). Mini vectors can have up to 16,000 dimensions.
+Each int vector takes `dimensions + 8` bytes of storage. Each element is a single byte signed integer. Int vectors can have up to 16,000 dimensions.
 
-### Minivec Operators
+### Intvec Operators
 
 Operator | Description | Added
 --- | --- | ---
-\+ | element-wise addition | 0.8.0
-\- | element-wise subtraction | 0.8.0
-\* | element-wise multiplication | 0.8.0
-\|\| | concatenate | 0.8.0
 <-> | Euclidean distance | 0.8.0
 <#> | negative inner product | 0.8.0
 <=> | cosine distance | 0.8.0
 <+> | taxicab distance | 0.8.0
 
-### Minivec Functions
+### Intvec Functions
 
 Function | Description | Added
 --- | --- | ---
-binary_quantize(minivec) → bit | binary quantize | 0.8.0
-cosine_distance(minivec, minivec) → double precision | cosine distance | 0.8.0
-inner_product(minivec, minivec) → double precision | inner product | 0.8.0
-l1_distance(minivec, minivec) → double precision | taxicab distance | 0.8.0
-l2_distance(minivec, minivec) → double precision | Euclidean distance | 0.8.0
-l2_norm(minivec) → double precision | Euclidean norm | 0.8.0
-l2_normalize(minivec) → minivec | Normalize with Euclidean norm | 0.8.0
-subvector(minivec, integer, integer) → minivec | subvector | 0.8.0
-vector_dims(minivec) → integer | number of dimensions | 0.8.0
+cosine_distance(intvec, intvec) → double precision | cosine distance | 0.8.0
+inner_product(intvec, intvec) → double precision | inner product | 0.8.0
+l1_distance(intvec, intvec) → double precision | taxicab distance | 0.8.0
+l2_distance(intvec, intvec) → double precision | Euclidean distance | 0.8.0
+l2_norm(intvec) → double precision | Euclidean norm | 0.8.0
+vector_dims(intvec) → integer | number of dimensions | 0.8.0
 
 ### Bit Type
 
@@ -1014,7 +1024,7 @@ l2_normalize(sparsevec) → sparsevec | Normalize with Euclidean norm | 0.7.0
 If your machine has multiple Postgres installations, specify the path to [pg_config](https://www.postgresql.org/docs/current/app-pgconfig.html) with:
 
 ```sh
-export PG_CONFIG=/Library/PostgreSQL/16/bin/pg_config
+export PG_CONFIG=/Library/PostgreSQL/17/bin/pg_config
 ```
 
 Then re-run the installation instructions (run `make clean` before `make` if needed). If `sudo` is needed for `make install`, use:
@@ -1025,11 +1035,11 @@ sudo --preserve-env=PG_CONFIG make install
 
 A few common paths on Mac are:
 
-- EDB installer - `/Library/PostgreSQL/16/bin/pg_config`
-- Homebrew (arm64) - `/opt/homebrew/opt/postgresql@16/bin/pg_config`
-- Homebrew (x86-64) - `/usr/local/opt/postgresql@16/bin/pg_config`
+- EDB installer - `/Library/PostgreSQL/17/bin/pg_config`
+- Homebrew (arm64) - `/opt/homebrew/opt/postgresql@17/bin/pg_config`
+- Homebrew (x86-64) - `/usr/local/opt/postgresql@17/bin/pg_config`
 
-Note: Replace `16` with your Postgres server version
+Note: Replace `17` with your Postgres server version
 
 ### Missing Header
 
@@ -1038,10 +1048,10 @@ If compilation fails with `fatal error: postgres.h: No such file or directory`,
 For Ubuntu and Debian, use:
 
 ```sh
-sudo apt install postgresql-server-dev-16
+sudo apt install postgresql-server-dev-17
 ```
 
-Note: Replace `16` with your Postgres server version
+Note: Replace `17` with your Postgres server version
 
 ### Missing SDK
 
@@ -1074,17 +1084,17 @@ If installation fails with `Access is denied`, re-run the installation instructi
 Get the [Docker image](https://hub.docker.com/r/pgvector/pgvector) with:
 
 ```sh
-docker pull pgvector/pgvector:pg16
+docker pull pgvector/pgvector:pg17
 ```
 
-This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (replace `16` with your Postgres server version, and run it the same way).
+This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (replace `17` with your Postgres server version, and run it the same way).
 
 You can also build the image manually:
 
 ```sh
 git clone --branch v0.7.4 https://github.com/pgvector/pgvector.git
 cd pgvector
-docker build --pull --build-arg PG_MAJOR=16 -t myuser/pgvector .
+docker build --pull --build-arg PG_MAJOR=17 -t myuser/pgvector .
 ```
 
 ### Homebrew
@@ -1095,7 +1105,7 @@ With Homebrew Postgres, you can use:
 brew install pgvector
 ```
 
-Note: This only adds it to the `postgresql@14` formula
+Note: This only adds it to the `postgresql@17` and `postgresql@14` formulas
 
 ### PGXN
 
@@ -1110,22 +1120,22 @@ pgxn install vector
 Debian and Ubuntu packages are available from the [PostgreSQL APT Repository](https://wiki.postgresql.org/wiki/Apt). Follow the [setup instructions](https://wiki.postgresql.org/wiki/Apt#Quickstart) and run:
 
 ```sh
-sudo apt install postgresql-16-pgvector
+sudo apt install postgresql-17-pgvector
 ```
 
-Note: Replace `16` with your Postgres server version
+Note: Replace `17` with your Postgres server version
 
 ### Yum
 
 RPM packages are available from the [PostgreSQL Yum Repository](https://yum.postgresql.org/). Follow the [setup instructions](https://www.postgresql.org/download/linux/redhat/) for your distribution and run:
 
 ```sh
-sudo yum install pgvector_16
+sudo yum install pgvector_17
 # or
-sudo dnf install pgvector_16
+sudo dnf install pgvector_17
 ```
 
-Note: Replace `16` with your Postgres server version
+Note: Replace `17` with your Postgres server version
 
 ### pkg
 

sql/vector--0.7.4--0.8.0.sql

@@ -1,7 +1,187 @@
 -- complain if script is sourced in psql, rather than via CREATE EXTENSION
 \echo Use "ALTER EXTENSION vector UPDATE TO '0.8.0'" to load this file. \quit
 
--- TODO minivec functions
+CREATE FUNCTION hnsw_intvec_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE TYPE intvec;
+
+CREATE FUNCTION intvec_in(cstring, oid, integer) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_out(intvec) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_recv(internal, oid, integer) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_send(intvec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE intvec (
+	INPUT     = intvec_in,
+	OUTPUT    = intvec_out,
+	TYPMOD_IN = intvec_typmod_in,
+	RECEIVE   = intvec_recv,
+	SEND      = intvec_send,
+	STORAGE   = external
+);
+
+CREATE FUNCTION l2_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_dims(intvec) RETURNS integer
+	AS 'MODULE_PATHNAME', 'intvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_lt(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_le(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_eq(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_ne(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_ge(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_gt(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_cmp(intvec, intvec) RETURNS int4
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_l2_squared_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_negative_inner_product(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec(intvec, integer, boolean) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_intvec(integer[], integer, boolean) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_to_integer(intvec, integer, boolean) RETURNS integer[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (intvec AS intvec)
+	WITH FUNCTION intvec(intvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (intvec AS integer[])
+	WITH FUNCTION intvec_to_integer(intvec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (integer[] AS intvec)
+	WITH FUNCTION array_to_intvec(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE OPERATOR <-> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+CREATE OPERATOR <+> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR < (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+CREATE OPERATOR CLASS intvec_ops
+	DEFAULT FOR TYPE intvec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 intvec_cmp(intvec, intvec);
+
+CREATE OPERATOR CLASS intvec_l2_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <-> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 intvec_l2_squared_distance(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_ip_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <#> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 intvec_negative_inner_product(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_cosine_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <=> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 cosine_distance(intvec, intvec),
+	FUNCTION 2 l2_norm(intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_l1_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <+> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
 
 CREATE FUNCTION array_to_sparsevec(integer[], integer, boolean) RETURNS sparsevec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;

sql/vector.sql

@@ -272,7 +272,7 @@ CREATE FUNCTION ivfflat_bit_support(internal) RETURNS internal
 CREATE FUNCTION hnsw_halfvec_support(internal) RETURNS internal
 	AS 'MODULE_PATHNAME' LANGUAGE C;
 
-CREATE FUNCTION hnsw_minivec_support(internal) RETURNS internal
+CREATE FUNCTION hnsw_intvec_support(internal) RETURNS internal
 	AS 'MODULE_PATHNAME' LANGUAGE C;
 
 CREATE FUNCTION hnsw_bit_support(internal) RETURNS internal
@@ -650,267 +650,198 @@ CREATE OPERATOR CLASS halfvec_l1_ops
 	FUNCTION 1 l1_distance(halfvec, halfvec),
 	FUNCTION 3 hnsw_halfvec_support(internal);
 
--- minivec type
+-- intvec type
 
-CREATE TYPE minivec;
+CREATE TYPE intvec;
 
-CREATE FUNCTION minivec_in(cstring, oid, integer) RETURNS minivec
+CREATE FUNCTION intvec_in(cstring, oid, integer) RETURNS intvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_out(minivec) RETURNS cstring
+CREATE FUNCTION intvec_out(intvec) RETURNS cstring
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_typmod_in(cstring[]) RETURNS integer
+CREATE FUNCTION intvec_typmod_in(cstring[]) RETURNS integer
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_recv(internal, oid, integer) RETURNS minivec
+CREATE FUNCTION intvec_recv(internal, oid, integer) RETURNS intvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_send(minivec) RETURNS bytea
+CREATE FUNCTION intvec_send(intvec) RETURNS bytea
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE TYPE minivec (
-	INPUT     = minivec_in,
-	OUTPUT    = minivec_out,
-	TYPMOD_IN = minivec_typmod_in,
-	RECEIVE   = minivec_recv,
-	SEND      = minivec_send,
+CREATE TYPE intvec (
+	INPUT     = intvec_in,
+	OUTPUT    = intvec_out,
+	TYPMOD_IN = intvec_typmod_in,
+	RECEIVE   = intvec_recv,
+	SEND      = intvec_send,
 	STORAGE   = external
 );
 
--- minivec functions
+-- intvec functions
 
-CREATE FUNCTION l2_distance(minivec, minivec) RETURNS float8
-	AS 'MODULE_PATHNAME', 'minivec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION l2_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION inner_product(minivec, minivec) RETURNS float8
-	AS 'MODULE_PATHNAME', 'minivec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION inner_product(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION cosine_distance(minivec, minivec) RETURNS float8
-	AS 'MODULE_PATHNAME', 'minivec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION cosine_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION l1_distance(minivec, minivec) RETURNS float8
-	AS 'MODULE_PATHNAME', 'minivec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION l1_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION vector_dims(minivec) RETURNS integer
-	AS 'MODULE_PATHNAME', 'minivec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION vector_dims(intvec) RETURNS integer
+	AS 'MODULE_PATHNAME', 'intvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION l2_norm(minivec) RETURNS float8
-	AS 'MODULE_PATHNAME', 'minivec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE FUNCTION l2_norm(intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION l2_normalize(minivec) RETURNS minivec
-	AS 'MODULE_PATHNAME', 'minivec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+-- intvec private functions
 
-CREATE FUNCTION binary_quantize(minivec) RETURNS bit
-	AS 'MODULE_PATHNAME', 'minivec_binary_quantize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
-CREATE FUNCTION subvector(minivec, int, int) RETURNS minivec
-	AS 'MODULE_PATHNAME', 'minivec_subvector' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
--- minivec private functions
-
-CREATE FUNCTION minivec_add(minivec, minivec) RETURNS minivec
+CREATE FUNCTION intvec_lt(intvec, intvec) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_sub(minivec, minivec) RETURNS minivec
+CREATE FUNCTION intvec_le(intvec, intvec) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_mul(minivec, minivec) RETURNS minivec
+CREATE FUNCTION intvec_eq(intvec, intvec) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_concat(minivec, minivec) RETURNS minivec
+CREATE FUNCTION intvec_ne(intvec, intvec) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_lt(minivec, minivec) RETURNS bool
+CREATE FUNCTION intvec_ge(intvec, intvec) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_le(minivec, minivec) RETURNS bool
+CREATE FUNCTION intvec_gt(intvec, intvec) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_eq(minivec, minivec) RETURNS bool
+CREATE FUNCTION intvec_cmp(intvec, intvec) RETURNS int4
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_ne(minivec, minivec) RETURNS bool
+CREATE FUNCTION intvec_l2_squared_distance(intvec, intvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_ge(minivec, minivec) RETURNS bool
+CREATE FUNCTION intvec_negative_inner_product(intvec, intvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_gt(minivec, minivec) RETURNS bool
+-- intvec cast functions
+
+CREATE FUNCTION intvec(intvec, integer, boolean) RETURNS intvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_cmp(minivec, minivec) RETURNS int4
+CREATE FUNCTION array_to_intvec(integer[], integer, boolean) RETURNS intvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_l2_squared_distance(minivec, minivec) RETURNS float8
+CREATE FUNCTION intvec_to_integer(intvec, integer, boolean) RETURNS integer[]
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
-CREATE FUNCTION minivec_negative_inner_product(minivec, minivec) RETURNS float8
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+-- intvec casts
 
--- minivec cast functions
+CREATE CAST (intvec AS intvec)
+	WITH FUNCTION intvec(intvec, integer, boolean) AS IMPLICIT;
 
-CREATE FUNCTION minivec(minivec, integer, boolean) RETURNS minivec
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE CAST (intvec AS integer[])
+	WITH FUNCTION intvec_to_integer(intvec, integer, boolean) AS ASSIGNMENT;
 
-CREATE FUNCTION minivec_to_vector(minivec, integer, boolean) RETURNS vector
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+CREATE CAST (integer[] AS intvec)
+	WITH FUNCTION array_to_intvec(integer[], integer, boolean) AS ASSIGNMENT;
 
-CREATE FUNCTION vector_to_minivec(vector, integer, boolean) RETURNS minivec
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
-CREATE FUNCTION array_to_minivec(integer[], integer, boolean) RETURNS minivec
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
-CREATE FUNCTION array_to_minivec(real[], integer, boolean) RETURNS minivec
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
-CREATE FUNCTION array_to_minivec(double precision[], integer, boolean) RETURNS minivec
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
-CREATE FUNCTION array_to_minivec(numeric[], integer, boolean) RETURNS minivec
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
-CREATE FUNCTION minivec_to_float4(minivec, integer, boolean) RETURNS real[]
-	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
-
--- minivec casts
-
-CREATE CAST (minivec AS minivec)
-	WITH FUNCTION minivec(minivec, integer, boolean) AS IMPLICIT;
-
-CREATE CAST (minivec AS vector)
-	WITH FUNCTION minivec_to_vector(minivec, integer, boolean) AS ASSIGNMENT;
-
-CREATE CAST (vector AS minivec)
-	WITH FUNCTION vector_to_minivec(vector, integer, boolean) AS IMPLICIT;
-
-CREATE CAST (minivec AS real[])
-	WITH FUNCTION minivec_to_float4(minivec, integer, boolean) AS ASSIGNMENT;
-
-CREATE CAST (integer[] AS minivec)
-	WITH FUNCTION array_to_minivec(integer[], integer, boolean) AS ASSIGNMENT;
-
-CREATE CAST (real[] AS minivec)
-	WITH FUNCTION array_to_minivec(real[], integer, boolean) AS ASSIGNMENT;
-
-CREATE CAST (double precision[] AS minivec)
-	WITH FUNCTION array_to_minivec(double precision[], integer, boolean) AS ASSIGNMENT;
-
-CREATE CAST (numeric[] AS minivec)
-	WITH FUNCTION array_to_minivec(numeric[], integer, boolean) AS ASSIGNMENT;
-
--- minivec operators
+-- intvec operators
 
 CREATE OPERATOR <-> (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = l2_distance,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = l2_distance,
 	COMMUTATOR = '<->'
 );
 
 CREATE OPERATOR <#> (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_negative_inner_product,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_negative_inner_product,
 	COMMUTATOR = '<#>'
 );
 
 CREATE OPERATOR <=> (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = cosine_distance,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = cosine_distance,
 	COMMUTATOR = '<=>'
 );
 
 CREATE OPERATOR <+> (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = l1_distance,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = l1_distance,
 	COMMUTATOR = '<+>'
 );
 
-CREATE OPERATOR + (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_add,
-	COMMUTATOR = +
-);
-
-CREATE OPERATOR - (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_sub
-);
-
-CREATE OPERATOR * (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_mul,
-	COMMUTATOR = *
-);
-
-CREATE OPERATOR || (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_concat
-);
-
 CREATE OPERATOR < (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_lt,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_lt,
 	COMMUTATOR = > , NEGATOR = >= ,
 	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
 );
 
 CREATE OPERATOR <= (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_le,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_le,
 	COMMUTATOR = >= , NEGATOR = > ,
 	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
 );
 
 CREATE OPERATOR = (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_eq,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_eq,
 	COMMUTATOR = = , NEGATOR = <> ,
 	RESTRICT = eqsel, JOIN = eqjoinsel
 );
 
 CREATE OPERATOR <> (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_ne,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_ne,
 	COMMUTATOR = <> , NEGATOR = = ,
 	RESTRICT = eqsel, JOIN = eqjoinsel
 );
 
 CREATE OPERATOR >= (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_ge,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_ge,
 	COMMUTATOR = <= , NEGATOR = < ,
 	RESTRICT = scalargesel, JOIN = scalargejoinsel
 );
 
 CREATE OPERATOR > (
-	LEFTARG = minivec, RIGHTARG = minivec, PROCEDURE = minivec_gt,
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_gt,
 	COMMUTATOR = < , NEGATOR = <= ,
 	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
 );
 
--- minivec op classes
+-- intvec opclasses
 
-CREATE OPERATOR CLASS minivec_ops
-	DEFAULT FOR TYPE minivec USING btree AS
+CREATE OPERATOR CLASS intvec_ops
+	DEFAULT FOR TYPE intvec USING btree AS
 	OPERATOR 1 < ,
 	OPERATOR 2 <= ,
 	OPERATOR 3 = ,
 	OPERATOR 4 >= ,
 	OPERATOR 5 > ,
-	FUNCTION 1 minivec_cmp(minivec, minivec);
+	FUNCTION 1 intvec_cmp(intvec, intvec);
 
-CREATE OPERATOR CLASS minivec_l2_ops
-	FOR TYPE minivec USING hnsw AS
-	OPERATOR 1 <-> (minivec, minivec) FOR ORDER BY float_ops,
-	FUNCTION 1 minivec_l2_squared_distance(minivec, minivec),
-	FUNCTION 3 hnsw_minivec_support(internal);
+CREATE OPERATOR CLASS intvec_l2_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <-> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 intvec_l2_squared_distance(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
 
-CREATE OPERATOR CLASS minivec_ip_ops
-	FOR TYPE minivec USING hnsw AS
-	OPERATOR 1 <#> (minivec, minivec) FOR ORDER BY float_ops,
-	FUNCTION 1 minivec_negative_inner_product(minivec, minivec),
-	FUNCTION 3 hnsw_minivec_support(internal);
+CREATE OPERATOR CLASS intvec_ip_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <#> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 intvec_negative_inner_product(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
 
-CREATE OPERATOR CLASS minivec_cosine_ops
-	FOR TYPE minivec USING hnsw AS
-	OPERATOR 1 <=> (minivec, minivec) FOR ORDER BY float_ops,
-	FUNCTION 1 minivec_negative_inner_product(minivec, minivec),
-	FUNCTION 2 l2_norm(minivec),
-	FUNCTION 3 hnsw_minivec_support(internal);
+CREATE OPERATOR CLASS intvec_cosine_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <=> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 cosine_distance(intvec, intvec),
+	FUNCTION 2 l2_norm(intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
 
-CREATE OPERATOR CLASS minivec_l1_ops
-	FOR TYPE minivec USING hnsw AS
-	OPERATOR 1 <+> (minivec, minivec) FOR ORDER BY float_ops,
-	FUNCTION 1 l1_distance(minivec, minivec),
-	FUNCTION 3 hnsw_minivec_support(internal);
+CREATE OPERATOR CLASS intvec_l1_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <+> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
 
 -- bit functions
 

src/hnsw.c

@@ -12,12 +12,22 @@
 #include "utils/float.h"
 #include "utils/guc.h"
 #include "utils/selfuncs.h"
+#include "utils/spccache.h"
 
 #if PG_VERSION_NUM < 150000
 #define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
 #endif
 
+static const struct config_enum_entry hnsw_iterative_search_options[] = {
+	{"off", HNSW_ITERATIVE_SEARCH_OFF, false},
+	{"relaxed_order", HNSW_ITERATIVE_SEARCH_RELAXED, false},
+	{"strict_order", HNSW_ITERATIVE_SEARCH_STRICT, false},
+	{NULL, 0, false}
+};
+
 int			hnsw_ef_search;
+int			hnsw_max_search_tuples;
+int			hnsw_iterative_search;
 int			hnsw_lock_tranche_id;
 static relopt_kind hnsw_relopt_kind;
 
@@ -68,6 +78,15 @@ HnswInit(void)
 							"Valid range is 1..1000.", &hnsw_ef_search,
 							HNSW_DEFAULT_EF_SEARCH, HNSW_MIN_EF_SEARCH, HNSW_MAX_EF_SEARCH, PGC_USERSET, 0, NULL, NULL, NULL);
 
+	DefineCustomEnumVariable("hnsw.iterative_search", "Sets the iterative search mode",
+							 NULL, &hnsw_iterative_search,
+							 HNSW_ITERATIVE_SEARCH_OFF, hnsw_iterative_search_options, PGC_USERSET, 0, NULL, NULL, NULL);
+
+	/* This is approximate and does not apply to the initial scan */
+	DefineCustomIntVariable("hnsw.max_search_tuples", "Sets the max number of candidates to visit for iterative search",
+							"-1 means no limit", &hnsw_max_search_tuples,
+							-1, -1, INT_MAX, PGC_USERSET, 0, NULL, NULL, NULL);
+
 	MarkGUCPrefixReserved("hnsw");
 }
 
@@ -99,7 +118,9 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 {
 	GenericCosts costs;
 	int			m;
-	int			entryLevel;
+	double		ratio;
+	double		startupPages;
+	double		spc_seq_page_cost;
 	Relation	index;
 
 	/* Never use index without order */
@@ -115,21 +136,71 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 
 	MemSet(&costs, 0, sizeof(costs));
 
+	genericcostestimate(root, path, loop_count, &costs);
+
 	index = index_open(path->indexinfo->indexoid, NoLock);
 	HnswGetMetaPageInfo(index, &m, NULL);
 	index_close(index, NoLock);
 
-	/* Approximate entry level */
-	entryLevel = (int) -log(1.0 / path->indexinfo->tuples) * HnswGetMl(m);
+	/*
+	 * HNSW cost estimation follows a formula that accounts for the total
+	 * number of tuples indexed combined with the parameters that most
+	 * influence the duration of the index scan, namely: m - the number of
+	 * tuples that are scanned in each step of the HNSW graph traversal
+	 * ef_search - which influences the total number of steps taken at layer 0
+	 *
+	 * The source of the vector data can impact how many steps it takes to
+	 * converge on the set of vectors to return to the executor. Currently, we
+	 * use a hardcoded scaling factor (HNSWScanScalingFactor) to help
+	 * influence that, but this could later become a configurable parameter
+	 * based on the cost estimations.
+	 *
+	 * The tuple estimator formula is below:
+	 *
+	 * numIndexTuples = entryLevel * m + layer0TuplesMax * layer0Selectivity
+	 *
+	 * "entryLevel * m" represents the floor of tuples we need to scan to get
+	 * to layer 0 (L0).
+	 *
+	 * "layer0TuplesMax" is the estimated total number of tuples we'd scan at
+	 * L0 if we weren't discarding already visited tuples as part of the scan.
+	 *
+	 * "layer0Selectivity" estimates the percentage of tuples that are scanned
+	 * at L0, accounting for previously visited tuples, multiplied by the
+	 * "scalingFactor" (currently hardcoded).
+	 */
+	if (path->indexinfo->tuples > 0)
+	{
+		double		scalingFactor = 0.55;
+		int			entryLevel = (int) (log(path->indexinfo->tuples) * HnswGetMl(m));
+		int			layer0TuplesMax = HnswGetLayerM(m, 0) * hnsw_ef_search;
+		double		layer0Selectivity = scalingFactor * log(path->indexinfo->tuples) / (log(m) * (1 + log(hnsw_ef_search)));
 
-	/* TODO Improve estimate of visited tuples (currently underestimates) */
-	/* Account for number of tuples (or entry level), m, and ef_search */
-	costs.numIndexTuples = (entryLevel + 2) * m;
+		ratio = (entryLevel * m + layer0TuplesMax * layer0Selectivity) / path->indexinfo->tuples;
 
-	genericcostestimate(root, path, loop_count, &costs);
+		if (ratio > 1)
+			ratio = 1;
+	}
+	else
+		ratio = 1;
 
-	/* Use total cost since most work happens before first tuple is returned */
-	*indexStartupCost = costs.indexTotalCost;
+	get_tablespace_page_costs(path->indexinfo->reltablespace, NULL, &spc_seq_page_cost);
+
+	/* Startup cost is cost before returning the first row */
+	costs.indexStartupCost = costs.indexTotalCost * ratio;
+
+	/* Adjust cost if needed since TOAST not included in seq scan cost */
+	startupPages = costs.numIndexPages * ratio;
+	if (startupPages > path->indexinfo->rel->pages && ratio < 0.5)
+	{
+		/* Change all page cost from random to sequential */
+		costs.indexStartupCost -= startupPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+
+		/* Remove cost of extra pages */
+		costs.indexStartupCost -= (startupPages - path->indexinfo->rel->pages) * spc_seq_page_cost;
+	}
+
+	*indexStartupCost = costs.indexStartupCost;
 	*indexTotalCost = costs.indexTotalCost;
 	*indexSelectivity = costs.indexSelectivity;
 	*indexCorrelation = costs.indexCorrelation;

src/hnsw.h

@@ -88,6 +88,9 @@
 /* Ensure fits on page and in uint8 */
 #define HnswGetMaxLevel(m) Min(((BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - offsetof(HnswNeighborTupleData, indextids) - sizeof(ItemIdData)) / (sizeof(ItemPointerData)) / (m)) - 2, 255)
 
+#define HnswGetSearchCandidate(membername, ptr) pairingheap_container(HnswSearchCandidate, membername, ptr)
+#define HnswGetSearchCandidateConst(membername, ptr) pairingheap_const_container(HnswSearchCandidate, membername, ptr)
+
 #define HnswGetValue(base, element) PointerGetDatum(HnswPtrAccess(base, (element)->value))
 
 #if PG_VERSION_NUM < 140005
@@ -106,8 +109,17 @@
 
 /* Variables */
 extern int	hnsw_ef_search;
+extern int	hnsw_iterative_search;
+extern int	hnsw_max_search_tuples;
 extern int	hnsw_lock_tranche_id;
 
+typedef enum HnswIterativeSearchMode
+{
+	HNSW_ITERATIVE_SEARCH_OFF,
+	HNSW_ITERATIVE_SEARCH_RELAXED,
+	HNSW_ITERATIVE_SEARCH_STRICT
+}			HnswIterativeSearchMode;
+
 typedef struct HnswElementData HnswElementData;
 typedef struct HnswNeighborArray HnswNeighborArray;
 
@@ -129,6 +141,7 @@ struct HnswElementData
 	uint8		heaptidsLength;
 	uint8		level;
 	uint8		deleted;
+	uint8		version;
 	uint32		hash;
 	HnswNeighborsPtr neighbors;
 	BlockNumber blkno;
@@ -160,7 +173,7 @@ typedef struct HnswSearchCandidate
 	pairingheap_node c_node;
 	pairingheap_node w_node;
 	HnswElementPtr element;
-	float		distance;
+	double		distance;
 }			HnswSearchCandidate;
 
 /* HNSW index options */
@@ -185,8 +198,8 @@ typedef struct HnswGraph
 
 	/* Allocations state */
 	LWLock		allocatorLock;
-	long		memoryUsed;
-	long		memoryTotal;
+	Size		memoryUsed;
+	Size		memoryTotal;
 
 	/* Flushed state */
 	LWLock		flushLock;
@@ -237,6 +250,18 @@ typedef struct HnswTypeInfo
 	void		(*checkValue) (Pointer v);
 }			HnswTypeInfo;
 
+typedef struct HnswSupport
+{
+	FmgrInfo   *procinfo;
+	FmgrInfo   *normprocinfo;
+	Oid			collation;
+}			HnswSupport;
+
+typedef struct HnswQuery
+{
+	Datum		value;
+}			HnswQuery;
+
 typedef struct HnswBuildState
 {
 	/* Info */
@@ -256,9 +281,7 @@ typedef struct HnswBuildState
 	double		reltuples;
 
 	/* Support functions */
-	FmgrInfo   *procinfo;
-	FmgrInfo   *normprocinfo;
-	Oid			collation;
+	HnswSupport support;
 
 	/* Variables */
 	HnswGraph	graphData;
@@ -306,10 +329,10 @@ typedef struct HnswElementTupleData
 	uint8		type;
 	uint8		level;
 	uint8		deleted;
-	uint8		unused;
+	uint8		version;
 	ItemPointerData heaptids[HNSW_HEAPTIDS];
 	ItemPointerData neighbortid;
-	uint16		unused2;
+	uint16		unused;
 	Vector		data;
 }			HnswElementTupleData;
 
@@ -318,24 +341,41 @@ typedef HnswElementTupleData * HnswElementTuple;
 typedef struct HnswNeighborTupleData
 {
 	uint8		type;
-	uint8		unused;
+	uint8		version;
 	uint16		count;
 	ItemPointerData indextids[FLEXIBLE_ARRAY_MEMBER];
 }			HnswNeighborTupleData;
 
 typedef HnswNeighborTupleData * HnswNeighborTuple;
 
+typedef union
+{
+	struct pointerhash_hash *pointers;
+	struct offsethash_hash *offsets;
+	struct tidhash_hash *tids;
+}			visited_hash;
+
+typedef union
+{
+	HnswElement element;
+	ItemPointerData indextid;
+}			HnswUnvisited;
+
 typedef struct HnswScanOpaqueData
 {
 	const		HnswTypeInfo *typeInfo;
 	bool		first;
 	List	   *w;
+	visited_hash v;
+	pairingheap *discarded;
+	HnswQuery	q;
+	int			m;
+	int64		tuples;
+	double		previousDistance;
 	MemoryContext tmpCtx;
 
 	/* Support functions */
-	FmgrInfo   *procinfo;
-	FmgrInfo   *normprocinfo;
-	Oid			collation;
+	HnswSupport support;
 }			HnswScanOpaqueData;
 
 typedef HnswScanOpaqueData * HnswScanOpaque;
@@ -353,8 +393,7 @@ typedef struct HnswVacuumState
 	int			efConstruction;
 
 	/* Support functions */
-	FmgrInfo   *procinfo;
-	Oid			collation;
+	HnswSupport support;
 
 	/* Variables */
 	struct tidhash_hash *deleted;
@@ -370,30 +409,33 @@ typedef struct HnswVacuumState
 int			HnswGetM(Relation index);
 int			HnswGetEfConstruction(Relation index);
 FmgrInfo   *HnswOptionalProcInfo(Relation index, uint16 procnum);
+void		HnswInitSupport(HnswSupport * support, Relation index);
 Datum		HnswNormValue(const HnswTypeInfo * typeInfo, Oid collation, Datum value);
-bool		HnswCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value);
+bool		HnswCheckNorm(HnswSupport * support, Datum value);
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);
 void		HnswInit(void);
-List	   *HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement);
+List	   *HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples);
 HnswElement HnswGetEntryPoint(Relation index);
 void		HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
 void	   *HnswAlloc(HnswAllocator * allocator, Size size);
 HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
 HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
-void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
-HnswSearchCandidate *HnswEntryCandidate(char *base, HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
+void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, HnswSupport * support, int m, int efConstruction, bool existing);
+HnswSearchCandidate *HnswEntryCandidate(char *base, HnswElement em, HnswQuery * q, Relation rel, HnswSupport * support, bool loadVec);
 void		HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum, bool building);
 void		HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m);
 void		HnswAddHeapTid(HnswElement element, ItemPointer heaptid);
+HnswNeighborArray *HnswInitNeighborArray(int lm, HnswAllocator * allocator);
 void		HnswInitNeighbors(char *base, HnswElement element, int m, HnswAllocator * alloc);
-bool		HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, bool building);
-void		HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building);
+bool		HnswInsertTupleOnDisk(Relation index, HnswSupport * support, Datum value, ItemPointer heaptid, bool building);
+void		HnswUpdateNeighborsOnDisk(Relation index, HnswSupport * support, HnswElement e, int m, bool checkExisting, bool building);
 void		HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHeaptids, bool loadVec);
-void		HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec, float *maxDistance);
+void		HnswLoadElement(HnswElement element, double *distance, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec, double *maxDistance);
+bool		HnswFormIndexValue(Datum *out, Datum *values, bool *isnull, const HnswTypeInfo * typeInfo, HnswSupport * support);
 void		HnswSetElementTuple(char *base, HnswElementTuple etup, HnswElement element);
-void		HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int lm, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation);
-void		HnswLoadNeighbors(HnswElement element, Relation index, int m);
+void		HnswUpdateConnection(char *base, HnswNeighborArray * neighbors, HnswElement newElement, float distance, int lm, int *updateIdx, Relation index, HnswSupport * support);
+bool		HnswLoadNeighborTids(HnswElement element, ItemPointerData *indextids, Relation index, int m, int lm, int lc);
 void		HnswInitLockTranche(void);
 const		HnswTypeInfo *HnswGetTypeInfo(Relation index);
 PGDLLEXPORT void HnswParallelBuildMain(dsm_segment *seg, shm_toc *toc);

src/hnswbuild.c

@@ -366,7 +366,7 @@ AddElementInMemory(char *base, HnswGraph * graph, HnswElement element)
  * Update neighbors
  */
 static void
-UpdateNeighborsInMemory(char *base, FmgrInfo *procinfo, Oid collation, HnswElement e, int m)
+UpdateNeighborsInMemory(char *base, HnswSupport * support, HnswElement e, int m)
 {
 	for (int lc = e->level; lc >= 0; lc--)
 	{
@@ -388,7 +388,7 @@ UpdateNeighborsInMemory(char *base, FmgrInfo *procinfo, Oid collation, HnswEleme
 			Assert(neighborElement);
 
 			LWLockAcquire(&neighborElement->lock, LW_EXCLUSIVE);
-			HnswUpdateConnection(base, e, hc, lm, lc, NULL, NULL, procinfo, collation);
+			HnswUpdateConnection(base, HnswGetNeighbors(base, neighborElement, lc), e, hc->distance, lm, NULL, NULL, support);
 			LWLockRelease(&neighborElement->lock);
 		}
 	}
@@ -398,7 +398,7 @@ UpdateNeighborsInMemory(char *base, FmgrInfo *procinfo, Oid collation, HnswEleme
  * Update graph in memory
  */
 static void
-UpdateGraphInMemory(FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement entryPoint, HnswBuildState * buildstate)
+UpdateGraphInMemory(HnswSupport * support, HnswElement element, int m, int efConstruction, HnswElement entryPoint, HnswBuildState * buildstate)
 {
 	HnswGraph  *graph = buildstate->graph;
 	char	   *base = buildstate->hnswarea;
@@ -411,7 +411,7 @@ UpdateGraphInMemory(FmgrInfo *procinfo, Oid collation, HnswElement element, int
 	AddElementInMemory(base, graph, element);
 
 	/* Update neighbors */
-	UpdateNeighborsInMemory(base, procinfo, collation, element, m);
+	UpdateNeighborsInMemory(base, support, element, m);
 
 	/* Update entry point if needed (already have lock) */
 	if (entryPoint == NULL || element->level > entryPoint->level)
@@ -424,9 +424,8 @@ UpdateGraphInMemory(FmgrInfo *procinfo, Oid collation, HnswElement element, int
 static void
 InsertTupleInMemory(HnswBuildState * buildstate, HnswElement element)
 {
-	FmgrInfo   *procinfo = buildstate->procinfo;
-	Oid			collation = buildstate->collation;
 	HnswGraph  *graph = buildstate->graph;
+	HnswSupport *support = &buildstate->support;
 	HnswElement entryPoint;
 	LWLock	   *entryLock = &graph->entryLock;
 	LWLock	   *entryWaitLock = &graph->entryWaitLock;
@@ -458,10 +457,10 @@ InsertTupleInMemory(HnswBuildState * buildstate, HnswElement element)
 	}
 
 	/* Find neighbors for element */
-	HnswFindElementNeighbors(base, element, entryPoint, NULL, procinfo, collation, m, efConstruction, false);
+	HnswFindElementNeighbors(base, element, entryPoint, NULL, support, m, efConstruction, false);
 
 	/* Update graph in memory */
-	UpdateGraphInMemory(procinfo, collation, element, m, efConstruction, entryPoint, buildstate);
+	UpdateGraphInMemory(support, element, m, efConstruction, entryPoint, buildstate);
 
 	/* Release entry lock */
 	LWLockRelease(entryLock);
@@ -473,30 +472,19 @@ InsertTupleInMemory(HnswBuildState * buildstate, HnswElement element)
 static bool
 InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, HnswBuildState * buildstate)
 {
-	const		HnswTypeInfo *typeInfo = buildstate->typeInfo;
 	HnswGraph  *graph = buildstate->graph;
 	HnswElement element;
 	HnswAllocator *allocator = &buildstate->allocator;
+	HnswSupport *support = &buildstate->support;
 	Size		valueSize;
 	Pointer		valuePtr;
 	LWLock	   *flushLock = &graph->flushLock;
 	char	   *base = buildstate->hnswarea;
+	Datum		value;
 
-	/* Detoast once for all calls */
-	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
-
-	/* Check value */
-	if (typeInfo->checkValue != NULL)
-		typeInfo->checkValue(DatumGetPointer(value));
-
-	/* Normalize if needed */
-	if (buildstate->normprocinfo != NULL)
-	{
-		if (!HnswCheckNorm(buildstate->normprocinfo, buildstate->collation, value))
-			return false;
-
-		value = HnswNormValue(typeInfo, buildstate->collation, value);
-	}
+	/* Form index value */
+	if (!HnswFormIndexValue(&value, values, isnull, buildstate->typeInfo, support))
+		return false;
 
 	/* Get datum size */
 	valueSize = VARSIZE_ANY(DatumGetPointer(value));
@@ -509,7 +497,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, Hn
 	{
 		LWLockRelease(flushLock);
 
-		return HnswInsertTupleOnDisk(index, value, values, isnull, heaptid, true);
+		return HnswInsertTupleOnDisk(index, support, value, heaptid, true);
 	}
 
 	/*
@@ -541,7 +529,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, Hn
 
 		LWLockRelease(flushLock);
 
-		return HnswInsertTupleOnDisk(index, value, values, isnull, heaptid, true);
+		return HnswInsertTupleOnDisk(index, support, value, heaptid, true);
 	}
 
 	/* Ok, we can proceed to allocate the element */
@@ -607,7 +595,7 @@ BuildCallback(Relation index, ItemPointer tid, Datum *values,
  * Initialize the graph
  */
 static void
-InitGraph(HnswGraph * graph, char *base, long memoryTotal)
+InitGraph(HnswGraph * graph, char *base, Size memoryTotal)
 {
 	/* Initialize the lock tranche if needed */
 	HnswInitLockTranche();
@@ -704,11 +692,9 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	buildstate->indtuples = 0;
 
 	/* Get support functions */
-	buildstate->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
-	buildstate->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
-	buildstate->collation = index->rd_indcollation[0];
+	HnswInitSupport(&buildstate->support, index);
 
-	InitGraph(&buildstate->graphData, NULL, maintenance_work_mem * 1024L);
+	InitGraph(&buildstate->graphData, NULL, (Size) maintenance_work_mem * 1024L);
 	buildstate->graph = &buildstate->graphData;
 	buildstate->ml = HnswGetMl(buildstate->m);
 	buildstate->maxLevel = HnswGetMaxLevel(buildstate->m);

src/hnswinsert.c

@@ -36,7 +36,7 @@ GetInsertPage(Relation index)
  * Check for a free offset
  */
 static bool
-HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size etupSize, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *newInsertPage)
+HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size etupSize, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *newInsertPage, uint8 *tupleVersion)
 {
 	OffsetNumber offno;
 	OffsetNumber maxoffno = PageGetMaxOffsetNumber(page);
@@ -98,6 +98,7 @@ HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size
 			{
 				*freeOffno = offno;
 				*freeNeighborOffno = neighborOffno;
+				*tupleVersion = etup->version;
 				return true;
 			}
 			else if (*nbuf != buf)
@@ -153,6 +154,7 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 	OffsetNumber freeOffno = InvalidOffsetNumber;
 	OffsetNumber freeNeighborOffno = InvalidOffsetNumber;
 	BlockNumber newInsertPage = InvalidBlockNumber;
+	uint8		tupleVersion;
 	char	   *base = NULL;
 
 	/* Calculate sizes */
@@ -202,7 +204,7 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 		}
 
 		/* Next, try space from a deleted element */
-		if (HnswFreeOffset(index, buf, page, e, etupSize, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage))
+		if (HnswFreeOffset(index, buf, page, e, etupSize, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage, &tupleVersion))
 		{
 			if (nbuf != buf)
 			{
@@ -212,6 +214,10 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 					npage = GenericXLogRegisterBuffer(state, nbuf, 0);
 			}
 
+			/* Set tuple version */
+			etup->version = tupleVersion;
+			ntup->version = tupleVersion;
+
 			break;
 		}
 
@@ -334,6 +340,107 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 		*updatedInsertPage = newInsertPage;
 }
 
+/*
+ * Load neighbors
+ */
+static HnswNeighborArray *
+HnswLoadNeighbors(HnswElement element, Relation index, int m, int lm, int lc)
+{
+	char	   *base = NULL;
+	HnswNeighborArray *neighbors = HnswInitNeighborArray(lm, NULL);
+	ItemPointerData indextids[HNSW_MAX_M * 2];
+
+	if (!HnswLoadNeighborTids(element, indextids, index, m, lm, lc))
+		return neighbors;
+
+	for (int i = 0; i < lm; i++)
+	{
+		ItemPointer indextid = &indextids[i];
+		HnswElement e;
+		HnswCandidate *hc;
+
+		if (!ItemPointerIsValid(indextid))
+			break;
+
+		e = HnswInitElementFromBlock(ItemPointerGetBlockNumber(indextid), ItemPointerGetOffsetNumber(indextid));
+		hc = &neighbors->items[neighbors->length++];
+		HnswPtrStore(base, hc->element, e);
+	}
+
+	return neighbors;
+}
+
+/*
+ * Load elements for insert
+ */
+static void
+LoadElementsForInsert(HnswNeighborArray * neighbors, HnswQuery * q, int *idx, Relation index, HnswSupport * support)
+{
+	char	   *base = NULL;
+
+	for (int i = 0; i < neighbors->length; i++)
+	{
+		HnswCandidate *hc = &neighbors->items[i];
+		HnswElement element = HnswPtrAccess(base, hc->element);
+		double		distance;
+
+		HnswLoadElement(element, &distance, q, index, support, true, NULL);
+		hc->distance = distance;
+
+		/* Prune element if being deleted */
+		if (element->heaptidsLength == 0)
+		{
+			*idx = i;
+			break;
+		}
+	}
+}
+
+/*
+ * Get update index
+ */
+static int
+GetUpdateIndex(HnswElement element, HnswElement newElement, float distance, int m, int lm, int lc, Relation index, HnswSupport * support, MemoryContext updateCtx)
+{
+	char	   *base = NULL;
+	int			idx = -1;
+	HnswNeighborArray *neighbors;
+	MemoryContext oldCtx = MemoryContextSwitchTo(updateCtx);
+
+	/*
+	 * Get latest neighbors since they may have changed. Do not lock yet since
+	 * selecting neighbors can take time. Could use optimistic locking to
+	 * retry if another update occurs before getting exclusive lock.
+	 */
+	neighbors = HnswLoadNeighbors(element, index, m, lm, lc);
+
+	/*
+	 * Could improve performance for vacuuming by checking neighbors against
+	 * list of elements being deleted to find index. It's important to exclude
+	 * already deleted elements for this since they can be replaced at any
+	 * time.
+	 */
+
+	if (neighbors->length < lm)
+		idx = -2;
+	else
+	{
+		HnswQuery	q;
+
+		q.value = HnswGetValue(base, element);
+
+		LoadElementsForInsert(neighbors, &q, &idx, index, support);
+
+		if (idx == -1)
+			HnswUpdateConnection(base, neighbors, newElement, distance, lm, &idx, index, support);
+	}
+
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextReset(updateCtx);
+
+	return idx;
+}
+
 /*
  * Check if connection already exists
  */
@@ -354,14 +461,94 @@ ConnectionExists(HnswElement e, HnswNeighborTuple ntup, int startIdx, int lm)
 	return false;
 }
 
+/*
+ * Update neighbor
+ */
+static void
+UpdateNeighborOnDisk(HnswElement element, HnswElement newElement, int idx, int m, int lm, int lc, Relation index, bool checkExisting, bool building)
+{
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	HnswNeighborTuple ntup;
+	int			startIdx;
+	OffsetNumber offno = element->neighborOffno;
+
+	/* Register page */
+	buf = ReadBuffer(index, element->neighborPage);
+	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+	if (building)
+	{
+		state = NULL;
+		page = BufferGetPage(buf);
+	}
+	else
+	{
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+	}
+
+	/* Get tuple */
+	ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, offno));
+
+	/* Calculate index for update */
+	startIdx = (element->level - lc) * m;
+
+	/* Check for existing connection */
+	if (checkExisting && ConnectionExists(newElement, ntup, startIdx, lm))
+		idx = -1;
+	else if (idx == -2)
+	{
+		/* Find free offset if still exists */
+		/* TODO Retry updating connections if not */
+		for (int j = 0; j < lm; j++)
+		{
+			if (!ItemPointerIsValid(&ntup->indextids[startIdx + j]))
+			{
+				idx = startIdx + j;
+				break;
+			}
+		}
+	}
+	else
+		idx += startIdx;
+
+	/* Make robust to issues */
+	if (idx >= 0 && idx < ntup->count)
+	{
+		ItemPointer indextid = &ntup->indextids[idx];
+
+		/* Update neighbor on the buffer */
+		ItemPointerSet(indextid, newElement->blkno, newElement->offno);
+
+		/* Commit */
+		if (building)
+			MarkBufferDirty(buf);
+		else
+			GenericXLogFinish(state);
+	}
+	else if (!building)
+		GenericXLogAbort(state);
+
+	UnlockReleaseBuffer(buf);
+}
+
 /*
  * Update neighbors
  */
 void
-HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building)
+HnswUpdateNeighborsOnDisk(Relation index, HnswSupport * support, HnswElement e, int m, bool checkExisting, bool building)
 {
 	char	   *base = NULL;
 
+	/* Use separate memory context to improve performance for larger vectors */
+	MemoryContext updateCtx = GenerationContextCreate(CurrentMemoryContext,
+													  "Hnsw insert update context",
+#if PG_VERSION_NUM >= 150000
+													  128 * 1024, 128 * 1024,
+#endif
+													  128 * 1024);
+
 	for (int lc = e->level; lc >= 0; lc--)
 	{
 		int			lm = HnswGetLayerM(m, lc);
@@ -370,96 +557,20 @@ HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, Hns
 		for (int i = 0; i < neighbors->length; i++)
 		{
 			HnswCandidate *hc = &neighbors->items[i];
-			Buffer		buf;
-			Page		page;
-			GenericXLogState *state;
-			HnswNeighborTuple ntup;
-			int			idx = -1;
-			int			startIdx;
 			HnswElement neighborElement = HnswPtrAccess(base, hc->element);
-			OffsetNumber offno = neighborElement->neighborOffno;
+			int			idx;
 
-			/*
-			 * Get latest neighbors since they may have changed. Do not lock
-			 * yet since selecting neighbors can take time. Could use
-			 * optimistic locking to retry if another update occurs before
-			 * getting exclusive lock.
-			 */
-			HnswLoadNeighbors(neighborElement, index, m);
-
-			/*
-			 * Could improve performance for vacuuming by checking neighbors
-			 * against list of elements being deleted to find index. It's
-			 * important to exclude already deleted elements for this since
-			 * they can be replaced at any time.
-			 */
-
-			/* Select neighbors */
-			HnswUpdateConnection(NULL, e, hc, lm, lc, &idx, index, procinfo, collation);
+			idx = GetUpdateIndex(neighborElement, e, hc->distance, m, lm, lc, index, support, updateCtx);
 
 			/* New element was not selected as a neighbor */
 			if (idx == -1)
 				continue;
 
-			/* Register page */
-			buf = ReadBuffer(index, neighborElement->neighborPage);
-			LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
-			if (building)
-			{
-				state = NULL;
-				page = BufferGetPage(buf);
-			}
-			else
-			{
-				state = GenericXLogStart(index);
-				page = GenericXLogRegisterBuffer(state, buf, 0);
-			}
-
-			/* Get tuple */
-			ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, offno));
-
-			/* Calculate index for update */
-			startIdx = (neighborElement->level - lc) * m;
-
-			/* Check for existing connection */
-			if (checkExisting && ConnectionExists(e, ntup, startIdx, lm))
-				idx = -1;
-			else if (idx == -2)
-			{
-				/* Find free offset if still exists */
-				/* TODO Retry updating connections if not */
-				for (int j = 0; j < lm; j++)
-				{
-					if (!ItemPointerIsValid(&ntup->indextids[startIdx + j]))
-					{
-						idx = startIdx + j;
-						break;
-					}
-				}
-			}
-			else
-				idx += startIdx;
-
-			/* Make robust to issues */
-			if (idx >= 0 && idx < ntup->count)
-			{
-				ItemPointer indextid = &ntup->indextids[idx];
-
-				/* Update neighbor on the buffer */
-				ItemPointerSet(indextid, e->blkno, e->offno);
-
-				/* Commit */
-				if (building)
-					MarkBufferDirty(buf);
-				else
-					GenericXLogFinish(state);
-			}
-			else if (!building)
-				GenericXLogAbort(state);
-
-			UnlockReleaseBuffer(buf);
+			UpdateNeighborOnDisk(neighborElement, e, idx, m, lm, lc, index, checkExisting, building);
 		}
 	}
+
+	MemoryContextDelete(updateCtx);
 }
 
 /*
@@ -549,7 +660,7 @@ FindDuplicateOnDisk(Relation index, HnswElement element, bool building)
  * Update graph on disk
  */
 static void
-UpdateGraphOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement entryPoint, bool building)
+UpdateGraphOnDisk(Relation index, HnswSupport * support, HnswElement element, int m, int efConstruction, HnswElement entryPoint, bool building)
 {
 	BlockNumber newInsertPage = InvalidBlockNumber;
 
@@ -565,7 +676,7 @@ UpdateGraphOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement
 		HnswUpdateMetaPage(index, 0, NULL, newInsertPage, MAIN_FORKNUM, building);
 
 	/* Update neighbors */
-	HnswUpdateNeighborsOnDisk(index, procinfo, collation, element, m, false, building);
+	HnswUpdateNeighborsOnDisk(index, support, element, m, false, building);
 
 	/* Update entry point if needed */
 	if (entryPoint == NULL || element->level > entryPoint->level)
@@ -576,14 +687,12 @@ UpdateGraphOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement
  * Insert a tuple into the index
  */
 bool
-HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, bool building)
+HnswInsertTupleOnDisk(Relation index, HnswSupport * support, Datum value, ItemPointer heaptid, bool building)
 {
 	HnswElement entryPoint;
 	HnswElement element;
 	int			m;
 	int			efConstruction = HnswGetEfConstruction(index);
-	FmgrInfo   *procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
-	Oid			collation = index->rd_indcollation[0];
 	LOCKMODE	lockmode = ShareLock;
 	char	   *base = NULL;
 
@@ -598,7 +707,7 @@ HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull,
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
 
 	/* Create an element */
-	element = HnswInitElement(base, heap_tid, m, HnswGetMl(m), HnswGetMaxLevel(m), NULL);
+	element = HnswInitElement(base, heaptid, m, HnswGetMl(m), HnswGetMaxLevel(m), NULL);
 	HnswPtrStore(base, element->value, DatumGetPointer(value));
 
 	/* Prevent concurrent inserts when likely updating entry point */
@@ -616,10 +725,10 @@ HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull,
 	}
 
 	/* Find neighbors for element */
-	HnswFindElementNeighbors(base, element, entryPoint, index, procinfo, collation, m, efConstruction, false);
+	HnswFindElementNeighbors(base, element, entryPoint, index, support, m, efConstruction, false);
 
 	/* Update graph on disk */
-	UpdateGraphOnDisk(index, procinfo, collation, element, m, efConstruction, entryPoint, building);
+	UpdateGraphOnDisk(index, support, element, m, efConstruction, entryPoint, building);
 
 	/* Release lock */
 	UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
@@ -631,31 +740,19 @@ HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull,
  * Insert a tuple into the index
  */
 static void
-HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid)
+HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid)
 {
 	Datum		value;
 	const		HnswTypeInfo *typeInfo = HnswGetTypeInfo(index);
-	FmgrInfo   *normprocinfo;
-	Oid			collation = index->rd_indcollation[0];
+	HnswSupport support;
 
-	/* Detoast once for all calls */
-	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+	HnswInitSupport(&support, index);
 
-	/* Check value */
-	if (typeInfo->checkValue != NULL)
-		typeInfo->checkValue(DatumGetPointer(value));
+	/* Form index value */
+	if (!HnswFormIndexValue(&value, values, isnull, typeInfo, &support))
+		return;
 
-	/* Normalize if needed */
-	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
-	if (normprocinfo != NULL)
-	{
-		if (!HnswCheckNorm(normprocinfo, collation, value))
-			return;
-
-		value = HnswNormValue(typeInfo, collation, value);
-	}
-
-	HnswInsertTupleOnDisk(index, value, values, isnull, heap_tid, false);
+	HnswInsertTupleOnDisk(index, &support, value, heaptid, false);
 }
 
 /*

src/hnswscan.c

@@ -5,39 +5,74 @@
 #include "pgstat.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
+#include "utils/float.h"
 #include "utils/memutils.h"
 
 /*
  * Algorithm 5 from paper
  */
 static List *
-GetScanItems(IndexScanDesc scan, Datum q)
+GetScanItems(IndexScanDesc scan, Datum value)
 {
 	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
 	Relation	index = scan->indexRelation;
-	FmgrInfo   *procinfo = so->procinfo;
-	Oid			collation = so->collation;
+	HnswSupport *support = &so->support;
 	List	   *ep;
 	List	   *w;
 	int			m;
 	HnswElement entryPoint;
 	char	   *base = NULL;
+	HnswQuery  *q = &so->q;
 
 	/* Get m and entry point */
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
 
+	q->value = value;
+	so->m = m;
+
 	if (entryPoint == NULL)
 		return NIL;
 
-	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, false));
+	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, support, false));
 
 	for (int lc = entryPoint->level; lc >= 1; lc--)
 	{
-		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, false, NULL);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, support, m, false, NULL, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
-	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, support, m, false, NULL, &so->v, hnsw_iterative_search != HNSW_ITERATIVE_SEARCH_OFF ? &so->discarded : NULL, true, &so->tuples);
+}
+
+/*
+ * Resume scan at ground level with discarded candidates
+ */
+static List *
+ResumeScanItems(IndexScanDesc scan)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	Relation	index = scan->indexRelation;
+	List	   *ep = NIL;
+	char	   *base = NULL;
+	int			batch_size = hnsw_ef_search;
+
+	if (pairingheap_is_empty(so->discarded))
+		return NIL;
+
+	/* Get next batch of candidates */
+	for (int i = 0; i < batch_size; i++)
+	{
+		HnswSearchCandidate *sc;
+
+		if (pairingheap_is_empty(so->discarded))
+			break;
+
+		sc = HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded));
+
+		ep = lappend(ep, sc);
+	}
+
+	return HnswSearchLayer(base, &so->q, ep, batch_size, 0, index, &so->support, so->m, false, NULL, &so->v, &so->discarded, false, &so->tuples);
 }
 
 /*
@@ -60,13 +95,24 @@ GetScanValue(IndexScanDesc scan)
 		Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
 
 		/* Normalize if needed */
-		if (so->normprocinfo != NULL)
-			value = HnswNormValue(so->typeInfo, so->collation, value);
+		if (so->support.normprocinfo != NULL)
+			value = HnswNormValue(so->typeInfo, so->support.collation, value);
 	}
 
 	return value;
 }
 
+#if defined(HNSW_MEMORY)
+/*
+ * Show memory usage
+ */
+static void
+ShowMemoryUsage(HnswScanOpaque so)
+{
+	elog(INFO, "memory: %zu KB, tuples: " INT64_FORMAT, MemoryContextMemAllocated(so->tmpCtx, false) / 1024, so->tuples);
+}
+#endif
+
 /*
  * Prepare for an index scan
  */
@@ -81,14 +127,19 @@ hnswbeginscan(Relation index, int nkeys, int norderbys)
 	so = (HnswScanOpaque) palloc(sizeof(HnswScanOpaqueData));
 	so->typeInfo = HnswGetTypeInfo(index);
 	so->first = true;
+	so->v.tids = NULL;
+	so->discarded = NULL;
+
+	/*
+	 * Use a lower max allocation size than default to allow scanning more
+	 * tuples for iterative search before exceeding work_mem
+	 */
 	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 									   "Hnsw scan temporary context",
-									   ALLOCSET_DEFAULT_SIZES);
+									   0, 8 * 1024, 512 * 1024);
 
 	/* Set support functions */
-	so->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
-	so->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
-	so->collation = index->rd_indcollation[0];
+	HnswInitSupport(&so->support, index);
 
 	scan->opaque = so;
 
@@ -103,7 +154,15 @@ hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int no
 {
 	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
 
+	if (so->v.tids != NULL)
+		tidhash_reset(so->v.tids);
+
+	if (so->discarded != NULL)
+		pairingheap_reset(so->discarded);
+
 	so->first = true;
+	so->tuples = 0;
+	so->previousDistance = -get_float8_infinity();
 	MemoryContextReset(so->tmpCtx);
 
 	if (keys && scan->numberOfKeys > 0)
@@ -161,26 +220,104 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		so->first = false;
 
 #if defined(HNSW_MEMORY)
-		elog(INFO, "memory: %zu KB", MemoryContextMemAllocated(so->tmpCtx, false) / 1024);
+		ShowMemoryUsage(so);
 #endif
 	}
 
-	while (list_length(so->w) > 0)
+	for (;;)
 	{
 		char	   *base = NULL;
-		HnswSearchCandidate *hc = llast(so->w);
-		HnswElement element = HnswPtrAccess(base, hc->element);
+		HnswSearchCandidate *sc;
+		HnswElement element;
 		ItemPointer heaptid;
 
+		if (list_length(so->w) == 0)
+		{
+			if (hnsw_iterative_search == HNSW_ITERATIVE_SEARCH_OFF)
+				break;
+
+			/* Empty index */
+			if (so->discarded == NULL)
+				break;
+
+			/* Reached max number of tuples */
+			if (hnsw_max_search_tuples != -1 && so->tuples >= hnsw_max_search_tuples)
+			{
+				if (pairingheap_is_empty(so->discarded))
+					break;
+
+				/* Return remaining tuples */
+				so->w = lappend(so->w, HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded)));
+			}
+			/* Prevent scans from consuming too much memory */
+			else if (MemoryContextMemAllocated(so->tmpCtx, false) > (Size) work_mem * 1024L)
+			{
+				if (pairingheap_is_empty(so->discarded))
+				{
+					ereport(DEBUG1,
+							(errmsg("hnsw index scan exceeded work_mem after " INT64_FORMAT " tuples", so->tuples),
+							 errhint("Increase work_mem to scan more tuples.")));
+
+					break;
+				}
+
+				/* Return remaining tuples */
+				so->w = lappend(so->w, HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded)));
+			}
+			else
+			{
+				/*
+				 * Locking ensures when neighbors are read, the elements they
+				 * reference will not be deleted (and replaced) during the
+				 * iteration.
+				 *
+				 * Elements loaded into memory on previous iterations may have
+				 * been deleted (and replaced), so when reading neighbors, the
+				 * element version must be checked.
+				 */
+				LockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+				so->w = ResumeScanItems(scan);
+
+				UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+#if defined(HNSW_MEMORY)
+				ShowMemoryUsage(so);
+#endif
+			}
+
+			if (list_length(so->w) == 0)
+				break;
+		}
+
+		sc = llast(so->w);
+		element = HnswPtrAccess(base, sc->element);
+
 		/* Move to next element if no valid heap TIDs */
 		if (element->heaptidsLength == 0)
 		{
 			so->w = list_delete_last(so->w);
+
+			/* Mark memory as free for next iteration */
+			if (hnsw_iterative_search != HNSW_ITERATIVE_SEARCH_OFF)
+			{
+				pfree(element);
+				pfree(sc);
+			}
+
 			continue;
 		}
 
 		heaptid = &element->heaptids[--element->heaptidsLength];
 
+		if (hnsw_iterative_search == HNSW_ITERATIVE_SEARCH_STRICT)
+		{
+			if (sc->distance < so->previousDistance)
+				continue;
+
+			so->previousDistance = sc->distance;
+		}
+
 		MemoryContextSwitchTo(oldCtx);
 
 		scan->xs_heaptid = *heaptid;

src/hnswutils.c

@@ -1,5 +1,6 @@
 #include "postgres.h"
 
+#include <float.h>
 #include <math.h>
 
 #include "access/generic_xlog.h"
@@ -100,19 +101,6 @@ hash_offset(Size offset)
 #define SH_DEFINE
 #include "lib/simplehash.h"
 
-typedef union
-{
-	pointerhash_hash *pointers;
-	offsethash_hash *offsets;
-	tidhash_hash *tids;
-}			visited_hash;
-
-typedef union
-{
-	HnswElement element;
-	ItemPointerData indextid;
-}			HnswUnvisited;
-
 /*
  * Get the max number of connections in an upper layer for each element in the index
  */
@@ -153,12 +141,26 @@ HnswOptionalProcInfo(Relation index, uint16 procnum)
 	return index_getprocinfo(index, 1, procnum);
 }
 
+/*
+ * Init support functions
+ */
+void
+HnswInitSupport(HnswSupport * support, Relation index)
+{
+	support->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
+	support->collation = index->rd_indcollation[0];
+	support->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+}
+
 /*
  * Normalize value
  */
 Datum
 HnswNormValue(const HnswTypeInfo * typeInfo, Oid collation, Datum value)
 {
+	if (!typeInfo->normalize)
+		return value;
+
 	return DirectFunctionCall1Coll(typeInfo->normalize, collation, value);
 }
 
@@ -166,9 +168,9 @@ HnswNormValue(const HnswTypeInfo * typeInfo, Oid collation, Datum value)
  * Check if non-zero norm
  */
 bool
-HnswCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value)
+HnswCheckNorm(HnswSupport * support, Datum value)
 {
-	return DatumGetFloat8(FunctionCall1Coll(procinfo, collation, value)) > 0;
+	return DatumGetFloat8(FunctionCall1Coll(support->normprocinfo, support->collation, value)) > 0;
 }
 
 /*
@@ -197,7 +199,7 @@ HnswInitPage(Buffer buf, Page page)
 /*
  * Allocate a neighbor array
  */
-static HnswNeighborArray *
+HnswNeighborArray *
 HnswInitNeighborArray(int lm, HnswAllocator * allocator)
 {
 	HnswNeighborArray *a = HnswAlloc(allocator, HNSW_NEIGHBOR_ARRAY_SIZE(lm));
@@ -253,6 +255,8 @@ HnswInitElement(char *base, ItemPointer heaptid, int m, double ml, int maxLevel,
 
 	element->level = level;
 	element->deleted = 0;
+	/* Start at one to make it easier to find issues */
+	element->version = 1;
 
 	HnswInitNeighbors(base, element, m, allocator);
 
@@ -394,6 +398,33 @@ HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, Bloc
 	UnlockReleaseBuffer(buf);
 }
 
+/*
+ * Form index value
+ */
+bool
+HnswFormIndexValue(Datum *out, Datum *values, bool *isnull, const HnswTypeInfo * typeInfo, HnswSupport * support)
+{
+	/* Detoast once for all calls */
+	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+
+	/* Check value */
+	if (typeInfo->checkValue != NULL)
+		typeInfo->checkValue(DatumGetPointer(value));
+
+	/* Normalize if needed */
+	if (support->normprocinfo != NULL)
+	{
+		if (!HnswCheckNorm(support, value))
+			return false;
+
+		value = HnswNormValue(typeInfo, support->collation, value);
+	}
+
+	*out = value;
+
+	return true;
+}
+
 /*
  * Set element tuple, except for neighbor info
  */
@@ -405,6 +436,7 @@ HnswSetElementTuple(char *base, HnswElementTuple etup, HnswElement element)
 	etup->type = HNSW_ELEMENT_TUPLE_TYPE;
 	etup->level = element->level;
 	etup->deleted = 0;
+	etup->version = element->version;
 	for (int i = 0; i < HNSW_HEAPTIDS; i++)
 	{
 		if (i < element->heaptidsLength)
@@ -447,69 +479,7 @@ HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m)
 	}
 
 	ntup->count = idx;
-}
-
-/*
- * Load neighbors from page
- */
-static void
-LoadNeighborsFromPage(HnswElement element, Relation index, Page page, int m)
-{
-	char	   *base = NULL;
-
-	HnswNeighborTuple ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
-	int			neighborCount = (element->level + 2) * m;
-
-	Assert(HnswIsNeighborTuple(ntup));
-
-	HnswInitNeighbors(base, element, m, NULL);
-
-	/* Ensure expected neighbors */
-	if (ntup->count != neighborCount)
-		return;
-
-	for (int i = 0; i < neighborCount; i++)
-	{
-		HnswElement e;
-		int			level;
-		HnswCandidate *hc;
-		ItemPointer indextid;
-		HnswNeighborArray *neighbors;
-
-		indextid = &ntup->indextids[i];
-
-		if (!ItemPointerIsValid(indextid))
-			continue;
-
-		e = HnswInitElementFromBlock(ItemPointerGetBlockNumber(indextid), ItemPointerGetOffsetNumber(indextid));
-
-		/* Calculate level based on offset */
-		level = element->level - i / m;
-		if (level < 0)
-			level = 0;
-
-		neighbors = HnswGetNeighbors(base, element, level);
-		hc = &neighbors->items[neighbors->length++];
-		HnswPtrStore(base, hc->element, e);
-	}
-}
-
-/*
- * Load neighbors
- */
-void
-HnswLoadNeighbors(HnswElement element, Relation index, int m)
-{
-	Buffer		buf;
-	Page		page;
-
-	buf = ReadBuffer(index, element->neighborPage);
-	LockBuffer(buf, BUFFER_LOCK_SHARE);
-	page = BufferGetPage(buf);
-
-	LoadNeighborsFromPage(element, index, page, m);
-
-	UnlockReleaseBuffer(buf);
+	ntup->version = e->version;
 }
 
 /*
@@ -520,6 +490,7 @@ HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHe
 {
 	element->level = etup->level;
 	element->deleted = etup->deleted;
+	element->version = etup->version;
 	element->neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
 	element->neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
 	element->heaptidsLength = 0;
@@ -545,11 +516,20 @@ HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHe
 	}
 }
 
+/*
+ * Calculate the distance between values
+ */
+static inline double
+HnswGetDistance(Datum a, Datum b, HnswSupport * support)
+{
+	return DatumGetFloat8(FunctionCall2Coll(support->procinfo, support->collation, a, b));
+}
+
 /*
  * Load an element and optionally get its distance from q
  */
 static void
-HnswLoadElementImpl(BlockNumber blkno, OffsetNumber offno, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec, float *maxDistance, HnswElement * element)
+HnswLoadElementImpl(BlockNumber blkno, OffsetNumber offno, double *distance, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec, double *maxDistance, HnswElement * element)
 {
 	Buffer		buf;
 	Page		page;
@@ -567,10 +547,17 @@ HnswLoadElementImpl(BlockNumber blkno, OffsetNumber offno, float *distance, Datu
 	/* Calculate distance */
 	if (distance != NULL)
 	{
-		if (DatumGetPointer(*q) == NULL)
+		if (DatumGetPointer(q->value) == NULL)
 			*distance = 0;
 		else
-			*distance = (float) DatumGetFloat8(FunctionCall2Coll(procinfo, collation, *q, PointerGetDatum(&etup->data)));
+		{
+			*distance = HnswGetDistance(q->value, PointerGetDatum(&etup->data), support);
+
+			/* Needed for intvec cosine distance */
+			/* TODO Improve */
+			if (isnan(*distance))
+				*distance = DBL_MAX;
+		}
 	}
 
 	/* Load element */
@@ -589,40 +576,51 @@ HnswLoadElementImpl(BlockNumber blkno, OffsetNumber offno, float *distance, Datu
  * Load an element and optionally get its distance from q
  */
 void
-HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec, float *maxDistance)
+HnswLoadElement(HnswElement element, double *distance, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec, double *maxDistance)
 {
-	HnswLoadElementImpl(element->blkno, element->offno, distance, q, index, procinfo, collation, loadVec, maxDistance, &element);
+	HnswLoadElementImpl(element->blkno, element->offno, distance, q, index, support, loadVec, maxDistance, &element);
 }
 
 /*
  * Get the distance for an element
  */
-static float
-GetElementDistance(char *base, HnswElement element, Datum q, FmgrInfo *procinfo, Oid collation)
+static double
+GetElementDistance(char *base, HnswElement element, HnswQuery * q, HnswSupport * support)
 {
 	Datum		value = HnswGetValue(base, element);
 
-	return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, q, value));
+	return HnswGetDistance(q->value, value, support);
+}
+
+/*
+ * Allocate a search candidate
+ */
+static HnswSearchCandidate *
+HnswInitSearchCandidate(char *base, HnswElement element, double distance)
+{
+	HnswSearchCandidate *sc = palloc(sizeof(HnswSearchCandidate));
+
+	HnswPtrStore(base, sc->element, element);
+	sc->distance = distance;
+	return sc;
 }
 
 /*
  * Create a candidate for the entry point
  */
 HnswSearchCandidate *
-HnswEntryCandidate(char *base, HnswElement entryPoint, Datum q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec)
+HnswEntryCandidate(char *base, HnswElement entryPoint, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec)
 {
-	HnswSearchCandidate *hc = palloc(sizeof(HnswSearchCandidate));
+	bool		inMemory = index == NULL;
+	double		distance;
 
-	HnswPtrStore(base, hc->element, entryPoint);
-	if (index == NULL)
-		hc->distance = GetElementDistance(base, entryPoint, q, procinfo, collation);
+	if (inMemory)
+		distance = GetElementDistance(base, entryPoint, q, support);
 	else
-		HnswLoadElement(entryPoint, &hc->distance, &q, index, procinfo, collation, loadVec, NULL);
-	return hc;
-}
+		HnswLoadElement(entryPoint, &distance, q, index, support, loadVec, NULL);
 
-#define HnswGetSearchCandidate(membername, ptr) pairingheap_container(HnswSearchCandidate, membername, ptr)
-#define HnswGetSearchCandidateConst(membername, ptr) pairingheap_const_container(HnswSearchCandidate, membername, ptr)
+	return HnswInitSearchCandidate(base, entryPoint, distance);
+}
 
 /*
  * Compare candidate distances
@@ -639,6 +637,21 @@ CompareNearestCandidates(const pairingheap_node *a, const pairingheap_node *b, v
 	return 0;
 }
 
+/*
+ * Compare discarded candidate distances
+ */
+static int
+CompareNearestDiscardedCandidates(const pairingheap_node *a, const pairingheap_node *b, void *arg)
+{
+	if (HnswGetSearchCandidateConst(w_node, a)->distance < HnswGetSearchCandidateConst(w_node, b)->distance)
+		return 1;
+
+	if (HnswGetSearchCandidateConst(w_node, a)->distance > HnswGetSearchCandidateConst(w_node, b)->distance)
+		return -1;
+
+	return 0;
+}
+
 /*
  * Compare candidate distances
  */
@@ -658,9 +671,9 @@ CompareFurthestCandidates(const pairingheap_node *a, const pairingheap_node *b,
  * Init visited
  */
 static inline void
-InitVisited(char *base, visited_hash * v, Relation index, int ef, int m)
+InitVisited(char *base, visited_hash * v, bool inMemory, int ef, int m)
 {
-	if (index != NULL)
+	if (!inMemory)
 		v->tids = tidhash_create(CurrentMemoryContext, ef * m * 2, NULL);
 	else if (base != NULL)
 		v->offsets = offsethash_create(CurrentMemoryContext, ef * m * 2, NULL);
@@ -672,9 +685,9 @@ InitVisited(char *base, visited_hash * v, Relation index, int ef, int m)
  * Add to visited
  */
 static inline void
-AddToVisited(char *base, visited_hash * v, HnswElementPtr elementPtr, Relation index, bool *found)
+AddToVisited(char *base, visited_hash * v, HnswElementPtr elementPtr, bool inMemory, bool *found)
 {
-	if (index != NULL)
+	if (!inMemory)
 	{
 		HnswElement element = HnswPtrAccess(base, elementPtr);
 		ItemPointerData indextid;
@@ -735,39 +748,61 @@ HnswLoadUnvisitedFromMemory(char *base, HnswElement element, HnswUnvisited * unv
 		HnswCandidate *hc = &localNeighborhood->items[i];
 		bool		found;
 
-		AddToVisited(base, v, hc->element, NULL, &found);
+		AddToVisited(base, v, hc->element, true, &found);
 
 		if (!found)
 			unvisited[(*unvisitedLength)++].element = HnswPtrAccess(base, hc->element);
 	}
 }
 
+/*
+ * Load neighbor index TIDs
+ */
+bool
+HnswLoadNeighborTids(HnswElement element, ItemPointerData *indextids, Relation index, int m, int lm, int lc)
+{
+	Buffer		buf;
+	Page		page;
+	HnswNeighborTuple ntup;
+	int			start;
+
+	buf = ReadBuffer(index, element->neighborPage);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+
+	ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
+
+	/*
+	 * Ensure the neighbor tuple has not been deleted or replaced between
+	 * index scan iterations
+	 */
+	if (ntup->version != element->version || ntup->count != (element->level + 2) * m)
+	{
+		UnlockReleaseBuffer(buf);
+		return false;
+	}
+
+	/* Copy to minimize lock time */
+	start = (element->level - lc) * m;
+	memcpy(indextids, ntup->indextids + start, lm * sizeof(ItemPointerData));
+
+	UnlockReleaseBuffer(buf);
+	return true;
+}
+
 /*
  * Load unvisited neighbors from disk
  */
 static void
 HnswLoadUnvisitedFromDisk(HnswElement element, HnswUnvisited * unvisited, int *unvisitedLength, visited_hash * v, Relation index, int m, int lm, int lc)
 {
-	Buffer		buf;
-	Page		page;
-	HnswNeighborTuple ntup;
-	int			start;
 	ItemPointerData indextids[HNSW_MAX_M * 2];
 
-	buf = ReadBuffer(index, element->neighborPage);
-	LockBuffer(buf, BUFFER_LOCK_SHARE);
-	page = BufferGetPage(buf);
-
-	ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
-	start = (element->level - lc) * m;
-
-	/* Copy to minimize lock time */
-	memcpy(&indextids, ntup->indextids + start, lm * sizeof(ItemPointerData));
-
-	UnlockReleaseBuffer(buf);
-
 	*unvisitedLength = 0;
 
+	if (!HnswLoadNeighborTids(element, indextids, index, m, lm, lc))
+		return;
+
 	for (int i = 0; i < lm; i++)
 	{
 		ItemPointer indextid = &indextids[i];
@@ -787,24 +822,37 @@ HnswLoadUnvisitedFromDisk(HnswElement element, HnswUnvisited * unvisited, int *u
  * Algorithm 2 from paper
  */
 List *
-HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement)
+HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples)
 {
 	List	   *w = NIL;
 	pairingheap *C = pairingheap_allocate(CompareNearestCandidates, NULL);
 	pairingheap *W = pairingheap_allocate(CompareFurthestCandidates, NULL);
 	int			wlen = 0;
-	visited_hash v;
+	visited_hash vh;
 	ListCell   *lc2;
 	HnswNeighborArray *localNeighborhood = NULL;
 	Size		neighborhoodSize = 0;
 	int			lm = HnswGetLayerM(m, lc);
 	HnswUnvisited *unvisited = palloc(lm * sizeof(HnswUnvisited));
 	int			unvisitedLength;
+	bool		inMemory = index == NULL;
 
-	InitVisited(base, &v, index, ef, m);
+	if (v == NULL)
+	{
+		v = &vh;
+		initVisited = true;
+	}
+
+	if (initVisited)
+	{
+		InitVisited(base, v, inMemory, ef, m);
+
+		if (discarded != NULL)
+			*discarded = pairingheap_allocate(CompareNearestDiscardedCandidates, NULL);
+	}
 
 	/* Create local memory for neighborhood if needed */
-	if (index == NULL)
+	if (inMemory)
 	{
 		neighborhoodSize = HNSW_NEIGHBOR_ARRAY_SIZE(lm);
 		localNeighborhood = palloc(neighborhoodSize);
@@ -813,20 +861,26 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 	/* Add entry points to v, C, and W */
 	foreach(lc2, ep)
 	{
-		HnswSearchCandidate *hc = (HnswSearchCandidate *) lfirst(lc2);
+		HnswSearchCandidate *sc = (HnswSearchCandidate *) lfirst(lc2);
 		bool		found;
 
-		AddToVisited(base, &v, hc->element, index, &found);
+		if (initVisited)
+		{
+			AddToVisited(base, v, sc->element, inMemory, &found);
 
-		pairingheap_add(C, &hc->c_node);
-		pairingheap_add(W, &hc->w_node);
+			if (tuples != NULL)
+				(*tuples)++;
+		}
+
+		pairingheap_add(C, &sc->c_node);
+		pairingheap_add(W, &sc->w_node);
 
 		/*
 		 * Do not count elements being deleted towards ef when vacuuming. It
 		 * would be ideal to do this for inserts as well, but this could
 		 * affect insert performance.
 		 */
-		if (CountElement(skipElement, HnswPtrAccess(base, hc->element)))
+		if (CountElement(skipElement, HnswPtrAccess(base, sc->element)))
 			wlen++;
 	}
 
@@ -841,24 +895,27 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 
 		cElement = HnswPtrAccess(base, c->element);
 
-		if (index == NULL)
-			HnswLoadUnvisitedFromMemory(base, cElement, unvisited, &unvisitedLength, &v, lc, localNeighborhood, neighborhoodSize);
+		if (inMemory)
+			HnswLoadUnvisitedFromMemory(base, cElement, unvisited, &unvisitedLength, v, lc, localNeighborhood, neighborhoodSize);
 		else
-			HnswLoadUnvisitedFromDisk(cElement, unvisited, &unvisitedLength, &v, index, m, lm, lc);
+			HnswLoadUnvisitedFromDisk(cElement, unvisited, &unvisitedLength, v, index, m, lm, lc);
+
+		if (tuples != NULL)
+			(*tuples) += unvisitedLength;
 
 		for (int i = 0; i < unvisitedLength; i++)
 		{
 			HnswElement eElement;
 			HnswSearchCandidate *e;
-			float		eDistance;
+			double		eDistance;
 			bool		alwaysAdd = wlen < ef;
 
 			f = HnswGetSearchCandidate(w_node, pairingheap_first(W));
 
-			if (index == NULL)
+			if (inMemory)
 			{
 				eElement = unvisited[i].element;
-				eDistance = GetElementDistance(base, eElement, q, procinfo, collation);
+				eDistance = GetElementDistance(base, eElement, q, support);
 			}
 			else
 			{
@@ -868,25 +925,30 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 
 				/* Avoid any allocations if not adding */
 				eElement = NULL;
-				HnswLoadElementImpl(blkno, offno, &eDistance, &q, index, procinfo, collation, inserting, alwaysAdd ? NULL : &f->distance, &eElement);
+				HnswLoadElementImpl(blkno, offno, &eDistance, q, index, support, inserting, alwaysAdd || discarded != NULL ? NULL : &f->distance, &eElement);
 
 				if (eElement == NULL)
 					continue;
 			}
 
-			if (!(eDistance < f->distance || alwaysAdd))
-				continue;
+			if (eElement == NULL || !(eDistance < f->distance || alwaysAdd))
+			{
+				if (discarded != NULL)
+				{
+					/* Create a new candidate */
+					e = HnswInitSearchCandidate(base, eElement, eDistance);
+					pairingheap_add(*discarded, &e->w_node);
+				}
 
-			Assert(!eElement->deleted);
+				continue;
+			}
 
 			/* Make robust to issues */
 			if (eElement->level < lc)
 				continue;
 
 			/* Create a new candidate */
-			e = palloc(sizeof(HnswSearchCandidate));
-			HnswPtrStore(base, e->element, eElement);
-			e->distance = eDistance;
+			e = HnswInitSearchCandidate(base, eElement, eDistance);
 			pairingheap_add(C, &e->c_node);
 			pairingheap_add(W, &e->w_node);
 
@@ -901,7 +963,12 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 
 				/* No need to decrement wlen */
 				if (wlen > ef)
-					pairingheap_remove_first(W);
+				{
+					HnswSearchCandidate *d = HnswGetSearchCandidate(w_node, pairingheap_remove_first(W));
+
+					if (discarded != NULL)
+						pairingheap_add(*discarded, &d->w_node);
+				}
 			}
 		}
 	}
@@ -909,9 +976,9 @@ HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, F
 	/* Add each element of W to w */
 	while (!pairingheap_is_empty(W))
 	{
-		HnswSearchCandidate *hc = HnswGetSearchCandidate(w_node, pairingheap_remove_first(W));
+		HnswSearchCandidate *sc = HnswGetSearchCandidate(w_node, pairingheap_remove_first(W));
 
-		w = lappend(w, hc);
+		w = lappend(w, sc);
 	}
 
 	return w;
@@ -965,32 +1032,22 @@ CompareCandidateDistancesOffset(const ListCell *a, const ListCell *b)
 	return 0;
 }
 
-/*
- * Calculate the distance between elements
- */
-static float
-HnswGetDistance(char *base, HnswElement a, HnswElement b, FmgrInfo *procinfo, Oid collation)
-{
-	Datum		aValue = HnswGetValue(base, a);
-	Datum		bValue = HnswGetValue(base, b);
-
-	return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, aValue, bValue));
-}
-
 /*
  * Check if an element is closer to q than any element from R
  */
 static bool
-CheckElementCloser(char *base, HnswCandidate * e, List *r, FmgrInfo *procinfo, Oid collation)
+CheckElementCloser(char *base, HnswCandidate * e, List *r, HnswSupport * support)
 {
 	HnswElement eElement = HnswPtrAccess(base, e->element);
+	Datum		eValue = HnswGetValue(base, eElement);
 	ListCell   *lc2;
 
 	foreach(lc2, r)
 	{
 		HnswCandidate *ri = lfirst(lc2);
 		HnswElement riElement = HnswPtrAccess(base, ri->element);
-		float		distance = HnswGetDistance(base, eElement, riElement, procinfo, collation);
+		Datum		riValue = HnswGetValue(base, riElement);
+		float		distance = HnswGetDistance(eValue, riValue, support);
 
 		if (distance <= e->distance)
 			return false;
@@ -1003,15 +1060,14 @@ CheckElementCloser(char *base, HnswCandidate * e, List *r, FmgrInfo *procinfo, O
  * Algorithm 4 from paper
  */
 static List *
-SelectNeighbors(char *base, List *c, int lm, int lc, FmgrInfo *procinfo, Oid collation, HnswElement e2, HnswCandidate * newCandidate, HnswCandidate * *pruned, bool sortCandidates)
+SelectNeighbors(char *base, List *c, int lm, HnswSupport * support, bool *closerSet, HnswCandidate * newCandidate, HnswCandidate * *pruned, bool sortCandidates)
 {
 	List	   *r = NIL;
 	List	   *w = list_copy(c);
 	HnswCandidate **wd;
 	int			wdlen = 0;
 	int			wdoff = 0;
-	HnswNeighborArray *neighbors = HnswGetNeighbors(base, e2, lc);
-	bool		mustCalculate = !neighbors->closerSet;
+	bool		mustCalculate = !(*closerSet);
 	List	   *added = NIL;
 	bool		removedAny = false;
 
@@ -1038,7 +1094,7 @@ SelectNeighbors(char *base, List *c, int lm, int lc, FmgrInfo *procinfo, Oid col
 
 		/* Use previous state of r and wd to skip work when possible */
 		if (mustCalculate)
-			e->closer = CheckElementCloser(base, e, r, procinfo, collation);
+			e->closer = CheckElementCloser(base, e, r, support);
 		else if (list_length(added) > 0)
 		{
 			/* Keep Valgrind happy for in-memory, parallel builds */
@@ -1051,7 +1107,7 @@ SelectNeighbors(char *base, List *c, int lm, int lc, FmgrInfo *procinfo, Oid col
 			 */
 			if (e->closer)
 			{
-				e->closer = CheckElementCloser(base, e, added, procinfo, collation);
+				e->closer = CheckElementCloser(base, e, added, support);
 
 				if (!e->closer)
 					removedAny = true;
@@ -1064,7 +1120,7 @@ SelectNeighbors(char *base, List *c, int lm, int lc, FmgrInfo *procinfo, Oid col
 				 */
 				if (removedAny)
 				{
-					e->closer = CheckElementCloser(base, e, r, procinfo, collation);
+					e->closer = CheckElementCloser(base, e, r, support);
 					if (e->closer)
 						added = lappend(added, e);
 				}
@@ -1072,7 +1128,7 @@ SelectNeighbors(char *base, List *c, int lm, int lc, FmgrInfo *procinfo, Oid col
 		}
 		else if (e == newCandidate)
 		{
-			e->closer = CheckElementCloser(base, e, r, procinfo, collation);
+			e->closer = CheckElementCloser(base, e, r, support);
 			if (e->closer)
 				added = lappend(added, e);
 		}
@@ -1088,7 +1144,7 @@ SelectNeighbors(char *base, List *c, int lm, int lc, FmgrInfo *procinfo, Oid col
 	}
 
 	/* Cached value can only be used in future if sorted deterministically */
-	neighbors->closerSet = sortCandidates;
+	*closerSet = sortCandidates;
 
 	/* Keep pruned connections */
 	while (wdoff < wdlen && list_length(r) < lm)
@@ -1123,18 +1179,16 @@ AddConnections(char *base, HnswElement element, List *neighbors, int lc)
  * Update connections
  */
 void
-HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int lm, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation)
+HnswUpdateConnection(char *base, HnswNeighborArray * neighbors, HnswElement newElement, float distance, int lm, int *updateIdx, Relation index, HnswSupport * support)
 {
-	HnswElement hce = HnswPtrAccess(base, hc->element);
-	HnswNeighborArray *currentNeighbors = HnswGetNeighbors(base, hce, lc);
-	HnswCandidate hc2;
+	HnswCandidate newHc;
 
-	HnswPtrStore(base, hc2.element, element);
-	hc2.distance = hc->distance;
+	HnswPtrStore(base, newHc.element, newElement);
+	newHc.distance = distance;
 
-	if (currentNeighbors->length < lm)
+	if (neighbors->length < lm)
 	{
-		currentNeighbors->items[currentNeighbors->length++] = hc2;
+		neighbors->items[neighbors->length++] = newHc;
 
 		/* Track update */
 		if (updateIdx != NULL)
@@ -1143,54 +1197,26 @@ HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int lm
 	else
 	{
 		/* Shrink connections */
+		List	   *c = NIL;
 		HnswCandidate *pruned = NULL;
 
-		/* Load elements on insert */
-		if (index != NULL)
-		{
-			Datum		q = HnswGetValue(base, hce);
+		/* Add candidates */
+		for (int i = 0; i < neighbors->length; i++)
+			c = lappend(c, &neighbors->items[i]);
+		c = lappend(c, &newHc);
 
-			for (int i = 0; i < currentNeighbors->length; i++)
-			{
-				HnswCandidate *hc3 = &currentNeighbors->items[i];
-				HnswElement hc3Element = HnswPtrAccess(base, hc3->element);
-
-				if (HnswPtrIsNull(base, hc3Element->value))
-					HnswLoadElement(hc3Element, &hc3->distance, &q, index, procinfo, collation, true, NULL);
-				else
-					hc3->distance = GetElementDistance(base, hc3Element, q, procinfo, collation);
-
-				/* Prune element if being deleted */
-				if (hc3Element->heaptidsLength == 0)
-				{
-					pruned = &currentNeighbors->items[i];
-					break;
-				}
-			}
-		}
+		SelectNeighbors(base, c, lm, support, &neighbors->closerSet, &newHc, &pruned, true);
 
+		/* Should not happen */
 		if (pruned == NULL)
-		{
-			List	   *c = NIL;
-
-			/* Add candidates */
-			for (int i = 0; i < currentNeighbors->length; i++)
-				c = lappend(c, &currentNeighbors->items[i]);
-			c = lappend(c, &hc2);
-
-			SelectNeighbors(base, c, lm, lc, procinfo, collation, hce, &hc2, &pruned, true);
-
-			/* Should not happen */
-			if (pruned == NULL)
-				return;
-		}
+			return;
 
 		/* Find and replace the pruned element */
-		for (int i = 0; i < currentNeighbors->length; i++)
+		for (int i = 0; i < neighbors->length; i++)
 		{
-			if (HnswPtrEqual(base, currentNeighbors->items[i].element, pruned->element))
+			if (HnswPtrEqual(base, neighbors->items[i].element, pruned->element))
 			{
-				currentNeighbors->items[i] = hc2;
+				neighbors->items[i] = newHc;
 
 				/* Track update */
 				if (updateIdx != NULL)
@@ -1250,17 +1276,20 @@ PrecomputeHash(char *base, HnswElement element)
  * Algorithm 1 from paper
  */
 void
-HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing)
+HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, HnswSupport * support, int m, int efConstruction, bool existing)
 {
 	List	   *ep;
 	List	   *w;
 	int			level = element->level;
 	int			entryLevel;
-	Datum		q = HnswGetValue(base, element);
+	HnswQuery	q;
 	HnswElement skipElement = existing ? element : NULL;
+	bool		inMemory = index == NULL;
+
+	q.value = HnswGetValue(base, element);
 
 	/* Precompute hash */
-	if (index == NULL)
+	if (inMemory)
 		PrecomputeHash(base, element);
 
 	/* No neighbors if no entry point */
@@ -1268,13 +1297,13 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 		return;
 
 	/* Get entry point and level */
-	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, true));
+	ep = list_make1(HnswEntryCandidate(base, entryPoint, &q, index, support, true));
 	entryLevel = entryPoint->level;
 
 	/* 1st phase: greedy search to insert level */
 	for (int lc = entryLevel; lc >= level + 1; lc--)
 	{
-		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, true, skipElement);
+		w = HnswSearchLayer(base, &q, ep, 1, lc, index, support, m, true, skipElement, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
@@ -1293,7 +1322,7 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 		List	   *lw = NIL;
 		ListCell   *lc2;
 
-		w = HnswSearchLayer(base, q, ep, efConstruction, lc, index, procinfo, collation, m, true, skipElement);
+		w = HnswSearchLayer(base, &q, ep, efConstruction, lc, index, support, m, true, skipElement, NULL, NULL, true, NULL);
 
 		/* Convert search candidates to candidates */
 		foreach(lc2, w)
@@ -1309,7 +1338,7 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 
 		/* Elements being deleted or skipped can help with search */
 		/* but should be removed before selecting neighbors */
-		if (index != NULL)
+		if (!inMemory)
 			lw = RemoveElements(base, lw, skipElement);
 
 		/*
@@ -1317,7 +1346,7 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 		 * sortCandidates to true for in-memory builds to enable closer
 		 * caching, but there does not seem to be a difference in performance.
 		 */
-		neighbors = SelectNeighbors(base, lw, lm, lc, procinfo, collation, element, NULL, NULL, false);
+		neighbors = SelectNeighbors(base, lw, lm, support, &HnswGetNeighbors(base, element, lc)->closerSet, NULL, NULL, false);
 
 		AddConnections(base, element, neighbors, lc);
 
@@ -1327,7 +1356,6 @@ HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint
 
 PGDLLEXPORT Datum l2_normalize(PG_FUNCTION_ARGS);
 PGDLLEXPORT Datum halfvec_l2_normalize(PG_FUNCTION_ARGS);
-PGDLLEXPORT Datum minivec_l2_normalize(PG_FUNCTION_ARGS);
 PGDLLEXPORT Datum sparsevec_l2_normalize(PG_FUNCTION_ARGS);
 
 static void
@@ -1376,13 +1404,13 @@ hnsw_halfvec_support(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(&typeInfo);
 };
 
-FUNCTION_PREFIX PG_FUNCTION_INFO_V1(hnsw_minivec_support);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(hnsw_intvec_support);
 Datum
-hnsw_minivec_support(PG_FUNCTION_ARGS)
+hnsw_intvec_support(PG_FUNCTION_ARGS)
 {
 	static const HnswTypeInfo typeInfo = {
 		.maxDimensions = HNSW_MAX_DIM * 4,
-		.normalize = minivec_l2_normalize,
+		.normalize = NULL,
 		.checkValue = NULL
 	};
 

src/hnswvacuum.c

@@ -184,13 +184,12 @@ static void
 RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswElement entryPoint)
 {
 	Relation	index = vacuumstate->index;
+	HnswSupport *support = &vacuumstate->support;
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
 	int			m = vacuumstate->m;
 	int			efConstruction = vacuumstate->efConstruction;
-	FmgrInfo   *procinfo = vacuumstate->procinfo;
-	Oid			collation = vacuumstate->collation;
 	BufferAccessStrategy bas = vacuumstate->bas;
 	HnswNeighborTuple ntup = vacuumstate->ntup;
 	Size		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(element->level, m);
@@ -205,7 +204,7 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	element->heaptidsLength = 0;
 
 	/* Find neighbors for element, skipping itself */
-	HnswFindElementNeighbors(base, element, entryPoint, index, procinfo, collation, m, efConstruction, true);
+	HnswFindElementNeighbors(base, element, entryPoint, index, support, m, efConstruction, true);
 
 	/* Zero memory for each element */
 	MemSet(ntup, 0, HNSW_TUPLE_ALLOC_SIZE);
@@ -229,7 +228,7 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	UnlockReleaseBuffer(buf);
 
 	/* Update neighbors */
-	HnswUpdateNeighborsOnDisk(index, procinfo, collation, element, m, true, false);
+	HnswUpdateNeighborsOnDisk(index, support, element, m, true, false);
 }
 
 /*
@@ -239,6 +238,7 @@ static void
 RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 {
 	Relation	index = vacuumstate->index;
+	HnswSupport *support = &vacuumstate->support;
 	HnswElement highestPoint = &vacuumstate->highestPoint;
 	HnswElement entryPoint;
 	MemoryContext oldCtx = MemoryContextSwitchTo(vacuumstate->tmpCtx);
@@ -256,7 +256,7 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 		LockPage(index, HNSW_UPDATE_LOCK, ShareLock);
 
 		/* Load element */
-		HnswLoadElement(highestPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true, NULL);
+		HnswLoadElement(highestPoint, NULL, NULL, index, support, true, NULL);
 
 		/* Repair if needed */
 		if (NeedsUpdated(vacuumstate, highestPoint))
@@ -294,7 +294,7 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 			 * is outdated, this can remove connections at higher levels in
 			 * the graph until they are repaired, but this should be fine.
 			 */
-			HnswLoadElement(entryPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true, NULL);
+			HnswLoadElement(entryPoint, NULL, NULL, index, support, true, NULL);
 
 			if (NeedsUpdated(vacuumstate, entryPoint))
 			{
@@ -527,6 +527,14 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 			for (int i = 0; i < ntup->count; i++)
 				ItemPointerSetInvalid(&ntup->indextids[i]);
 
+			/* Increment version */
+			/* This is used to avoid incorrect reads for iterative scans */
+			/* Reserve some bits for future use */
+			etup->version++;
+			if (etup->version > 15)
+				etup->version = 1;
+			ntup->version = etup->version;
+
 			/*
 			 * We modified the tuples in place, no need to call
 			 * PageIndexTupleOverwrite
@@ -573,13 +581,13 @@ InitVacuumState(HnswVacuumState * vacuumstate, IndexVacuumInfo *info, IndexBulkD
 	vacuumstate->callback_state = callback_state;
 	vacuumstate->efConstruction = HnswGetEfConstruction(index);
 	vacuumstate->bas = GetAccessStrategy(BAS_BULKREAD);
-	vacuumstate->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
-	vacuumstate->collation = index->rd_indcollation[0];
 	vacuumstate->ntup = palloc0(HNSW_TUPLE_ALLOC_SIZE);
 	vacuumstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 												"Hnsw vacuum temporary context",
 												ALLOCSET_DEFAULT_SIZES);
 
+	HnswInitSupport(&vacuumstate->support, index);
+
 	/* Get m from metapage */
 	HnswGetMetaPageInfo(index, &vacuumstate->m, NULL);
 

src/intvec.c

@@ -0,0 +1,754 @@
+#include "postgres.h"
+
+#include <limits.h>
+#include <math.h>
+
+#include "catalog/pg_type.h"
+#include "fmgr.h"
+#include "intvec.h"
+#include "lib/stringinfo.h"
+#include "libpq/pqformat.h"
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "utils/lsyscache.h"
+
+/*
+ * Ensure same dimensions
+ */
+static inline void
+CheckDims(IntVector * a, IntVector * b)
+{
+	if (a->dim != b->dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different intvec dimensions %d and %d", a->dim, b->dim)));
+}
+
+/*
+ * Ensure expected dimensions
+ */
+static inline void
+CheckExpectedDim(int32 typmod, int dim)
+{
+	if (typmod != -1 && typmod != dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected %d dimensions, not %d", typmod, dim)));
+}
+
+/*
+ * Ensure valid dimensions
+ */
+static inline void
+CheckDim(int dim)
+{
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("intvec must have at least 1 dimension")));
+
+	if (dim > INTVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("intvec cannot have more than %d dimensions", INTVEC_MAX_DIM)));
+}
+
+/*
+ * Ensure element in range
+ */
+static inline void
+CheckElement(long value)
+{
+	if (value < SCHAR_MIN || value > SCHAR_MAX)
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("value \"%ld\" is out of range for type intvec", value)));
+}
+
+/*
+ * Allocate and initialize a new int vector
+ */
+IntVector *
+InitIntVector(int dim)
+{
+	IntVector  *result;
+	int			size;
+
+	size = INTVEC_SIZE(dim);
+	result = (IntVector *) palloc0(size);
+	SET_VARSIZE(result, size);
+	result->dim = dim;
+
+	return result;
+}
+
+/*
+ * Check for whitespace, since array_isspace() is static
+ */
+static inline bool
+intvec_isspace(char ch)
+{
+	if (ch == ' ' ||
+		ch == '\t' ||
+		ch == '\n' ||
+		ch == '\r' ||
+		ch == '\v' ||
+		ch == '\f')
+		return true;
+	return false;
+}
+
+/*
+ * Convert textual representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_in);
+Datum
+intvec_in(PG_FUNCTION_ARGS)
+{
+	char	   *lit = PG_GETARG_CSTRING(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	int8		x[INTVEC_MAX_DIM];
+	int			dim = 0;
+	char	   *pt = lit;
+	IntVector  *result;
+
+	while (intvec_isspace(*pt))
+		pt++;
+
+	if (*pt != '[')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type intvec: \"%s\"", lit),
+				 errdetail("Vector contents must start with \"[\".")));
+
+	pt++;
+
+	while (intvec_isspace(*pt))
+		pt++;
+
+	if (*pt == ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("intvec must have at least 1 dimension")));
+
+	for (;;)
+	{
+		long		val;
+		char	   *stringEnd;
+
+		if (dim == INTVEC_MAX_DIM)
+			ereport(ERROR,
+					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+					 errmsg("intvec cannot have more than %d dimensions", VECTOR_MAX_DIM)));
+
+		while (intvec_isspace(*pt))
+			pt++;
+
+		/* Check for empty string like float4in */
+		if (*pt == '\0')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type intvec: \"%s\"", lit)));
+
+		errno = 0;
+
+		/* Use similar logic as int2vectorin */
+		val = strtol(pt, &stringEnd, 10);
+
+		if (stringEnd == pt)
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type intvec: \"%s\"", lit)));
+
+		/* Check for range error like float4in */
+		if (errno == ERANGE || val < SCHAR_MIN || val > SCHAR_MAX)
+			ereport(ERROR,
+					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+					 errmsg("\"%s\" is out of range for type intvec", pnstrdup(pt, stringEnd - pt))));
+
+		CheckElement(val);
+		x[dim++] = val;
+
+		pt = stringEnd;
+
+		while (intvec_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 intvec: \"%s\"", lit)));
+	}
+
+	/* Only whitespace is allowed after the closing brace */
+	while (intvec_isspace(*pt))
+		pt++;
+
+	if (*pt != '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type intvec: \"%s\"", lit),
+				 errdetail("Junk after closing right brace.")));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	result = InitIntVector(dim);
+	for (int i = 0; i < dim; i++)
+		result->x[i] = x[i];
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert internal representation to textual representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_out);
+Datum
+intvec_out(PG_FUNCTION_ARGS)
+{
+	IntVector  *vector = PG_GETARG_INTVEC_P(0);
+	int			dim = vector->dim;
+	char	   *buf;
+	char	   *ptr;
+
+	/*
+	 * Need:
+	 *
+	 * dim * 4 bytes for elements (-128 to 127)
+	 *
+	 * dim - 1 bytes for separator
+	 *
+	 * 3 bytes for [, ], and \0
+	 */
+	buf = (char *) palloc(5 * dim + 2);
+	ptr = buf;
+
+	*ptr = '[';
+	ptr++;
+	for (int i = 0; i < dim; i++)
+	{
+		if (i > 0)
+		{
+			*ptr = ',';
+			ptr++;
+		}
+
+#if PG_VERSION_NUM >= 140000
+		ptr += pg_ltoa(vector->x[i], ptr);
+#else
+		pg_ltoa(vector->x[i], ptr);
+		while (*ptr != '\0')
+			ptr++;
+#endif
+	}
+	*ptr = ']';
+	ptr++;
+	*ptr = '\0';
+
+	PG_FREE_IF_COPY(vector, 0);
+	PG_RETURN_CSTRING(buf);
+}
+
+/*
+ * Convert type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_typmod_in);
+Datum
+intvec_typmod_in(PG_FUNCTION_ARGS)
+{
+	ArrayType  *ta = PG_GETARG_ARRAYTYPE_P(0);
+	int32	   *tl;
+	int			n;
+
+	tl = ArrayGetIntegerTypmods(ta, &n);
+
+	if (n != 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("invalid type modifier")));
+
+	if (*tl < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type intvec must be at least 1")));
+
+	if (*tl > INTVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type intvec cannot exceed %d", INTVEC_MAX_DIM)));
+
+	PG_RETURN_INT32(*tl);
+}
+
+/*
+ * Convert external binary representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_recv);
+Datum
+intvec_recv(PG_FUNCTION_ARGS)
+{
+	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	IntVector  *result;
+	int16		dim;
+	int16		unused;
+
+	dim = pq_getmsgint(buf, sizeof(int16));
+	unused = pq_getmsgint(buf, sizeof(int16));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	if (unused != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected unused to be 0, not %d", unused)));
+
+	result = InitIntVector(dim);
+	for (int i = 0; i < dim; i++)
+		result->x[i] = pq_getmsgint(buf, sizeof(int8));
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert internal representation to the external binary representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_send);
+Datum
+intvec_send(PG_FUNCTION_ARGS)
+{
+	IntVector  *vec = PG_GETARG_INTVEC_P(0);
+	StringInfoData buf;
+
+	pq_begintypsend(&buf);
+	pq_sendint(&buf, vec->dim, sizeof(int16));
+	pq_sendint(&buf, vec->unused, sizeof(int16));
+	for (int i = 0; i < vec->dim; i++)
+		pq_sendint8(&buf, vec->x[i]);
+
+	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
+}
+
+/*
+ * Convert int vector to int vector
+ * This is needed to check the type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec);
+Datum
+intvec(PG_FUNCTION_ARGS)
+{
+	IntVector  *vec = PG_GETARG_INTVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+
+	CheckExpectedDim(typmod, vec->dim);
+
+	PG_RETURN_POINTER(vec);
+}
+
+/*
+ * Convert array to intvec vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(array_to_intvec);
+Datum
+array_to_intvec(PG_FUNCTION_ARGS)
+{
+	ArrayType  *array = PG_GETARG_ARRAYTYPE_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	IntVector  *result;
+	int16		typlen;
+	bool		typbyval;
+	char		typalign;
+	Datum	   *elemsp;
+	int			nelemsp;
+
+	if (ARR_NDIM(array) > 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("array must be 1-D")));
+
+	if (ARR_HASNULL(array) && array_contains_nulls(array))
+		ereport(ERROR,
+				(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
+				 errmsg("array must not contain nulls")));
+
+	get_typlenbyvalalign(ARR_ELEMTYPE(array), &typlen, &typbyval, &typalign);
+	deconstruct_array(array, ARR_ELEMTYPE(array), typlen, typbyval, typalign, &elemsp, NULL, &nelemsp);
+
+	CheckDim(nelemsp);
+	CheckExpectedDim(typmod, nelemsp);
+
+	result = InitIntVector(nelemsp);
+
+	if (ARR_ELEMTYPE(array) == INT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+		{
+			long		l = DatumGetInt32(elemsp[i]);
+
+			CheckElement(l);
+
+			result->x[i] = l;
+		}
+	}
+	else
+	{
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("unsupported array type")));
+	}
+
+	/*
+	 * Free allocation from deconstruct_array. Do not free individual elements
+	 * when pass-by-reference since they point to original array.
+	 */
+	pfree(elemsp);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert int vector to integer[]
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_to_integer);
+Datum
+intvec_to_integer(PG_FUNCTION_ARGS)
+{
+	IntVector  *vec = PG_GETARG_INTVEC_P(0);
+	Datum	   *datums;
+	ArrayType  *result;
+
+	datums = (Datum *) palloc(sizeof(Datum) * vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		datums[i] = Int32GetDatum((int) vec->x[i]);
+
+	result = construct_array(datums, vec->dim, INT4OID, sizeof(int32), true, TYPALIGN_INT);
+
+	pfree(datums);
+
+	PG_RETURN_POINTER(result);
+}
+
+static int
+IntvecL2SquaredDistance(int dim, int8 *ax, int8 *bx)
+{
+	int			distance = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		int			diff = (int) ax[i] - (int) bx[i];
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+
+/*
+ * Get the L2 distance between int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_l2_distance);
+Datum
+intvec_l2_distance(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(sqrt((double) IntvecL2SquaredDistance(a->dim, a->x, b->x)));
+}
+
+/*
+ * Get the L2 squared distance between int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_l2_squared_distance);
+Datum
+intvec_l2_squared_distance(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) IntvecL2SquaredDistance(a->dim, a->x, b->x));
+}
+
+static int
+IntvecInnerProduct(int dim, int8 *ax, int8 *bx)
+{
+	int			distance = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += (int) ax[i] * (int) bx[i];
+
+	return distance;
+}
+
+/*
+ * Get the inner product of two int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_inner_product);
+Datum
+intvec_inner_product(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) IntvecInnerProduct(a->dim, a->x, b->x));
+}
+
+/*
+ * Get the negative inner product of two int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_negative_inner_product);
+Datum
+intvec_negative_inner_product(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) -IntvecInnerProduct(a->dim, a->x, b->x));
+}
+
+static double
+IntvecCosineSimilarity(int dim, int8 *ax, int8 *bx)
+{
+	int			similarity = 0;
+	int			norma = 0;
+	int			normb = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		int			axi = ax[i];
+		int			bxi = 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);
+}
+
+/*
+ * Get the cosine distance between two int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_cosine_distance);
+Datum
+intvec_cosine_distance(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+	double		similarity;
+
+	CheckDims(a, b);
+
+	similarity = IntvecCosineSimilarity(a->dim, a->x, b->x);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	if (isnan(similarity))
+		PG_RETURN_FLOAT8(NAN);
+#endif
+
+	/* Keep in range */
+	if (similarity > 1)
+		similarity = 1;
+	else if (similarity < -1)
+		similarity = -1;
+
+	PG_RETURN_FLOAT8(1 - similarity);
+}
+
+static int
+IntvecL1Distance(int dim, int8 *ax, int8 *bx)
+{
+	int			distance = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += abs((int) ax[i] - (int) bx[i]);
+
+	return distance;
+}
+
+/*
+ * Get the L1 distance between two int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_l1_distance);
+Datum
+intvec_l1_distance(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) IntvecL1Distance(a->dim, a->x, b->x));
+}
+
+/*
+ * Get the dimensions of an int vector
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_vector_dims);
+Datum
+intvec_vector_dims(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+
+	PG_RETURN_INT32(a->dim);
+}
+
+/*
+ * Get the L2 norm of an int vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_l2_norm);
+Datum
+intvec_l2_norm(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	int8	   *ax = a->x;
+	int			norm = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		norm += (int) ax[i] * (int) ax[i];
+
+	PG_RETURN_FLOAT8(sqrt((double) norm));
+}
+
+/*
+ * Internal helper to compare int vectors
+ */
+static int
+intvec_cmp_internal(IntVector * a, IntVector * b)
+{
+	int			dim = Min(a->dim, b->dim);
+
+	/* Check values before dimensions to be consistent with Postgres arrays */
+	for (int i = 0; i < dim; i++)
+	{
+		if (a->x[i] < b->x[i])
+			return -1;
+
+		if (a->x[i] > b->x[i])
+			return 1;
+	}
+
+	if (a->dim < b->dim)
+		return -1;
+
+	if (a->dim > b->dim)
+		return 1;
+
+	return 0;
+}
+
+/*
+ * Less than
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_lt);
+Datum
+intvec_lt(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) < 0);
+}
+
+/*
+ * Less than or equal
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_le);
+Datum
+intvec_le(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) <= 0);
+}
+
+/*
+ * Equal
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_eq);
+Datum
+intvec_eq(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) == 0);
+}
+
+/*
+ * Not equal
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_ne);
+Datum
+intvec_ne(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) != 0);
+}
+
+/*
+ * Greater than or equal
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_ge);
+Datum
+intvec_ge(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) >= 0);
+}
+
+/*
+ * Greater than
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_gt);
+Datum
+intvec_gt(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) > 0);
+}
+
+/*
+ * Compare int vectors
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_cmp);
+Datum
+intvec_cmp(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_INT32(intvec_cmp_internal(a, b));
+}

src/intvec.h

@@ -0,0 +1,23 @@
+#ifndef INTVEC_H
+#define INTVEC_H
+
+#include "vector.h"
+
+#define INTVEC_MAX_DIM VECTOR_MAX_DIM
+
+#define INTVEC_SIZE(_dim)		(offsetof(IntVector, x) + sizeof(int8)*(_dim))
+#define DatumGetIntVector(x)	((IntVector *) PG_DETOAST_DATUM(x))
+#define PG_GETARG_INTVEC_P(x)	DatumGetIntVector(PG_GETARG_DATUM(x))
+#define PG_RETURN_INTVEC_P(x)	PG_RETURN_POINTER(x)
+
+typedef struct IntVector
+{
+	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int16		dim;			/* number of dimensions */
+	int16		unused;
+	int8		x[FLEXIBLE_ARRAY_MEMBER];
+}			IntVector;
+
+IntVector  *InitIntVector(int dim);
+
+#endif

src/ivfbuild.c

@@ -228,11 +228,11 @@ BuildCallback(Relation index, ItemPointer tid, Datum *values,
 static inline void
 GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot, IndexTuple *itup, int *list)
 {
-	Datum		value;
-	bool		isnull;
-
 	if (tuplesort_gettupleslot(sortstate, true, false, slot, NULL))
 	{
+		Datum		value;
+		bool		isnull;
+
 		*list = DatumGetInt32(slot_getattr(slot, 1, &isnull));
 		value = slot_getattr(slot, 3, &isnull);
 
@@ -254,8 +254,8 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 	IndexTuple	itup = NULL;	/* silence compiler warning */
 	int64		inserted = 0;
 
-	TupleTableSlot *slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsMinimalTuple);
-	TupleDesc	tupdesc = RelationGetDescr(index);
+	TupleTableSlot *slot = MakeSingleTupleTableSlot(buildstate->sortdesc, &TTSOpsMinimalTuple);
+	TupleDesc	tupdesc = buildstate->tupdesc;
 
 	pgstat_progress_update_param(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_LOAD);
 
@@ -319,6 +319,7 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->index = index;
 	buildstate->indexInfo = indexInfo;
 	buildstate->typeInfo = IvfflatGetTypeInfo(index);
+	buildstate->tupdesc = RelationGetDescr(index);
 
 	buildstate->lists = IvfflatGetLists(index);
 	buildstate->dimensions = TupleDescAttr(index->rd_att, 0)->atttypmod;
@@ -356,12 +357,12 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 				 errmsg("dimensions must be greater than one for this opclass")));
 
 	/* Create tuple description for sorting */
-	buildstate->tupdesc = CreateTemplateTupleDesc(3);
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 1, "list", INT4OID, -1, 0);
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 3, "vector", RelationGetDescr(index)->attrs[0].atttypid, -1, 0);
+	buildstate->sortdesc = CreateTemplateTupleDesc(3);
+	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 1, "list", INT4OID, -1, 0);
+	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
+	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 3, "vector", buildstate->tupdesc->attrs[0].atttypid, -1, 0);
 
-	buildstate->slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsVirtual);
+	buildstate->slot = MakeSingleTupleTableSlot(buildstate->sortdesc, &TTSOpsVirtual);
 
 	buildstate->centers = VectorArrayInit(buildstate->lists, buildstate->dimensions, buildstate->typeInfo->itemSize(buildstate->dimensions));
 	buildstate->listInfo = palloc(sizeof(ListInfo) * buildstate->lists);
@@ -633,7 +634,7 @@ IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, S
 	InitBuildState(&buildstate, ivfspool->heap, ivfspool->index, indexInfo);
 	memcpy(buildstate.centers->items, ivfcenters, buildstate.centers->itemsize * buildstate.centers->maxlen);
 	buildstate.centers->length = buildstate.centers->maxlen;
-	ivfspool->sortstate = InitBuildSortState(buildstate.tupdesc, sortmem, coordinate);
+	ivfspool->sortstate = InitBuildSortState(buildstate.sortdesc, sortmem, coordinate);
 	buildstate.sortstate = ivfspool->sortstate;
 	scan = table_beginscan_parallel(ivfspool->heap,
 									ParallelTableScanFromIvfflatShared(ivfshared));
@@ -950,7 +951,7 @@ AssignTuples(IvfflatBuildState * buildstate)
 	}
 
 	/* Begin serial/leader tuplesort */
-	buildstate->sortstate = InitBuildSortState(buildstate->tupdesc, maintenance_work_mem, coordinate);
+	buildstate->sortstate = InitBuildSortState(buildstate->sortdesc, maintenance_work_mem, coordinate);
 
 	/* Add tuples to sort */
 	if (buildstate->heap != NULL)

src/ivfflat.c

@@ -17,8 +17,16 @@
 #endif
 
 int			ivfflat_probes;
+int			ivfflat_iterative_search;
+int			ivfflat_max_probes;
 static relopt_kind ivfflat_relopt_kind;
 
+static const struct config_enum_entry ivfflat_iterative_search_options[] = {
+	{"off", IVFFLAT_ITERATIVE_SEARCH_OFF, false},
+	{"relaxed_order", IVFFLAT_ITERATIVE_SEARCH_RELAXED, false},
+	{NULL, 0, false}
+};
+
 /*
  * Initialize index options and variables
  */
@@ -33,6 +41,15 @@ IvfflatInit(void)
 							"Valid range is 1..lists.", &ivfflat_probes,
 							IVFFLAT_DEFAULT_PROBES, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
 
+	DefineCustomEnumVariable("ivfflat.iterative_search", "Sets the iterative search mode",
+							 NULL, &ivfflat_iterative_search,
+							 IVFFLAT_ITERATIVE_SEARCH_OFF, ivfflat_iterative_search_options, PGC_USERSET, 0, NULL, NULL, NULL);
+
+	/* If this is less than probes, probes is used */
+	DefineCustomIntVariable("ivfflat.max_probes", "Sets the max number of probes for iterative search",
+							"-1 means no limit", &ivfflat_max_probes,
+							-1, -1, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
+
 	MarkGUCPrefixReserved("ivfflat");
 }
 
@@ -69,6 +86,8 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	GenericCosts costs;
 	int			lists;
 	double		ratio;
+	double		sequentialRatio = 0.5;
+	double		startupPages;
 	double		spc_seq_page_cost;
 	Relation	index;
 
@@ -85,6 +104,8 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 
 	MemSet(&costs, 0, sizeof(costs));
 
+	genericcostestimate(root, path, loop_count, &costs);
+
 	index = index_open(path->indexinfo->indexoid, NoLock);
 	IvfflatGetMetaPageInfo(index, &lists, NULL);
 	index_close(index, NoLock);
@@ -94,41 +115,26 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	if (ratio > 1.0)
 		ratio = 1.0;
 
-	/*
-	 * This gives us the subset of tuples to visit. This value is passed into
-	 * the generic cost estimator to determine the number of pages to visit
-	 * during the index scan.
-	 */
-	costs.numIndexTuples = path->indexinfo->tuples * ratio;
-
-	genericcostestimate(root, path, loop_count, &costs);
-
 	get_tablespace_page_costs(path->indexinfo->reltablespace, NULL, &spc_seq_page_cost);
 
+	/* Change some page cost from random to sequential */
+	costs.indexTotalCost -= sequentialRatio * costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+
+	/* Startup cost is cost before returning the first row */
+	costs.indexStartupCost = costs.indexTotalCost * ratio;
+
 	/* Adjust cost if needed since TOAST not included in seq scan cost */
-	if (costs.numIndexPages > path->indexinfo->rel->pages && ratio < 0.5)
+	startupPages = costs.numIndexPages * ratio;
+	if (startupPages > path->indexinfo->rel->pages && ratio < 0.5)
 	{
-		/* Change all page cost from random to sequential */
-		costs.indexTotalCost -= costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+		/* Change rest of page cost from random to sequential */
+		costs.indexStartupCost -= (1 - sequentialRatio) * startupPages * (costs.spc_random_page_cost - spc_seq_page_cost);
 
 		/* Remove cost of extra pages */
-		costs.indexTotalCost -= (costs.numIndexPages - path->indexinfo->rel->pages) * spc_seq_page_cost;
-	}
-	else
-	{
-		/* Change some page cost from random to sequential */
-		costs.indexTotalCost -= 0.5 * costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+		costs.indexStartupCost -= (startupPages - path->indexinfo->rel->pages) * spc_seq_page_cost;
 	}
 
-	/*
-	 * If the list selectivity is lower than what is returned from the generic
-	 * cost estimator, use that.
-	 */
-	if (ratio < costs.indexSelectivity)
-		costs.indexSelectivity = ratio;
-
-	/* Use total cost since most work happens before first tuple is returned */
-	*indexStartupCost = costs.indexTotalCost;
+	*indexStartupCost = costs.indexStartupCost;
 	*indexTotalCost = costs.indexTotalCost;
 	*indexSelectivity = costs.indexSelectivity;
 	*indexCorrelation = costs.indexCorrelation;

src/ivfflat.h

@@ -80,6 +80,14 @@
 
 /* Variables */
 extern int	ivfflat_probes;
+extern int	ivfflat_iterative_search;
+extern int	ivfflat_max_probes;
+
+typedef enum IvfflatIterativeSearchMode
+{
+	IVFFLAT_ITERATIVE_SEARCH_OFF,
+	IVFFLAT_ITERATIVE_SEARCH_RELAXED
+}			IvfflatIterativeSearchMode;
 
 typedef struct VectorArrayData
 {
@@ -165,6 +173,7 @@ typedef struct IvfflatBuildState
 	Relation	index;
 	IndexInfo  *indexInfo;
 	const		IvfflatTypeInfo *typeInfo;
+	TupleDesc	tupdesc;
 
 	/* Settings */
 	int			dimensions;
@@ -198,7 +207,7 @@ typedef struct IvfflatBuildState
 
 	/* Sorting */
 	Tuplesortstate *sortstate;
-	TupleDesc	tupdesc;
+	TupleDesc	sortdesc;
 	TupleTableSlot *slot;
 
 	/* Memory */
@@ -247,8 +256,11 @@ typedef struct IvfflatScanOpaqueData
 {
 	const		IvfflatTypeInfo *typeInfo;
 	int			probes;
+	int			maxProbes;
 	int			dimensions;
 	bool		first;
+	Datum		value;
+	MemoryContext tmpCtx;
 
 	/* Sorting */
 	Tuplesortstate *sortstate;
@@ -265,7 +277,9 @@ typedef struct IvfflatScanOpaqueData
 
 	/* Lists */
 	pairingheap *listQueue;
-	IvfflatScanList lists[FLEXIBLE_ARRAY_MEMBER];	/* must come last */
+	BlockNumber *listPages;
+	int			listIndex;
+	IvfflatScanList *lists;
 }			IvfflatScanOpaqueData;
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;

src/ivfinsert.c

@@ -98,7 +98,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 	IvfflatGetMetaPageInfo(index, NULL, NULL);
 
 	/* Find the insert page - sets the page and list info */
-	FindInsertPage(index, values, &insertPage, &listInfo);
+	FindInsertPage(index, &value, &insertPage, &listInfo);
 	Assert(BlockNumberIsValid(insertPage));
 	originalInsertPage = insertPage;
 

src/ivfscan.c

@@ -10,10 +10,7 @@
 #include "miscadmin.h"
 #include "pgstat.h"
 #include "storage/bufmgr.h"
-
-#ifdef IVFFLAT_MEMORY
 #include "utils/memutils.h"
-#endif
 
 #define GetScanList(ptr) pairingheap_container(IvfflatScanList, ph_node, ptr)
 #define GetScanListConst(ptr) pairingheap_const_container(IvfflatScanList, ph_node, ptr)
@@ -65,7 +62,7 @@ GetScanLists(IndexScanDesc scan, Datum value)
 			/* Use procinfo from the index instead of scan key for performance */
 			distance = DatumGetFloat8(so->distfunc(so->procinfo, so->collation, PointerGetDatum(&list->center), value));
 
-			if (listCount < so->probes)
+			if (listCount < so->maxProbes)
 			{
 				IvfflatScanList *scanlist;
 
@@ -78,7 +75,7 @@ GetScanLists(IndexScanDesc scan, Datum value)
 				pairingheap_add(so->listQueue, &scanlist->ph_node);
 
 				/* Calculate max distance */
-				if (listCount == so->probes)
+				if (listCount == so->maxProbes)
 					maxDistance = GetScanList(pairingheap_first(so->listQueue))->distance;
 			}
 			else if (distance < maxDistance)
@@ -102,6 +99,11 @@ GetScanLists(IndexScanDesc scan, Datum value)
 
 		UnlockReleaseBuffer(cbuf);
 	}
+
+	for (int i = listCount - 1; i >= 0; i--)
+		so->listPages[i] = GetScanList(pairingheap_remove_first(so->listQueue))->startPage;
+
+	Assert(pairingheap_is_empty(so->listQueue));
 }
 
 /*
@@ -114,11 +116,14 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	TupleDesc	tupdesc = RelationGetDescr(scan->indexRelation);
 	double		tuples = 0;
 	TupleTableSlot *slot = so->vslot;
+	int			batchProbes = 0;
+
+	tuplesort_reset(so->sortstate);
 
 	/* Search closest probes lists */
-	while (!pairingheap_is_empty(so->listQueue))
+	while (so->listIndex < so->maxProbes && (++batchProbes) <= so->probes)
 	{
-		BlockNumber searchPage = GetScanList(pairingheap_remove_first(so->listQueue))->startPage;
+		BlockNumber searchPage = so->listPages[so->listIndex++];
 
 		/* Search all entry pages for list */
 		while (BlockNumberIsValid(searchPage))
@@ -166,13 +171,17 @@ GetScanItems(IndexScanDesc scan, Datum value)
 		}
 	}
 
-	if (tuples < 100)
+	if (tuples < 100 && ivfflat_iterative_search == IVFFLAT_ITERATIVE_SEARCH_OFF)
 		ereport(DEBUG1,
 				(errmsg("index scan found few tuples"),
 				 errdetail("Index may have been created with little data."),
 				 errhint("Recreate the index and possibly decrease lists.")));
 
 	tuplesort_performsort(so->sortstate);
+
+#if defined(IVFFLAT_MEMORY)
+	elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
+#endif
 }
 
 /*
@@ -209,7 +218,13 @@ GetScanValue(IndexScanDesc scan)
 
 		/* Normalize if needed */
 		if (so->normprocinfo != NULL)
+		{
+			MemoryContext oldCtx = MemoryContextSwitchTo(so->tmpCtx);
+
 			value = IvfflatNormValue(so->typeInfo, so->collation, value);
+
+			MemoryContextSwitchTo(oldCtx);
+		}
 	}
 
 	return value;
@@ -240,19 +255,40 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	int			lists;
 	int			dimensions;
 	int			probes = ivfflat_probes;
+	int			maxProbes;
+	MemoryContext oldCtx;
 
 	scan = RelationGetIndexScan(index, nkeys, norderbys);
 
 	/* Get lists and dimensions from metapage */
 	IvfflatGetMetaPageInfo(index, &lists, &dimensions);
 
+	if (ivfflat_iterative_search != IVFFLAT_ITERATIVE_SEARCH_OFF)
+	{
+		maxProbes = ivfflat_max_probes;
+
+		if (maxProbes < 0)
+			maxProbes = lists;
+		else if (maxProbes < probes)
+		{
+			/* TODO Show notice */
+			maxProbes = probes;
+		}
+	}
+	else
+		maxProbes = probes;
+
 	if (probes > lists)
 		probes = lists;
 
-	so = (IvfflatScanOpaque) palloc(offsetof(IvfflatScanOpaqueData, lists) + probes * sizeof(IvfflatScanList));
+	if (maxProbes > lists)
+		maxProbes = lists;
+
+	so = (IvfflatScanOpaque) palloc(sizeof(IvfflatScanOpaqueData));
 	so->typeInfo = IvfflatGetTypeInfo(index);
 	so->first = true;
 	so->probes = probes;
+	so->maxProbes = maxProbes;
 	so->dimensions = dimensions;
 
 	/* Set support functions */
@@ -260,6 +296,12 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	so->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	so->collation = index->rd_indcollation[0];
 
+	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+									   "Ivfflat scan temporary context",
+									   ALLOCSET_DEFAULT_SIZES);
+
+	oldCtx = MemoryContextSwitchTo(so->tmpCtx);
+
 	/* Create tuple description for sorting */
 	so->tupdesc = CreateTemplateTupleDesc(2);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
@@ -280,6 +322,11 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	so->bas = GetAccessStrategy(BAS_BULKREAD);
 
 	so->listQueue = pairingheap_allocate(CompareLists, scan);
+	so->listPages = palloc(maxProbes * sizeof(BlockNumber));
+	so->listIndex = 0;
+	so->lists = palloc(maxProbes * sizeof(IvfflatScanList));
+
+	MemoryContextSwitchTo(oldCtx);
 
 	scan->opaque = so;
 
@@ -294,11 +341,9 @@ ivfflatrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 
-	if (!so->first)
-		tuplesort_reset(so->sortstate);
-
 	so->first = true;
 	pairingheap_reset(so->listQueue);
+	so->listIndex = 0;
 
 	if (keys && scan->numberOfKeys > 0)
 		memmove(scan->keyData, keys, scan->numberOfKeys * sizeof(ScanKeyData));
@@ -314,6 +359,8 @@ bool
 ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
+	ItemPointer heaptid;
+	bool		isnull;
 
 	/*
 	 * Index can be used to scan backward, but Postgres doesn't support
@@ -341,28 +388,23 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
 		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;
-
-#if defined(IVFFLAT_MEMORY)
-		elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
-#endif
-
-		/* Clean up if we allocated a new value */
-		if (value != scan->orderByData->sk_argument)
-			pfree(DatumGetPointer(value));
+		so->value = value;
 	}
 
-	if (tuplesort_gettupleslot(so->sortstate, true, false, so->mslot, NULL))
+	while (!tuplesort_gettupleslot(so->sortstate, true, false, so->mslot, NULL))
 	{
-		bool		isnull;
-		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->mslot, 2, &isnull));
+		if (so->listIndex == so->maxProbes)
+			return false;
 
-		scan->xs_heaptid = *heaptid;
-		scan->xs_recheck = false;
-		scan->xs_recheckorderby = false;
-		return true;
+		IvfflatBench("GetScanItems", GetScanItems(scan, so->value));
 	}
 
-	return false;
+	heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->mslot, 2, &isnull));
+
+	scan->xs_heaptid = *heaptid;
+	scan->xs_recheck = false;
+	scan->xs_recheckorderby = false;
+	return true;
 }
 
 /*
@@ -373,12 +415,10 @@ ivfflatendscan(IndexScanDesc scan)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 
-	pairingheap_free(so->listQueue);
+	/* Free any temporary files */
 	tuplesort_end(so->sortstate);
-	FreeAccessStrategy(so->bas);
-	FreeTupleDesc(so->tupdesc);
 
-	/* TODO Free vslot and mslot without freeing TupleDesc */
+	MemoryContextDelete(so->tmpCtx);
 
 	pfree(so);
 	scan->opaque = NULL;

src/ivfvacuum.c

@@ -26,7 +26,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 		Page		cpage;
 		OffsetNumber coffno;
 		OffsetNumber cmaxoffno;
-		BlockNumber startPages[MaxOffsetNumber];
+		BlockNumber listPages[MaxOffsetNumber];
 		ListInfo	listInfo;
 
 		cbuf = ReadBuffer(index, blkno);
@@ -40,7 +40,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 		{
 			IvfflatList list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, coffno));
 
-			startPages[coffno - FirstOffsetNumber] = list->startPage;
+			listPages[coffno - FirstOffsetNumber] = list->startPage;
 		}
 
 		listInfo.blkno = blkno;
@@ -50,7 +50,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 
 		for (coffno = FirstOffsetNumber; coffno <= cmaxoffno; coffno = OffsetNumberNext(coffno))
 		{
-			BlockNumber searchPage = startPages[coffno - FirstOffsetNumber];
+			BlockNumber searchPage = listPages[coffno - FirstOffsetNumber];
 			BlockNumber insertPage = InvalidBlockNumber;
 
 			/* Iterate over entry pages */

src/minivec.h

@@ -1,156 +0,0 @@
-#ifndef MINIVEC_H
-#define MINIVEC_H
-
-#include <float.h>
-
-#define MINIVEC_MAX_DIM 16000
-
-#define fp8 uint8
-
-#define MINIVEC_SIZE(_dim)		(offsetof(MiniVector, x) + sizeof(fp8)*(_dim))
-#define DatumGetMiniVector(x)		((MiniVector *) PG_DETOAST_DATUM(x))
-#define PG_GETARG_MINIVEC_P(x)	DatumGetMiniVector(PG_GETARG_DATUM(x))
-#define PG_RETURN_MINIVEC_P(x)	PG_RETURN_POINTER(x)
-
-typedef struct MiniVector
-{
-	int32		vl_len_;		/* varlena header (do not touch directly!) */
-	int16		dim;			/* number of dimensions */
-	int16		unused;			/* reserved for future use, always zero */
-	fp8			x[FLEXIBLE_ARRAY_MEMBER];
-}			MiniVector;
-
-MiniVector *InitMiniVector(int dim);
-
-/*
- * Check if fp8 is NaN
- */
-static inline bool
-Fp8IsNan(fp8 num)
-{
-	return (num & 0x7F) == 0x7F;
-}
-
-/*
- * Check if fp8 is zero
- */
-static inline bool
-Fp8IsZero(fp8 num)
-{
-	return num == 0;
-}
-
-/*
- * Convert a fp8 to a float4
- */
-static inline float
-Fp8ToFloat4(fp8 num)
-{
-	float		lookup[128] = {0, 0.00195312, 0.00390625, 0.00585938, 0.0078125, 0.00976562, 0.0117188, 0.0136719, 0.015625, 0.0175781, 0.0195312, 0.0214844, 0.0234375, 0.0253906, 0.0273438, 0.0292969, 0.03125, 0.0351562, 0.0390625, 0.0429688, 0.046875, 0.0507812, 0.0546875, 0.0585938, 0.0625, 0.0703125, 0.078125, 0.0859375, 0.09375, 0.101562, 0.109375, 0.117188, 0.125, 0.140625, 0.15625, 0.171875, 0.1875, 0.203125, 0.21875, 0.234375, 0.25, 0.28125, 0.3125, 0.34375, 0.375, 0.40625, 0.4375, 0.46875, 0.5, 0.5625, 0.625, 0.6875, 0.75, 0.8125, 0.875, 0.9375, 1, 1.125, 1.25, 1.375, 1.5, 1.625, 1.75, 1.875, 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 36, 40, 44, 48, 52, 56, 60, 64, 72, 80, 88, 96, 104, 112, 120, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288, 320, 352, 384, 416, 448, NAN};
-	float		v = lookup[num & 0x7F];
-
-	return (num & 0x80) == 0x80 ? -v : v;
-}
-
-/*
- * Convert a float4 to a fp8
- */
-static inline fp8
-Float4ToFp8Unchecked(float num)
-{
-	union
-	{
-		float		f;
-		uint32		i;
-	}			swapfloat;
-
-	uint32		bin;
-	int			exponent;
-	int			mantissa;
-	uint8		result;
-
-	swapfloat.f = num;
-	bin = swapfloat.i;
-	exponent = (bin & 0x7F800000) >> 23;
-	mantissa = bin & 0x007FFFFF;
-
-	/* Sign */
-	result = (bin & 0x80000000) >> 24;
-
-	if (isinf(num) || isnan(num))
-	{
-		/* NaN */
-		result |= 0x7F;
-	}
-	else if (exponent > 116)
-	{
-		int			m;
-		int			gr;
-		int			s;
-
-		exponent -= 127;
-		s = mantissa & 0x000FFFFF;
-
-		/* Subnormal */
-		if (exponent < -6)
-		{
-			int			diff = -exponent - 6;
-
-			mantissa >>= diff;
-			mantissa += 1 << (23 - diff);
-			s |= mantissa & 0x000FFFFF;
-		}
-
-		m = mantissa >> 20;
-
-		/* Round */
-		gr = (mantissa >> 19) % 4;
-		if (gr == 3 || (gr == 1 && s != 0))
-			m += 1;
-
-		if (m == 8)
-		{
-			m = 0;
-			exponent += 1;
-		}
-
-		if (exponent > 8)
-		{
-			/* Infinite, which is NaN */
-			result |= 0x7F;
-		}
-		else
-		{
-			if (exponent >= -7)
-				result |= (exponent + 7) << 3;
-
-			result |= m;
-		}
-	}
-
-	return result;
-}
-
-/*
- * Convert a float4 to a fp8
- */
-static inline fp8
-Float4ToFp8(float num)
-{
-	fp8			result = Float4ToFp8Unchecked(num);
-
-	if (unlikely(Fp8IsNan(result)) && !isnan(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 minivec", buf)));
-	}
-
-	return result;
-}
-
-#endif

src/vector.c

@@ -13,7 +13,6 @@
 #include "ivfflat.h"
 #include "lib/stringinfo.h"
 #include "libpq/pqformat.h"
-#include "minivec.h"
 #include "port.h"				/* for strtof() */
 #include "sparsevec.h"
 #include "utils/array.h"
@@ -543,28 +542,6 @@ halfvec_to_vector(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
-/*
- * Convert fp8 vector to vector
- */
-FUNCTION_PREFIX PG_FUNCTION_INFO_V1(minivec_to_vector);
-Datum
-minivec_to_vector(PG_FUNCTION_ARGS)
-{
-	MiniVector *vec = PG_GETARG_MINIVEC_P(0);
-	int32		typmod = PG_GETARG_INT32(1);
-	Vector	   *result;
-
-	CheckDim(vec->dim);
-	CheckExpectedDim(typmod, vec->dim);
-
-	result = InitVector(vec->dim);
-
-	for (int i = 0; i < vec->dim; i++)
-		result->x[i] = Fp8ToFloat4(vec->x[i]);
-
-	PG_RETURN_POINTER(result);
-}
-
 VECTOR_TARGET_CLONES static float
 VectorL2SquaredDistance(int dim, float *ax, float *bx)
 {

test/expected/btree.out

@@ -38,26 +38,6 @@ SELECT * FROM t ORDER BY val;
  
 (4 rows)
 
-DROP TABLE t;
--- minivec
-CREATE TABLE t (val minivec(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;
 -- sparsevec
 CREATE TABLE t (val sparsevec(3));

test/expected/cast.out

@@ -140,64 +140,34 @@ SELECT '{1e-8,-1e-8}'::real[]::halfvec;
  [0,-0]
 (1 row)
 
-SELECT '[1,2,3]'::vector::minivec;
- minivec 
+SELECT '[1,2,3]'::intvec::integer[];
+  int4   
+---------
+ {1,2,3}
+(1 row)
+
+SELECT '{1,2,3}'::integer[]::intvec;
+ intvec  
 ---------
  [1,2,3]
 (1 row)
 
-SELECT '[1,2,3]'::vector::minivec(3);
- minivec 
+SELECT '{1,2,3}'::integer[]::intvec(3);
+ intvec  
 ---------
  [1,2,3]
 (1 row)
 
-SELECT '[1,2,3]'::vector::minivec(2);
+SELECT '{1,2,3}'::integer[]::intvec(2);
 ERROR:  expected 2 dimensions, not 3
-SELECT '[465]'::vector::minivec;
-ERROR:  "465" is out of range for type minivec
-SELECT '[1e-8]'::vector::minivec;
- minivec 
----------
- [0]
-(1 row)
-
-SELECT '[1,2,3]'::minivec::vector;
- vector  
----------
- [1,2,3]
-(1 row)
-
-SELECT '[1,2,3]'::minivec::vector(3);
- vector  
----------
- [1,2,3]
-(1 row)
-
-SELECT '[1,2,3]'::minivec::vector(2);
-ERROR:  expected 2 dimensions, not 3
-SELECT '{1,2,3}'::real[]::minivec;
- minivec 
----------
- [1,2,3]
-(1 row)
-
-SELECT '{1,2,3}'::real[]::minivec(3);
- minivec 
----------
- [1,2,3]
-(1 row)
-
-SELECT '{1,2,3}'::real[]::minivec(2);
-ERROR:  expected 2 dimensions, not 3
-SELECT '{465,-465}'::real[]::minivec;
-ERROR:  "465" is out of range for type minivec
-SELECT '{1e-8,-1e-8}'::real[]::minivec;
- minivec 
----------
- [0,-0]
+SELECT '{127,-128}'::integer[]::intvec;
+   intvec   
+------------
+ [127,-128]
 (1 row)
 
+SELECT '{128,-129}'::integer[]::intvec;
+ERROR:  value "128" is out of range for type intvec
 SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
     sparsevec    
 -----------------

test/expected/copy.out

@@ -32,12 +32,12 @@ SELECT * FROM t2 ORDER BY val;
 
 DROP TABLE t;
 DROP TABLE t2;
--- minivec
-CREATE TABLE t (val minivec(3));
+-- intvec
+CREATE TABLE t (val intvec(3));
 INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE TABLE t2 (val minivec(3));
-\copy t TO 'results/minivec.bin' WITH (FORMAT binary)
-\copy t2 FROM 'results/minivec.bin' WITH (FORMAT binary)
+CREATE TABLE t2 (val intvec(3));
+\copy t TO 'results/intvec.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/intvec.bin' WITH (FORMAT binary)
 SELECT * FROM t2 ORDER BY val;
    val   
 ---------

test/expected/hnsw_intvec.out

@@ -0,0 +1,102 @@
+SET enable_seqscan = off;
+-- L2
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_l2_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::intvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+SELECT COUNT(*) FROM t;
+ count 
+-------
+     5
+(1 row)
+
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+ val 
+-----
+(0 rows)
+
+DROP TABLE t;
+-- inner product
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_ip_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <#> '[3,3,3]';
+   val   
+---------
+ [1,2,4]
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <#> (SELECT NULL::intvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;
+-- cosine
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_cosine_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <=> '[3,3,3]';
+   val   
+---------
+ [1,1,1]
+ [1,2,3]
+ [1,2,4]
+(3 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
+ count 
+-------
+     3
+(1 row)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::intvec)) t2;
+ count 
+-------
+     3
+(1 row)
+
+DROP TABLE t;
+-- L1
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_vector.out

@@ -99,6 +99,32 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::vector)) t2
      4
 (1 row)
 
+DROP TABLE t;
+-- iterative
+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_l2_ops);
+SET hnsw.iterative_search = strict_order;
+SET hnsw.ef_search = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+SET hnsw.iterative_search = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+RESET hnsw.iterative_search;
+RESET hnsw.ef_search;
 DROP TABLE t;
 -- unlogged
 CREATE UNLOGGED TABLE t (val vector(3));
@@ -139,4 +165,21 @@ SET hnsw.ef_search = 0;
 ERROR:  0 is outside the valid range for parameter "hnsw.ef_search" (1 .. 1000)
 SET hnsw.ef_search = 1001;
 ERROR:  1001 is outside the valid range for parameter "hnsw.ef_search" (1 .. 1000)
+SHOW hnsw.iterative_search;
+ hnsw.iterative_search 
+-----------------------
+ off
+(1 row)
+
+SET hnsw.iterative_search = on;
+ERROR:  invalid value for parameter "hnsw.iterative_search": "on"
+HINT:  Available values: off, relaxed_order, strict_order.
+SHOW hnsw.max_search_tuples;
+ hnsw.max_search_tuples 
+------------------------
+ -1
+(1 row)
+
+SET hnsw.max_search_tuples = -2;
+ERROR:  -2 is outside the valid range for parameter "hnsw.max_search_tuples" (-1 .. 2147483647)
 DROP TABLE t;

test/expected/intvec.out

@@ -0,0 +1,328 @@
+SELECT '[1,2,3]'::intvec;
+ intvec  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[-1,-2,-3]'::intvec;
+   intvec   
+------------
+ [-1,-2,-3]
+(1 row)
+
+SELECT ' [ 1,  2 ,    3  ] '::intvec;
+ intvec  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1.23456]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1.23456]"
+LINE 1: SELECT '[1.23456]'::intvec;
+               ^
+SELECT '[hello,1]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[hello,1]"
+LINE 1: SELECT '[hello,1]'::intvec;
+               ^
+SELECT '[127,-128]'::intvec;
+   intvec   
+------------
+ [127,-128]
+(1 row)
+
+SELECT '[128,-129]'::intvec;
+ERROR:  "128" is out of range for type intvec
+LINE 1: SELECT '[128,-129]'::intvec;
+               ^
+SELECT '[1,2,3'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1,2,3"
+LINE 1: SELECT '[1,2,3'::intvec;
+               ^
+SELECT '[1,2,3]9'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1,2,3]9"
+LINE 1: SELECT '[1,2,3]9'::intvec;
+               ^
+DETAIL:  Junk after closing right brace.
+SELECT '1,2,3'::intvec;
+ERROR:  invalid input syntax for type intvec: "1,2,3"
+LINE 1: SELECT '1,2,3'::intvec;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT ''::intvec;
+ERROR:  invalid input syntax for type intvec: ""
+LINE 1: SELECT ''::intvec;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT '['::intvec;
+ERROR:  invalid input syntax for type intvec: "["
+LINE 1: SELECT '['::intvec;
+               ^
+SELECT '[,'::intvec;
+ERROR:  invalid input syntax for type intvec: "[,"
+LINE 1: SELECT '[,'::intvec;
+               ^
+SELECT '[]'::intvec;
+ERROR:  intvec must have at least 1 dimension
+LINE 1: SELECT '[]'::intvec;
+               ^
+SELECT '[1,]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1,]"
+LINE 1: SELECT '[1,]'::intvec;
+               ^
+SELECT '[1a]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1a]"
+LINE 1: SELECT '[1a]'::intvec;
+               ^
+SELECT '[1,,3]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1,,3]"
+LINE 1: SELECT '[1,,3]'::intvec;
+               ^
+SELECT '[1, ,3]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1, ,3]"
+LINE 1: SELECT '[1, ,3]'::intvec;
+               ^
+SELECT '[1,2,3]'::intvec(3);
+ intvec  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::intvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::intvec(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '[1,2,3]'::intvec(3, 2);
+                          ^
+SELECT '[1,2,3]'::intvec('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '[1,2,3]'::intvec('a');
+                          ^
+SELECT '[1,2,3]'::intvec(0);
+ERROR:  dimensions for type intvec must be at least 1
+LINE 1: SELECT '[1,2,3]'::intvec(0);
+                          ^
+SELECT '[1,2,3]'::intvec(16001);
+ERROR:  dimensions for type intvec cannot exceed 16000
+LINE 1: SELECT '[1,2,3]'::intvec(16001);
+                          ^
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::intvec[]);
+ unnest  
+---------
+ [1,2,3]
+ [4,5,6]
+(2 rows)
+
+SELECT '{"[1,2,3]"}'::intvec(2)[];
+ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::intvec < '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec < '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec <= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec <= '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec = '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec = '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec != '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec != '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec >= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec >= '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec > '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec > '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT intvec_cmp('[1,2,3]', '[1,2,3]');
+ intvec_cmp 
+------------
+          0
+(1 row)
+
+SELECT intvec_cmp('[1,2,3]', '[0,0,0]');
+ intvec_cmp 
+------------
+          1
+(1 row)
+
+SELECT intvec_cmp('[0,0,0]', '[1,2,3]');
+ intvec_cmp 
+------------
+         -1
+(1 row)
+
+SELECT intvec_cmp('[1,2]', '[1,2,3]');
+ intvec_cmp 
+------------
+         -1
+(1 row)
+
+SELECT intvec_cmp('[1,2,3]', '[1,2]');
+ intvec_cmp 
+------------
+          1
+(1 row)
+
+SELECT intvec_cmp('[1,2]', '[2,3,4]');
+ intvec_cmp 
+------------
+         -1
+(1 row)
+
+SELECT intvec_cmp('[2,3]', '[1,2,3]');
+ intvec_cmp 
+------------
+          1
+(1 row)
+
+SELECT vector_dims('[1,2,3]'::intvec);
+ vector_dims 
+-------------
+           3
+(1 row)
+
+SELECT l2_distance('[0,0]'::intvec, '[3,4]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('[0,0]'::intvec, '[0,1]');
+ l2_distance 
+-------------
+           1
+(1 row)
+
+SELECT l2_distance('[1,2]'::intvec, '[3]');
+ERROR:  different intvec dimensions 2 and 1
+SELECT '[0,0]'::intvec <-> '[3,4]';
+ ?column? 
+----------
+        5
+(1 row)
+
+SELECT inner_product('[1,2]'::intvec, '[3,4]');
+ inner_product 
+---------------
+            11
+(1 row)
+
+SELECT inner_product('[1,2]'::intvec, '[3]');
+ERROR:  different intvec dimensions 2 and 1
+SELECT inner_product('[127]'::intvec, '[127]');
+ inner_product 
+---------------
+         16129
+(1 row)
+
+SELECT '[1,2]'::intvec <#> '[3,4]';
+ ?column? 
+----------
+      -11
+(1 row)
+
+SELECT cosine_distance('[1,2]'::intvec, '[2,4]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,2]'::intvec, '[0,0]');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('[1,1]'::intvec, '[1,1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,0]'::intvec, '[0,2]');
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
+SELECT cosine_distance('[1,1]'::intvec, '[-1,-1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('[1,2]'::intvec, '[3]');
+ERROR:  different intvec dimensions 2 and 1
+SELECT '[1,2]'::intvec <=> '[2,4]';
+ ?column? 
+----------
+        0
+(1 row)
+
+SELECT l1_distance('[0,0]'::intvec, '[3,4]');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('[0,0]'::intvec, '[0,1]');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('[1,2]'::intvec, '[3]');
+ERROR:  different intvec dimensions 2 and 1

test/expected/ivfflat_vector.out

@@ -81,6 +81,44 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2
      3
 (1 row)
 
+DROP TABLE t;
+-- iterative
+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 ivfflat (val vector_l2_ops) WITH (lists = 3);
+SET ivfflat.iterative_search = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+SET ivfflat.max_probes = 0;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+(1 row)
+
+SET ivfflat.max_probes = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+(1 row)
+
+SET ivfflat.max_probes = 2;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+(2 rows)
+
+RESET ivfflat.iterative_search;
+RESET ivfflat.max_probes;
 DROP TABLE t;
 -- unlogged
 CREATE UNLOGGED TABLE t (val vector(3));
@@ -109,4 +147,27 @@ SHOW ivfflat.probes;
  1
 (1 row)
 
+SET ivfflat.probes = 0;
+ERROR:  0 is outside the valid range for parameter "ivfflat.probes" (1 .. 32768)
+SET ivfflat.probes = 32769;
+ERROR:  32769 is outside the valid range for parameter "ivfflat.probes" (1 .. 32768)
+SHOW ivfflat.iterative_search;
+ ivfflat.iterative_search 
+--------------------------
+ off
+(1 row)
+
+SET ivfflat.iterative_search = on;
+ERROR:  invalid value for parameter "ivfflat.iterative_search": "on"
+HINT:  Available values: off, relaxed_order.
+SHOW ivfflat.max_probes;
+ ivfflat.max_probes 
+--------------------
+ -1
+(1 row)
+
+SET ivfflat.max_probes = -2;
+ERROR:  -2 is outside the valid range for parameter "ivfflat.max_probes" (-1 .. 32768)
+SET ivfflat.max_probes = 32769;
+ERROR:  32769 is outside the valid range for parameter "ivfflat.max_probes" (-1 .. 32768)
 DROP TABLE t;

test/expected/minivec.out

@@ -1,588 +0,0 @@
-SELECT '[1,2,3]'::minivec;
- minivec 
----------
- [1,2,3]
-(1 row)
-
-SELECT '[-1,-2,-3]'::minivec;
-  minivec   
-------------
- [-1,-2,-3]
-(1 row)
-
-SELECT '[1.,2.,3.]'::minivec;
- minivec 
----------
- [1,2,3]
-(1 row)
-
-SELECT ' [ 1,  2 ,    3  ] '::minivec;
- minivec 
----------
- [1,2,3]
-(1 row)
-
-SELECT '[1.23456]'::minivec;
- minivec 
----------
- [1.25]
-(1 row)
-
-SELECT '[hello,1]'::minivec;
-ERROR:  invalid input syntax for type minivec: "[hello,1]"
-LINE 1: SELECT '[hello,1]'::minivec;
-               ^
-SELECT '[NaN,1]'::minivec;
-ERROR:  NaN not allowed in minivec
-LINE 1: SELECT '[NaN,1]'::minivec;
-               ^
-SELECT '[Infinity,1]'::minivec;
-ERROR:  "Infinity" is out of range for type minivec
-LINE 1: SELECT '[Infinity,1]'::minivec;
-               ^
-SELECT '[-Infinity,1]'::minivec;
-ERROR:  "-Infinity" is out of range for type minivec
-LINE 1: SELECT '[-Infinity,1]'::minivec;
-               ^
-SELECT '[65519,-65519]'::minivec;
-ERROR:  "65519" is out of range for type minivec
-LINE 1: SELECT '[65519,-65519]'::minivec;
-               ^
-SELECT '[65520,-65520]'::minivec;
-ERROR:  "65520" is out of range for type minivec
-LINE 1: SELECT '[65520,-65520]'::minivec;
-               ^
-SELECT '[1e-8,-1e-8]'::minivec;
- minivec 
----------
- [0,-0]
-(1 row)
-
-SELECT '[4e38,1]'::minivec;
-ERROR:  "4e38" is out of range for type minivec
-LINE 1: SELECT '[4e38,1]'::minivec;
-               ^
-SELECT '[1e-46,1]'::minivec;
- minivec 
----------
- [0,1]
-(1 row)
-
-SELECT '[1,2,3'::minivec;
-ERROR:  invalid input syntax for type minivec: "[1,2,3"
-LINE 1: SELECT '[1,2,3'::minivec;
-               ^
-SELECT '[1,2,3]9'::minivec;
-ERROR:  invalid input syntax for type minivec: "[1,2,3]9"
-LINE 1: SELECT '[1,2,3]9'::minivec;
-               ^
-DETAIL:  Junk after closing right brace.
-SELECT '1,2,3'::minivec;
-ERROR:  invalid input syntax for type minivec: "1,2,3"
-LINE 1: SELECT '1,2,3'::minivec;
-               ^
-DETAIL:  Vector contents must start with "[".
-SELECT ''::minivec;
-ERROR:  invalid input syntax for type minivec: ""
-LINE 1: SELECT ''::minivec;
-               ^
-DETAIL:  Vector contents must start with "[".
-SELECT '['::minivec;
-ERROR:  invalid input syntax for type minivec: "["
-LINE 1: SELECT '['::minivec;
-               ^
-SELECT '[ '::minivec;
-ERROR:  invalid input syntax for type minivec: "[ "
-LINE 1: SELECT '[ '::minivec;
-               ^
-SELECT '[,'::minivec;
-ERROR:  invalid input syntax for type minivec: "[,"
-LINE 1: SELECT '[,'::minivec;
-               ^
-SELECT '[]'::minivec;
-ERROR:  minivec must have at least 1 dimension
-LINE 1: SELECT '[]'::minivec;
-               ^
-SELECT '[ ]'::minivec;
-ERROR:  minivec must have at least 1 dimension
-LINE 1: SELECT '[ ]'::minivec;
-               ^
-SELECT '[,]'::minivec;
-ERROR:  invalid input syntax for type minivec: "[,]"
-LINE 1: SELECT '[,]'::minivec;
-               ^
-SELECT '[1,]'::minivec;
-ERROR:  invalid input syntax for type minivec: "[1,]"
-LINE 1: SELECT '[1,]'::minivec;
-               ^
-SELECT '[1a]'::minivec;
-ERROR:  invalid input syntax for type minivec: "[1a]"
-LINE 1: SELECT '[1a]'::minivec;
-               ^
-SELECT '[1,,3]'::minivec;
-ERROR:  invalid input syntax for type minivec: "[1,,3]"
-LINE 1: SELECT '[1,,3]'::minivec;
-               ^
-SELECT '[1, ,3]'::minivec;
-ERROR:  invalid input syntax for type minivec: "[1, ,3]"
-LINE 1: SELECT '[1, ,3]'::minivec;
-               ^
-SELECT '[1,2,3]'::minivec(3);
- minivec 
----------
- [1,2,3]
-(1 row)
-
-SELECT '[1,2,3]'::minivec(2);
-ERROR:  expected 2 dimensions, not 3
-SELECT '[1,2,3]'::minivec(3, 2);
-ERROR:  invalid type modifier
-LINE 1: SELECT '[1,2,3]'::minivec(3, 2);
-                          ^
-SELECT '[1,2,3]'::minivec('a');
-ERROR:  invalid input syntax for type integer: "a"
-LINE 1: SELECT '[1,2,3]'::minivec('a');
-                          ^
-SELECT '[1,2,3]'::minivec(0);
-ERROR:  dimensions for type minivec must be at least 1
-LINE 1: SELECT '[1,2,3]'::minivec(0);
-                          ^
-SELECT '[1,2,3]'::minivec(16001);
-ERROR:  dimensions for type minivec cannot exceed 16000
-LINE 1: SELECT '[1,2,3]'::minivec(16001);
-                          ^
-SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::minivec[]);
- unnest  
----------
- [1,2,3]
- [4,5,6]
-(2 rows)
-
-SELECT '{"[1,2,3]"}'::minivec(2)[];
-ERROR:  expected 2 dimensions, not 3
-SELECT '[1,2,3]'::minivec + '[4,5,6]';
- ?column? 
-----------
- [5,7,9]
-(1 row)
-
-SELECT '[448]'::minivec + '[448]';
-ERROR:  value out of range: overflow
-SELECT '[1,2]'::minivec + '[3]';
-ERROR:  different minivec dimensions 2 and 1
-SELECT '[1,2,3]'::minivec - '[4,5,6]';
-  ?column?  
-------------
- [-3,-3,-3]
-(1 row)
-
-SELECT '[-448]'::minivec - '[448]';
-ERROR:  value out of range: overflow
-SELECT '[1,2]'::minivec - '[3]';
-ERROR:  different minivec dimensions 2 and 1
-SELECT '[1,2,3]'::minivec * '[4,5,6]';
- ?column?  
------------
- [4,10,18]
-(1 row)
-
-SELECT '[448]'::minivec * '[448]';
-ERROR:  value out of range: overflow
-SELECT '[1e-7]'::minivec * '[1e-7]';
- ?column? 
-----------
- [0]
-(1 row)
-
-SELECT '[1,2]'::minivec * '[3]';
-ERROR:  different minivec dimensions 2 and 1
-SELECT '[1,2,3]'::minivec || '[4,5]';
-  ?column?   
--------------
- [1,2,3,4,5]
-(1 row)
-
-SELECT array_fill(0, ARRAY[16000])::minivec || '[1]';
-ERROR:  minivec cannot have more than 16000 dimensions
-SELECT '[1,2,3]'::minivec < '[1,2,3]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::minivec < '[1,2]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::minivec <= '[1,2,3]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::minivec <= '[1,2]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::minivec = '[1,2,3]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::minivec = '[1,2]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::minivec != '[1,2,3]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::minivec != '[1,2]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::minivec >= '[1,2,3]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::minivec >= '[1,2]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::minivec > '[1,2,3]';
- ?column? 
-----------
- f
-(1 row)
-
-SELECT '[1,2,3]'::minivec > '[1,2]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT minivec_cmp('[1,2,3]', '[1,2,3]');
- minivec_cmp 
--------------
-           0
-(1 row)
-
-SELECT minivec_cmp('[1,2,3]', '[0,0,0]');
- minivec_cmp 
--------------
-           1
-(1 row)
-
-SELECT minivec_cmp('[0,0,0]', '[1,2,3]');
- minivec_cmp 
--------------
-          -1
-(1 row)
-
-SELECT minivec_cmp('[1,2]', '[1,2,3]');
- minivec_cmp 
--------------
-          -1
-(1 row)
-
-SELECT minivec_cmp('[1,2,3]', '[1,2]');
- minivec_cmp 
--------------
-           1
-(1 row)
-
-SELECT minivec_cmp('[1,2]', '[2,3,4]');
- minivec_cmp 
--------------
-          -1
-(1 row)
-
-SELECT minivec_cmp('[2,3]', '[1,2,3]');
- minivec_cmp 
--------------
-           1
-(1 row)
-
-SELECT vector_dims('[1,2,3]'::minivec);
- vector_dims 
--------------
-           3
-(1 row)
-
-SELECT round(l2_norm('[1,1]'::minivec)::numeric, 5);
-  round  
----------
- 1.41421
-(1 row)
-
-SELECT l2_norm('[3,4]'::minivec);
- l2_norm 
----------
-       5
-(1 row)
-
-SELECT l2_norm('[0,1]'::minivec);
- l2_norm 
----------
-       1
-(1 row)
-
-SELECT l2_norm('[0,0]'::minivec);
- l2_norm 
----------
-       0
-(1 row)
-
-SELECT l2_norm('[2]'::minivec);
- l2_norm 
----------
-       2
-(1 row)
-
-SELECT l2_distance('[0,0]'::minivec, '[3,4]');
- l2_distance 
--------------
-           5
-(1 row)
-
-SELECT l2_distance('[0,0]'::minivec, '[0,1]');
- l2_distance 
--------------
-           1
-(1 row)
-
-SELECT l2_distance('[1,2]'::minivec, '[3]');
-ERROR:  different minivec dimensions 2 and 1
-SELECT l2_distance('[1,1,1,1,1,1,1,1,1]'::minivec, '[1,1,1,1,1,1,1,4,5]');
- l2_distance 
--------------
-           5
-(1 row)
-
-SELECT '[0,0]'::minivec <-> '[3,4]';
- ?column? 
-----------
-        5
-(1 row)
-
-SELECT inner_product('[1,2]'::minivec, '[3,4]');
- inner_product 
----------------
-            11
-(1 row)
-
-SELECT inner_product('[1,2]'::minivec, '[3]');
-ERROR:  different minivec dimensions 2 and 1
-SELECT inner_product('[448]'::minivec, '[448]');
- inner_product 
----------------
-        200704
-(1 row)
-
-SELECT inner_product('[1,1,1,1,1,1,1,1,1]'::minivec, '[1,2,3,4,5,6,7,8,9]');
- inner_product 
----------------
-            45
-(1 row)
-
-SELECT '[1,2]'::minivec <#> '[3,4]';
- ?column? 
-----------
-      -11
-(1 row)
-
-SELECT cosine_distance('[1,2]'::minivec, '[2,4]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,2]'::minivec, '[0,0]');
- cosine_distance 
------------------
-             NaN
-(1 row)
-
-SELECT cosine_distance('[1,1]'::minivec, '[1,1]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,0]'::minivec, '[0,2]');
- cosine_distance 
------------------
-               1
-(1 row)
-
-SELECT cosine_distance('[1,1]'::minivec, '[-1,-1]');
- cosine_distance 
------------------
-               2
-(1 row)
-
-SELECT cosine_distance('[1,2]'::minivec, '[3]');
-ERROR:  different minivec dimensions 2 and 1
-SELECT cosine_distance('[1,1]'::minivec, '[1.1,1.1]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,1]'::minivec, '[-1.1,-1.1]');
- cosine_distance 
------------------
-               2
-(1 row)
-
-SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::minivec, '[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]'::minivec, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
- cosine_distance 
------------------
-               2
-(1 row)
-
-SELECT '[1,2]'::minivec <=> '[2,4]';
- ?column? 
-----------
-        0
-(1 row)
-
-SELECT l1_distance('[0,0]'::minivec, '[3,4]');
- l1_distance 
--------------
-           7
-(1 row)
-
-SELECT l1_distance('[0,0]'::minivec, '[0,1]');
- l1_distance 
--------------
-           1
-(1 row)
-
-SELECT l1_distance('[1,2]'::minivec, '[3]');
-ERROR:  different minivec dimensions 2 and 1
-SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::minivec, '[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]'::minivec, '[0,3,2,5,4,7,6,9,8]');
- l1_distance 
--------------
-           9
-(1 row)
-
-SELECT '[0,0]'::minivec <+> '[3,4]';
- ?column? 
-----------
-        7
-(1 row)
-
-SELECT l2_normalize('[3,4]'::minivec);
-  l2_normalize  
-----------------
- [0.625,0.8125]
-(1 row)
-
-SELECT l2_normalize('[3,0]'::minivec);
- l2_normalize 
---------------
- [1,0]
-(1 row)
-
-SELECT l2_normalize('[0,0.1]'::minivec);
- l2_normalize 
---------------
- [0,1]
-(1 row)
-
-SELECT l2_normalize('[0,0]'::minivec);
- l2_normalize 
---------------
- [0,0]
-(1 row)
-
-SELECT l2_normalize('[448]'::minivec);
- l2_normalize 
---------------
- [1]
-(1 row)
-
-SELECT binary_quantize('[1,0,-1]'::minivec);
- binary_quantize 
------------------
- 100
-(1 row)
-
-SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::minivec);
- binary_quantize 
------------------
- 01001110101
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]'::minivec, 1, 3);
- subvector 
------------
- [1,2,3]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]'::minivec, 3, 2);
- subvector 
------------
- [3,4]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]'::minivec, -1, 3);
- subvector 
------------
- [1]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]'::minivec, 3, 9);
- subvector 
------------
- [3,4,5]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]'::minivec, 1, 0);
-ERROR:  minivec must have at least 1 dimension
-SELECT subvector('[1,2,3,4,5]'::minivec, 3, -1);
-ERROR:  minivec must have at least 1 dimension
-SELECT subvector('[1,2,3,4,5]'::minivec, -1, 2);
-ERROR:  minivec must have at least 1 dimension
-SELECT subvector('[1,2,3,4,5]'::minivec, 2147483647, 10);
-ERROR:  minivec must have at least 1 dimension
-SELECT subvector('[1,2,3,4,5]'::minivec, 3, 2147483647);
- subvector 
------------
- [3,4,5]
-(1 row)
-
-SELECT subvector('[1,2,3,4,5]'::minivec, -2147483644, 2147483647);
- subvector 
------------
- [1,2]
-(1 row)
-

test/sql/btree.sql

@@ -22,17 +22,6 @@ SELECT * FROM t ORDER BY val;
 
 DROP TABLE t;
 
--- minivec
-
-CREATE TABLE t (val minivec(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;
-
 -- sparsevec
 
 CREATE TABLE t (val sparsevec(3));

test/sql/cast.sql

@@ -38,21 +38,13 @@ SELECT '{1,2,3}'::real[]::halfvec(2);
 SELECT '{65520,-65520}'::real[]::halfvec;
 SELECT '{1e-8,-1e-8}'::real[]::halfvec;
 
-SELECT '[1,2,3]'::vector::minivec;
-SELECT '[1,2,3]'::vector::minivec(3);
-SELECT '[1,2,3]'::vector::minivec(2);
-SELECT '[465]'::vector::minivec;
-SELECT '[1e-8]'::vector::minivec;
+SELECT '[1,2,3]'::intvec::integer[];
 
-SELECT '[1,2,3]'::minivec::vector;
-SELECT '[1,2,3]'::minivec::vector(3);
-SELECT '[1,2,3]'::minivec::vector(2);
-
-SELECT '{1,2,3}'::real[]::minivec;
-SELECT '{1,2,3}'::real[]::minivec(3);
-SELECT '{1,2,3}'::real[]::minivec(2);
-SELECT '{465,-465}'::real[]::minivec;
-SELECT '{1e-8,-1e-8}'::real[]::minivec;
+SELECT '{1,2,3}'::integer[]::intvec;
+SELECT '{1,2,3}'::integer[]::intvec(3);
+SELECT '{1,2,3}'::integer[]::intvec(2);
+SELECT '{127,-128}'::integer[]::intvec;
+SELECT '{128,-129}'::integer[]::intvec;
 
 SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
 SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(5);

test/sql/copy.sql

@@ -28,15 +28,15 @@ SELECT * FROM t2 ORDER BY val;
 DROP TABLE t;
 DROP TABLE t2;
 
--- minivec
+-- intvec
 
-CREATE TABLE t (val minivec(3));
+CREATE TABLE t (val intvec(3));
 INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
 
-CREATE TABLE t2 (val minivec(3));
+CREATE TABLE t2 (val intvec(3));
 
-\copy t TO 'results/minivec.bin' WITH (FORMAT binary)
-\copy t2 FROM 'results/minivec.bin' WITH (FORMAT binary)
+\copy t TO 'results/intvec.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/intvec.bin' WITH (FORMAT binary)
 
 SELECT * FROM t2 ORDER BY val;
 

test/sql/hnsw_intvec.sql

@@ -0,0 +1,58 @@
+SET enable_seqscan = off;
+
+-- L2
+
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_l2_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::intvec)) t2;
+SELECT COUNT(*) FROM t;
+
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+DROP TABLE t;
+
+-- inner product
+
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_ip_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <#> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <#> (SELECT NULL::intvec)) t2;
+
+DROP TABLE t;
+
+-- cosine
+
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_cosine_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <=> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::intvec)) t2;
+
+DROP TABLE t;
+
+-- L1
+
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) t2;
+
+DROP TABLE t;

test/sql/hnsw_vector.sql

@@ -57,6 +57,23 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::vector)) t2
 
 DROP TABLE t;
 
+-- iterative
+
+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_l2_ops);
+
+SET hnsw.iterative_search = strict_order;
+SET hnsw.ef_search = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+SET hnsw.iterative_search = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+RESET hnsw.iterative_search;
+RESET hnsw.ef_search;
+DROP TABLE t;
+
 -- unlogged
 
 CREATE UNLOGGED TABLE t (val vector(3));
@@ -81,4 +98,12 @@ SHOW hnsw.ef_search;
 SET hnsw.ef_search = 0;
 SET hnsw.ef_search = 1001;
 
+SHOW hnsw.iterative_search;
+
+SET hnsw.iterative_search = on;
+
+SHOW hnsw.max_search_tuples;
+
+SET hnsw.max_search_tuples = -2;
+
 DROP TABLE t;

test/sql/intvec.sql

@@ -0,0 +1,73 @@
+SELECT '[1,2,3]'::intvec;
+SELECT '[-1,-2,-3]'::intvec;
+SELECT ' [ 1,  2 ,    3  ] '::intvec;
+SELECT '[1.23456]'::intvec;
+SELECT '[hello,1]'::intvec;
+SELECT '[127,-128]'::intvec;
+SELECT '[128,-129]'::intvec;
+SELECT '[1,2,3'::intvec;
+SELECT '[1,2,3]9'::intvec;
+SELECT '1,2,3'::intvec;
+SELECT ''::intvec;
+SELECT '['::intvec;
+SELECT '[,'::intvec;
+SELECT '[]'::intvec;
+SELECT '[1,]'::intvec;
+SELECT '[1a]'::intvec;
+SELECT '[1,,3]'::intvec;
+SELECT '[1, ,3]'::intvec;
+
+SELECT '[1,2,3]'::intvec(3);
+SELECT '[1,2,3]'::intvec(2);
+SELECT '[1,2,3]'::intvec(3, 2);
+SELECT '[1,2,3]'::intvec('a');
+SELECT '[1,2,3]'::intvec(0);
+SELECT '[1,2,3]'::intvec(16001);
+
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::intvec[]);
+SELECT '{"[1,2,3]"}'::intvec(2)[];
+
+SELECT '[1,2,3]'::intvec < '[1,2,3]';
+SELECT '[1,2,3]'::intvec < '[1,2]';
+SELECT '[1,2,3]'::intvec <= '[1,2,3]';
+SELECT '[1,2,3]'::intvec <= '[1,2]';
+SELECT '[1,2,3]'::intvec = '[1,2,3]';
+SELECT '[1,2,3]'::intvec = '[1,2]';
+SELECT '[1,2,3]'::intvec != '[1,2,3]';
+SELECT '[1,2,3]'::intvec != '[1,2]';
+SELECT '[1,2,3]'::intvec >= '[1,2,3]';
+SELECT '[1,2,3]'::intvec >= '[1,2]';
+SELECT '[1,2,3]'::intvec > '[1,2,3]';
+SELECT '[1,2,3]'::intvec > '[1,2]';
+
+SELECT intvec_cmp('[1,2,3]', '[1,2,3]');
+SELECT intvec_cmp('[1,2,3]', '[0,0,0]');
+SELECT intvec_cmp('[0,0,0]', '[1,2,3]');
+SELECT intvec_cmp('[1,2]', '[1,2,3]');
+SELECT intvec_cmp('[1,2,3]', '[1,2]');
+SELECT intvec_cmp('[1,2]', '[2,3,4]');
+SELECT intvec_cmp('[2,3]', '[1,2,3]');
+
+SELECT vector_dims('[1,2,3]'::intvec);
+
+SELECT l2_distance('[0,0]'::intvec, '[3,4]');
+SELECT l2_distance('[0,0]'::intvec, '[0,1]');
+SELECT l2_distance('[1,2]'::intvec, '[3]');
+SELECT '[0,0]'::intvec <-> '[3,4]';
+
+SELECT inner_product('[1,2]'::intvec, '[3,4]');
+SELECT inner_product('[1,2]'::intvec, '[3]');
+SELECT inner_product('[127]'::intvec, '[127]');
+SELECT '[1,2]'::intvec <#> '[3,4]';
+
+SELECT cosine_distance('[1,2]'::intvec, '[2,4]');
+SELECT cosine_distance('[1,2]'::intvec, '[0,0]');
+SELECT cosine_distance('[1,1]'::intvec, '[1,1]');
+SELECT cosine_distance('[1,0]'::intvec, '[0,2]');
+SELECT cosine_distance('[1,1]'::intvec, '[-1,-1]');
+SELECT cosine_distance('[1,2]'::intvec, '[3]');
+SELECT '[1,2]'::intvec <=> '[2,4]';
+
+SELECT l1_distance('[0,0]'::intvec, '[3,4]');
+SELECT l1_distance('[0,0]'::intvec, '[0,1]');
+SELECT l1_distance('[1,2]'::intvec, '[3]');

test/sql/ivfflat_vector.sql

@@ -44,6 +44,28 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2
 
 DROP TABLE t;
 
+-- iterative
+
+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 ivfflat (val vector_l2_ops) WITH (lists = 3);
+
+SET ivfflat.iterative_search = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+SET ivfflat.max_probes = 0;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+SET ivfflat.max_probes = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+SET ivfflat.max_probes = 2;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+RESET ivfflat.iterative_search;
+RESET ivfflat.max_probes;
+DROP TABLE t;
+
 -- unlogged
 
 CREATE UNLOGGED TABLE t (val vector(3));
@@ -62,4 +84,16 @@ CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 32769);
 
 SHOW ivfflat.probes;
 
+SET ivfflat.probes = 0;
+SET ivfflat.probes = 32769;
+
+SHOW ivfflat.iterative_search;
+
+SET ivfflat.iterative_search = on;
+
+SHOW ivfflat.max_probes;
+
+SET ivfflat.max_probes = -2;
+SET ivfflat.max_probes = 32769;
+
 DROP TABLE t;

test/sql/minivec.sql

@@ -1,134 +0,0 @@
-SELECT '[1,2,3]'::minivec;
-SELECT '[-1,-2,-3]'::minivec;
-SELECT '[1.,2.,3.]'::minivec;
-SELECT ' [ 1,  2 ,    3  ] '::minivec;
-SELECT '[1.23456]'::minivec;
-SELECT '[hello,1]'::minivec;
-SELECT '[NaN,1]'::minivec;
-SELECT '[Infinity,1]'::minivec;
-SELECT '[-Infinity,1]'::minivec;
-SELECT '[65519,-65519]'::minivec;
-SELECT '[65520,-65520]'::minivec;
-SELECT '[1e-8,-1e-8]'::minivec;
-SELECT '[4e38,1]'::minivec;
-SELECT '[1e-46,1]'::minivec;
-SELECT '[1,2,3'::minivec;
-SELECT '[1,2,3]9'::minivec;
-SELECT '1,2,3'::minivec;
-SELECT ''::minivec;
-SELECT '['::minivec;
-SELECT '[ '::minivec;
-SELECT '[,'::minivec;
-SELECT '[]'::minivec;
-SELECT '[ ]'::minivec;
-SELECT '[,]'::minivec;
-SELECT '[1,]'::minivec;
-SELECT '[1a]'::minivec;
-SELECT '[1,,3]'::minivec;
-SELECT '[1, ,3]'::minivec;
-
-SELECT '[1,2,3]'::minivec(3);
-SELECT '[1,2,3]'::minivec(2);
-SELECT '[1,2,3]'::minivec(3, 2);
-SELECT '[1,2,3]'::minivec('a');
-SELECT '[1,2,3]'::minivec(0);
-SELECT '[1,2,3]'::minivec(16001);
-
-SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::minivec[]);
-SELECT '{"[1,2,3]"}'::minivec(2)[];
-
-SELECT '[1,2,3]'::minivec + '[4,5,6]';
-SELECT '[448]'::minivec + '[448]';
-SELECT '[1,2]'::minivec + '[3]';
-
-SELECT '[1,2,3]'::minivec - '[4,5,6]';
-SELECT '[-448]'::minivec - '[448]';
-SELECT '[1,2]'::minivec - '[3]';
-
-SELECT '[1,2,3]'::minivec * '[4,5,6]';
-SELECT '[448]'::minivec * '[448]';
-SELECT '[1e-7]'::minivec * '[1e-7]';
-SELECT '[1,2]'::minivec * '[3]';
-
-SELECT '[1,2,3]'::minivec || '[4,5]';
-SELECT array_fill(0, ARRAY[16000])::minivec || '[1]';
-
-SELECT '[1,2,3]'::minivec < '[1,2,3]';
-SELECT '[1,2,3]'::minivec < '[1,2]';
-SELECT '[1,2,3]'::minivec <= '[1,2,3]';
-SELECT '[1,2,3]'::minivec <= '[1,2]';
-SELECT '[1,2,3]'::minivec = '[1,2,3]';
-SELECT '[1,2,3]'::minivec = '[1,2]';
-SELECT '[1,2,3]'::minivec != '[1,2,3]';
-SELECT '[1,2,3]'::minivec != '[1,2]';
-SELECT '[1,2,3]'::minivec >= '[1,2,3]';
-SELECT '[1,2,3]'::minivec >= '[1,2]';
-SELECT '[1,2,3]'::minivec > '[1,2,3]';
-SELECT '[1,2,3]'::minivec > '[1,2]';
-
-SELECT minivec_cmp('[1,2,3]', '[1,2,3]');
-SELECT minivec_cmp('[1,2,3]', '[0,0,0]');
-SELECT minivec_cmp('[0,0,0]', '[1,2,3]');
-SELECT minivec_cmp('[1,2]', '[1,2,3]');
-SELECT minivec_cmp('[1,2,3]', '[1,2]');
-SELECT minivec_cmp('[1,2]', '[2,3,4]');
-SELECT minivec_cmp('[2,3]', '[1,2,3]');
-
-SELECT vector_dims('[1,2,3]'::minivec);
-
-SELECT round(l2_norm('[1,1]'::minivec)::numeric, 5);
-SELECT l2_norm('[3,4]'::minivec);
-SELECT l2_norm('[0,1]'::minivec);
-SELECT l2_norm('[0,0]'::minivec);
-SELECT l2_norm('[2]'::minivec);
-
-SELECT l2_distance('[0,0]'::minivec, '[3,4]');
-SELECT l2_distance('[0,0]'::minivec, '[0,1]');
-SELECT l2_distance('[1,2]'::minivec, '[3]');
-SELECT l2_distance('[1,1,1,1,1,1,1,1,1]'::minivec, '[1,1,1,1,1,1,1,4,5]');
-SELECT '[0,0]'::minivec <-> '[3,4]';
-
-SELECT inner_product('[1,2]'::minivec, '[3,4]');
-SELECT inner_product('[1,2]'::minivec, '[3]');
-SELECT inner_product('[448]'::minivec, '[448]');
-SELECT inner_product('[1,1,1,1,1,1,1,1,1]'::minivec, '[1,2,3,4,5,6,7,8,9]');
-SELECT '[1,2]'::minivec <#> '[3,4]';
-
-SELECT cosine_distance('[1,2]'::minivec, '[2,4]');
-SELECT cosine_distance('[1,2]'::minivec, '[0,0]');
-SELECT cosine_distance('[1,1]'::minivec, '[1,1]');
-SELECT cosine_distance('[1,0]'::minivec, '[0,2]');
-SELECT cosine_distance('[1,1]'::minivec, '[-1,-1]');
-SELECT cosine_distance('[1,2]'::minivec, '[3]');
-SELECT cosine_distance('[1,1]'::minivec, '[1.1,1.1]');
-SELECT cosine_distance('[1,1]'::minivec, '[-1.1,-1.1]');
-SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::minivec, '[1,2,3,4,5,6,7,8,9]');
-SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::minivec, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
-SELECT '[1,2]'::minivec <=> '[2,4]';
-
-SELECT l1_distance('[0,0]'::minivec, '[3,4]');
-SELECT l1_distance('[0,0]'::minivec, '[0,1]');
-SELECT l1_distance('[1,2]'::minivec, '[3]');
-SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::minivec, '[1,2,3,4,5,6,7,8,9]');
-SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::minivec, '[0,3,2,5,4,7,6,9,8]');
-SELECT '[0,0]'::minivec <+> '[3,4]';
-
-SELECT l2_normalize('[3,4]'::minivec);
-SELECT l2_normalize('[3,0]'::minivec);
-SELECT l2_normalize('[0,0.1]'::minivec);
-SELECT l2_normalize('[0,0]'::minivec);
-SELECT l2_normalize('[448]'::minivec);
-
-SELECT binary_quantize('[1,0,-1]'::minivec);
-SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::minivec);
-
-SELECT subvector('[1,2,3,4,5]'::minivec, 1, 3);
-SELECT subvector('[1,2,3,4,5]'::minivec, 3, 2);
-SELECT subvector('[1,2,3,4,5]'::minivec, -1, 3);
-SELECT subvector('[1,2,3,4,5]'::minivec, 3, 9);
-SELECT subvector('[1,2,3,4,5]'::minivec, 1, 0);
-SELECT subvector('[1,2,3,4,5]'::minivec, 3, -1);
-SELECT subvector('[1,2,3,4,5]'::minivec, -1, 2);
-SELECT subvector('[1,2,3,4,5]'::minivec, 2147483647, 10);
-SELECT subvector('[1,2,3,4,5]'::minivec, 3, 2147483647);
-SELECT subvector('[1,2,3,4,5]'::minivec, -2147483644, 2147483647);

test/t/002_ivfflat_vacuum.pl

@@ -6,13 +6,7 @@ use Test::More;
 
 my $dim = 3;
 
-my @r = ();
-for (1 .. $dim)
-{
-	my $v = int(rand(1000)) + 1;
-	push(@r, "i % $v");
-}
-my $array_sql = join(", ", @r);
+my $array_sql = join(",", ('random()') x $dim);
 
 # Initialize node
 my $node = PostgreSQL::Test::Cluster->new('node');
@@ -23,19 +17,20 @@ $node->start;
 $node->safe_psql("postgres", "CREATE EXTENSION vector;");
 $node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
 $node->safe_psql("postgres",
-	"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
 );
 $node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_l2_ops);");
 
 # Get size
 my $size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");
 
+# Store values
+$node->safe_psql("postgres", "CREATE TABLE tmp AS SELECT * FROM tst;");
+
 # Delete all, vacuum, and insert same data
 $node->safe_psql("postgres", "DELETE FROM tst;");
 $node->safe_psql("postgres", "VACUUM tst;");
-$node->safe_psql("postgres",
-	"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
-);
+$node->safe_psql("postgres", "INSERT INTO tst SELECT * FROM tmp;");
 
 # Check size
 my $new_size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");

test/t/009_ivfflat_filtering.pl

@@ -94,8 +94,7 @@ like($explain, qr/Seq Scan/);
 $explain = $node->safe_psql("postgres", qq(
 	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1 ORDER BY v <-> '$query';
 ));
-# TODO Do not use index
-like($explain, qr/Index Scan using idx/);
+like($explain, qr/Seq Scan/);
 
 # Test attribute index
 $node->safe_psql("postgres", "CREATE INDEX attribute_idx ON tst (c);");
@@ -110,7 +109,6 @@ $node->safe_psql("postgres", "CREATE INDEX partial_idx ON tst USING ivfflat (v v
 $explain = $node->safe_psql("postgres", qq(
 	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
 ));
-# TODO Use partial index
-like($explain, qr/Index Scan using idx/);
+like($explain, qr/Index Scan using partial_idx/);
 
 done_testing();

test/t/017_hnsw_filtering.pl

@@ -18,9 +18,13 @@ $node->start;
 # Create table and index
 $node->safe_psql("postgres", "CREATE EXTENSION vector;");
 $node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim), c int4, t text);");
+$node->safe_psql("postgres", "CREATE TABLE cat (i int4 PRIMARY KEY, t text, b boolean);");
 $node->safe_psql("postgres",
 	"INSERT INTO tst SELECT i, ARRAY[$array_sql], i % $nc, 'test ' || i FROM generate_series(1, 10000) i;"
 );
+$node->safe_psql("postgres",
+	"INSERT INTO cat SELECT i, 'cat ' || i, i % 5 = 0 FROM generate_series(1, $nc) i;"
+);
 $node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v vector_l2_ops);");
 $node->safe_psql("postgres", "ANALYZE tst;");
 
@@ -37,8 +41,7 @@ my $c = int(rand() * $nc);
 my $explain = $node->safe_psql("postgres", qq(
 	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
 ));
-# TODO Do not use index
-like($explain, qr/Index Scan using idx/);
+like($explain, qr/Seq Scan/);
 
 # Test attribute filtering with few rows removed
 $explain = $node->safe_psql("postgres", qq(
@@ -56,8 +59,7 @@ like($explain, qr/Index Scan using idx/);
 $explain = $node->safe_psql("postgres", qq(
 	EXPLAIN ANALYZE SELECT i FROM tst WHERE c < 1 ORDER BY v <-> '$query' LIMIT $limit;
 ));
-# TODO Do not use index
-like($explain, qr/Index Scan using idx/);
+like($explain, qr/Seq Scan/);
 
 # Test attribute filtering with few rows removed like
 $explain = $node->safe_psql("postgres", qq(
@@ -96,13 +98,25 @@ $explain = $node->safe_psql("postgres", qq(
 ));
 like($explain, qr/Seq Scan/);
 
+# Test join
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT cat.t FROM cat INNER JOIN tst ON cat.i = tst.c ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test join with attribute filtering
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT cat.t FROM cat INNER JOIN tst ON cat.i = tst.c WHERE cat.b = 't' ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
 # Test attribute index
 $node->safe_psql("postgres", "CREATE INDEX attribute_idx ON tst (c);");
 $explain = $node->safe_psql("postgres", qq(
 	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
 ));
-# TODO Use attribute index
-like($explain, qr/Index Scan using idx/);
+# Use attribute index
+like($explain, qr/Bitmap Index Scan on attribute_idx/);
 
 # Test partial index
 $node->safe_psql("postgres", "CREATE INDEX partial_idx ON tst USING hnsw (v vector_l2_ops) WHERE (c = $c);");

test/t/033_comparison.pl

@@ -40,6 +40,10 @@ for (1 .. 50)
 	$actual = $node->safe_psql("postgres", "SELECT halfvec_cmp(v::halfvec, '$query'::real[]::halfvec) FROM tst");
 	is($expected, $actual);
 
+	# Test intvec
+	$actual = $node->safe_psql("postgres", "SELECT intvec_cmp(v::integer[]::intvec, '$query'::integer[]::intvec) 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);

test/t/034_distance_functions.pl

@@ -45,6 +45,10 @@ for my $function (@functions)
 		my $actual = $node->safe_psql("postgres", "SELECT $function(v::halfvec, '$query'::vector::halfvec) FROM tst");
 		is($expected, $actual, "halfvec $function");
 
+		# Test intvec
+		$actual = $node->safe_psql("postgres", "SELECT $function(v::real[]::integer[]::intvec, '$query'::vector::real[]::integer[]::intvec) FROM tst");
+		is($expected, $actual, "intvec $function");
+
 		# Test sparsevec
 		$actual = $node->safe_psql("postgres", "SELECT $function(v::sparsevec, '$query'::vector::sparsevec) FROM tst");
 		is($expected, $actual, "sparsevec $function");

test/t/037_inputs.pl

@@ -12,8 +12,8 @@ $node->start;
 # Create extension
 $node->safe_psql("postgres", "CREATE EXTENSION vector;");
 
-my @types = ("vector", "halfvec", "sparsevec");
-my @inputs = ("[1.23,4.56,7.89]", "[1.23,4.56,7.89]", "{1:1.23,2:4.56,3:7.89}/3");
+my @types = ("vector", "halfvec", "intvec", "sparsevec");
+my @inputs = ("[1.23,4.56,7.89]", "[1.23,4.56,7.89]", "[1,2,3]", "{1:1.23,2:4.56,3:7.89}/3");
 my @subs = (" ", " ", ",", ":", "-", "1", "9", "\0", "2147483648", "-2147483649");
 
 for my $i (0 .. $#types)

test/t/039_hnsw_cost.pl

@@ -0,0 +1,60 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my @dims = (384, 1536);
+my $limit = 10;
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+
+for my $dim (@dims)
+{
+	my $array_sql = join(",", ('random()') x $dim);
+
+	# Create table and index
+	$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
+	$node->safe_psql("postgres",
+		"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 2000) i;"
+	);
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v vector_l2_ops);");
+	$node->safe_psql("postgres", "ANALYZE tst;");
+
+	# Generate query
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	my $query = "[" . join(",", @r) . "]";
+
+	my $explain = $node->safe_psql("postgres", qq(
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$query' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx/);
+
+	# 3x the rows are needed for distance filters
+	# since the planner uses DEFAULT_INEQ_SEL for the selectivity (should be 1)
+	# Recreate index for performance
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres",
+		"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(2001, 6000) i;"
+	);
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v vector_l2_ops);");
+	$node->safe_psql("postgres", "ANALYZE tst;");
+
+	$explain = $node->safe_psql("postgres", qq(
+		EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1 ORDER BY v <-> '$query' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx/);
+
+	$node->safe_psql("postgres", "DROP TABLE tst;");
+}
+
+done_testing();

test/t/040_ivfflat_cost.pl

@@ -0,0 +1,50 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my @dims = (384, 1536);
+my $limit = 10;
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+
+for my $dim (@dims)
+{
+	my $array_sql = join(",", ('random()') x $dim);
+
+	# Create table and index
+	$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
+	$node->safe_psql("postgres",
+		"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 5000) i;"
+	);
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING ivfflat (v vector_l2_ops) WITH (lists = 5);");
+	$node->safe_psql("postgres", "ANALYZE tst;");
+
+	# Generate query
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	my $query = "[" . join(",", @r) . "]";
+
+	my $explain = $node->safe_psql("postgres", qq(
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$query' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx/);
+
+	$explain = $node->safe_psql("postgres", qq(
+		EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1 ORDER BY v <-> '$query' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx/);
+
+	$node->safe_psql("postgres", "DROP TABLE tst;");
+}
+
+done_testing();

test/t/041_ivfflat_iterative_search.pl

@@ -0,0 +1,54 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $dim = 3;
+my $array_sql = join(",", ('random()') x $dim);
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4 PRIMARY KEY, v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
+);
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_l2_ops);");
+
+my $count = $node->safe_psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET ivfflat.probes = 10;
+	SET ivfflat.iterative_search = relaxed_order;
+	SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst LIMIT 1) LIMIT 11) t;
+));
+is($count, 10);
+
+foreach ((30, 50, 70))
+{
+	my $max_probes = $_;
+	my $expected = $max_probes / 10;
+	my $sum = 0;
+
+	for my $i (1 .. 20)
+	{
+		$count = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET ivfflat.probes = 10;
+			SET ivfflat.iterative_search = relaxed_order;
+			SET ivfflat.max_probes = $max_probes;
+			SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst WHERE i = $i) LIMIT 11) t;
+		));
+		$sum += $count;
+	}
+
+	my $avg = $sum / 20;
+	cmp_ok($avg, '>', $expected - 2);
+	cmp_ok($avg, '<', $expected + 2);
+}
+
+done_testing();

test/t/042_ivfflat_iterative_search_recall.pl

@@ -0,0 +1,125 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my @cs = (100, 1000);
+
+sub test_recall
+{
+	my ($c, $probes, $min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET ivfflat.probes = $probes;
+		SET ivfflat.iterative_search = relaxed_order;
+		EXPLAIN ANALYZE SELECT i FROM tst WHERE i % $c = 0 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;
+			SET ivfflat.iterative_search = relaxed_order;
+			SELECT i FROM tst WHERE i % $c = 0 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 $c");
+}
+
+# Initialize node
+$node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector(3));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 100000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "[$r1,$r2,$r3]");
+}
+
+# Check each index type
+my @operators = ("<->", "<=>");
+my @opclasses = ("vector_l2_ops", "vector_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING ivfflat (v $opclass);");
+
+	foreach (@cs)
+	{
+		my $c = $_;
+
+		# Get exact results
+		@expected = ();
+		foreach (@queries)
+		{
+			my $res = $node->safe_psql("postgres", qq(
+				SET enable_indexscan = off;
+				WITH top AS (
+					SELECT v $operator '$_' AS distance FROM tst WHERE i % $c = 0 ORDER BY distance LIMIT $limit
+				)
+				SELECT i FROM tst WHERE (v $operator '$_') <= (SELECT MAX(distance) FROM top)
+			));
+			push(@expected, $res);
+		}
+
+		if ($c == 100)
+		{
+			test_recall($c, 1, 0.57, $operator);
+			test_recall($c, 10, 0.98, $operator);
+		}
+		else
+		{
+			if ($operator eq "<->")
+			{
+				test_recall($c, 1, 0.80, $operator);
+			}
+			else
+			{
+				test_recall($c, 1, 0.88, $operator);
+			}
+		}
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();

test/t/043_hnsw_iterative_search.pl

@@ -0,0 +1,67 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $dim = 3;
+my $array_sql = join(",", ('random()') x $dim);
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4 PRIMARY KEY, v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
+);
+$node->safe_psql("postgres", qq(
+	SET maintenance_work_mem = '128MB';
+	SET max_parallel_maintenance_workers = 2;
+	CREATE INDEX ON tst USING hnsw (v vector_l2_ops)
+));
+
+my $count = $node->safe_psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET hnsw.iterative_search = relaxed_order;
+	SET work_mem = '8MB';
+	SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst LIMIT 1) LIMIT 11) t;
+));
+is($count, 10);
+
+foreach ((30000, 50000, 70000))
+{
+	my $max_tuples = $_;
+	my $expected = $max_tuples / 10000;
+	my $sum = 0;
+
+	for my $i (1 .. 20)
+	{
+		$count = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.iterative_search = relaxed_order;
+			SET hnsw.max_search_tuples = $max_tuples;
+			SET work_mem = '8MB';
+			SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst WHERE i = $i) LIMIT 11) t;
+		));
+		$sum += $count;
+	}
+
+	my $avg = $sum / 20;
+	cmp_ok($avg, '>', $expected - 2);
+	cmp_ok($avg, '<', $expected + 2);
+}
+
+my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET hnsw.iterative_search = relaxed_order;
+	SET client_min_messages = debug1;
+	SET work_mem = '2MB';
+	SELECT COUNT(*) FROM (SELECT v FROM tst WHERE i % 10000 = 0 ORDER BY v <-> (SELECT v FROM tst LIMIT 1) LIMIT 11) t;
+));
+like($stderr, qr/hnsw index scan exceeded work_mem after \d+ tuples/);
+
+done_testing();

test/t/044_hnsw_iterative_search_recall.pl

@@ -0,0 +1,118 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 3;
+my $array_sql = join(",", ('random()') x $dim);
+my @cs = (50, 500);
+
+sub test_recall
+{
+	my ($c, $ef_search, $min, $operator, $mode) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = $ef_search;
+		SET hnsw.iterative_search = $mode;
+		EXPLAIN ANALYZE SELECT i FROM tst WHERE i % $c = 0 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 hnsw.ef_search = $ef_search;
+			SET hnsw.iterative_search = $mode;
+			SELECT i FROM tst WHERE i % $c = 0 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 $mode $c");
+}
+
+# Initialize node
+$node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 50000) 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 = ("vector_l2_ops", "vector_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	$node->safe_psql("postgres", qq(
+		SET maintenance_work_mem = '128MB';
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+
+	foreach (@cs)
+	{
+		my $c = $_;
+
+		# Get exact results
+		@expected = ();
+		foreach (@queries)
+		{
+			my $res = $node->safe_psql("postgres", qq(
+				SET enable_indexscan = off;
+				WITH top AS (
+					SELECT v $operator '$_' AS distance FROM tst WHERE i % $c = 0 ORDER BY distance LIMIT $limit
+				)
+				SELECT i FROM tst WHERE (v $operator '$_') <= (SELECT MAX(distance) FROM top)
+			));
+			push(@expected, $res);
+		}
+
+		test_recall($c, 40, 0.99, $operator, "strict_order");
+		test_recall($c, 40, 0.99, $operator, "relaxed_order");
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();

test/t/045_hnsw_intvec_build_recall.pl

@@ -9,7 +9,7 @@ my @queries = ();
 my @expected;
 my $limit = 20;
 my $dim = 10;
-my $array_sql = join(",", ('2 * random() * random()') x $dim);
+my $array_sql = join(",", ('(random() * 255)::int - 128') x $dim);
 
 sub test_recall
 {
@@ -54,7 +54,7 @@ $node->start;
 
 # Create table
 $node->safe_psql("postgres", "CREATE EXTENSION vector;");
-$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v minivec($dim));");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v intvec($dim));");
 $node->safe_psql("postgres",
 	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
 );
@@ -65,14 +65,14 @@ for (1 .. 20)
 	my @r = ();
 	for (1 .. $dim)
 	{
-		push(@r, rand());
+		push(@r, int(rand(256)) - 128);
 	}
 	push(@queries, "[" . join(",", @r) . "]");
 }
 
 # Check each index type
 my @operators = ("<->", "<#>", "<=>", "<+>");
-my @opclasses = ("minivec_l2_ops", "minivec_ip_ops", "minivec_cosine_ops", "minivec_l1_ops");
+my @opclasses = ("intvec_l2_ops", "intvec_ip_ops", "intvec_cosine_ops", "intvec_l1_ops");
 
 for my $i (0 .. $#operators)
 {
@@ -95,10 +95,6 @@ for my $i (0 .. $#operators)
 
 	# Test approximate results
 	my $min = 0.98;
-	if ($operator eq '<=>')
-	{
-		$min = 0.65;
-	}
 	test_recall($min, $operator);
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");

test/t/046_hnsw_intvec_insert_recall.pl

@@ -0,0 +1,113 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 10;
+my $array_sql = join(",", ('(random() * 255)::int - 128') 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 = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i serial, v intvec($dim));");
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, int(rand(256)) - 128);
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>", "<+>");
+my @opclasses = ("intvec_l2_ops", "intvec_ip_ops", "intvec_cosine_ops", "intvec_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",
+		{
+			"040_hnsw_intvec_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 $min = 0.98;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres", "TRUNCATE tst;");
+}
+
+done_testing();

test/t/047_hnsw_intvec_vacuum_recall.pl

@@ -0,0 +1,101 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 10;
+my $array_sql = join(",", ('(random() * 255)::int - 128') x $dim);
+
+sub test_recall
+{
+	my ($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 %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 = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v intvec($dim));");
+$node->safe_psql("postgres", "ALTER TABLE tst SET (autovacuum_enabled = false);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
+);
+
+# Add index
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v intvec_l2_ops) WITH (m = 4, ef_construction = 8);");
+
+# Delete data
+$node->safe_psql("postgres", "DELETE FROM tst WHERE i > 2500;");
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, int(rand(256)) - 128);
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# 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, $limit, "before vacuum");
+test_recall(0.84, 100, "before vacuum");
+
+# TODO Test concurrent inserts with vacuum
+$node->safe_psql("postgres", "VACUUM tst;");
+
+test_recall(0.84, $limit, "after vacuum");
+
+done_testing();

test/t/048_hnsw_intvec_duplicates.pl

@@ -0,0 +1,58 @@
+use strict;
+use warnings FATAL => 'all';
+use PostgreSQL::Test::Cluster;
+use PostgreSQL::Test::Utils;
+use Test::More;
+
+# Initialize node
+my $node = PostgreSQL::Test::Cluster->new('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (v intvec(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();
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v intvec_l2_ops);");
+test_duplicates();
+
+# Reset
+$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",
+	{
+		"042_hnsw_intvec_duplicates" => "INSERT INTO tst VALUES ('[1,1,1]');"
+	}
+);
+
+done_testing();