Use normalize_l2 for ivfflat

Co-authored-by: Xiaoran Wang <wxiaoran@vmware.com>

.github/workflows/build.yml

@@ -8,6 +8,8 @@ jobs:
       fail-fast: false
       matrix:
         include:
+          - postgres: 16
+            os: ubuntu-22.04
           - postgres: 15
             os: ubuntu-22.04
           - postgres: 14
@@ -25,6 +27,8 @@ jobs:
           postgres-version: ${{ matrix.postgres }}
           dev-files: true
       - run: make
+        env:
+          PG_CFLAGS: -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
       - run: |
           export PG_CONFIG=`which pg_config`
           sudo --preserve-env=PG_CONFIG make install
@@ -44,6 +48,8 @@ jobs:
         with:
           postgres-version: 14
       - run: make
+        env:
+          PG_CFLAGS: -Wall -Wextra -Werror -Wno-unused-parameter
       - run: make install
       - run: make installcheck
       - if: ${{ failure() }}
@@ -54,6 +60,7 @@ jobs:
           wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_14_5.tar.gz
           tar xf REL_14_5.tar.gz
       - run: make prove_installcheck PROVE_FLAGS="-I ./postgres-REL_14_5/src/test/perl" PERL5LIB="/Users/runner/perl5/lib/perl5"
+      - run: make clean && /usr/local/opt/llvm@15/bin/scan-build --status-bugs make
   windows:
     runs-on: windows-latest
     if: ${{ !startsWith(github.ref_name, 'mac') }}
@@ -70,3 +77,23 @@ jobs:
           nmake /NOLOGO /F Makefile.win clean && ^
           nmake /NOLOGO /F Makefile.win uninstall
         shell: cmd
+  i386:
+    runs-on: ubuntu-latest
+    container:
+      image: debian:11
+      options: --platform linux/386
+    steps:
+      - run: apt-get update && apt-get install -y build-essential git libipc-run-perl postgresql-13 postgresql-server-dev-13 sudo
+      - run: service postgresql start
+      - run: |
+          git clone https://github.com/${{ github.repository }}.git pgvector
+          cd pgvector
+          git fetch origin ${{ github.ref }}
+          git reset --hard FETCH_HEAD
+          make
+          make install
+          chown -R postgres .
+          sudo -u postgres make installcheck
+          sudo -u postgres make prove_installcheck
+        env:
+          PG_CFLAGS: -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare

CHANGELOG.md

@@ -1,3 +1,32 @@
+## 0.5.0 (unreleased)
+
+- Added HNSW index type
+- Added support for parallel index builds
+- Added `l1_distance` function
+- Added `normalize_l2` function
+- Added element-wise multiplication for vectors
+- Added `sum` aggregate
+- Improved performance of distance functions
+- Fixed out of range results for cosine distance
+- Fixed results for NULL and NaN distances
+
+## 0.4.4 (2023-06-12)
+
+- Improved error message for malformed vector literal
+- Fixed segmentation fault with text input
+- Fixed consecutive delimiters with text input
+
+## 0.4.3 (2023-06-10)
+
+- Improved cost estimation
+- Improved support for spaces with text input
+- Fixed infinite and NaN values with binary input
+- Fixed infinite values with vector addition and subtraction
+- Fixed infinite values with list centers
+- Fixed compilation error when `float8` is pass by reference
+- Fixed compilation error on PowerPC
+- Fixed segmentation fault with index creation on i386
+
 ## 0.4.2 (2023-05-13)
 
 - Added notice when index created with little data

Dockerfile

@@ -5,6 +5,7 @@ ARG PG_MAJOR
 COPY . /tmp/pgvector
 
 RUN apt-get update && \
+		apt-mark hold locales && \
 		apt-get install -y --no-install-recommends build-essential postgresql-server-dev-$PG_MAJOR && \
 		cd /tmp/pgvector && \
 		make clean && \
@@ -15,4 +16,5 @@ RUN apt-get update && \
 		rm -r /tmp/pgvector && \
 		apt-get remove -y build-essential postgresql-server-dev-$PG_MAJOR && \
 		apt-get autoremove -y && \
+		apt-mark unhold locales && \
 		rm -rf /var/lib/apt/lists/*

LICENSE

@@ -1,4 +1,4 @@
-Portions Copyright (c) 1996-2022, PostgreSQL Global Development Group
+Portions Copyright (c) 1996-2023, PostgreSQL Global Development Group
 
 Portions Copyright (c) 1994, The Regents of the University of California
 

META.json

@@ -2,7 +2,7 @@
 	"name": "vector",
 	"abstract": "Open-source vector similarity search for Postgres",
 	"description": "Supports L2 distance, inner product, and cosine distance",
-	"version": "0.4.2",
+	"version": "0.4.4",
 	"maintainer": [
 		"Andrew Kane <andrew@ankane.org>"
 	],
@@ -20,7 +20,7 @@
 		"vector": {
 			"file": "sql/vector.sql",
 			"docfile": "README.md",
-			"version": "0.4.2",
+			"version": "0.4.4",
 			"abstract": "Open-source vector similarity search for Postgres"
 		}
 	},

Makefile

@@ -1,9 +1,9 @@
 EXTENSION = vector
-EXTVERSION = 0.4.2
+EXTVERSION = 0.4.4
 
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
-OBJS = src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
+OBJS = src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
 
 TESTS = $(wildcard test/sql/*.sql)
 REGRESS = $(patsubst test/sql/%.sql,%,$(TESTS))
@@ -19,6 +19,11 @@ ifeq ($(shell uname -s), Darwin)
 	endif
 endif
 
+# PowerPC doesn't support -march=native
+ifneq ($(filter ppc64%, $(shell uname -m)), )
+	OPTFLAGS =
+endif
+
 # For auto-vectorization:
 # - GCC (needs -ftree-vectorize OR -O3) - https://gcc.gnu.org/projects/tree-ssa/vectorization.html
 # - Clang (could use pragma instead) - https://llvm.org/docs/Vectorizers.html

Makefile.win

@@ -1,7 +1,7 @@
 EXTENSION = vector
-EXTVERSION = 0.4.2
+EXTVERSION = 0.4.4
 
-OBJS = src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\vector.obj
+OBJS = src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\vector.obj
 
 REGRESS = btree cast copy functions input ivfflat_cosine ivfflat_ip ivfflat_l2 ivfflat_options ivfflat_unlogged
 REGRESS_OPTS = --inputdir=test --load-extension=vector

README.md

@@ -2,12 +2,14 @@
 
 Open-source vector similarity search for Postgres
 
-Supports
+Store all of your application data in one place. Supports:
 
 - exact and approximate nearest neighbor search
 - L2 distance, inner product, and cosine distance
 - any [language](#languages) with a Postgres client
 
+Plus [ACID](https://en.wikipedia.org/wiki/ACID) compliance, point-in-time recovery, JOINs, and all of the other [great features](https://www.postgresql.org/about/) of Postgres
+
 [![Build Status](https://github.com/pgvector/pgvector/workflows/build/badge.svg?branch=master)](https://github.com/pgvector/pgvector/actions)
 
 ## Installation
@@ -16,24 +18,24 @@ Compile and install the extension (supports Postgres 11+)
 
 ```sh
 cd /tmp
-git clone --branch v0.4.2 https://github.com/pgvector/pgvector.git
+git clone --branch v0.4.4 https://github.com/pgvector/pgvector.git
 cd pgvector
 make
 make install # may need sudo
 ```
 
-Then load it in databases where you want to use it
-
-```sql
-CREATE EXTENSION vector;
-```
-
 See the [installation notes](#installation-notes) if you run into issues
 
-You can also install it with [Docker](#docker), [Homebrew](#homebrew), [PGXN](#pgxn), [Yum](#yum), or [conda-forge](#conda-forge)
+You can also install it with [Docker](#docker), [Homebrew](#homebrew), [PGXN](#pgxn), [APT](#apt), [Yum](#yum), or [conda-forge](#conda-forge), and it comes preinstalled with [Postgres.app](#postgresapp) and many [hosted providers](#hosted-postgres)
 
 ## Getting Started
 
+Enable the extension (do this once in each database where you want to use it)
+
+```tsql
+CREATE EXTENSION vector;
+```
+
 Create a vector column with 3 dimensions
 
 ```sql
@@ -127,7 +129,7 @@ SELECT embedding <-> '[3,1,2]' AS distance FROM items;
 
 For inner product, multiply by -1 (since `<#>` returns the negative inner product)
 
-```sql
+```tsql
 SELECT (embedding <#> '[3,1,2]') * -1 AS inner_product FROM items;
 ```
 
@@ -161,7 +163,7 @@ Three keys to achieving good recall are:
 
 1. Create the index *after* the table has some data
 2. Choose an appropriate number of lists - a good place to start is `rows / 1000` for up to 1M rows and `sqrt(rows)` for over 1M rows
-3. When querying, specify an appropriate number of [probes](#query-options) (higher is better for recall, lower is better for speed) - a good place to start is `lists / 10` for up to 1M rows and `sqrt(lists)` for over 1M rows
+3. When querying, specify an appropriate number of [probes](#query-options) (higher is better for recall, lower is better for speed) - a good place to start is `sqrt(lists)`
 
 Add an index for each distance function you want to use.
 
@@ -221,26 +223,42 @@ The phases are:
 
 Note: `tuples_done` and `tuples_total` are only populated during the `loading tuples` phase
 
-### Partial Indexes
+## Filtering
 
-Consider [partial indexes](https://www.postgresql.org/docs/current/indexes-partial.html) for queries with a `WHERE` clause
+There are a few ways to index nearest neighbor queries with a `WHERE` clause
 
 ```sql
 SELECT * FROM items WHERE category_id = 123 ORDER BY embedding <-> '[3,1,2]' LIMIT 5;
 ```
 
-can be indexed with:
+Create an index on one [or more](https://www.postgresql.org/docs/current/indexes-multicolumn.html) of the `WHERE` columns for exact search
 
 ```sql
-CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 100) WHERE (category_id = 123);
+CREATE INDEX ON items (category_id);
 ```
 
-To index many different values of `category_id`, consider [partitioning](https://www.postgresql.org/docs/current/ddl-partitioning.html) on `category_id`.
+Or a [partial index](https://www.postgresql.org/docs/current/indexes-partial.html) on the vector column for approximate search
+
+```sql
+CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 100)
+    WHERE (category_id = 123);
+```
+
+Use [partitioning](https://www.postgresql.org/docs/current/ddl-partitioning.html) for approximate search on many different values of the `WHERE` columns
 
 ```sql
 CREATE TABLE items (embedding vector(3), category_id int) PARTITION BY LIST(category_id);
 ```
 
+## Hybrid Search
+
+Use together with Postgres [full-text search](https://www.postgresql.org/docs/current/textsearch-intro.html) for hybrid search ([Python example](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search.py)).
+
+```sql
+SELECT id, content FROM items, plainto_tsquery('hello search') query
+    WHERE textsearch @@ query ORDER BY ts_rank_cd(textsearch, query) DESC LIMIT 5;
+```
+
 ## Performance
 
 Use `EXPLAIN ANALYZE` to debug performance.
@@ -259,7 +277,7 @@ SET max_parallel_workers_per_gather = 4;
 
 If vectors are normalized to length 1 (like [OpenAI embeddings](https://platform.openai.com/docs/guides/embeddings/which-distance-function-should-i-use)), use inner product for best performance.
 
-```sql
+```tsql
 SELECT * FROM items ORDER BY embedding <#> '[3,1,2]' LIMIT 5;
 ```
 
@@ -280,6 +298,7 @@ Language | Libraries / Examples
 C++ | [pgvector-cpp](https://github.com/pgvector/pgvector-cpp)
 C# | [pgvector-dotnet](https://github.com/pgvector/pgvector-dotnet)
 Crystal | [pgvector-crystal](https://github.com/pgvector/pgvector-crystal)
+Dart | [pgvector-dart](https://github.com/pgvector/pgvector-dart)
 Elixir | [pgvector-elixir](https://github.com/pgvector/pgvector-elixir)
 Go | [pgvector-go](https://github.com/pgvector/pgvector-go)
 Haskell | [pgvector-haskell](https://github.com/pgvector/pgvector-haskell)
@@ -309,10 +328,45 @@ Yes, pgvector uses the write-ahead log (WAL), which allows for replication and p
 
 You’ll need to use [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction) at the moment.
 
-#### Why am I seeing less results after adding an index?
+## Troubleshooting
+
+#### Why isn’t a query using an index?
+
+The cost estimation in pgvector < 0.4.3 does not always work well with the planner. You can encourage the planner to use an index for a query with:
+
+```sql
+BEGIN;
+SET LOCAL enable_seqscan = off;
+SELECT ...
+COMMIT;
+```
+
+#### Why isn’t a query using a parallel table scan?
+
+The planner doesn’t consider [out-of-line storage](https://www.postgresql.org/docs/current/storage-toast.html) in cost estimates, which can make a serial scan look cheaper. You can reduce the cost of a parallel scan for a query with:
+
+```sql
+BEGIN;
+SET LOCAL min_parallel_table_scan_size = 1;
+SET LOCAL parallel_setup_cost = 1;
+SELECT ...
+COMMIT;
+```
+
+or choose to store vectors inline:
+
+```sql
+ALTER TABLE items ALTER COLUMN embedding SET STORAGE PLAIN;
+```
+
+#### Why are there less results for a query after adding an index?
 
 The index was likely created with too little data for the number of lists. Drop the index until the table has more data.
 
+```sql
+DROP INDEX index_name;
+```
+
 ## Reference
 
 ### Vector Type
@@ -325,6 +379,7 @@ Operator | Description
 --- | ---
 \+ | element-wise addition
 \- | element-wise subtraction
+\* | element-wise multiplication [unreleased]
 <-> | Euclidean distance
 <#> | negative inner product
 <=> | cosine distance
@@ -336,6 +391,8 @@ Function | Description
 cosine_distance(vector, vector) → double precision | cosine distance
 inner_product(vector, vector) → double precision | inner product
 l2_distance(vector, vector) → double precision | Euclidean distance
+l1_distance(vector, vector) → double precision | taxicab distance [unreleased]
+normalize_l2(vector) → vector | normalize with Euclidean norm [unreleased]
 vector_dims(vector) → integer | number of dimensions
 vector_norm(vector) → double precision | Euclidean norm
 
@@ -344,6 +401,7 @@ vector_norm(vector) → double precision | Euclidean norm
 Function | Description
 --- | ---
 avg(vector) → vector | arithmetic mean
+sum(vector) → vector | sum [unreleased]
 
 ## Installation Notes
 
@@ -368,18 +426,26 @@ If compilation fails with `fatal error: postgres.h: No such file or directory`,
 For Ubuntu and Debian, use:
 
 ```sh
-sudo apt-get install postgresql-server-dev-15
+sudo apt install postgresql-server-dev-15
 ```
 
 Note: Replace `15` with your Postgres server version
 
 ### Windows
 
-Support for Windows is currently experimental. Use `nmake` to build:
+Support for Windows is currently experimental. Ensure [C++ support in Visual Studio](https://learn.microsoft.com/en-us/cpp/build/building-on-the-command-line?view=msvc-170#download-and-install-the-tools) is installed, and run:
+
+```cmd
+call "C:\Program Files\Microsoft Visual Studio\2022\Community\VC\Auxiliary\Build\vcvars64.bat"
+```
+
+Note: The exact path will vary depending on your Visual Studio version and edition
+
+Then use `nmake` to build:
 
 ```cmd
 set "PGROOT=C:\Program Files\PostgreSQL\15"
-git clone --branch v0.4.2 https://github.com/pgvector/pgvector.git
+git clone --branch v0.4.4 https://github.com/pgvector/pgvector.git
 cd pgvector
 nmake /F Makefile.win
 nmake /F Makefile.win install
@@ -400,9 +466,10 @@ This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (r
 You can also build the image manually:
 
 ```sh
-git clone --branch v0.4.2 https://github.com/pgvector/pgvector.git
+git clone --branch v0.4.4 https://github.com/pgvector/pgvector.git
 cd pgvector
-docker build -t pgvector .
+git cherry-pick 237a6df
+docker build --build-arg PG_MAJOR=15 -t myuser/pgvector .
 ```
 
 ### Homebrew
@@ -423,6 +490,16 @@ Install from the [PostgreSQL Extension Network](https://pgxn.org/dist/vector) wi
 pgxn install vector
 ```
 
+### APT
+
+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-15-pgvector
+```
+
+Note: Replace `15` 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:
@@ -445,17 +522,14 @@ conda install -c conda-forge pgvector
 
 This method is [community-maintained](https://github.com/conda-forge/pgvector-feedstock) by [@mmcauliffe](https://github.com/mmcauliffe)
 
+### Postgres.app
+
+Download the [latest release](https://postgresapp.com/downloads.html) with Postgres 15+.
+
 ## Hosted Postgres
 
 pgvector is available on [these providers](https://github.com/pgvector/pgvector/issues/54).
 
-To request a new extension on other providers:
-
-- Google Cloud SQL - vote or comment on [this page](https://issuetracker.google.com/issues/265172065)
-- Azure Database - vote or comment on [this page](https://feedback.azure.com/d365community/idea/7b423322-6189-ed11-a81b-000d3ae49307)
-- DigitalOcean Managed Databases - vote or comment on [this page](https://ideas.digitalocean.com/managed-database/p/pgvector-extension-for-postgresql)
-- Heroku Postgres - vote or comment on [this page](https://github.com/heroku/roadmap/issues/156)
-
 ## Upgrading
 
 Install the latest version and run:
@@ -496,9 +570,10 @@ Thanks to:
 
 - [PASE: PostgreSQL Ultra-High-Dimensional Approximate Nearest Neighbor Search Extension](https://dl.acm.org/doi/pdf/10.1145/3318464.3386131)
 - [Faiss: A Library for Efficient Similarity Search and Clustering of Dense Vectors](https://github.com/facebookresearch/faiss)
-- [Using the Triangle Inequality to Accelerate k-means](https://www.aaai.org/Papers/ICML/2003/ICML03-022.pdf)
+- [Using the Triangle Inequality to Accelerate k-means](https://cdn.aaai.org/ICML/2003/ICML03-022.pdf)
 - [k-means++: The Advantage of Careful Seeding](https://theory.stanford.edu/~sergei/papers/kMeansPP-soda.pdf)
 - [Concept Decompositions for Large Sparse Text Data using Clustering](https://www.cs.utexas.edu/users/inderjit/public_papers/concept_mlj.pdf)
+- [Efficient and Robust Approximate Nearest Neighbor Search using Hierarchical Navigable Small World Graphs](https://arxiv.org/ftp/arxiv/papers/1603/1603.09320.pdf)
 
 ## History
 
@@ -546,4 +621,4 @@ Resources for contributors
 
 - [Extension Building Infrastructure](https://www.postgresql.org/docs/current/extend-pgxs.html)
 - [Index Access Method Interface Definition](https://www.postgresql.org/docs/current/indexam.html)
-- [Generic WAL Records](https://www.postgresql.org/docs/13/generic-wal.html)
+- [Generic WAL Records](https://www.postgresql.org/docs/current/generic-wal.html)

sql/vector--0.4.2--0.4.3.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.4.3'" to load this file. \quit

sql/vector--0.4.3--0.4.4.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.4.4'" to load this file. \quit

sql/vector--0.4.4--0.5.0.sql

@@ -0,0 +1,46 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.5.0'" to load this file. \quit
+
+CREATE FUNCTION l1_distance(vector, vector) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION normalize_l2(vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE OPERATOR * (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_mul,
+	COMMUTATOR = *
+);
+
+CREATE AGGREGATE sum(vector) (
+	SFUNC = vector_add,
+	STYPE = vector,
+	COMBINEFUNC = vector_add,
+	PARALLEL = SAFE
+);
+
+CREATE FUNCTION hnswhandler(internal) RETURNS index_am_handler
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE ACCESS METHOD hnsw TYPE INDEX HANDLER hnswhandler;
+
+COMMENT ON ACCESS METHOD hnsw IS 'hnsw index access method';
+
+CREATE OPERATOR CLASS vector_l2_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <-> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_l2_squared_distance(vector, vector);
+
+CREATE OPERATOR CLASS vector_ip_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <#> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_negative_inner_product(vector, vector);
+
+CREATE OPERATOR CLASS vector_cosine_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_negative_inner_product(vector, vector),
+	FUNCTION 2 vector_norm(vector);

sql/vector.sql

@@ -40,18 +40,27 @@ CREATE FUNCTION inner_product(vector, vector) RETURNS float8
 CREATE FUNCTION cosine_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION l1_distance(vector, vector) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE FUNCTION vector_dims(vector) RETURNS integer
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION vector_norm(vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION normalize_l2(vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE FUNCTION vector_add(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION vector_sub(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 -- private functions
 
 CREATE FUNCTION vector_lt(vector, vector) RETURNS bool
@@ -104,6 +113,13 @@ CREATE AGGREGATE avg(vector) (
 	PARALLEL = SAFE
 );
 
+CREATE AGGREGATE sum(vector) (
+	SFUNC = vector_add,
+	STYPE = vector,
+	COMBINEFUNC = vector_add,
+	PARALLEL = SAFE
+);
+
 -- cast functions
 
 CREATE FUNCTION vector(vector, integer, boolean) RETURNS vector
@@ -171,6 +187,11 @@ CREATE OPERATOR - (
 	COMMUTATOR = -
 );
 
+CREATE OPERATOR * (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_mul,
+	COMMUTATOR = *
+);
+
 CREATE OPERATOR < (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_lt,
 	COMMUTATOR = > , NEGATOR = >= ,
@@ -209,7 +230,7 @@ CREATE OPERATOR > (
 	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
 );
 
--- access method
+-- access methods
 
 CREATE FUNCTION ivfflathandler(internal) RETURNS index_am_handler
 	AS 'MODULE_PATHNAME' LANGUAGE C;
@@ -218,6 +239,13 @@ CREATE ACCESS METHOD ivfflat TYPE INDEX HANDLER ivfflathandler;
 
 COMMENT ON ACCESS METHOD ivfflat IS 'ivfflat index access method';
 
+CREATE FUNCTION hnswhandler(internal) RETURNS index_am_handler
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE ACCESS METHOD hnsw TYPE INDEX HANDLER hnswhandler;
+
+COMMENT ON ACCESS METHOD hnsw IS 'hnsw index access method';
+
 -- opclasses
 
 CREATE OPERATOR CLASS vector_ops
@@ -240,12 +268,28 @@ CREATE OPERATOR CLASS vector_ip_ops
 	OPERATOR 1 <#> (vector, vector) FOR ORDER BY float_ops,
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
 	FUNCTION 3 vector_spherical_distance(vector, vector),
-	FUNCTION 4 vector_norm(vector);
+	FUNCTION 6 normalize_l2(vector);
 
 CREATE OPERATOR CLASS vector_cosine_ops
 	FOR TYPE vector USING ivfflat AS
 	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
-	FUNCTION 2 vector_norm(vector),
 	FUNCTION 3 vector_spherical_distance(vector, vector),
-	FUNCTION 4 vector_norm(vector);
+	FUNCTION 5 normalize_l2(vector),
+	FUNCTION 6 normalize_l2(vector);
+
+CREATE OPERATOR CLASS vector_l2_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <-> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_l2_squared_distance(vector, vector);
+
+CREATE OPERATOR CLASS vector_ip_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <#> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_negative_inner_product(vector, vector);
+
+CREATE OPERATOR CLASS vector_cosine_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_negative_inner_product(vector, vector),
+	FUNCTION 3 normalize_l2(vector);

src/hnsw.c

@@ -0,0 +1,224 @@
+#include "postgres.h"
+
+#include <float.h>
+#include <math.h>
+
+#include "access/amapi.h"
+#include "commands/vacuum.h"
+#include "hnsw.h"
+#include "utils/guc.h"
+#include "utils/selfuncs.h"
+
+#if PG_VERSION_NUM >= 120000
+#include "commands/progress.h"
+#endif
+
+int			hnsw_ef_search;
+static relopt_kind hnsw_relopt_kind;
+
+/*
+ * Initialize index options and variables
+ */
+void
+HnswInit(void)
+{
+	hnsw_relopt_kind = add_reloption_kind();
+	add_int_reloption(hnsw_relopt_kind, "m", "Max number of connections",
+					  HNSW_DEFAULT_M, HNSW_MIN_M, HNSW_MAX_M
+#if PG_VERSION_NUM >= 130000
+					  ,AccessExclusiveLock
+#endif
+		);
+	add_int_reloption(hnsw_relopt_kind, "ef_construction", "Size of the dynamic candidate list for construction",
+					  HNSW_DEFAULT_EF_CONSTRUCTION, HNSW_MIN_EF_CONSTRUCTION, HNSW_MAX_EF_CONSTRUCTION
+#if PG_VERSION_NUM >= 130000
+					  ,AccessExclusiveLock
+#endif
+		);
+
+	DefineCustomIntVariable("hnsw.ef_search", "Sets the size of the dynamic candidate list for search",
+							"Valid range is 10..1000.", &hnsw_ef_search,
+							HNSW_DEFAULT_EF_SEARCH, HNSW_MIN_EF_SEARCH, HNSW_MAX_EF_SEARCH, PGC_USERSET, 0, NULL, NULL, NULL);
+}
+
+/*
+ * Get the name of index build phase
+ */
+#if PG_VERSION_NUM >= 120000
+static char *
+hnswbuildphasename(int64 phasenum)
+{
+	switch (phasenum)
+	{
+		case PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE:
+			return "initializing";
+		case PROGRESS_HNSW_PHASE_LOAD:
+			return "loading tuples";
+		default:
+			return NULL;
+	}
+}
+#endif
+
+/*
+ * Estimate the cost of an index scan
+ */
+static void
+hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
+				 Cost *indexStartupCost, Cost *indexTotalCost,
+				 Selectivity *indexSelectivity, double *indexCorrelation,
+				 double *indexPages)
+{
+	GenericCosts costs;
+	int			m;
+	int			entryLevel;
+	Relation	index;
+#if PG_VERSION_NUM < 120000
+	List	   *qinfos;
+#endif
+
+	/* Never use index without order */
+	if (path->indexorderbys == NULL)
+	{
+		*indexStartupCost = DBL_MAX;
+		*indexTotalCost = DBL_MAX;
+		*indexSelectivity = 0;
+		*indexCorrelation = 0;
+		*indexPages = 0;
+		return;
+	}
+
+	MemSet(&costs, 0, sizeof(costs));
+
+	index = index_open(path->indexinfo->indexoid, NoLock);
+	m = HnswGetM(index);
+	index_close(index, NoLock);
+
+	/* Approximate entry level */
+	entryLevel = (int) -log(1.0 / path->indexinfo->tuples) * HnswGetMl(m);
+
+	/* 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;
+
+#if PG_VERSION_NUM >= 120000
+	genericcostestimate(root, path, loop_count, &costs);
+#else
+	qinfos = deconstruct_indexquals(path);
+	genericcostestimate(root, path, loop_count, qinfos, &costs);
+#endif
+
+	/* Use total cost since most work happens before first tuple is returned */
+	*indexStartupCost = costs.indexTotalCost;
+	*indexTotalCost = costs.indexTotalCost;
+	*indexSelectivity = costs.indexSelectivity;
+	*indexCorrelation = costs.indexCorrelation;
+	*indexPages = costs.numIndexPages;
+}
+
+/*
+ * Parse and validate the reloptions
+ */
+static bytea *
+hnswoptions(Datum reloptions, bool validate)
+{
+	static const relopt_parse_elt tab[] = {
+		{"m", RELOPT_TYPE_INT, offsetof(HnswOptions, m)},
+		{"ef_construction", RELOPT_TYPE_INT, offsetof(HnswOptions, efConstruction)},
+	};
+
+#if PG_VERSION_NUM >= 130000
+	return (bytea *) build_reloptions(reloptions, validate,
+									  hnsw_relopt_kind,
+									  sizeof(HnswOptions),
+									  tab, lengthof(tab));
+#else
+	relopt_value *options;
+	int			numoptions;
+	HnswOptions *rdopts;
+
+	options = parseRelOptions(reloptions, validate, hnsw_relopt_kind, &numoptions);
+	rdopts = allocateReloptStruct(sizeof(HnswOptions), options, numoptions);
+	fillRelOptions((void *) rdopts, sizeof(HnswOptions), options, numoptions,
+				   validate, tab, lengthof(tab));
+
+	return (bytea *) rdopts;
+#endif
+}
+
+/*
+ * Validate catalog entries for the specified operator class
+ */
+static bool
+hnswvalidate(Oid opclassoid)
+{
+	return true;
+}
+
+/*
+ * Define index handler
+ *
+ * See https://www.postgresql.org/docs/current/index-api.html
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(hnswhandler);
+Datum
+hnswhandler(PG_FUNCTION_ARGS)
+{
+	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);
+
+	amroutine->amstrategies = 0;
+	amroutine->amsupport = 3;
+#if PG_VERSION_NUM >= 130000
+	amroutine->amoptsprocnum = 0;
+#endif
+	amroutine->amcanorder = false;
+	amroutine->amcanorderbyop = true;
+	amroutine->amcanbackward = false;	/* can change direction mid-scan */
+	amroutine->amcanunique = false;
+	amroutine->amcanmulticol = false;
+	amroutine->amoptionalkey = true;
+	amroutine->amsearcharray = false;
+	amroutine->amsearchnulls = false;
+	amroutine->amstorage = false;
+	amroutine->amclusterable = false;
+	amroutine->ampredlocks = false;
+	amroutine->amcanparallel = false;
+	amroutine->amcaninclude = false;
+#if PG_VERSION_NUM >= 130000
+	amroutine->amusemaintenanceworkmem = false; /* not used during VACUUM */
+	amroutine->amparallelvacuumoptions = VACUUM_OPTION_PARALLEL_BULKDEL;
+#endif
+	amroutine->amkeytype = InvalidOid;
+
+	/* Interface functions */
+	amroutine->ambuild = hnswbuild;
+	amroutine->ambuildempty = hnswbuildempty;
+	amroutine->aminsert = hnswinsert;
+	amroutine->ambulkdelete = hnswbulkdelete;
+	amroutine->amvacuumcleanup = hnswvacuumcleanup;
+	amroutine->amcanreturn = NULL;	/* tuple not included in heapsort */
+	amroutine->amcostestimate = hnswcostestimate;
+	amroutine->amoptions = hnswoptions;
+	amroutine->amproperty = NULL;	/* TODO AMPROP_DISTANCE_ORDERABLE */
+#if PG_VERSION_NUM >= 120000
+	amroutine->ambuildphasename = hnswbuildphasename;
+#endif
+	amroutine->amvalidate = hnswvalidate;
+#if PG_VERSION_NUM >= 140000
+	amroutine->amadjustmembers = NULL;
+#endif
+	amroutine->ambeginscan = hnswbeginscan;
+	amroutine->amrescan = hnswrescan;
+	amroutine->amgettuple = hnswgettuple;
+	amroutine->amgetbitmap = NULL;
+	amroutine->amendscan = hnswendscan;
+	amroutine->ammarkpos = NULL;
+	amroutine->amrestrpos = NULL;
+
+	/* Interface functions to support parallel index scans */
+	amroutine->amestimateparallelscan = NULL;
+	amroutine->aminitparallelscan = NULL;
+	amroutine->amparallelrescan = NULL;
+
+	PG_RETURN_POINTER(amroutine);
+}

src/hnsw.h

@@ -0,0 +1,297 @@
+#ifndef HNSW_H
+#define HNSW_H
+
+#include "postgres.h"
+
+#include "access/generic_xlog.h"
+#include "access/reloptions.h"
+#include "nodes/execnodes.h"
+#include "port.h"				/* for random() */
+#include "utils/sampling.h"
+#include "vector.h"
+
+#if PG_VERSION_NUM < 110000
+#error "Requires PostgreSQL 11+"
+#endif
+
+#define HNSW_MAX_DIM 2000
+
+/* Support functions */
+#define HNSW_DISTANCE_PROC 1
+#define HNSW_NORM_PROC 2
+#define HNSW_NORMALIZE_PROC 3
+
+#define HNSW_VERSION	1
+#define HNSW_MAGIC_NUMBER 0xA953A953
+#define HNSW_PAGE_ID	0xFF85
+
+/* Preserved page numbers */
+#define HNSW_METAPAGE_BLKNO	0
+#define HNSW_HEAD_BLKNO		1	/* first element page */
+
+#define HNSW_DEFAULT_M	16
+#define HNSW_MIN_M	4
+#define HNSW_MAX_M		100
+#define HNSW_DEFAULT_EF_CONSTRUCTION	40
+#define HNSW_MIN_EF_CONSTRUCTION	10
+#define HNSW_MAX_EF_CONSTRUCTION		1000
+#define HNSW_DEFAULT_EF_SEARCH	40
+#define HNSW_MIN_EF_SEARCH		10
+#define HNSW_MAX_EF_SEARCH		1000
+
+#define HNSW_ELEMENT_TUPLE_TYPE  1
+#define HNSW_NEIGHBOR_TUPLE_TYPE 2
+
+/* Make graph robust against non-HOT updates */
+#define HNSW_HEAPTIDS 10
+
+/* Build phases */
+/* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
+#define PROGRESS_HNSW_PHASE_LOAD		2
+
+#define HNSW_ELEMENT_TUPLE_SIZE(_dim)	MAXALIGN(offsetof(HnswElementTupleData, vec) + VECTOR_SIZE(_dim))
+#define HNSW_NEIGHBOR_TUPLE_SIZE(level, m)	MAXALIGN(offsetof(HnswNeighborTupleData, indextids) + ((level) + 2) * (m) * sizeof(ItemPointerData))
+
+#define HnswPageGetOpaque(page)	((HnswPageOpaque) PageGetSpecialPointer(page))
+#define HnswPageGetMeta(page)	((HnswMetaPageData *) PageGetContents(page))
+
+#if PG_VERSION_NUM >= 150000
+#define RandomDouble() pg_prng_double(&pg_global_prng_state)
+#else
+#define RandomDouble() (((double) random()) / MAX_RANDOM_VALUE)
+#endif
+
+#if PG_VERSION_NUM < 130000
+#define list_delete_last(list) list_truncate(list, list_length(list) - 1)
+#define list_sort(list, cmp) list_qsort(list, cmp)
+#endif
+
+#define HnswIsElementTuple(tup) ((tup)->type == HNSW_ELEMENT_TUPLE_TYPE)
+#define HnswIsNeighborTuple(tup) ((tup)->type == HNSW_NEIGHBOR_TUPLE_TYPE)
+
+#define HnswGetLayerM(m, layer) (layer == 0 ? m * 2 : m)
+#define HnswGetMl(m) (1 / log(m))
+
+/* Ensure fits in uint8 */
+#define HnswGetMaxLevel(m) Min(((BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - offsetof(HnswNeighborTupleData, indextids) - sizeof(ItemIdData)) / (sizeof(ItemPointerData)) / m) - 2, 255)
+
+/* Variables */
+extern int	hnsw_ef_search;
+
+typedef struct HnswNeighborArray HnswNeighborArray;
+
+typedef struct HnswElementData
+{
+	List	   *heaptids;
+	uint8		level;
+	uint8		deleted;
+	HnswNeighborArray *neighbors;
+	BlockNumber blkno;
+	OffsetNumber offno;
+	OffsetNumber neighborOffno;
+	BlockNumber neighborPage;
+	Vector	   *vec;
+}			HnswElementData;
+
+typedef HnswElementData * HnswElement;
+
+typedef struct HnswCandidate
+{
+	HnswElement element;
+	float		distance;
+}			HnswCandidate;
+
+typedef struct HnswNeighborArray
+{
+	int			length;
+	HnswCandidate *items;
+}			HnswNeighborArray;
+
+typedef struct HnswUpdate
+{
+	HnswCandidate hc;
+	int			level;
+	int			index;
+}			HnswUpdate;
+
+typedef struct HnswPairingHeapNode
+{
+	pairingheap_node ph_node;
+	HnswCandidate *inner;
+}			HnswPairingHeapNode;
+
+/* HNSW index options */
+typedef struct HnswOptions
+{
+	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int			m;				/* number of connections */
+	int			efConstruction; /* size of dynamic candidate list */
+}			HnswOptions;
+
+typedef struct HnswBuildState
+{
+	/* Info */
+	Relation	heap;
+	Relation	index;
+	IndexInfo  *indexInfo;
+	ForkNumber	forkNum;
+
+	/* Settings */
+	int			dimensions;
+	int			m;
+	int			efConstruction;
+
+	/* Statistics */
+	double		indtuples;
+	double		reltuples;
+
+	/* Support functions */
+	FmgrInfo   *procinfo;
+	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
+	Oid			collation;
+
+	/* Variables */
+	List	   *elements;
+	HnswElement entryPoint;
+	double		ml;
+	int			maxLevel;
+	double		maxInMemoryElements;
+	bool		flushed;
+	Vector	   *normvec;
+
+	/* Memory */
+	MemoryContext tmpCtx;
+}			HnswBuildState;
+
+typedef struct HnswMetaPageData
+{
+	uint32		magicNumber;
+	uint32		version;
+	uint32		dimensions;
+	uint16		m;
+	uint16		efConstruction;
+	BlockNumber entryBlkno;
+	OffsetNumber entryOffno;
+	int16		entryLevel;
+	BlockNumber insertPage;
+}			HnswMetaPageData;
+
+typedef HnswMetaPageData * HnswMetaPage;
+
+typedef struct HnswPageOpaqueData
+{
+	BlockNumber nextblkno;
+	uint16		unused;
+	uint16		page_id;		/* for identification of HNSW indexes */
+}			HnswPageOpaqueData;
+
+typedef HnswPageOpaqueData * HnswPageOpaque;
+
+typedef struct HnswElementTupleData
+{
+	uint8		type;
+	uint8		level;
+	uint8		deleted;
+	uint8		unused;
+	ItemPointerData heaptids[HNSW_HEAPTIDS];
+	ItemPointerData neighbortid;
+	uint16		unused2;
+	Vector		vec;
+}			HnswElementTupleData;
+
+typedef HnswElementTupleData * HnswElementTuple;
+
+typedef struct HnswNeighborTupleData
+{
+	uint8		type;
+	uint8		unused;
+	uint16		count;
+	ItemPointerData indextids[FLEXIBLE_ARRAY_MEMBER];
+}			HnswNeighborTupleData;
+
+typedef HnswNeighborTupleData * HnswNeighborTuple;
+
+typedef struct HnswScanOpaqueData
+{
+	bool		first;
+	Buffer		buf;
+	List	   *w;
+	MemoryContext tmpCtx;
+
+	/* Support functions */
+	FmgrInfo   *procinfo;
+	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
+	Oid			collation;
+}			HnswScanOpaqueData;
+
+typedef HnswScanOpaqueData * HnswScanOpaque;
+
+typedef struct HnswVacuumState
+{
+	/* Info */
+	Relation	index;
+	IndexBulkDeleteResult *stats;
+	IndexBulkDeleteCallback callback;
+	void	   *callback_state;
+
+	/* Settings */
+	int			m;
+	int			efConstruction;
+
+	/* Support functions */
+	FmgrInfo   *procinfo;
+	Oid			collation;
+
+	/* Variables */
+	HTAB	   *deleted;
+	BufferAccessStrategy bas;
+	HnswNeighborTuple ntup;
+	HnswElementData highestPoint;
+
+	/* Memory */
+	MemoryContext tmpCtx;
+}			HnswVacuumState;
+
+/* Methods */
+int			HnswGetM(Relation index);
+int			HnswGetEfConstruction(Relation index);
+FmgrInfo   *HnswOptionalProcInfo(Relation rel, uint16 procnum);
+void		HnswNormValue(FmgrInfo *procinfo, FmgrInfo *normalizeprocinfo, Oid collation, Datum *value, Vector * result);
+void		HnswCommitBuffer(Buffer buf, GenericXLogState *state);
+Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
+void		HnswInitPage(Buffer buf, Page page);
+void		HnswInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state);
+void		HnswInit(void);
+List	   *HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, bool inserting, BlockNumber *skipPage, OffsetNumber *skipOffno);
+HnswElement HnswGetEntryPoint(Relation index);
+HnswElement HnswInitElement(ItemPointer tid, int m, double ml, int maxLevel);
+void		HnswFreeElement(HnswElement element);
+HnswElement HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, List **updates, bool vacuuming);
+HnswCandidate *HnswEntryCandidate(HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadvec);
+void		HnswUpdateMetaPage(Relation index, bool updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum);
+void		HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m);
+void		HnswAddHeapTid(HnswElement element, ItemPointer heaptid);
+void		HnswInitNeighbors(HnswElement element, int m);
+bool		HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel);
+void		HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec);
+void		HnswSetElementTuple(HnswElementTuple etup, HnswElement element);
+
+/* Index access methods */
+IndexBuildResult *hnswbuild(Relation heap, Relation index, IndexInfo *indexInfo);
+void		hnswbuildempty(Relation index);
+bool		hnswinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heap, IndexUniqueCheck checkUnique
+#if PG_VERSION_NUM >= 140000
+					   ,bool indexUnchanged
+#endif
+					   ,IndexInfo *indexInfo
+);
+IndexBulkDeleteResult *hnswbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats, IndexBulkDeleteCallback callback, void *callback_state);
+IndexBulkDeleteResult *hnswvacuumcleanup(IndexVacuumInfo *info, IndexBulkDeleteResult *stats);
+IndexScanDesc hnswbeginscan(Relation index, int nkeys, int norderbys);
+void		hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int norderbys);
+bool		hnswgettuple(IndexScanDesc scan, ScanDirection dir);
+void		hnswendscan(IndexScanDesc scan);
+
+#endif

src/hnswbuild.c

@@ -0,0 +1,503 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "catalog/index.h"
+#include "hnsw.h"
+#include "miscadmin.h"
+#include "lib/pairingheap.h"
+#include "nodes/pg_list.h"
+#include "storage/bufmgr.h"
+#include "utils/memutils.h"
+
+#if PG_VERSION_NUM >= 140000
+#include "utils/backend_progress.h"
+#elif PG_VERSION_NUM >= 120000
+#include "pgstat.h"
+#endif
+
+#if PG_VERSION_NUM >= 120000
+#include "access/tableam.h"
+#include "commands/progress.h"
+#else
+#define PROGRESS_CREATEIDX_TUPLES_DONE 0
+#endif
+
+#if PG_VERSION_NUM >= 130000
+#define CALLBACK_ITEM_POINTER ItemPointer tid
+#else
+#define CALLBACK_ITEM_POINTER HeapTuple hup
+#endif
+
+#if PG_VERSION_NUM >= 120000
+#define UpdateProgress(index, val) pgstat_progress_update_param(index, val)
+#else
+#define UpdateProgress(index, val) ((void)val)
+#endif
+
+/*
+ * Create the metapage
+ */
+static void
+CreateMetaPage(HnswBuildState * buildstate)
+{
+	Relation	index = buildstate->index;
+	ForkNumber	forkNum = buildstate->forkNum;
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	HnswMetaPage metap;
+
+	buf = HnswNewBuffer(index, forkNum);
+	HnswInitRegisterPage(index, &buf, &page, &state);
+
+	/* Set metapage data */
+	metap = HnswPageGetMeta(page);
+	metap->magicNumber = HNSW_MAGIC_NUMBER;
+	metap->version = HNSW_VERSION;
+	metap->dimensions = buildstate->dimensions;
+	metap->m = buildstate->m;
+	metap->efConstruction = buildstate->efConstruction;
+	metap->entryBlkno = InvalidBlockNumber;
+	metap->entryOffno = InvalidOffsetNumber;
+	metap->insertPage = InvalidBlockNumber;
+	((PageHeader) page)->pd_lower =
+		((char *) metap + sizeof(HnswMetaPageData)) - (char *) page;
+
+	HnswCommitBuffer(buf, state);
+}
+
+/*
+ * Add a new page
+ */
+static void
+HnswBuildAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state, ForkNumber forkNum)
+{
+	/* Add a new page */
+	Buffer		newbuf = HnswNewBuffer(index, forkNum);
+
+	/* Update previous page */
+	HnswPageGetOpaque(*page)->nextblkno = BufferGetBlockNumber(newbuf);
+
+	/* Commit */
+	MarkBufferDirty(*buf);
+	GenericXLogFinish(*state);
+	UnlockReleaseBuffer(*buf);
+
+	/* Can take a while, so ensure we can interrupt */
+	/* Needs to be called when no buffer locks are held */
+	LockBuffer(newbuf, BUFFER_LOCK_UNLOCK);
+	CHECK_FOR_INTERRUPTS();
+	LockBuffer(newbuf, BUFFER_LOCK_EXCLUSIVE);
+
+	/* Prepare new page */
+	*buf = newbuf;
+	*state = GenericXLogStart(index);
+	*page = GenericXLogRegisterBuffer(*state, *buf, GENERIC_XLOG_FULL_IMAGE);
+	HnswInitPage(*buf, *page);
+}
+
+/*
+ * Create element pages
+ */
+static void
+CreateElementPages(HnswBuildState * buildstate)
+{
+	Relation	index = buildstate->index;
+	ForkNumber	forkNum = buildstate->forkNum;
+	int			dimensions = buildstate->dimensions;
+	Size		etupSize;
+	Size		maxSize;
+	HnswElementTuple etup;
+	HnswNeighborTuple ntup;
+	BlockNumber insertPage;
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	ListCell   *lc;
+
+	/* Calculate sizes */
+	maxSize = BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData));
+	etupSize = HNSW_ELEMENT_TUPLE_SIZE(dimensions);
+
+	/* Allocate once */
+	etup = palloc0(etupSize);
+	ntup = palloc0(maxSize);
+
+	/* Prepare first page */
+	buf = HnswNewBuffer(index, forkNum);
+	state = GenericXLogStart(index);
+	page = GenericXLogRegisterBuffer(state, buf, GENERIC_XLOG_FULL_IMAGE);
+	HnswInitPage(buf, page);
+
+	foreach(lc, buildstate->elements)
+	{
+		HnswElement element = lfirst(lc);
+		Size		ntupSize;
+		Size		combinedSize;
+
+		HnswSetElementTuple(etup, element);
+
+		/* Calculate sizes */
+		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(element->level, buildstate->m);
+		combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
+
+		/* Keep element and neighbors on the same page if possible */
+		if (PageGetFreeSpace(page) < etupSize || (combinedSize <= maxSize && PageGetFreeSpace(page) < combinedSize))
+			HnswBuildAppendPage(index, &buf, &page, &state, forkNum);
+
+		/* Calculate offsets */
+		element->blkno = BufferGetBlockNumber(buf);
+		element->offno = OffsetNumberNext(PageGetMaxOffsetNumber(page));
+		if (combinedSize <= maxSize)
+		{
+			element->neighborPage = element->blkno;
+			element->neighborOffno = OffsetNumberNext(element->offno);
+		}
+		else
+		{
+			element->neighborPage = element->blkno + 1;
+			element->neighborOffno = FirstOffsetNumber;
+		}
+
+		ItemPointerSet(&etup->neighbortid, element->neighborPage, element->neighborOffno);
+
+		/* Add element */
+		if (PageAddItem(page, (Item) etup, etupSize, InvalidOffsetNumber, false, false) != element->offno)
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+		/* Add new page if needed */
+		if (PageGetFreeSpace(page) < ntupSize)
+			HnswBuildAppendPage(index, &buf, &page, &state, forkNum);
+
+		/* Add placeholder for neighbors */
+		if (PageAddItem(page, (Item) ntup, ntupSize, InvalidOffsetNumber, false, false) != element->neighborOffno)
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+	}
+
+	insertPage = BufferGetBlockNumber(buf);
+
+	/* Commit */
+	MarkBufferDirty(buf);
+	GenericXLogFinish(state);
+	UnlockReleaseBuffer(buf);
+
+	HnswUpdateMetaPage(index, true, buildstate->entryPoint, insertPage, forkNum);
+
+	pfree(etup);
+	pfree(ntup);
+}
+
+/*
+ * Create neighbor pages
+ */
+static void
+CreateNeighborPages(HnswBuildState * buildstate)
+{
+	Relation	index = buildstate->index;
+	ForkNumber	forkNum = buildstate->forkNum;
+	int			m = buildstate->m;
+	ListCell   *lc;
+	HnswNeighborTuple ntup;
+
+	/* Allocate once */
+	ntup = palloc0(BLCKSZ);
+
+	foreach(lc, buildstate->elements)
+	{
+		HnswElement e = lfirst(lc);
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		Size		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(e->level, m);
+
+		/* Can take a while, so ensure we can interrupt */
+		/* Needs to be called when no buffer locks are held */
+		CHECK_FOR_INTERRUPTS();
+
+		buf = ReadBufferExtended(index, forkNum, e->neighborPage, RBM_NORMAL, NULL);
+		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+
+		HnswSetNeighborTuple(ntup, e, m);
+
+		if (!PageIndexTupleOverwrite(page, e->neighborOffno, (Item) ntup, ntupSize))
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+		/* Commit */
+		MarkBufferDirty(buf);
+		GenericXLogFinish(state);
+		UnlockReleaseBuffer(buf);
+	}
+
+	pfree(ntup);
+}
+
+/*
+ * Free elements
+ */
+static void
+FreeElements(HnswBuildState * buildstate)
+{
+	ListCell   *lc;
+
+	foreach(lc, buildstate->elements)
+		HnswFreeElement(lfirst(lc));
+
+	list_free(buildstate->elements);
+}
+
+/*
+ * Flush pages
+ */
+static void
+FlushPages(HnswBuildState * buildstate)
+{
+	CreateMetaPage(buildstate);
+	CreateElementPages(buildstate);
+	CreateNeighborPages(buildstate);
+
+	buildstate->flushed = true;
+	FreeElements(buildstate);
+}
+
+/*
+ * Insert tuple
+ */
+static bool
+InsertTuple(Relation index, Datum *values, HnswElement element, HnswBuildState * buildstate, HnswElement * dup)
+{
+	FmgrInfo   *procinfo = buildstate->procinfo;
+	Oid			collation = buildstate->collation;
+	HnswElement entryPoint = buildstate->entryPoint;
+	int			efConstruction = buildstate->efConstruction;
+	int			m = buildstate->m;
+
+	/* Detoast once for all calls */
+	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+
+	/* Normalize if needed */
+	HnswNormValue(buildstate->normprocinfo, buildstate->normalizeprocinfo, collation, &value, buildstate->normvec);
+
+	/* Copy value to element so accessible outside of memory context */
+	memcpy(element->vec, DatumGetVector(value), VECTOR_SIZE(buildstate->dimensions));
+
+	/* Insert element in graph */
+	*dup = HnswInsertElement(element, entryPoint, NULL, procinfo, collation, m, efConstruction, NULL, false);
+
+	/* Update entry point if needed */
+	if (*dup == NULL && (entryPoint == NULL || element->level > entryPoint->level))
+		buildstate->entryPoint = element;
+
+	UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++buildstate->indtuples);
+
+	return *dup == NULL;
+}
+
+/*
+ * Callback for table_index_build_scan
+ */
+static void
+BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
+			  bool *isnull, bool tupleIsAlive, void *state)
+{
+	HnswBuildState *buildstate = (HnswBuildState *) state;
+	MemoryContext oldCtx;
+	HnswElement element;
+	HnswElement dup = NULL;
+	bool		inserted;
+
+#if PG_VERSION_NUM < 130000
+	ItemPointer tid = &hup->t_self;
+#endif
+
+	/* Skip nulls */
+	if (isnull[0])
+		return;
+
+	if (buildstate->indtuples >= buildstate->maxInMemoryElements)
+	{
+		if (!buildstate->flushed)
+		{
+			ereport(NOTICE,
+					(errmsg("hnsw graph no longer fits into maintenance_work_mem after " INT64_FORMAT " tuples", (int64) buildstate->indtuples),
+					 errdetail("Building will take significantly more time."),
+					 errhint("Increase maintenance_work_mem to speed up builds.")));
+
+			FlushPages(buildstate);
+		}
+
+		oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
+
+		if (HnswInsertTuple(buildstate->index, values, isnull, tid, buildstate->heap))
+			UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++buildstate->indtuples);
+
+		/* Reset memory context */
+		MemoryContextSwitchTo(oldCtx);
+		MemoryContextReset(buildstate->tmpCtx);
+
+		return;
+	}
+
+	/* Allocate necessary memory outside of memory context */
+	element = HnswInitElement(tid, buildstate->m, buildstate->ml, buildstate->maxLevel);
+	element->vec = palloc(VECTOR_SIZE(buildstate->dimensions));
+
+	/* Use memory context since detoast can allocate */
+	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
+
+	/* Insert tuple */
+	inserted = InsertTuple(index, values, element, buildstate, &dup);
+
+	/* Reset memory context */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextReset(buildstate->tmpCtx);
+
+	/* Add outside memory context */
+	if (dup != NULL)
+		HnswAddHeapTid(dup, tid);
+
+	/* Add to buildstate or free */
+	if (inserted)
+		buildstate->elements = lappend(buildstate->elements, element);
+	else
+		HnswFreeElement(element);
+}
+
+/*
+ * Get the max number of elements that fit into maintenance_work_mem
+ */
+static double
+HnswGetMaxInMemoryElements(int m, double ml, int dimensions)
+{
+	Size		elementSize = sizeof(HnswElementData);
+	double		avgLevel = -log(0.5) * ml;
+
+	elementSize += sizeof(HnswNeighborArray) * (avgLevel + 1);
+	elementSize += sizeof(HnswCandidate) * (m * (avgLevel + 2));
+	elementSize += sizeof(ItemPointerData);
+	elementSize += VECTOR_SIZE(dimensions);
+	return (maintenance_work_mem * 1024L) / elementSize;
+}
+
+/*
+ * Initialize the build state
+ */
+static void
+InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, IndexInfo *indexInfo, ForkNumber forkNum)
+{
+	buildstate->heap = heap;
+	buildstate->index = index;
+	buildstate->indexInfo = indexInfo;
+	buildstate->forkNum = forkNum;
+
+	buildstate->m = HnswGetM(index);
+	buildstate->efConstruction = HnswGetEfConstruction(index);
+	buildstate->dimensions = TupleDescAttr(index->rd_att, 0)->atttypmod;
+
+	/* Require column to have dimensions to be indexed */
+	if (buildstate->dimensions < 0)
+		elog(ERROR, "column does not have dimensions");
+
+	if (buildstate->dimensions > HNSW_MAX_DIM)
+		elog(ERROR, "column cannot have more than %d dimensions for hnsw index", HNSW_MAX_DIM);
+
+	buildstate->reltuples = 0;
+	buildstate->indtuples = 0;
+
+	/* Get support functions */
+	buildstate->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
+	buildstate->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	buildstate->normalizeprocinfo = HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC);
+	buildstate->collation = index->rd_indcollation[0];
+
+	buildstate->elements = NIL;
+	buildstate->entryPoint = NULL;
+	buildstate->ml = HnswGetMl(buildstate->m);
+	buildstate->maxLevel = HnswGetMaxLevel(buildstate->m);
+	buildstate->maxInMemoryElements = HnswGetMaxInMemoryElements(buildstate->m, buildstate->ml, buildstate->dimensions);
+	buildstate->flushed = false;
+
+	/* Reuse for each tuple */
+	buildstate->normvec = InitVector(buildstate->dimensions);
+
+	buildstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+											   "Hnsw build temporary context",
+											   ALLOCSET_DEFAULT_SIZES);
+}
+
+/*
+ * Free resources
+ */
+static void
+FreeBuildState(HnswBuildState * buildstate)
+{
+	pfree(buildstate->normvec);
+	MemoryContextDelete(buildstate->tmpCtx);
+}
+
+/*
+ * Build graph
+ */
+static void
+BuildGraph(HnswBuildState * buildstate, ForkNumber forkNum)
+{
+	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_HNSW_PHASE_LOAD);
+
+#if PG_VERSION_NUM >= 120000
+	buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+												   true, true, BuildCallback, (void *) buildstate, NULL);
+#else
+	buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+											   true, BuildCallback, (void *) buildstate, NULL);
+#endif
+}
+
+/*
+ * Build the index
+ */
+static void
+BuildIndex(Relation heap, Relation index, IndexInfo *indexInfo,
+		   HnswBuildState * buildstate, ForkNumber forkNum)
+{
+	InitBuildState(buildstate, heap, index, indexInfo, forkNum);
+
+	if (buildstate->heap != NULL)
+		BuildGraph(buildstate, forkNum);
+
+	if (!buildstate->flushed)
+		FlushPages(buildstate);
+
+	FreeBuildState(buildstate);
+}
+
+/*
+ * Build the index for a logged table
+ */
+IndexBuildResult *
+hnswbuild(Relation heap, Relation index, IndexInfo *indexInfo)
+{
+	IndexBuildResult *result;
+	HnswBuildState buildstate;
+
+	BuildIndex(heap, index, indexInfo, &buildstate, MAIN_FORKNUM);
+
+	result = (IndexBuildResult *) palloc(sizeof(IndexBuildResult));
+	result->heap_tuples = buildstate.reltuples;
+	result->index_tuples = buildstate.indtuples;
+
+	return result;
+}
+
+/*
+ * Build the index for an unlogged table
+ */
+void
+hnswbuildempty(Relation index)
+{
+	IndexInfo  *indexInfo = BuildIndexInfo(index);
+	HnswBuildState buildstate;
+
+	BuildIndex(NULL, index, indexInfo, &buildstate, INIT_FORKNUM);
+}

src/hnswinsert.c

@@ -0,0 +1,488 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "hnsw.h"
+#include "storage/bufmgr.h"
+#include "storage/lmgr.h"
+#include "utils/memutils.h"
+
+/*
+ * Get the insert page
+ */
+static BlockNumber
+GetInsertPage(Relation index)
+{
+	Buffer		buf;
+	Page		page;
+	HnswMetaPage metap;
+	BlockNumber insertPage;
+
+	buf = ReadBuffer(index, HNSW_METAPAGE_BLKNO);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	metap = HnswPageGetMeta(page);
+
+	insertPage = metap->insertPage;
+
+	UnlockReleaseBuffer(buf);
+
+	return insertPage;
+}
+
+/*
+ * Check for a free offset
+ */
+static bool
+HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *firstFreePage)
+{
+	OffsetNumber offno;
+	OffsetNumber maxoffno = PageGetMaxOffsetNumber(page);
+
+	for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+	{
+		HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+
+		/* Skip neighbor tuples */
+		if (!HnswIsElementTuple(etup))
+			continue;
+
+		if (etup->deleted)
+		{
+			BlockNumber neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
+			OffsetNumber neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
+			ItemId		itemid;
+
+			if (!BlockNumberIsValid(*firstFreePage))
+				*firstFreePage = neighborPage;
+
+			if (neighborPage == BufferGetBlockNumber(buf))
+			{
+				*nbuf = buf;
+				*npage = page;
+			}
+			else
+			{
+				*nbuf = ReadBuffer(index, neighborPage);
+				LockBuffer(*nbuf, BUFFER_LOCK_EXCLUSIVE);
+
+				/* Skip WAL for now */
+				*npage = BufferGetPage(*nbuf);
+			}
+
+			itemid = PageGetItemId(*npage, neighborOffno);
+
+			/* Check for space on neighbor tuple page */
+			if (PageGetFreeSpace(*npage) + ItemIdGetLength(itemid) - sizeof(ItemIdData) >= ntupSize)
+			{
+				*freeOffno = offno;
+				*freeNeighborOffno = neighborOffno;
+				return true;
+			}
+			else if (*nbuf != buf)
+				UnlockReleaseBuffer(*nbuf);
+		}
+	}
+
+	return false;
+}
+
+/*
+ * Add a new page
+ */
+static void
+HnswInsertAppendPage(Relation index, Buffer *nbuf, Page *npage, GenericXLogState *state, Page page)
+{
+	/* Add a new page */
+	LockRelationForExtension(index, ExclusiveLock);
+	*nbuf = HnswNewBuffer(index, MAIN_FORKNUM);
+	UnlockRelationForExtension(index, ExclusiveLock);
+
+	/* Init new page */
+	*npage = GenericXLogRegisterBuffer(state, *nbuf, GENERIC_XLOG_FULL_IMAGE);
+	HnswInitPage(*nbuf, *npage);
+
+	/* Update previous buffer */
+	HnswPageGetOpaque(page)->nextblkno = BufferGetBlockNumber(*nbuf);
+}
+
+/*
+ * Add to element and neighbor pages
+ */
+static void
+WriteNewElementPages(Relation index, HnswElement e, int m)
+{
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	Size		etupSize;
+	Size		ntupSize;
+	Size		combinedSize;
+	HnswElementTuple etup;
+	BlockNumber insertPage = GetInsertPage(index);
+	BlockNumber originalInsertPage = insertPage;
+	int			dimensions = e->vec->dim;
+	HnswNeighborTuple ntup;
+	Buffer		nbuf;
+	Page		npage;
+	OffsetNumber freeOffno = InvalidOffsetNumber;
+	OffsetNumber freeNeighborOffno = InvalidOffsetNumber;
+	BlockNumber firstFreePage = InvalidBlockNumber;
+
+	/* Calculate sizes */
+	etupSize = HNSW_ELEMENT_TUPLE_SIZE(dimensions);
+	ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(e->level, m);
+	combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
+
+	/* Prepare element tuple */
+	etup = palloc0(etupSize);
+	HnswSetElementTuple(etup, e);
+
+	/* Prepare neighbor tuple */
+	ntup = palloc0(ntupSize);
+	HnswSetNeighborTuple(ntup, e, m);
+
+	/* Find a page to insert the item */
+	for (;;)
+	{
+		buf = ReadBuffer(index, insertPage);
+		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+
+		/* Space for both */
+		if (PageGetFreeSpace(page) >= combinedSize)
+		{
+			nbuf = buf;
+			npage = page;
+			break;
+		}
+
+		/* Space for element but not neighbors and last page */
+		if (PageGetFreeSpace(page) >= etupSize && !BlockNumberIsValid(HnswPageGetOpaque(page)->nextblkno))
+		{
+			HnswInsertAppendPage(index, &nbuf, &npage, state, page);
+			break;
+		}
+
+		/* Space from deleted item */
+		if (HnswFreeOffset(index, buf, page, e, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &firstFreePage))
+		{
+			if (nbuf != buf)
+				npage = GenericXLogRegisterBuffer(state, nbuf, 0);
+
+			break;
+		}
+
+		insertPage = HnswPageGetOpaque(page)->nextblkno;
+
+		if (BlockNumberIsValid(insertPage))
+		{
+			/* Move to next page */
+			GenericXLogAbort(state);
+			UnlockReleaseBuffer(buf);
+		}
+		else
+		{
+			Buffer		newbuf;
+			Page		newpage;
+
+			HnswInsertAppendPage(index, &newbuf, &newpage, state, page);
+
+			/* Commit */
+			MarkBufferDirty(newbuf);
+			MarkBufferDirty(buf);
+			GenericXLogFinish(state);
+
+			/* Unlock previous buffer */
+			UnlockReleaseBuffer(buf);
+
+			/* Prepare new buffer */
+			state = GenericXLogStart(index);
+			buf = newbuf;
+			page = GenericXLogRegisterBuffer(state, buf, 0);
+
+			/* Create new page for neighbors if needed */
+			if (PageGetFreeSpace(page) < combinedSize)
+				HnswInsertAppendPage(index, &nbuf, &npage, state, page);
+			else
+			{
+				nbuf = buf;
+				npage = page;
+			}
+
+			break;
+		}
+	}
+
+	e->blkno = BufferGetBlockNumber(buf);
+	e->neighborPage = BufferGetBlockNumber(nbuf);
+
+	insertPage = e->neighborPage;
+
+	if (OffsetNumberIsValid(freeOffno))
+	{
+		e->offno = freeOffno;
+		e->neighborOffno = freeNeighborOffno;
+	}
+	else
+	{
+		e->offno = OffsetNumberNext(PageGetMaxOffsetNumber(page));
+		if (nbuf == buf)
+			e->neighborOffno = OffsetNumberNext(e->offno);
+		else
+			e->neighborOffno = FirstOffsetNumber;
+	}
+
+	ItemPointerSet(&etup->neighbortid, e->neighborPage, e->neighborOffno);
+
+	/* Add element and neighbors */
+	if (OffsetNumberIsValid(freeOffno))
+	{
+		if (!PageIndexTupleOverwrite(page, e->offno, (Item) etup, etupSize))
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+		if (!PageIndexTupleOverwrite(npage, e->neighborOffno, (Item) ntup, ntupSize))
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+	}
+	else
+	{
+		if (PageAddItem(page, (Item) etup, etupSize, InvalidOffsetNumber, false, false) != e->offno)
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+		if (PageAddItem(npage, (Item) ntup, ntupSize, InvalidOffsetNumber, false, false) != e->neighborOffno)
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+	}
+
+	/* Commit */
+	MarkBufferDirty(buf);
+	if (nbuf != buf)
+		MarkBufferDirty(nbuf);
+	GenericXLogFinish(state);
+	UnlockReleaseBuffer(buf);
+	if (nbuf != buf)
+		UnlockReleaseBuffer(nbuf);
+
+	/* Update the insert page */
+	if (insertPage != originalInsertPage && (!OffsetNumberIsValid(freeOffno) || firstFreePage == insertPage))
+		HnswUpdateMetaPage(index, false, NULL, insertPage, MAIN_FORKNUM);
+}
+
+/*
+ * Calculate index for update
+ */
+static int
+HnswGetIndex(HnswUpdate * update, int m)
+{
+	return (update->hc.element->level - update->level) * m + update->index;
+}
+
+/*
+ * Update neighbors
+ */
+static void
+UpdateNeighborPages(Relation index, HnswElement e, int m, List *updates)
+{
+	ListCell   *lc;
+
+	/* Could update multiple at once for same element */
+	/* but should only happen a low percent of time, so keep simple for now */
+	foreach(lc, updates)
+	{
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		HnswUpdate *update = lfirst(lc);
+		ItemId		itemid;
+		HnswNeighborTuple ntup;
+		Size		ntupSize;
+		int			idx;
+		OffsetNumber offno = update->hc.element->neighborOffno;
+
+		/* Register page */
+		buf = ReadBuffer(index, update->hc.element->neighborPage);
+		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+
+		/* Get tuple */
+		itemid = PageGetItemId(page, offno);
+		ntup = (HnswNeighborTuple) PageGetItem(page, itemid);
+		ntupSize = ItemIdGetLength(itemid);
+
+		/* Calculate index */
+		idx = HnswGetIndex(update, m);
+
+		/* Make robust to issues */
+		if (idx < ntup->count)
+		{
+			ItemPointer indextid = &ntup->indextids[idx];
+
+			/* Update neighbor */
+			ItemPointerSet(indextid, e->blkno, e->offno);
+
+			/* Overwrite tuple */
+			if (!PageIndexTupleOverwrite(page, offno, (Item) ntup, ntupSize))
+				elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+			/* Commit */
+			MarkBufferDirty(buf);
+			GenericXLogFinish(state);
+		}
+		else
+			GenericXLogAbort(state);
+
+		UnlockReleaseBuffer(buf);
+	}
+}
+
+/*
+ * Add a heap TID to an existing element
+ */
+static bool
+HnswAddDuplicate(Relation index, HnswElement element, HnswElement dup)
+{
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	Size		etupSize = HNSW_ELEMENT_TUPLE_SIZE(dup->vec->dim);
+	HnswElementTuple etup;
+	int			i;
+
+	/* Read page */
+	buf = ReadBuffer(index, dup->blkno);
+	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+	state = GenericXLogStart(index);
+	page = GenericXLogRegisterBuffer(state, buf, 0);
+
+	/* Find space */
+	etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, dup->offno));
+	for (i = 0; i < HNSW_HEAPTIDS; i++)
+	{
+		if (!ItemPointerIsValid(&etup->heaptids[i]))
+			break;
+	}
+
+	/* Either being deleted or we lost our chance to another backend */
+	if (i == 0 || i == HNSW_HEAPTIDS)
+	{
+		GenericXLogAbort(state);
+		UnlockReleaseBuffer(buf);
+		return false;
+	}
+
+	/* Add heap TID */
+	etup->heaptids[i] = *((ItemPointer) linitial(element->heaptids));
+
+	/* Overwrite tuple */
+	if (!PageIndexTupleOverwrite(page, dup->offno, (Item) etup, etupSize))
+		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+	/* Commit */
+	MarkBufferDirty(buf);
+	GenericXLogFinish(state);
+	UnlockReleaseBuffer(buf);
+
+	return true;
+}
+
+/*
+ * Write changes to disk
+ */
+static void
+WriteElement(Relation index, HnswElement element, int m, List *updates, HnswElement dup, HnswElement entryPoint)
+{
+	/* Try to add to existing page */
+	if (dup != NULL)
+	{
+		if (HnswAddDuplicate(index, element, dup))
+			return;
+	}
+
+	/* If fails, take this path */
+	WriteNewElementPages(index, element, m);
+	UpdateNeighborPages(index, element, m, updates);
+
+	/* Update metapage if needed */
+	if (entryPoint == NULL || element->level > entryPoint->level)
+		HnswUpdateMetaPage(index, true, element, InvalidBlockNumber, MAIN_FORKNUM);
+}
+
+/*
+ * Insert a tuple into the index
+ */
+bool
+HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel)
+{
+	Datum		value;
+	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
+	HnswElement entryPoint;
+	HnswElement element;
+	int			m = HnswGetM(index);
+	int			efConstruction = HnswGetEfConstruction(index);
+	double		ml = HnswGetMl(m);
+	FmgrInfo   *procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
+	Oid			collation = index->rd_indcollation[0];
+	List	   *updates = NIL;
+	HnswElement dup;
+
+	/* Detoast once for all calls */
+	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+
+	/* Normalize if needed */
+	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	normalizeprocinfo = HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC);
+	HnswNormValue(normprocinfo, normalizeprocinfo, collation, &value, NULL);
+
+	/* Create an element */
+	element = HnswInitElement(heap_tid, m, ml, HnswGetMaxLevel(m));
+	element->vec = DatumGetVector(value);
+
+	/* Get entry point */
+	entryPoint = HnswGetEntryPoint(index);
+
+	/* Insert element in graph */
+	dup = HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, &updates, false);
+
+	/* Write to disk */
+	WriteElement(index, element, m, updates, dup, entryPoint);
+
+	return true;
+}
+
+/*
+ * Insert a tuple into the index
+ */
+bool
+hnswinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid,
+		   Relation heap, IndexUniqueCheck checkUnique
+#if PG_VERSION_NUM >= 140000
+		   ,bool indexUnchanged
+#endif
+		   ,IndexInfo *indexInfo
+)
+{
+	MemoryContext oldCtx;
+	MemoryContext insertCtx;
+
+	/* Skip nulls */
+	if (isnull[0])
+		return false;
+
+	/* Create memory context */
+	insertCtx = AllocSetContextCreate(CurrentMemoryContext,
+									  "Hnsw insert temporary context",
+									  ALLOCSET_DEFAULT_SIZES);
+	oldCtx = MemoryContextSwitchTo(insertCtx);
+
+	/* Insert tuple */
+	HnswInsertTuple(index, values, isnull, heap_tid, heap);
+
+	/* Delete memory context */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(insertCtx);
+
+	return false;
+}

src/hnswscan.c

@@ -0,0 +1,212 @@
+#include "postgres.h"
+
+#include "access/relscan.h"
+#include "hnsw.h"
+#include "pgstat.h"
+#include "storage/bufmgr.h"
+#include "utils/memutils.h"
+
+/*
+ * Algorithm 5 from paper
+ */
+static void
+GetScanItems(IndexScanDesc scan, Datum q)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	Relation	index = scan->indexRelation;
+	FmgrInfo   *procinfo = so->procinfo;
+	Oid			collation = so->collation;
+	List	   *ep = NIL;
+	List	   *w;
+	HnswElement entryPoint = HnswGetEntryPoint(index);
+
+	if (entryPoint == NULL)
+		return;
+
+	ep = lappend(ep, HnswEntryCandidate(entryPoint, q, index, procinfo, collation, false));
+
+	for (int lc = entryPoint->level; lc >= 1; lc--)
+	{
+		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, false, NULL, NULL);
+		ep = w;
+	}
+
+	so->w = HnswSearchLayer(q, ep, hnsw_ef_search, 0, index, procinfo, collation, false, NULL, NULL);
+}
+
+/*
+ * Get dimensions from metapage
+ */
+static int
+GetDimensions(Relation index)
+{
+	Buffer		buf;
+	Page		page;
+	HnswMetaPage metap;
+	int			dimensions;
+
+	buf = ReadBuffer(index, HNSW_METAPAGE_BLKNO);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	metap = HnswPageGetMeta(page);
+
+	dimensions = metap->dimensions;
+
+	UnlockReleaseBuffer(buf);
+
+	return dimensions;
+}
+
+/*
+ * Prepare for an index scan
+ */
+IndexScanDesc
+hnswbeginscan(Relation index, int nkeys, int norderbys)
+{
+	IndexScanDesc scan;
+	HnswScanOpaque so;
+
+	scan = RelationGetIndexScan(index, nkeys, norderbys);
+
+	so = (HnswScanOpaque) palloc(sizeof(HnswScanOpaqueData));
+	so->buf = InvalidBuffer;
+	so->first = true;
+	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+									   "Hnsw scan temporary context",
+									   ALLOCSET_DEFAULT_SIZES);
+
+	/* Set support functions */
+	so->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
+	so->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	so->normalizeprocinfo = HnswOptionalProcInfo(index, HNSW_NORMALIZE_PROC);
+	so->collation = index->rd_indcollation[0];
+
+	scan->opaque = so;
+
+	return scan;
+}
+
+/*
+ * Start or restart an index scan
+ */
+void
+hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int norderbys)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+
+	so->first = true;
+	MemoryContextReset(so->tmpCtx);
+
+	if (keys && scan->numberOfKeys > 0)
+		memmove(scan->keyData, keys, scan->numberOfKeys * sizeof(ScanKeyData));
+
+	if (orderbys && scan->numberOfOrderBys > 0)
+		memmove(scan->orderByData, orderbys, scan->numberOfOrderBys * sizeof(ScanKeyData));
+}
+
+/*
+ * Fetch the next tuple in the given scan
+ */
+bool
+hnswgettuple(IndexScanDesc scan, ScanDirection dir)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	MemoryContext oldCtx = MemoryContextSwitchTo(so->tmpCtx);
+
+	/*
+	 * Index can be used to scan backward, but Postgres doesn't support
+	 * backward scan on operators
+	 */
+	Assert(ScanDirectionIsForward(dir));
+
+	if (so->first)
+	{
+		Datum		value;
+
+		/* Count index scan for stats */
+		pgstat_count_index_scan(scan->indexRelation);
+
+		/* Safety check */
+		if (scan->orderByData == NULL)
+			elog(ERROR, "cannot scan hnsw index without order");
+
+		if (scan->orderByData->sk_flags & SK_ISNULL)
+			value = PointerGetDatum(InitVector(GetDimensions(scan->indexRelation)));
+		else
+		{
+			value = scan->orderByData->sk_argument;
+
+			/* Value should not be compressed or toasted */
+			Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
+			Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
+
+			/* Fine if normalization fails */
+			HnswNormValue(so->normprocinfo, so->normalizeprocinfo, so->collation, &value, NULL);
+		}
+
+		GetScanItems(scan, value);
+		so->first = false;
+	}
+
+	while (list_length(so->w) > 0)
+	{
+		HnswCandidate *hc = llast(so->w);
+		ItemPointer tid;
+		BlockNumber indexblkno;
+
+		/* Move to next element if no valid heap tids */
+		if (list_length(hc->element->heaptids) == 0)
+		{
+			so->w = list_delete_last(so->w);
+			continue;
+		}
+
+		tid = llast(hc->element->heaptids);
+		indexblkno = hc->element->blkno;
+
+		hc->element->heaptids = list_delete_last(hc->element->heaptids);
+
+		MemoryContextSwitchTo(oldCtx);
+
+#if PG_VERSION_NUM >= 120000
+		scan->xs_heaptid = *tid;
+#else
+		scan->xs_ctup.t_self = *tid;
+#endif
+
+		if (BufferIsValid(so->buf))
+			ReleaseBuffer(so->buf);
+
+		/*
+		 * An index scan must maintain a pin on the index page holding the
+		 * item last returned by amgettuple
+		 *
+		 * https://www.postgresql.org/docs/current/index-locking.html
+		 */
+		so->buf = ReadBuffer(scan->indexRelation, indexblkno);
+
+		scan->xs_recheckorderby = false;
+		return true;
+	}
+
+	MemoryContextSwitchTo(oldCtx);
+	return false;
+}
+
+/*
+ * End a scan and release resources
+ */
+void
+hnswendscan(IndexScanDesc scan)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+
+	/* Release pin */
+	if (BufferIsValid(so->buf))
+		ReleaseBuffer(so->buf);
+
+	MemoryContextDelete(so->tmpCtx);
+
+	pfree(so);
+	scan->opaque = NULL;
+}

src/hnswutils.c

@@ -0,0 +1,986 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "hnsw.h"
+#include "storage/bufmgr.h"
+#include "vector.h"
+
+/*
+ * Get the number of connection in the index
+ */
+int
+HnswGetM(Relation index)
+{
+	HnswOptions *opts = (HnswOptions *) index->rd_options;
+
+	if (opts)
+		return opts->m;
+
+	return HNSW_DEFAULT_M;
+}
+
+/*
+ * Get the size of the dynamic candidate list in the index
+ */
+int
+HnswGetEfConstruction(Relation index)
+{
+	HnswOptions *opts = (HnswOptions *) index->rd_options;
+
+	if (opts)
+		return opts->efConstruction;
+
+	return HNSW_DEFAULT_EF_CONSTRUCTION;
+}
+
+/*
+ * Get proc
+ */
+FmgrInfo *
+HnswOptionalProcInfo(Relation rel, uint16 procnum)
+{
+	if (!OidIsValid(index_getprocid(rel, 1, procnum)))
+		return NULL;
+
+	return index_getprocinfo(rel, 1, procnum);
+}
+
+/*
+ * Normalize a vector
+ *
+ * The caller needs to free the pointer stored in value
+ * if it's different than the original value
+ */
+void
+HnswNormValue(FmgrInfo *procinfo, FmgrInfo *normalizeprocinfo, Oid collation, Datum *value, Vector * result)
+{
+	double		norm;
+
+	if (normalizeprocinfo != NULL)
+	{
+		*value = FunctionCall1Coll(normalizeprocinfo, collation, *value);
+		return;
+	}
+
+	if (procinfo == NULL)
+		return;
+
+	norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
+
+	if (norm > 0)
+	{
+		Vector	   *v = DatumGetVector(*value);
+
+		if (result == NULL)
+			result = InitVector(v->dim);
+
+		for (int i = 0; i < v->dim; i++)
+			result->x[i] = v->x[i] / norm;
+
+		*value = PointerGetDatum(result);
+	}
+}
+
+/*
+ * New buffer
+ */
+Buffer
+HnswNewBuffer(Relation index, ForkNumber forkNum)
+{
+	Buffer		buf = ReadBufferExtended(index, forkNum, P_NEW, RBM_NORMAL, NULL);
+
+	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+	return buf;
+}
+
+/*
+ * Init page
+ */
+void
+HnswInitPage(Buffer buf, Page page)
+{
+	PageInit(page, BufferGetPageSize(buf), sizeof(HnswPageOpaqueData));
+	HnswPageGetOpaque(page)->nextblkno = InvalidBlockNumber;
+	HnswPageGetOpaque(page)->page_id = HNSW_PAGE_ID;
+}
+
+/*
+ * Init and register page
+ */
+void
+HnswInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state)
+{
+	*state = GenericXLogStart(index);
+	*page = GenericXLogRegisterBuffer(*state, *buf, GENERIC_XLOG_FULL_IMAGE);
+	HnswInitPage(*buf, *page);
+}
+
+/*
+ * Commit buffer
+ */
+void
+HnswCommitBuffer(Buffer buf, GenericXLogState *state)
+{
+	MarkBufferDirty(buf);
+	GenericXLogFinish(state);
+	UnlockReleaseBuffer(buf);
+}
+
+/*
+ * Allocate neighbors
+ */
+void
+HnswInitNeighbors(HnswElement element, int m)
+{
+	int			level = element->level;
+
+	element->neighbors = palloc(sizeof(HnswNeighborArray) * (level + 1));
+
+	for (int lc = 0; lc <= level; lc++)
+	{
+		HnswNeighborArray *a;
+		int			lm = HnswGetLayerM(m, lc);
+
+		a = &element->neighbors[lc];
+		a->length = 0;
+		a->items = palloc(sizeof(HnswCandidate) * lm);
+	}
+}
+
+/*
+ * Allocate an element
+ */
+HnswElement
+HnswInitElement(ItemPointer heaptid, int m, double ml, int maxLevel)
+{
+	HnswElement element = palloc(sizeof(HnswElementData));
+
+	int			level = (int) (-log(RandomDouble()) * ml);
+
+	/* Cap level */
+	if (level > maxLevel)
+		level = maxLevel;
+
+	element->heaptids = NIL;
+	HnswAddHeapTid(element, heaptid);
+
+	element->level = level;
+	element->deleted = 0;
+
+	HnswInitNeighbors(element, m);
+
+	return element;
+}
+
+/*
+ * Free an element
+ */
+void
+HnswFreeElement(HnswElement element)
+{
+	list_free_deep(element->heaptids);
+	for (int lc = 0; lc <= element->level; lc++)
+		pfree(element->neighbors[lc].items);
+	pfree(element->neighbors);
+	pfree(element->vec);
+	pfree(element);
+}
+
+/*
+ * Add a heap TID to an element
+ */
+void
+HnswAddHeapTid(HnswElement element, ItemPointer heaptid)
+{
+	ItemPointer copy = palloc(sizeof(ItemPointerData));
+
+	ItemPointerCopy(heaptid, copy);
+	element->heaptids = lappend(element->heaptids, copy);
+}
+
+/*
+ * Allocate an element from block and offset numbers
+ */
+static HnswElement
+InitElementFromBlock(BlockNumber blkno, OffsetNumber offno)
+{
+	HnswElement element = palloc(sizeof(HnswElementData));
+
+	element->blkno = blkno;
+	element->offno = offno;
+	element->neighbors = NULL;
+	element->vec = NULL;
+	return element;
+}
+
+/*
+ * Get the entry point
+ */
+HnswElement
+HnswGetEntryPoint(Relation index)
+{
+	Buffer		buf;
+	Page		page;
+	HnswMetaPage metap;
+	HnswElement entryPoint = NULL;
+
+	buf = ReadBuffer(index, HNSW_METAPAGE_BLKNO);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	metap = HnswPageGetMeta(page);
+
+	if (BlockNumberIsValid(metap->entryBlkno))
+		entryPoint = InitElementFromBlock(metap->entryBlkno, metap->entryOffno);
+
+	UnlockReleaseBuffer(buf);
+
+	return entryPoint;
+}
+
+/*
+ * Update the metapage
+ */
+void
+HnswUpdateMetaPage(Relation index, bool updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum)
+{
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	HnswMetaPage metap;
+
+	buf = ReadBufferExtended(index, forkNum, HNSW_METAPAGE_BLKNO, RBM_NORMAL, NULL);
+	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+	state = GenericXLogStart(index);
+	page = GenericXLogRegisterBuffer(state, buf, 0);
+
+	metap = HnswPageGetMeta(page);
+
+	if (updateEntry)
+	{
+		if (entryPoint == NULL)
+		{
+			metap->entryBlkno = InvalidBlockNumber;
+			metap->entryOffno = InvalidOffsetNumber;
+			metap->entryLevel = -1;
+		}
+		else
+		{
+			metap->entryBlkno = entryPoint->blkno;
+			metap->entryOffno = entryPoint->offno;
+			metap->entryLevel = entryPoint->level;
+		}
+	}
+
+	if (BlockNumberIsValid(insertPage))
+		metap->insertPage = insertPage;
+
+	HnswCommitBuffer(buf, state);
+}
+
+/*
+ * Set element tuple, except for neighbor info
+ */
+void
+HnswSetElementTuple(HnswElementTuple etup, HnswElement element)
+{
+	etup->type = HNSW_ELEMENT_TUPLE_TYPE;
+	etup->level = element->level;
+	etup->deleted = 0;
+	for (int i = 0; i < HNSW_HEAPTIDS; i++)
+	{
+		if (i < list_length(element->heaptids))
+			etup->heaptids[i] = *((ItemPointer) list_nth(element->heaptids, i));
+		else
+			ItemPointerSetInvalid(&etup->heaptids[i]);
+	}
+	memcpy(&etup->vec, element->vec, VECTOR_SIZE(element->vec->dim));
+}
+
+/*
+ * Set neighbor tuple
+ */
+void
+HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m)
+{
+	int			idx = 0;
+
+	ntup->type = HNSW_NEIGHBOR_TUPLE_TYPE;
+
+	for (int lc = e->level; lc >= 0; lc--)
+	{
+		HnswNeighborArray *neighbors = &e->neighbors[lc];
+		int			lm = HnswGetLayerM(m, lc);
+
+		for (int i = 0; i < lm; i++)
+		{
+			ItemPointer indextid = &ntup->indextids[idx++];
+
+			if (i < neighbors->length)
+			{
+				HnswCandidate *hc = &neighbors->items[i];
+
+				ItemPointerSet(indextid, hc->element->blkno, hc->element->offno);
+			}
+			else
+				ItemPointerSetInvalid(indextid);
+		}
+	}
+
+	ntup->count = idx;
+}
+
+/*
+ * Load neighbors from page
+ */
+static void
+LoadNeighborsFromPage(HnswElement element, Relation index, Page page)
+{
+	HnswNeighborTuple ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
+	int			m = HnswGetM(index);
+	int			neighborCount = (element->level + 2) * m;
+
+	Assert(HnswIsNeighborTuple(ntup));
+
+	HnswInitNeighbors(element, m);
+
+	/* 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 = InitElementFromBlock(ItemPointerGetBlockNumber(indextid), ItemPointerGetOffsetNumber(indextid));
+
+		/* Calculate level based on offset */
+		level = element->level - i / m;
+		if (level < 0)
+			level = 0;
+
+		neighbors = &element->neighbors[level];
+		hc = &neighbors->items[neighbors->length++];
+		hc->element = e;
+	}
+}
+
+/*
+ * Load neighbors
+ */
+static void
+LoadNeighbors(HnswElement element, Relation index)
+{
+	Buffer		buf;
+	Page		page;
+
+	buf = ReadBuffer(index, element->neighborPage);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+
+	LoadNeighborsFromPage(element, index, page);
+
+	UnlockReleaseBuffer(buf);
+}
+
+/*
+ * 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)
+{
+	Buffer		buf;
+	Page		page;
+	HnswElementTuple etup;
+
+	/* Read vector */
+	buf = ReadBuffer(index, element->blkno);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+
+	etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, element->offno));
+
+	Assert(HnswIsElementTuple(etup));
+
+	/* Load element */
+	element->heaptids = NIL;
+	for (int i = 0; i < HNSW_HEAPTIDS; i++)
+	{
+		/* Can stop at first invalid */
+		if (!ItemPointerIsValid(&etup->heaptids[i]))
+			break;
+
+		HnswAddHeapTid(element, &etup->heaptids[i]);
+	}
+	element->level = etup->level;
+	element->neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
+	element->neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
+	element->deleted = etup->deleted;
+
+	if (loadVec)
+	{
+		element->vec = palloc(VECTOR_SIZE(etup->vec.dim));
+		memcpy(element->vec, &etup->vec, VECTOR_SIZE(etup->vec.dim));
+	}
+
+	/* Calculate distance */
+	if (distance != NULL)
+		*distance = (float) DatumGetFloat8(FunctionCall2Coll(procinfo, collation, *q, PointerGetDatum(&etup->vec)));
+
+	UnlockReleaseBuffer(buf);
+}
+
+/*
+ * Get the distance for a candidate
+ */
+static float
+GetCandidateDistance(HnswCandidate * hc, Datum q, FmgrInfo *procinfo, Oid collation)
+{
+	return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, q, PointerGetDatum(hc->element->vec)));
+}
+
+/*
+ * Create a candidate for the entry point
+ */
+HnswCandidate *
+HnswEntryCandidate(HnswElement entryPoint, Datum q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadvec)
+{
+	HnswCandidate *hc = palloc(sizeof(HnswCandidate));
+
+	hc->element = entryPoint;
+	if (index == NULL)
+		hc->distance = GetCandidateDistance(hc, q, procinfo, collation);
+	else
+		HnswLoadElement(hc->element, &hc->distance, &q, index, procinfo, collation, loadvec);
+	return hc;
+}
+
+/*
+ * Compare candidate distances
+ */
+static int
+CompareNearestCandidates(const pairingheap_node *a, const pairingheap_node *b, void *arg)
+{
+	if (((const HnswPairingHeapNode *) a)->inner->distance < ((const HnswPairingHeapNode *) b)->inner->distance)
+		return 1;
+
+	if (((const HnswPairingHeapNode *) a)->inner->distance > ((const HnswPairingHeapNode *) b)->inner->distance)
+		return -1;
+
+	return 0;
+}
+
+/*
+ * Compare candidate distances
+ */
+static int
+CompareFurthestCandidates(const pairingheap_node *a, const pairingheap_node *b, void *arg)
+{
+	if (((const HnswPairingHeapNode *) a)->inner->distance < ((const HnswPairingHeapNode *) b)->inner->distance)
+		return -1;
+
+	if (((const HnswPairingHeapNode *) a)->inner->distance > ((const HnswPairingHeapNode *) b)->inner->distance)
+		return 1;
+
+	return 0;
+}
+
+/*
+ * Create a pairing heap node for a candidate
+ */
+static HnswPairingHeapNode *
+CreatePairingHeapNode(HnswCandidate * c)
+{
+	HnswPairingHeapNode *node = palloc(sizeof(HnswPairingHeapNode));
+
+	node->inner = c;
+	return node;
+}
+
+/*
+ * Add to visited
+ */
+static inline void
+AddToVisited(HTAB *v, HnswCandidate * hc, Relation index, bool *found)
+{
+	if (index == NULL)
+		hash_search(v, &hc->element, HASH_ENTER, found);
+	else
+	{
+		ItemPointerData indextid;
+
+		ItemPointerSet(&indextid, hc->element->blkno, hc->element->offno);
+		hash_search(v, &indextid, HASH_ENTER, found);
+	}
+}
+
+/*
+ * Algorithm 2 from paper
+ */
+List *
+HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, bool inserting, BlockNumber *skipPage, OffsetNumber *skipOffno)
+{
+	ListCell   *lc2;
+
+	List	   *w = NIL;
+	pairingheap *C = pairingheap_allocate(CompareNearestCandidates, NULL);
+	pairingheap *W = pairingheap_allocate(CompareFurthestCandidates, NULL);
+	int			wlen = 0;
+	HASHCTL		hash_ctl;
+	HTAB	   *v;
+
+	/* Create hash table */
+	if (index == NULL)
+	{
+		hash_ctl.keysize = sizeof(HnswElement *);
+		hash_ctl.entrysize = sizeof(HnswElement *);
+	}
+	else
+	{
+		hash_ctl.keysize = sizeof(ItemPointerData);
+		hash_ctl.entrysize = sizeof(ItemPointerData);
+	}
+
+	hash_ctl.hcxt = CurrentMemoryContext;
+	v = hash_create("hnsw visited", 256, &hash_ctl, HASH_ELEM | HASH_BLOBS | HASH_CONTEXT);
+
+	/* Add entry points to v, C, and W */
+	foreach(lc2, ep)
+	{
+		HnswCandidate *hc = (HnswCandidate *) lfirst(lc2);
+
+		AddToVisited(v, hc, index, NULL);
+
+		pairingheap_add(C, &(CreatePairingHeapNode(hc)->ph_node));
+		pairingheap_add(W, &(CreatePairingHeapNode(hc)->ph_node));
+
+		wlen++;
+	}
+
+	while (!pairingheap_is_empty(C))
+	{
+		HnswNeighborArray *neighborhood;
+		HnswCandidate *c = ((HnswPairingHeapNode *) pairingheap_remove_first(C))->inner;
+		HnswCandidate *f = ((HnswPairingHeapNode *) pairingheap_first(W))->inner;
+
+		if (c->distance > f->distance)
+			break;
+
+		if (c->element->neighbors == NULL)
+			LoadNeighbors(c->element, index);
+
+		/* Get the neighborhood at layer lc */
+		neighborhood = &c->element->neighbors[lc];
+
+		for (int i = 0; i < neighborhood->length; i++)
+		{
+			HnswCandidate *e = &neighborhood->items[i];
+			bool		visited;
+
+			AddToVisited(v, e, index, &visited);
+
+			if (!visited)
+			{
+				float		eDistance;
+
+				f = ((HnswPairingHeapNode *) pairingheap_first(W))->inner;
+
+				if (index == NULL)
+					eDistance = GetCandidateDistance(e, q, procinfo, collation);
+				else
+					HnswLoadElement(e->element, &eDistance, &q, index, procinfo, collation, inserting);
+
+				/* Skip if fully deleted */
+				if (e->element->deleted)
+					continue;
+
+				/* Skip for inserts if deleting */
+				if (inserting && list_length(e->element->heaptids) == 0)
+					continue;
+
+				/* Skip self for vacuuming update */
+				if (skipPage != NULL && e->element->neighborPage == *skipPage && e->element->neighborOffno == *skipOffno)
+					continue;
+
+				/* Make robust to issues */
+				if (e->element->level < lc)
+					continue;
+
+				if (eDistance < f->distance || wlen < ef)
+				{
+					/* Copy e */
+					HnswCandidate *ec = palloc(sizeof(HnswCandidate));
+
+					ec->element = e->element;
+					ec->distance = eDistance;
+
+					pairingheap_add(C, &(CreatePairingHeapNode(ec)->ph_node));
+					pairingheap_add(W, &(CreatePairingHeapNode(ec)->ph_node));
+					wlen++;
+
+					/* No need to decrement wlen */
+					if (wlen > ef)
+						pairingheap_remove_first(W);
+				}
+			}
+		}
+	}
+
+	/* Add each element of W to w */
+	while (!pairingheap_is_empty(W))
+	{
+		HnswCandidate *hc = ((HnswPairingHeapNode *) pairingheap_remove_first(W))->inner;
+
+		w = lappend(w, hc);
+	}
+
+	return w;
+}
+
+/*
+ * Calculate the distance between elements
+ */
+static float
+HnswGetDistance(HnswElement a, HnswElement b, int lc, FmgrInfo *procinfo, Oid collation)
+{
+	/* Look for cached distance */
+	if (a->neighbors != NULL)
+	{
+		Assert(a->level >= lc);
+
+		for (int i = 0; i < a->neighbors[lc].length; i++)
+		{
+			if (a->neighbors[lc].items[i].element == b)
+				return a->neighbors[lc].items[i].distance;
+		}
+	}
+
+	if (b->neighbors != NULL)
+	{
+		Assert(b->level >= lc);
+
+		for (int i = 0; i < b->neighbors[lc].length; i++)
+		{
+			if (b->neighbors[lc].items[i].element == a)
+				return b->neighbors[lc].items[i].distance;
+		}
+	}
+
+	return DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(a->vec), PointerGetDatum(b->vec)));
+}
+
+/*
+ * Check if an element is closer to q than any element from R
+ */
+static bool
+CheckElementCloser(HnswCandidate * e, List *r, int lc, FmgrInfo *procinfo, Oid collation)
+{
+	ListCell   *lc2;
+
+	foreach(lc2, r)
+	{
+		HnswCandidate *ri = lfirst(lc2);
+		float		distance = HnswGetDistance(e->element, ri->element, lc, procinfo, collation);
+
+		if (distance <= e->distance)
+			return false;
+	}
+
+	return true;
+}
+
+/*
+ * Algorithm 4 from paper
+ */
+static List *
+SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswCandidate * *pruned)
+{
+	List	   *r = NIL;
+	List	   *w = list_copy(c);
+	pairingheap *wd;
+
+	if (list_length(w) < m)
+		return w;
+
+	wd = pairingheap_allocate(CompareNearestCandidates, NULL);
+
+	while (list_length(w) > 0 && list_length(r) < m)
+	{
+		/* Assumes w is already ordered desc */
+		HnswCandidate *e = llast(w);
+		bool		closer;
+
+		w = list_delete_last(w);
+
+		closer = CheckElementCloser(e, r, lc, procinfo, collation);
+
+		if (closer)
+			r = lappend(r, e);
+		else
+			pairingheap_add(wd, &(CreatePairingHeapNode(e)->ph_node));
+	}
+
+	/* Keep pruned connections */
+	while (!pairingheap_is_empty(wd) && list_length(r) < m)
+		r = lappend(r, ((HnswPairingHeapNode *) pairingheap_remove_first(wd))->inner);
+
+	/* Return pruned for update connections */
+	if (pruned != NULL)
+	{
+		if (!pairingheap_is_empty(wd))
+			*pruned = ((HnswPairingHeapNode *) pairingheap_first(wd))->inner;
+		else
+			*pruned = linitial(w);
+	}
+
+	return r;
+}
+
+/*
+ * Find duplicate element
+ */
+static HnswElement
+HnswFindDuplicate(HnswElement e, List *neighbors)
+{
+	ListCell   *lc;
+
+	foreach(lc, neighbors)
+	{
+		HnswCandidate *neighbor = lfirst(lc);
+
+		/* Exit early since ordered by distance */
+		if (vector_cmp_internal(e->vec, neighbor->element->vec) != 0)
+			break;
+
+		/* Check for space */
+		if (list_length(neighbor->element->heaptids) < HNSW_HEAPTIDS)
+			return neighbor->element;
+	}
+
+	return NULL;
+}
+
+/*
+ * Add connections
+ */
+static void
+AddConnections(HnswElement element, List *neighbors, int m, int lc)
+{
+	ListCell   *lc2;
+	HnswNeighborArray *a = &element->neighbors[lc];
+
+	foreach(lc2, neighbors)
+		a->items[a->length++] = *((HnswCandidate *) lfirst(lc2));
+}
+
+/*
+ * Compare candidate distances
+ */
+static int
+#if PG_VERSION_NUM >= 130000
+CompareCandidateDistances(const ListCell *a, const ListCell *b)
+#else
+CompareCandidateDistances(const void *a, const void *b)
+#endif
+{
+	HnswCandidate *hca = lfirst((ListCell *) a);
+	HnswCandidate *hcb = lfirst((ListCell *) b);
+
+	if (hca->distance < hcb->distance)
+		return 1;
+
+	if (hca->distance > hcb->distance)
+		return -1;
+
+	return 0;
+}
+
+/*
+ * Create update
+ */
+static HnswUpdate *
+CreateUpdate(HnswCandidate * hc, int level, int index)
+{
+	HnswUpdate *update = palloc(sizeof(HnswUpdate));
+
+	update->hc = *hc;
+	update->level = level;
+	update->index = index;
+	return update;
+}
+
+/*
+ * Update connections
+ */
+static void
+UpdateConnections(HnswElement element, List *neighbors, int m, int lc, List **updates, Relation index, FmgrInfo *procinfo, Oid collation)
+{
+	ListCell   *lc2;
+
+	foreach(lc2, neighbors)
+	{
+		HnswCandidate *hc = (HnswCandidate *) lfirst(lc2);
+		HnswNeighborArray *currentNeighbors = &hc->element->neighbors[lc];
+
+		HnswCandidate hc2;
+
+		hc2.element = element;
+		hc2.distance = hc->distance;
+
+		if (currentNeighbors->length < m)
+		{
+			currentNeighbors->items[currentNeighbors->length++] = hc2;
+
+			/* Track updates */
+			if (updates != NULL)
+				*updates = lappend(*updates, CreateUpdate(hc, lc, currentNeighbors->length - 1));
+		}
+		else
+		{
+			/* Shrink connections */
+			HnswCandidate *pruned = NULL;
+			List	   *c = NIL;
+
+			/* Load elements on insert */
+			if (index != NULL)
+			{
+				Datum		q = PointerGetDatum(hc->element->vec);
+
+				for (int i = 0; i < currentNeighbors->length; i++)
+				{
+					HnswCandidate *hc3 = &currentNeighbors->items[i];
+
+					if (hc3->element->vec == NULL)
+						HnswLoadElement(hc3->element, &hc3->distance, &q, index, procinfo, collation, true);
+					else
+						hc3->distance = GetCandidateDistance(hc3, q, procinfo, collation);
+
+					/* Prune element if being deleted */
+					if (list_length(hc3->element->heaptids) == 0)
+					{
+						pruned = &currentNeighbors->items[i];
+						break;
+					}
+				}
+			}
+
+			if (pruned == NULL)
+			{
+				/* Add and sort candidates */
+				for (int i = 0; i < currentNeighbors->length; i++)
+					c = lappend(c, &currentNeighbors->items[i]);
+				c = lappend(c, &hc2);
+				list_sort(c, CompareCandidateDistances);
+
+				SelectNeighbors(c, m, lc, procinfo, collation, &pruned);
+
+				/* Should not happen */
+				if (pruned == NULL)
+					continue;
+			}
+
+			/* Find and replace the pruned element */
+			for (int i = 0; i < currentNeighbors->length; i++)
+			{
+				if (currentNeighbors->items[i].element == pruned->element)
+				{
+					currentNeighbors->items[i] = hc2;
+
+					/* Track updates */
+					if (updates != NULL)
+						*updates = lappend(*updates, CreateUpdate(hc, lc, i));
+
+					break;
+				}
+			}
+		}
+	}
+}
+
+/*
+ * Algorithm 1 from paper
+ */
+HnswElement
+HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, List **updates, bool vacuuming)
+{
+	List	   *ep = NIL;
+	List	   *w;
+	int			level = element->level;
+	int			entryLevel;
+	List	  **newNeighbors = palloc(sizeof(List *) * (level + 1));
+	Datum		q = PointerGetDatum(element->vec);
+	HnswElement dup;
+	BlockNumber *skipPage = vacuuming ? &element->neighborPage : NULL;
+	OffsetNumber *skipOffno = vacuuming ? &element->neighborOffno : NULL;
+	bool		removeEntryPoint;
+	HnswCandidate *entryCandidate;
+
+	/* Get entry point and level */
+	if (entryPoint != NULL)
+	{
+		entryCandidate = HnswEntryCandidate(entryPoint, q, index, procinfo, collation, true);
+		ep = lappend(ep, entryCandidate);
+		entryLevel = entryPoint->level;
+		removeEntryPoint = vacuuming && list_length(entryPoint->heaptids) == 0;
+	}
+	else
+	{
+		entryLevel = -1;
+		removeEntryPoint = false;
+	}
+
+	/* 1st phase: greedy search to insert level */
+	for (int lc = entryLevel; lc >= level + 1; lc--)
+	{
+		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, true, skipPage, skipOffno);
+		ep = w;
+	}
+
+	if (level > entryLevel)
+		level = entryLevel;
+
+	/* 2nd phase */
+	for (int lc = level; lc >= 0; lc--)
+	{
+		int			lm = HnswGetLayerM(m, lc);
+
+		w = HnswSearchLayer(q, ep, efConstruction, lc, index, procinfo, collation, true, skipPage, skipOffno);
+
+		/* Remove entry point if it's being deleted */
+		if (removeEntryPoint)
+			w = list_delete_ptr(w, entryCandidate);
+
+		newNeighbors[lc] = SelectNeighbors(w, lm, lc, procinfo, collation, NULL);
+		ep = w;
+	}
+
+	/* Look for duplicate */
+	if (level >= 0 && !vacuuming)
+	{
+		dup = HnswFindDuplicate(element, newNeighbors[0]);
+		if (dup != NULL)
+			return dup;
+	}
+
+	/* Update connections */
+	for (int lc = level; lc >= 0; lc--)
+	{
+		int			lm = HnswGetLayerM(m, lc);
+
+		AddConnections(element, newNeighbors[lc], lm, lc);
+
+		if (!vacuuming)
+			UpdateConnections(element, newNeighbors[lc], lm, lc, updates, index, procinfo, collation);
+	}
+
+	return NULL;
+}

src/hnswvacuum.c

@@ -0,0 +1,581 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "commands/vacuum.h"
+#include "hnsw.h"
+#include "storage/bufmgr.h"
+#include "utils/memutils.h"
+
+/*
+ * Check if deleted list contains an index tid
+ */
+static bool
+DeletedContains(HTAB *deleted, ItemPointer indextid)
+{
+	bool		found;
+
+	hash_search(deleted, indextid, HASH_FIND, &found);
+	return found;
+}
+
+/*
+ * Remove deleted heap TIDs
+ *
+ * OK to remove for entry point, since always considered for searches and inserts
+ */
+static void
+RemoveHeapTids(HnswVacuumState * vacuumstate)
+{
+	BlockNumber blkno = HNSW_HEAD_BLKNO;
+	HnswElement highestPoint = &vacuumstate->highestPoint;
+	Relation	index = vacuumstate->index;
+	BufferAccessStrategy bas = vacuumstate->bas;
+	HnswElement entryPoint = HnswGetEntryPoint(vacuumstate->index);
+
+	/* Store separately since highestPoint.level is uint8 */
+	int			highestLevel = -1;
+
+	/* Initialize highest point */
+	highestPoint->blkno = InvalidBlockNumber;
+	highestPoint->offno = InvalidOffsetNumber;
+
+	while (BlockNumberIsValid(blkno))
+	{
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		OffsetNumber offno;
+		OffsetNumber maxoffno;
+		bool		updated = false;
+
+		vacuum_delay_point();
+
+		buf = ReadBufferExtended(index, MAIN_FORKNUM, blkno, RBM_NORMAL, bas);
+		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+		maxoffno = PageGetMaxOffsetNumber(page);
+
+		/* Iterate over nodes */
+		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+		{
+			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+			int			idx = 0;
+			bool		itemUpdated = false;
+
+			/* Skip neighbor tuples */
+			if (!HnswIsElementTuple(etup))
+				continue;
+
+			if (ItemPointerIsValid(&etup->heaptids[0]))
+			{
+				for (int i = 0; i < HNSW_HEAPTIDS; i++)
+				{
+					/* Stop at first unused */
+					if (!ItemPointerIsValid(&etup->heaptids[i]))
+						break;
+
+					if (vacuumstate->callback(&etup->heaptids[i], vacuumstate->callback_state))
+						itemUpdated = true;
+					else
+					{
+						/* Move to front of list */
+						etup->heaptids[idx++] = etup->heaptids[i];
+					}
+				}
+
+				if (itemUpdated)
+				{
+					Size		etupSize = HNSW_ELEMENT_TUPLE_SIZE(etup->vec.dim);
+
+					/* Mark rest as invalid */
+					for (int i = idx; i < HNSW_HEAPTIDS; i++)
+						ItemPointerSetInvalid(&etup->heaptids[i]);
+
+					if (!PageIndexTupleOverwrite(page, offno, (Item) etup, etupSize))
+						elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+					updated = true;
+				}
+			}
+
+			if (!ItemPointerIsValid(&etup->heaptids[0]))
+			{
+				ItemPointerData ip;
+
+				/* Add to deleted list */
+				ItemPointerSet(&ip, blkno, offno);
+
+				(void) hash_search(vacuumstate->deleted, &ip, HASH_ENTER, NULL);
+			}
+			else if (etup->level > highestLevel && !(blkno == entryPoint->blkno && offno == entryPoint->offno))
+			{
+				/* Keep track of highest non-entry point */
+				highestPoint->blkno = blkno;
+				highestPoint->offno = offno;
+				highestPoint->level = etup->level;
+				highestLevel = etup->level;
+			}
+		}
+
+		blkno = HnswPageGetOpaque(page)->nextblkno;
+
+		if (updated)
+		{
+			MarkBufferDirty(buf);
+			GenericXLogFinish(state);
+		}
+		else
+			GenericXLogAbort(state);
+
+		UnlockReleaseBuffer(buf);
+	}
+}
+
+/*
+ * Check for deleted neighbors
+ */
+static bool
+NeedsUpdated(HnswVacuumState * vacuumstate, HnswElement element)
+{
+	Relation	index = vacuumstate->index;
+	BufferAccessStrategy bas = vacuumstate->bas;
+	Buffer		buf;
+	Page		page;
+	HnswNeighborTuple ntup;
+	bool		needsUpdated = false;
+
+	buf = ReadBufferExtended(index, MAIN_FORKNUM, element->neighborPage, RBM_NORMAL, bas);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
+
+	Assert(HnswIsNeighborTuple(ntup));
+
+	/* Check neighbors */
+	for (int i = 0; i < ntup->count; i++)
+	{
+		ItemPointer indextid = &ntup->indextids[i];
+
+		if (!ItemPointerIsValid(indextid))
+			continue;
+
+		/* Check if in deleted list */
+		if (DeletedContains(vacuumstate->deleted, indextid))
+		{
+			needsUpdated = true;
+			break;
+		}
+	}
+
+	UnlockReleaseBuffer(buf);
+
+	return needsUpdated;
+}
+
+/*
+ * Repair graph for a single element
+ */
+static void
+RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element)
+{
+	Relation	index = vacuumstate->index;
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	int			m = vacuumstate->m;
+	int			efConstruction = vacuumstate->efConstruction;
+	FmgrInfo   *procinfo = vacuumstate->procinfo;
+	Oid			collation = vacuumstate->collation;
+	HnswElement entryPoint;
+	BufferAccessStrategy bas = vacuumstate->bas;
+	HnswNeighborTuple ntup = vacuumstate->ntup;
+	Size		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(element->level, m);
+
+	/* Check if any neighbors point to deleted values */
+	if (!NeedsUpdated(vacuumstate, element))
+		return;
+
+	/* Refresh entry point for each element */
+	entryPoint = HnswGetEntryPoint(index);
+
+	/* Special case for entry point */
+	if (element->blkno == entryPoint->blkno && element->offno == entryPoint->offno)
+	{
+		if (BlockNumberIsValid(vacuumstate->highestPoint.blkno))
+		{
+			/* Already updated */
+			if (vacuumstate->highestPoint.blkno == element->blkno && vacuumstate->highestPoint.offno == element->offno)
+				return;
+
+			entryPoint = &vacuumstate->highestPoint;
+
+			/* Reset neighbors from previous update */
+			entryPoint->neighbors = NULL;
+		}
+		else
+			entryPoint = NULL;
+	}
+
+	/* Init fields */
+	HnswInitNeighbors(element, m);
+	element->heaptids = NIL;
+
+	/* Add element to graph, skipping itself */
+	HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, NULL, true);
+
+	/* Update neighbor tuple */
+	/* Do this before getting page to minimize locking */
+	HnswSetNeighborTuple(ntup, element, m);
+
+	/* Get neighbor page */
+	buf = ReadBufferExtended(index, MAIN_FORKNUM, element->neighborPage, RBM_NORMAL, bas);
+	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+	state = GenericXLogStart(index);
+	page = GenericXLogRegisterBuffer(state, buf, 0);
+
+	/* Overwrite tuple */
+	if (!PageIndexTupleOverwrite(page, element->neighborOffno, (Item) ntup, ntupSize))
+		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+	/* Commit */
+	MarkBufferDirty(buf);
+	GenericXLogFinish(state);
+	UnlockReleaseBuffer(buf);
+}
+
+/*
+ * Repair graph entry point
+ */
+static void
+RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
+{
+	Relation	index = vacuumstate->index;
+	HnswElement highestPoint = &vacuumstate->highestPoint;
+	HnswElement entryPoint;
+	MemoryContext oldCtx = MemoryContextSwitchTo(vacuumstate->tmpCtx);
+
+	/* Repair graph for highest non-entry point */
+	/* This may not be the highest with new inserts, but should be fine */
+	if (BlockNumberIsValid(highestPoint->blkno))
+	{
+		HnswLoadElement(highestPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true);
+		RepairGraphElement(vacuumstate, highestPoint);
+	}
+
+	/* See if entry point needs updated */
+	entryPoint = HnswGetEntryPoint(index);
+	if (entryPoint != NULL)
+	{
+		ItemPointerData epData;
+
+		ItemPointerSet(&epData, entryPoint->blkno, entryPoint->offno);
+
+		if (DeletedContains(vacuumstate->deleted, &epData))
+			HnswUpdateMetaPage(index, true, highestPoint, InvalidBlockNumber, MAIN_FORKNUM);
+		else
+		{
+			/* Highest point will be used to repair */
+			HnswLoadElement(entryPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true);
+			RepairGraphElement(vacuumstate, entryPoint);
+		}
+	}
+
+	/* Reset memory context */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextReset(vacuumstate->tmpCtx);
+}
+
+/*
+ * Repair graph for all elements
+ */
+static void
+RepairGraph(HnswVacuumState * vacuumstate)
+{
+	Relation	index = vacuumstate->index;
+	BufferAccessStrategy bas = vacuumstate->bas;
+	BlockNumber blkno = HNSW_HEAD_BLKNO;
+
+	RepairGraphEntryPoint(vacuumstate);
+
+	while (BlockNumberIsValid(blkno))
+	{
+		Buffer		buf;
+		Page		page;
+		OffsetNumber offno;
+		OffsetNumber maxoffno;
+		List	   *elements = NIL;
+		ListCell   *lc2;
+		MemoryContext oldCtx;
+
+		vacuum_delay_point();
+
+		oldCtx = MemoryContextSwitchTo(vacuumstate->tmpCtx);
+
+		buf = ReadBufferExtended(index, MAIN_FORKNUM, blkno, RBM_NORMAL, bas);
+		LockBuffer(buf, BUFFER_LOCK_SHARE);
+		page = BufferGetPage(buf);
+		maxoffno = PageGetMaxOffsetNumber(page);
+
+		/* Load items into memory to minimize locking */
+		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+		{
+			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+			HnswElement element;
+
+			/* Skip neighbor tuples */
+			if (!HnswIsElementTuple(etup))
+				continue;
+
+			/* Skip updating neighbors if being deleted */
+			if (!ItemPointerIsValid(&etup->heaptids[0]))
+				continue;
+
+			/* Create an element */
+			element = palloc(sizeof(HnswElementData));
+			element->neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
+			element->neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
+			element->level = etup->level;
+			element->blkno = blkno;
+			element->offno = offno;
+			element->vec = palloc(VECTOR_SIZE(etup->vec.dim));
+			memcpy(element->vec, &etup->vec, VECTOR_SIZE(etup->vec.dim));
+
+			elements = lappend(elements, element);
+		}
+
+		blkno = HnswPageGetOpaque(page)->nextblkno;
+
+		UnlockReleaseBuffer(buf);
+
+		/* Update neighbor pages */
+		foreach(lc2, elements)
+			RepairGraphElement(vacuumstate, (HnswElement) lfirst(lc2));
+
+		/* Reset memory context */
+		MemoryContextSwitchTo(oldCtx);
+		MemoryContextReset(vacuumstate->tmpCtx);
+	}
+}
+
+/*
+ * Mark items as deleted
+ */
+static void
+MarkDeleted(HnswVacuumState * vacuumstate)
+{
+	BlockNumber blkno = HNSW_HEAD_BLKNO;
+	BlockNumber insertPage = InvalidBlockNumber;
+	Relation	index = vacuumstate->index;
+	BufferAccessStrategy bas = vacuumstate->bas;
+	IndexBulkDeleteResult *stats = vacuumstate->stats;
+
+	while (BlockNumberIsValid(blkno))
+	{
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		OffsetNumber offno;
+		OffsetNumber maxoffno;
+
+		vacuum_delay_point();
+
+		buf = ReadBufferExtended(index, MAIN_FORKNUM, blkno, RBM_NORMAL, bas);
+
+		/*
+		 * ambulkdelete cannot delete entries from pages that are pinned by
+		 * other backends
+		 *
+		 * https://www.postgresql.org/docs/current/index-locking.html
+		 */
+		LockBufferForCleanup(buf);
+
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+		maxoffno = PageGetMaxOffsetNumber(page);
+
+		/* Update element and neighbors together */
+		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+		{
+			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+			HnswNeighborTuple ntup;
+			Size		etupSize;
+			Size		ntupSize;
+			Buffer		nbuf;
+			Page		npage;
+			BlockNumber neighborPage;
+			OffsetNumber neighborOffno;
+
+			/* Skip neighbor tuples */
+			if (!HnswIsElementTuple(etup))
+				continue;
+
+			/* Skip deleted tuples */
+			if (etup->deleted)
+				continue;
+
+			/* Skip live tuples */
+			if (ItemPointerIsValid(&etup->heaptids[0]))
+			{
+				stats->num_index_tuples++;
+				continue;
+			}
+
+			/* Update stats */
+			stats->tuples_removed++;
+
+			/* Calculate sizes */
+			etupSize = HNSW_ELEMENT_TUPLE_SIZE(etup->vec.dim);
+			ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(etup->level, vacuumstate->m);
+
+			/* Get neighbor page */
+			neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
+			neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
+
+			if (neighborPage == blkno)
+			{
+				nbuf = buf;
+				npage = page;
+			}
+			else
+			{
+				nbuf = ReadBufferExtended(index, MAIN_FORKNUM, neighborPage, RBM_NORMAL, bas);
+				LockBuffer(nbuf, BUFFER_LOCK_EXCLUSIVE);
+				npage = GenericXLogRegisterBuffer(state, nbuf, 0);
+			}
+
+			ntup = (HnswNeighborTuple) PageGetItem(npage, PageGetItemId(npage, neighborOffno));
+
+			/* Overwrite element */
+			etup->deleted = 1;
+			MemSet(&etup->vec.x, 0, etup->vec.dim * sizeof(float));
+
+			/* Overwrite neighbors */
+			for (int i = 0; i < ntup->count; i++)
+				ItemPointerSetInvalid(&ntup->indextids[i]);
+
+			/* Overwrite element tuple */
+			if (!PageIndexTupleOverwrite(page, offno, (Item) etup, etupSize))
+				elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+			/* Overwrite neighbor tuple */
+			if (!PageIndexTupleOverwrite(npage, neighborOffno, (Item) ntup, ntupSize))
+				elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+			/* Commit */
+			MarkBufferDirty(buf);
+			if (nbuf != buf)
+				MarkBufferDirty(nbuf);
+			GenericXLogFinish(state);
+			if (nbuf != buf)
+				UnlockReleaseBuffer(nbuf);
+
+			/* Set to first free page */
+			if (!BlockNumberIsValid(insertPage))
+				insertPage = blkno;
+
+			/* Prepare new xlog */
+			state = GenericXLogStart(index);
+			page = GenericXLogRegisterBuffer(state, buf, 0);
+		}
+
+		blkno = HnswPageGetOpaque(page)->nextblkno;
+
+		GenericXLogAbort(state);
+		UnlockReleaseBuffer(buf);
+	}
+
+	HnswUpdateMetaPage(index, false, NULL, insertPage, MAIN_FORKNUM);
+}
+
+/*
+ * Initialize the vacuum state
+ */
+static void
+InitVacuumState(HnswVacuumState * vacuumstate, IndexVacuumInfo *info, IndexBulkDeleteResult *stats, IndexBulkDeleteCallback callback, void *callback_state)
+{
+	Relation	index = info->index;
+	HASHCTL		hash_ctl;
+
+	if (stats == NULL)
+		stats = (IndexBulkDeleteResult *) palloc0(sizeof(IndexBulkDeleteResult));
+
+	vacuumstate->index = index;
+	vacuumstate->stats = stats;
+	vacuumstate->callback = callback;
+	vacuumstate->callback_state = callback_state;
+	vacuumstate->m = HnswGetM(index);
+	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(BLCKSZ);
+	vacuumstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+												"Hnsw vacuum temporary context",
+												ALLOCSET_DEFAULT_SIZES);
+
+	/* Create hash table */
+	hash_ctl.keysize = sizeof(ItemPointerData);
+	hash_ctl.entrysize = sizeof(ItemPointerData);
+	hash_ctl.hcxt = CurrentMemoryContext;
+	vacuumstate->deleted = hash_create("hnswbulkdelete indextids", 256, &hash_ctl, HASH_ELEM | HASH_BLOBS | HASH_CONTEXT);
+}
+
+/*
+ * Free resources
+ */
+static void
+FreeVacuumState(HnswVacuumState * vacuumstate)
+{
+	hash_destroy(vacuumstate->deleted);
+	FreeAccessStrategy(vacuumstate->bas);
+	pfree(vacuumstate->ntup);
+	MemoryContextDelete(vacuumstate->tmpCtx);
+}
+
+/*
+ * Bulk delete tuples from the index
+ */
+IndexBulkDeleteResult *
+hnswbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
+			   IndexBulkDeleteCallback callback, void *callback_state)
+{
+	HnswVacuumState vacuumstate;
+
+	InitVacuumState(&vacuumstate, info, stats, callback, callback_state);
+
+	/* Pass 1: Remove heap TIDs */
+	RemoveHeapTids(&vacuumstate);
+
+	/* Pass 2: Repair graph */
+	RepairGraph(&vacuumstate);
+
+	/* Pass 3: Mark as deleted */
+	MarkDeleted(&vacuumstate);
+
+	FreeVacuumState(&vacuumstate);
+
+	return vacuumstate.stats;
+}
+
+/*
+ * Clean up after a VACUUM operation
+ */
+IndexBulkDeleteResult *
+hnswvacuumcleanup(IndexVacuumInfo *info, IndexBulkDeleteResult *stats)
+{
+	Relation	rel = info->index;
+
+	if (info->analyze_only)
+		return stats;
+
+	/* stats is NULL if ambulkdelete not called */
+	/* OK to return NULL if index not changed */
+	if (stats == NULL)
+		return NULL;
+
+	stats->num_pages = RelationGetNumberOfBlocks(rel);
+
+	return stats;
+}

src/ivfbuild.c

@@ -2,11 +2,16 @@
 
 #include <float.h>
 
+#include "access/parallel.h"
+#include "access/xact.h"
 #include "catalog/index.h"
+#include "catalog/pg_operator_d.h"
+#include "catalog/pg_type_d.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
 #include "storage/bufmgr.h"
 #include "utils/memutils.h"
+#include "tcop/tcopprot.h"
 
 #if PG_VERSION_NUM >= 140000
 #include "utils/backend_progress.h"
@@ -23,9 +28,6 @@
 #define PROGRESS_CREATEIDX_TUPLES_DONE 0
 #endif
 
-#include "catalog/pg_operator_d.h"
-#include "catalog/pg_type_d.h"
-
 #if PG_VERSION_NUM >= 130000
 #define CALLBACK_ITEM_POINTER ItemPointer tid
 #else
@@ -38,6 +40,25 @@
 #define UpdateProgress(index, val) ((void)val)
 #endif
 
+#if PG_VERSION_NUM >= 140000
+#include "utils/backend_status.h"
+#include "utils/wait_event.h"
+#endif
+
+#if PG_VERSION_NUM >= 120000
+#include "access/table.h"
+#include "optimizer/optimizer.h"
+#else
+#include "access/heapam.h"
+#include "optimizer/planner.h"
+#include "pgstat.h"
+#endif
+
+#define PARALLEL_KEY_IVFFLAT_SHARED		UINT64CONST(0xA000000000000001)
+#define PARALLEL_KEY_TUPLESORT			UINT64CONST(0xA000000000000002)
+#define PARALLEL_KEY_IVFFLAT_CENTERS	UINT64CONST(0xA000000000000003)
+#define PARALLEL_KEY_QUERY_TEXT			UINT64CONST(0xA000000000000004)
+
 /*
  * Add sample
  */
@@ -54,11 +75,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 	 * Normalize with KMEANS_NORM_PROC since spherical distance function
 	 * expects unit vectors
 	 */
-	if (buildstate->kmeansnormprocinfo != NULL)
+	IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->kmeansnormalizeprocinfo, buildstate->collation, &value, buildstate->normvec);
-	{
-		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->normvec))
-			return;
-	}
 
 	if (samples->length < targsamples)
 	{
@@ -147,23 +164,18 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState
 {
 	double		distance;
 	double		minDistance = DBL_MAX;
-	int			closestCenter = -1;
+	int			closestCenter = 0;
 	VectorArray centers = buildstate->centers;
 	TupleTableSlot *slot = buildstate->slot;
-	int			i;
 
 	/* Detoast once for all calls */
 	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
 
 	/* Normalize if needed */
-	if (buildstate->normprocinfo != NULL)
+	IvfflatNormValue(buildstate->normprocinfo, buildstate->normalizeprocinfo, buildstate->collation, &value, buildstate->normvec);
-	{
-		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->normvec))
-			return;
-	}
 
 	/* Find the list that minimizes the distance */
-	for (i = 0; i < centers->length; i++)
+	for (int i = 0; i < centers->length; i++)
 	{
 		distance = DatumGetFloat8(FunctionCall2Coll(buildstate->procinfo, buildstate->collation, value, PointerGetDatum(VectorArrayGet(centers, i))));
 
@@ -258,15 +270,8 @@ GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot,
 static void
 InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 {
-	Buffer		buf;
-	Page		page;
-	GenericXLogState *state;
 	int			list;
 	IndexTuple	itup = NULL;	/* silence compiler warning */
-	BlockNumber startPage;
-	BlockNumber insertPage;
-	Size		itemsz;
-	int			i;
 	int64		inserted = 0;
 
 #if PG_VERSION_NUM >= 120000
@@ -282,8 +287,14 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 
 	GetNextTuple(buildstate->sortstate, tupdesc, slot, &itup, &list);
 
-	for (i = 0; i < buildstate->centers->length; i++)
+	for (int i = 0; i < buildstate->centers->length; i++)
 	{
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		BlockNumber startPage;
+		BlockNumber insertPage;
+
 		/* Can take a while, so ensure we can interrupt */
 		/* Needs to be called when no buffer locks are held */
 		CHECK_FOR_INTERRUPTS();
@@ -297,7 +308,8 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 		while (list == i)
 		{
 			/* Check for free space */
-			itemsz = MAXALIGN(IndexTupleSize(itup));
+			Size		itemsz = MAXALIGN(IndexTupleSize(itup));
+
 			if (PageGetFreeSpace(page) < itemsz)
 				IvfflatAppendPage(index, &buf, &page, &state, forkNum);
 
@@ -317,7 +329,7 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 		IvfflatCommitBuffer(buf, state);
 
 		/* Set the start and insert pages */
-		IvfflatUpdateList(index, state, buildstate->listInfo[i], insertPage, InvalidBlockNumber, startPage, forkNum);
+		IvfflatUpdateList(index, buildstate->listInfo[i], insertPage, InvalidBlockNumber, startPage, forkNum);
 	}
 }
 
@@ -348,12 +360,12 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
 	buildstate->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	buildstate->kmeansnormprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
+	buildstate->normalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC);
+	buildstate->kmeansnormalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORMALIZE_PROC);
 	buildstate->collation = index->rd_indcollation[0];
 
 	/* Require more than one dimension for spherical k-means */
-	/* Lists check for backwards compatibility */
+	if (buildstate->kmeansnormprocinfo != NULL && buildstate->dimensions == 1)
-	/* TODO Remove lists check in 0.3.0 */
-	if (buildstate->kmeansnormprocinfo != NULL && buildstate->dimensions == 1 && buildstate->lists > 1)
 		elog(ERROR, "dimensions must be greater than one for this opclass");
 
 	/* Create tuple description for sorting */
@@ -387,6 +399,8 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->listSums = palloc0(sizeof(double) * buildstate->lists);
 	buildstate->listCounts = palloc0(sizeof(int) * buildstate->lists);
 #endif
+
+	buildstate->ivfleader = NULL;
 }
 
 /*
@@ -483,7 +497,6 @@ static void
 CreateListPages(Relation index, VectorArray centers, int dimensions,
 				int lists, ForkNumber forkNum, ListInfo * *listInfo)
 {
-	int			i;
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
@@ -497,7 +510,7 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	buf = IvfflatNewBuffer(index, forkNum);
 	IvfflatInitRegisterPage(index, &buf, &page, &state);
 
-	for (i = 0; i < lists; i++)
+	for (int i = 0; i < lists; i++)
 	{
 		/* Load list */
 		list->startPage = InvalidBlockNumber;
@@ -533,7 +546,7 @@ PrintKmeansMetrics(IvfflatBuildState * buildstate)
 	elog(INFO, "inertia: %.3e", buildstate->inertia);
 
 	/* Calculate Davies-Bouldin index */
-	if (buildstate->lists > 1)
+	if (buildstate->lists > 1 && !buildstate->ivfleader)
 	{
 		double		db = 0.0;
 
@@ -568,43 +581,478 @@ PrintKmeansMetrics(IvfflatBuildState * buildstate)
 }
 #endif
 
+/*
+ * Within leader, wait for end of heap scan
+ */
+static double
+ParallelHeapScan(IvfflatBuildState * buildstate)
+{
+	IvfflatShared *ivfshared = buildstate->ivfleader->ivfshared;
+	int			nparticipanttuplesorts;
+	double		reltuples;
+
+	nparticipanttuplesorts = buildstate->ivfleader->nparticipanttuplesorts;
+	for (;;)
+	{
+		SpinLockAcquire(&ivfshared->mutex);
+		if (ivfshared->nparticipantsdone == nparticipanttuplesorts)
+		{
+			buildstate->indtuples = ivfshared->indtuples;
+			reltuples = ivfshared->reltuples;
+#ifdef IVFFLAT_KMEANS_DEBUG
+			buildstate->inertia = ivfshared->inertia;
+#endif
+			SpinLockRelease(&ivfshared->mutex);
+			break;
+		}
+		SpinLockRelease(&ivfshared->mutex);
+
+		ConditionVariableSleep(&ivfshared->workersdonecv,
+							   WAIT_EVENT_PARALLEL_CREATE_INDEX_SCAN);
+	}
+
+	ConditionVariableCancelSleep();
+
+	return reltuples;
+}
+
+/*
+ * Perform a worker's portion of a parallel sort
+ */
+static void
+IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, Sharedsort *sharedsort, Vector * ivfcenters, int sortmem, bool progress)
+{
+	SortCoordinate coordinate;
+	IvfflatBuildState buildstate;
+#if PG_VERSION_NUM >= 120000
+	TableScanDesc scan;
+#else
+	HeapScanDesc scan;
+#endif
+	double		reltuples;
+	IndexInfo  *indexInfo;
+
+	/* Sort options, which must match AssignTuples */
+	AttrNumber	attNums[] = {1};
+	Oid			sortOperators[] = {Int4LessOperator};
+	Oid			sortCollations[] = {InvalidOid};
+	bool		nullsFirstFlags[] = {false};
+
+	/* Initialize local tuplesort coordination state */
+	coordinate = palloc0(sizeof(SortCoordinateData));
+	coordinate->isWorker = true;
+	coordinate->nParticipants = -1;
+	coordinate->sharedsort = sharedsort;
+
+	/* Join parallel scan */
+	indexInfo = BuildIndexInfo(ivfspool->index);
+	indexInfo->ii_Concurrent = ivfshared->isconcurrent;
+	InitBuildState(&buildstate, ivfspool->heap, ivfspool->index, indexInfo);
+	memcpy(buildstate.centers->items, ivfcenters, VECTOR_SIZE(buildstate.centers->dim) * buildstate.centers->maxlen);
+	buildstate.centers->length = buildstate.centers->maxlen;
+	ivfspool->sortstate = tuplesort_begin_heap(buildstate.tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, sortmem, coordinate, false);
+	buildstate.sortstate = ivfspool->sortstate;
+#if PG_VERSION_NUM >= 120000
+	scan = table_beginscan_parallel(ivfspool->heap,
+									ParallelTableScanFromIvfflatShared(ivfshared));
+	reltuples = table_index_build_scan(ivfspool->heap, ivfspool->index, indexInfo,
+									   true, progress, BuildCallback,
+									   (void *) &buildstate, scan);
+#else
+	scan = heap_beginscan_parallel(ivfspool->heap, &ivfshared->heapdesc);
+	reltuples = IndexBuildHeapScan(ivfspool->heap, ivfspool->index, indexInfo,
+								   true, BuildCallback,
+								   (void *) &buildstate, scan);
+#endif
+
+	/* Execute this worker's part of the sort */
+	tuplesort_performsort(ivfspool->sortstate);
+
+	/* Record statistics */
+	SpinLockAcquire(&ivfshared->mutex);
+	ivfshared->nparticipantsdone++;
+	ivfshared->reltuples += reltuples;
+	ivfshared->indtuples += buildstate.indtuples;
+#ifdef IVFFLAT_KMEANS_DEBUG
+	ivfshared->inertia += buildstate.inertia;
+#endif
+	SpinLockRelease(&ivfshared->mutex);
+
+	/* Log statistics */
+	if (progress)
+		ereport(DEBUG1, (errmsg("leader processed " INT64_FORMAT " tuples", (int64) reltuples)));
+	else
+		ereport(DEBUG1, (errmsg("worker processed " INT64_FORMAT " tuples", (int64) reltuples)));
+
+	/* Notify leader */
+	ConditionVariableSignal(&ivfshared->workersdonecv);
+
+	/* We can end tuplesorts immediately */
+	tuplesort_end(ivfspool->sortstate);
+
+	FreeBuildState(&buildstate);
+}
+
+/*
+ * Perform work within a launched parallel process
+ */
+void
+IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc)
+{
+	char	   *sharedquery;
+	IvfflatSpool *ivfspool;
+	IvfflatShared *ivfshared;
+	Sharedsort *sharedsort;
+	Vector	   *ivfcenters;
+	Relation	heapRel;
+	Relation	indexRel;
+	LOCKMODE	heapLockmode;
+	LOCKMODE	indexLockmode;
+	int			sortmem;
+
+	/* Set debug_query_string for individual workers first */
+	sharedquery = shm_toc_lookup(toc, PARALLEL_KEY_QUERY_TEXT, true);
+	debug_query_string = sharedquery;
+
+	/* Report the query string from leader */
+	pgstat_report_activity(STATE_RUNNING, debug_query_string);
+
+	/* Look up shared state */
+	ivfshared = shm_toc_lookup(toc, PARALLEL_KEY_IVFFLAT_SHARED, false);
+
+	/* Open relations using lock modes known to be obtained by index.c */
+	if (!ivfshared->isconcurrent)
+	{
+		heapLockmode = ShareLock;
+		indexLockmode = AccessExclusiveLock;
+	}
+	else
+	{
+		heapLockmode = ShareUpdateExclusiveLock;
+		indexLockmode = RowExclusiveLock;
+	}
+
+	/* Open relations within worker */
+#if PG_VERSION_NUM >= 120000
+	heapRel = table_open(ivfshared->heaprelid, heapLockmode);
+#else
+	heapRel = heap_open(ivfshared->heaprelid, heapLockmode);
+#endif
+	indexRel = index_open(ivfshared->indexrelid, indexLockmode);
+
+	/* Initialize worker's own spool */
+	ivfspool = (IvfflatSpool *) palloc0(sizeof(IvfflatSpool));
+	ivfspool->heap = heapRel;
+	ivfspool->index = indexRel;
+
+	/* Look up shared state private to tuplesort.c */
+	sharedsort = shm_toc_lookup(toc, PARALLEL_KEY_TUPLESORT, false);
+	tuplesort_attach_shared(sharedsort, seg);
+
+	ivfcenters = shm_toc_lookup(toc, PARALLEL_KEY_IVFFLAT_CENTERS, false);
+
+	/* Perform sorting */
+	sortmem = maintenance_work_mem / ivfshared->scantuplesortstates;
+	IvfflatParallelScanAndSort(ivfspool, ivfshared, sharedsort, ivfcenters, sortmem, false);
+
+	/* Close relations within worker */
+	index_close(indexRel, indexLockmode);
+#if PG_VERSION_NUM >= 120000
+	table_close(heapRel, heapLockmode);
+#else
+	heap_close(heapRel, heapLockmode);
+#endif
+}
+
+/*
+ * End parallel build
+ */
+static void
+IvfflatEndParallel(IvfflatLeader * ivfleader)
+{
+	/* Shutdown worker processes */
+	WaitForParallelWorkersToFinish(ivfleader->pcxt);
+
+	/* Free last reference to MVCC snapshot, if one was used */
+	if (IsMVCCSnapshot(ivfleader->snapshot))
+		UnregisterSnapshot(ivfleader->snapshot);
+	DestroyParallelContext(ivfleader->pcxt);
+	ExitParallelMode();
+}
+
+/*
+ * Return size of shared memory required for parallel index build
+ */
+static Size
+ParallelEstimateShared(Relation heap, Snapshot snapshot)
+{
+#if PG_VERSION_NUM >= 120000
+	return add_size(BUFFERALIGN(sizeof(IvfflatShared)), table_parallelscan_estimate(heap, snapshot));
+#else
+	if (!IsMVCCSnapshot(snapshot))
+	{
+		Assert(snapshot == SnapshotAny);
+		return sizeof(IvfflatShared);
+	}
+
+	return add_size(offsetof(IvfflatShared, heapdesc) +
+					offsetof(ParallelHeapScanDescData, phs_snapshot_data),
+					EstimateSnapshotSpace(snapshot));
+#endif
+}
+
+/*
+ * Within leader, participate as a parallel worker
+ */
+static void
+IvfflatLeaderParticipateAsWorker(IvfflatBuildState * buildstate)
+{
+	IvfflatLeader *ivfleader = buildstate->ivfleader;
+	IvfflatSpool *leaderworker;
+	int			sortmem;
+
+	/* Allocate memory and initialize private spool */
+	leaderworker = (IvfflatSpool *) palloc0(sizeof(IvfflatSpool));
+	leaderworker->heap = buildstate->heap;
+	leaderworker->index = buildstate->index;
+
+	/* Perform work common to all participants */
+	sortmem = maintenance_work_mem / ivfleader->nparticipanttuplesorts;
+	IvfflatParallelScanAndSort(leaderworker, ivfleader->ivfshared,
+							   ivfleader->sharedsort, ivfleader->ivfcenters,
+							   sortmem, true);
+}
+
+/*
+ * Begin parallel build
+ */
+static void
+IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int request)
+{
+	ParallelContext *pcxt;
+	int			scantuplesortstates;
+	Snapshot	snapshot;
+	Size		estivfshared;
+	Size		estsort;
+	Size		estcenters;
+	IvfflatShared *ivfshared;
+	Sharedsort *sharedsort;
+	Vector	   *ivfcenters;
+	IvfflatLeader *ivfleader = (IvfflatLeader *) palloc0(sizeof(IvfflatLeader));
+	bool		leaderparticipates = true;
+	int			querylen;
+
+#ifdef DISABLE_LEADER_PARTICIPATION
+	leaderparticipates = false;
+#endif
+
+	/* Enter parallel mode and create context */
+	EnterParallelMode();
+	Assert(request > 0);
+#if PG_VERSION_NUM >= 120000
+	pcxt = CreateParallelContext("vector", "IvfflatParallelBuildMain", request);
+#else
+	pcxt = CreateParallelContext("vector", "IvfflatParallelBuildMain", request, true);
+#endif
+
+	scantuplesortstates = leaderparticipates ? request + 1 : request;
+
+	/* Get snapshot for table scan */
+	if (!isconcurrent)
+		snapshot = SnapshotAny;
+	else
+		snapshot = RegisterSnapshot(GetTransactionSnapshot());
+
+	/* Estimate size of workspaces */
+	estivfshared = ParallelEstimateShared(buildstate->heap, snapshot);
+	shm_toc_estimate_chunk(&pcxt->estimator, estivfshared);
+	estsort = tuplesort_estimate_shared(scantuplesortstates);
+	shm_toc_estimate_chunk(&pcxt->estimator, estsort);
+	estcenters = VECTOR_SIZE(buildstate->dimensions) * buildstate->lists;
+	shm_toc_estimate_chunk(&pcxt->estimator, estcenters);
+	shm_toc_estimate_keys(&pcxt->estimator, 3);
+
+	/* Finally, estimate PARALLEL_KEY_QUERY_TEXT space */
+	if (debug_query_string)
+	{
+		querylen = strlen(debug_query_string);
+		shm_toc_estimate_chunk(&pcxt->estimator, querylen + 1);
+		shm_toc_estimate_keys(&pcxt->estimator, 1);
+	}
+	else
+		querylen = 0;			/* keep compiler quiet */
+
+	/* Everyone's had a chance to ask for space, so now create the DSM */
+	InitializeParallelDSM(pcxt);
+
+	/* If no DSM segment was available, back out (do serial build) */
+	if (pcxt->seg == NULL)
+	{
+		if (IsMVCCSnapshot(snapshot))
+			UnregisterSnapshot(snapshot);
+		DestroyParallelContext(pcxt);
+		ExitParallelMode();
+		return;
+	}
+
+	/* Store shared build state, for which we reserved space */
+	ivfshared = (IvfflatShared *) shm_toc_allocate(pcxt->toc, estivfshared);
+	/* Initialize immutable state */
+	ivfshared->heaprelid = RelationGetRelid(buildstate->heap);
+	ivfshared->indexrelid = RelationGetRelid(buildstate->index);
+	ivfshared->isconcurrent = isconcurrent;
+	ivfshared->scantuplesortstates = scantuplesortstates;
+	ConditionVariableInit(&ivfshared->workersdonecv);
+	SpinLockInit(&ivfshared->mutex);
+	/* Initialize mutable state */
+	ivfshared->nparticipantsdone = 0;
+	ivfshared->reltuples = 0;
+	ivfshared->indtuples = 0;
+#ifdef IVFFLAT_KMEANS_DEBUG
+	ivfshared->inertia = 0;
+#endif
+#if PG_VERSION_NUM >= 120000
+	table_parallelscan_initialize(buildstate->heap,
+								  ParallelTableScanFromIvfflatShared(ivfshared),
+								  snapshot);
+#else
+	heap_parallelscan_initialize(&ivfshared->heapdesc, buildstate->heap, snapshot);
+#endif
+
+	/* Store shared tuplesort-private state, for which we reserved space */
+	sharedsort = (Sharedsort *) shm_toc_allocate(pcxt->toc, estsort);
+	tuplesort_initialize_shared(sharedsort, scantuplesortstates,
+								pcxt->seg);
+
+	ivfcenters = (Vector *) shm_toc_allocate(pcxt->toc, estcenters);
+	memcpy(ivfcenters, buildstate->centers->items, estcenters);
+
+	shm_toc_insert(pcxt->toc, PARALLEL_KEY_IVFFLAT_SHARED, ivfshared);
+	shm_toc_insert(pcxt->toc, PARALLEL_KEY_TUPLESORT, sharedsort);
+	shm_toc_insert(pcxt->toc, PARALLEL_KEY_IVFFLAT_CENTERS, ivfcenters);
+
+	/* Store query string for workers */
+	if (debug_query_string)
+	{
+		char	   *sharedquery;
+
+		sharedquery = (char *) shm_toc_allocate(pcxt->toc, querylen + 1);
+		memcpy(sharedquery, debug_query_string, querylen + 1);
+		shm_toc_insert(pcxt->toc, PARALLEL_KEY_QUERY_TEXT, sharedquery);
+	}
+
+	/* Launch workers, saving status for leader/caller */
+	LaunchParallelWorkers(pcxt);
+	ivfleader->pcxt = pcxt;
+	ivfleader->nparticipanttuplesorts = pcxt->nworkers_launched;
+	if (leaderparticipates)
+		ivfleader->nparticipanttuplesorts++;
+	ivfleader->ivfshared = ivfshared;
+	ivfleader->sharedsort = sharedsort;
+	ivfleader->snapshot = snapshot;
+	ivfleader->ivfcenters = ivfcenters;
+
+	/* If no workers were successfully launched, back out (do serial build) */
+	if (pcxt->nworkers_launched == 0)
+	{
+		IvfflatEndParallel(ivfleader);
+		return;
+	}
+
+	/* Log participants */
+	ereport(DEBUG1, (errmsg("using %d parallel workers", pcxt->nworkers_launched)));
+
+	/* Save leader state now that it's clear build will be parallel */
+	buildstate->ivfleader = ivfleader;
+
+	/* Join heap scan ourselves */
+	if (leaderparticipates)
+		IvfflatLeaderParticipateAsWorker(buildstate);
+
+	/* Wait for all launched workers */
+	WaitForParallelWorkersToAttach(pcxt);
+}
+
+/*
+ * Scan table for tuples to index
+ */
+static void
+AssignTuples(IvfflatBuildState * buildstate)
+{
+	int			parallel_workers = 0;
+	SortCoordinate coordinate = NULL;
+
+	/* Sort options, which must match IvfflatParallelScanAndSort */
+	AttrNumber	attNums[] = {1};
+	Oid			sortOperators[] = {Int4LessOperator};
+	Oid			sortCollations[] = {InvalidOid};
+	bool		nullsFirstFlags[] = {false};
+
+	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_ASSIGN);
+
+	/* Calculate parallel workers */
+	if (buildstate->heap != NULL)
+		parallel_workers = plan_create_index_workers(RelationGetRelid(buildstate->heap), RelationGetRelid(buildstate->index));
+
+	/* Attempt to launch parallel worker scan when required */
+	if (parallel_workers > 0)
+		IvfflatBeginParallel(buildstate, buildstate->indexInfo->ii_Concurrent, parallel_workers);
+
+	/* Set up coordination state if at least one worker launched */
+	if (buildstate->ivfleader)
+	{
+		coordinate = (SortCoordinate) palloc0(sizeof(SortCoordinateData));
+		coordinate->isWorker = false;
+		coordinate->nParticipants = buildstate->ivfleader->nparticipanttuplesorts;
+		coordinate->sharedsort = buildstate->ivfleader->sharedsort;
+	}
+
+	/* Begin serial/leader tuplesort */
+	buildstate->sortstate = tuplesort_begin_heap(buildstate->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, maintenance_work_mem, coordinate, false);
+
+	/* Add tuples to sort */
+	if (buildstate->heap != NULL)
+	{
+		if (buildstate->ivfleader)
+			buildstate->reltuples = ParallelHeapScan(buildstate);
+		else
+		{
+#if PG_VERSION_NUM >= 120000
+			buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+														   true, true, BuildCallback, (void *) buildstate, NULL);
+#else
+			buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+													   true, BuildCallback, (void *) buildstate, NULL);
+#endif
+		}
+
+#ifdef IVFFLAT_KMEANS_DEBUG
+		PrintKmeansMetrics(buildstate);
+#endif
+	}
+}
+
 /*
  * Create entry pages
  */
 static void
 CreateEntryPages(IvfflatBuildState * buildstate, ForkNumber forkNum)
 {
-	AttrNumber	attNums[] = {1};
+	/* Assign */
-	Oid			sortOperators[] = {Float8LessOperator};
+	IvfflatBench("assign tuples", AssignTuples(buildstate));
-	Oid			sortCollations[] = {InvalidOid};
-	bool		nullsFirstFlags[] = {false};
-
-	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_SORT);
-
-	buildstate->sortstate = tuplesort_begin_heap(buildstate->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, maintenance_work_mem, NULL, false);
-
-	/* Add tuples to sort */
-	if (buildstate->heap != NULL)
-	{
-#if PG_VERSION_NUM >= 120000
-		buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-													   true, true, BuildCallback, (void *) buildstate, NULL);
-#else
-		buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-												   true, BuildCallback, (void *) buildstate, NULL);
-#endif
-	}
 
 	/* Sort */
-	tuplesort_performsort(buildstate->sortstate);
+	IvfflatBench("sort tuples", tuplesort_performsort(buildstate->sortstate));
 
-#ifdef IVFFLAT_KMEANS_DEBUG
+	/* Load */
-	PrintKmeansMetrics(buildstate);
+	IvfflatBench("load tuples", InsertTuples(buildstate->index, buildstate, forkNum));
-#endif
 
-	/* Insert */
+	/* End sort */
-	InsertTuples(buildstate->index, buildstate, forkNum);
 	tuplesort_end(buildstate->sortstate);
+
+	/* End parallel build */
+	if (buildstate->ivfleader)
+		IvfflatEndParallel(buildstate->ivfleader);
 }
 
 /*
@@ -621,7 +1069,7 @@ BuildIndex(Relation heap, Relation index, IndexInfo *indexInfo,
 	/* Create pages */
 	CreateMetaPage(index, buildstate->dimensions, buildstate->lists, forkNum);
 	CreateListPages(index, buildstate->centers, buildstate->dimensions, buildstate->lists, forkNum, &buildstate->listInfo);
-	IvfflatBench("CreateEntryPages", CreateEntryPages(buildstate, forkNum));
+	CreateEntryPages(buildstate, forkNum);
 
 	FreeBuildState(buildstate);
 }

src/ivfflat.c

@@ -7,6 +7,7 @@
 #include "ivfflat.h"
 #include "utils/guc.h"
 #include "utils/selfuncs.h"
+#include "utils/spccache.h"
 
 #if PG_VERSION_NUM >= 120000
 #include "commands/progress.h"
@@ -19,7 +20,7 @@ static relopt_kind ivfflat_relopt_kind;
  * Initialize index options and variables
  */
 void
-_PG_init(void)
+IvfflatInit(void)
 {
 	ivfflat_relopt_kind = add_reloption_kind();
 	add_int_reloption(ivfflat_relopt_kind, "lists", "Number of inverted lists",
@@ -47,8 +48,8 @@ ivfflatbuildphasename(int64 phasenum)
 			return "initializing";
 		case PROGRESS_IVFFLAT_PHASE_KMEANS:
 			return "performing k-means";
-		case PROGRESS_IVFFLAT_PHASE_SORT:
+		case PROGRESS_IVFFLAT_PHASE_ASSIGN:
-			return "sorting tuples";
+			return "assigning tuples";
 		case PROGRESS_IVFFLAT_PHASE_LOAD:
 			return "loading tuples";
 		default:
@@ -63,13 +64,13 @@ ivfflatbuildphasename(int64 phasenum)
 static void
 ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 					Cost *indexStartupCost, Cost *indexTotalCost,
-					Selectivity *indexSelectivity, double *indexCorrelation
+					Selectivity *indexSelectivity, double *indexCorrelation,
-					,double *indexPages
+					double *indexPages)
-)
 {
 	GenericCosts costs;
 	int			lists;
 	double		ratio;
+	double		spc_seq_page_cost;
 	Relation	indexRel;
 #if PG_VERSION_NUM < 120000
 	List	   *qinfos;
@@ -88,6 +89,22 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 
 	MemSet(&costs, 0, sizeof(costs));
 
+	indexRel = index_open(path->indexinfo->indexoid, NoLock);
+	lists = IvfflatGetLists(indexRel);
+	index_close(indexRel, NoLock);
+
+	/* Get the ratio of lists that we need to visit */
+	ratio = ((double) ivfflat_probes) / lists;
+	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;
+
 #if PG_VERSION_NUM >= 120000
 	genericcostestimate(root, path, loop_count, &costs);
 #else
@@ -95,17 +112,31 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	genericcostestimate(root, path, loop_count, qinfos, &costs);
 #endif
 
-	indexRel = index_open(path->indexinfo->indexoid, NoLock);
+	get_tablespace_page_costs(path->indexinfo->reltablespace, NULL, &spc_seq_page_cost);
-	lists = IvfflatGetLists(indexRel);
-	index_close(indexRel, NoLock);
 
-	ratio = ((double) ivfflat_probes) / lists;
+	/* Adjust cost if needed since TOAST not included in seq scan cost */
-	if (ratio > 1)
+	if (costs.numIndexPages > path->indexinfo->rel->pages && ratio < 0.5)
-		ratio = 1;
+	{
+		/* Change all page cost from random to sequential */
+		costs.indexTotalCost -= costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
 
-	costs.indexTotalCost *= ratio;
+		/* 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);
+	}
 
-	/* Startup cost and total cost are same */
+	/*
+	 * 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;
 	*indexTotalCost = costs.indexTotalCost;
 	*indexSelectivity = costs.indexSelectivity;
@@ -163,7 +194,7 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);
 
 	amroutine->amstrategies = 0;
-	amroutine->amsupport = 4;
+	amroutine->amsupport = 6;
 #if PG_VERSION_NUM >= 130000
 	amroutine->amoptsprocnum = 0;
 #endif

src/ivfflat.h

@@ -3,14 +3,11 @@
 
 #include "postgres.h"
 
-#if PG_VERSION_NUM < 110000
-#error "Requires PostgreSQL 11+"
-#endif
-
 #include "access/generic_xlog.h"
+#include "access/parallel.h"
 #include "access/reloptions.h"
 #include "nodes/execnodes.h"
-#include "port.h"				/* for strtof() and random() */
+#include "port.h"				/* for random() */
 #include "utils/sampling.h"
 #include "utils/tuplesort.h"
 #include "vector.h"
@@ -19,6 +16,10 @@
 #include "common/pg_prng.h"
 #endif
 
+#if PG_VERSION_NUM < 120000
+#include "access/relscan.h"
+#endif
+
 #ifdef IVFFLAT_BENCH
 #include "portability/instr_time.h"
 #endif
@@ -30,6 +31,8 @@
 #define IVFFLAT_NORM_PROC 2
 #define IVFFLAT_KMEANS_DISTANCE_PROC 3
 #define IVFFLAT_KMEANS_NORM_PROC 4
+#define IVFFLAT_NORMALIZE_PROC 5
+#define IVFFLAT_KMEANS_NORMALIZE_PROC 6
 
 #define IVFFLAT_VERSION	1
 #define IVFFLAT_MAGIC_NUMBER 0x14FF1A7
@@ -45,7 +48,7 @@
 /* Build phases */
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
 #define PROGRESS_IVFFLAT_PHASE_KMEANS	2
-#define PROGRESS_IVFFLAT_PHASE_SORT		3
+#define PROGRESS_IVFFLAT_PHASE_ASSIGN	3
 #define PROGRESS_IVFFLAT_PHASE_LOAD		4
 
 #define IVFFLAT_LIST_SIZE(_dim)	(offsetof(IvfflatListData, center) + VECTOR_SIZE(_dim))
@@ -79,9 +82,6 @@
 /* Variables */
 extern int	ivfflat_probes;
 
-/* Exported functions */
-PGDLLEXPORT void _PG_init(void);
-
 typedef struct VectorArrayData
 {
 	int			length;
@@ -105,6 +105,56 @@ typedef struct IvfflatOptions
 	int			lists;			/* number of lists */
 }			IvfflatOptions;
 
+typedef struct IvfflatSpool
+{
+	Tuplesortstate *sortstate;
+	Relation	heap;
+	Relation	index;
+}			IvfflatSpool;
+
+typedef struct IvfflatShared
+{
+	/* Immutable state */
+	Oid			heaprelid;
+	Oid			indexrelid;
+	bool		isconcurrent;
+	int			scantuplesortstates;
+
+	/* Worker progress */
+	ConditionVariable workersdonecv;
+
+	/* Mutex for mutable state */
+	slock_t		mutex;
+
+	/* Mutable state */
+	int			nparticipantsdone;
+	double		reltuples;
+	double		indtuples;
+
+#ifdef IVFFLAT_KMEANS_DEBUG
+	double		inertia;
+#endif
+
+#if PG_VERSION_NUM < 120000
+	ParallelHeapScanDescData heapdesc;	/* must come last */
+#endif
+}			IvfflatShared;
+
+#if PG_VERSION_NUM >= 120000
+#define ParallelTableScanFromIvfflatShared(shared) \
+	(ParallelTableScanDesc) ((char *) (shared) + BUFFERALIGN(sizeof(IvfflatShared)))
+#endif
+
+typedef struct IvfflatLeader
+{
+	ParallelContext *pcxt;
+	int			nparticipanttuplesorts;
+	IvfflatShared *ivfshared;
+	Sharedsort *sharedsort;
+	Snapshot	snapshot;
+	Vector	   *ivfcenters;
+}			IvfflatLeader;
+
 typedef struct IvfflatBuildState
 {
 	/* Info */
@@ -124,6 +174,8 @@ typedef struct IvfflatBuildState
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
 	FmgrInfo   *kmeansnormprocinfo;
+	FmgrInfo   *normalizeprocinfo;
+	FmgrInfo   *kmeansnormalizeprocinfo;
 	Oid			collation;
 
 	/* Variables */
@@ -150,6 +202,9 @@ typedef struct IvfflatBuildState
 
 	/* Memory */
 	MemoryContext tmpCtx;
+
+	/* Parallel builds */
+	IvfflatLeader *ivfleader;
 }			IvfflatBuildState;
 
 typedef struct IvfflatMetaPageData
@@ -202,6 +257,7 @@ typedef struct IvfflatScanOpaqueData
 	/* Support functions */
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Oid			collation;
 
 	/* Lists */
@@ -222,14 +278,16 @@ void		VectorArrayFree(VectorArray arr);
 void		PrintVectorArray(char *msg, VectorArray arr);
 void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
 FmgrInfo   *IvfflatOptionalProcInfo(Relation rel, uint16 procnum);
-bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+void		IvfflatNormValue(FmgrInfo *procinfo, FmgrInfo *normalizeprocinfo, Oid collation, Datum *value, Vector * result);
 int			IvfflatGetLists(Relation index);
-void		IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);
+void		IvfflatUpdateList(Relation index, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);
 void		IvfflatCommitBuffer(Buffer buf, GenericXLogState *state);
 void		IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state, ForkNumber forkNum);
 Buffer		IvfflatNewBuffer(Relation index, ForkNumber forkNum);
 void		IvfflatInitPage(Buffer buf, Page page);
 void		IvfflatInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state);
+void		IvfflatInit(void);
+PGDLLEXPORT void IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc);
 
 /* Index access methods */
 IndexBuildResult *ivfflatbuild(Relation heap, Relation index, IndexInfo *indexInfo);

src/ivfinsert.c

@@ -4,6 +4,7 @@
 
 #include "ivfflat.h"
 #include "storage/bufmgr.h"
+#include "storage/lmgr.h"
 #include "utils/memutils.h"
 
 /*
@@ -23,6 +24,10 @@ FindInsertPage(Relation rel, Datum *values, BlockNumber *insertPage, ListInfo *
 	OffsetNumber offno;
 	OffsetNumber maxoffno;
 
+	/* Avoid compiler warning */
+	listInfo->blkno = nextblkno;
+	listInfo->offno = FirstOffsetNumber;
+
 	procinfo = index_getprocinfo(rel, 1, IVFFLAT_DISTANCE_PROC);
 	collation = rel->rd_indcollation[0];
 
@@ -39,7 +44,7 @@ FindInsertPage(Relation rel, Datum *values, BlockNumber *insertPage, ListInfo *
 			list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, offno));
 			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, values[0], PointerGetDatum(&list->center)));
 
-			if (distance < minDistance)
+			if (distance < minDistance || !BlockNumberIsValid(*insertPage))
 			{
 				*insertPage = list->insertPage;
 				listInfo->blkno = nextblkno;
@@ -63,6 +68,7 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 	IndexTuple	itup;
 	Datum		value;
 	FmgrInfo   *normprocinfo;
+	FmgrInfo   *normalizeprocinfo;
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
@@ -76,11 +82,8 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 
 	/* Normalize if needed */
 	normprocinfo = IvfflatOptionalProcInfo(rel, IVFFLAT_NORM_PROC);
-	if (normprocinfo != NULL)
+	normalizeprocinfo = IvfflatOptionalProcInfo(rel, IVFFLAT_NORMALIZE_PROC);
-	{
+	IvfflatNormValue(normprocinfo, normalizeprocinfo, rel->rd_indcollation[0], &value, NULL);
-		if (!IvfflatNormValue(normprocinfo, rel->rd_indcollation[0], &value, NULL))
-			return;
-	}
 
 	/* Find the insert page - sets the page and list info */
 	FindInsertPage(rel, values, &insertPage, &listInfo);
@@ -117,23 +120,16 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 		}
 		else
 		{
-			Buffer		metabuf;
 			Buffer		newbuf;
 			Page		newpage;
 
-			/*
-			 * From ReadBufferExtended: Caller is responsible for ensuring
-			 * that only one backend tries to extend a relation at the same
-			 * time!
-			 */
-			metabuf = ReadBuffer(rel, IVFFLAT_METAPAGE_BLKNO);
-			LockBuffer(metabuf, BUFFER_LOCK_EXCLUSIVE);
-
 			/* Add a new page */
+			LockRelationForExtension(rel, ExclusiveLock);
 			newbuf = IvfflatNewBuffer(rel, MAIN_FORKNUM);
-			newpage = GenericXLogRegisterBuffer(state, newbuf, GENERIC_XLOG_FULL_IMAGE);
+			UnlockRelationForExtension(rel, ExclusiveLock);
 
 			/* Init new page */
+			newpage = GenericXLogRegisterBuffer(state, newbuf, GENERIC_XLOG_FULL_IMAGE);
 			IvfflatInitPage(newbuf, newpage);
 
 			/* Update insert page */
@@ -147,9 +143,6 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 			MarkBufferDirty(buf);
 			GenericXLogFinish(state);
 
-			/* Unlock extend relation lock as early as possible */
-			UnlockReleaseBuffer(metabuf);
-
 			/* Unlock previous buffer */
 			UnlockReleaseBuffer(buf);
 
@@ -169,7 +162,7 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 
 	/* Update the insert page */
 	if (insertPage != originalInsertPage)
-		IvfflatUpdateList(rel, state, listInfo, insertPage, originalInsertPage, InvalidBlockNumber, MAIN_FORKNUM);
+		IvfflatUpdateList(rel, listInfo, insertPage, originalInsertPage, InvalidBlockNumber, MAIN_FORKNUM);
 }
 
 /*

src/ivfkmeans.c

@@ -1,6 +1,7 @@
 #include "postgres.h"
 
 #include <float.h>
+#include <math.h>
 
 #include "ivfflat.h"
 #include "miscadmin.h"
@@ -15,7 +16,6 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 {
 	FmgrInfo   *procinfo;
 	Oid			collation;
-	int			i;
 	int64		j;
 	double		distance;
 	double		sum;
@@ -35,7 +35,7 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 	for (j = 0; j < numSamples; j++)
 		weight[j] = DBL_MAX;
 
-	for (i = 0; i < numCenters; i++)
+	for (int i = 0; i < numCenters; i++)
 	{
 		CHECK_FOR_INTERRUPTS();
 
@@ -87,13 +87,12 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 static inline void
 ApplyNorm(FmgrInfo *normprocinfo, Oid collation, Vector * vec)
 {
-	int			i;
 	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(vec)));
 
 	/* TODO Handle zero norm */
 	if (norm > 0)
 	{
-		for (i = 0; i < vec->dim; i++)
+		for (int i = 0; i < vec->dim; i++)
 			vec->x[i] /= norm;
 	}
 }
@@ -113,8 +112,6 @@ CompareVectors(const void *a, const void *b)
 static void
 QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 {
-	int			i;
-	int			j;
 	Vector	   *vec;
 	int			dimensions = centers->dim;
 	Oid			collation = index->rd_indcollation[0];
@@ -124,7 +121,7 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	if (samples->length > 0)
 	{
 		qsort(samples->items, samples->length, VECTOR_SIZE(samples->dim), CompareVectors);
-		for (i = 0; i < samples->length; i++)
+		for (int i = 0; i < samples->length; i++)
 		{
 			vec = VectorArrayGet(samples, i);
 
@@ -144,7 +141,7 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
 		vec->dim = dimensions;
 
-		for (j = 0; j < dimensions; j++)
+		for (int j = 0; j < dimensions; j++)
 			vec->x[j] = RandomDouble();
 
 		/* Normalize if needed (only needed for random centers) */
@@ -211,7 +208,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 	/* Check memory requirements */
 	/* Add one to error message to ceil */
-	if (totalSize / 1024 > maintenance_work_mem)
+	if (totalSize > (Size) maintenance_work_mem * 1024L)
 		ereport(ERROR,
 				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
 				 errmsg("memory required is %zu MB, maintenance_work_mem is %d MB",
@@ -251,7 +248,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	for (j = 0; j < numSamples; j++)
 	{
 		minDistance = DBL_MAX;
-		closestCenter = -1;
+		closestCenter = 0;
 
 		/* Find closest center */
 		for (k = 0; k < numCenters; k++)
@@ -398,6 +395,14 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 			if (centerCounts[j] > 0)
 			{
+				/* Double avoids overflow, but requires more memory */
+				/* TODO Update bounds */
+				for (k = 0; k < dimensions; k++)
+				{
+					if (isinf(vec->x[k]))
+						vec->x[k] = vec->x[k] > 0 ? FLT_MAX : -FLT_MAX;
+				}
+
 				for (k = 0; k < dimensions; k++)
 					vec->x[k] /= centerCounts[j];
 			}
@@ -461,16 +466,31 @@ CheckCenters(Relation index, VectorArray centers)
 {
 	FmgrInfo   *normprocinfo;
 	Oid			collation;
-	int			i;
+	Vector	   *vec;
 	double		norm;
 
 	if (centers->length != centers->maxlen)
 		elog(ERROR, "Not enough centers. Please report a bug.");
 
+	/* Ensure no NaN or infinite values */
+	for (int i = 0; i < centers->length; i++)
+	{
+		vec = VectorArrayGet(centers, i);
+
+		for (int j = 0; j < vec->dim; j++)
+		{
+			if (isnan(vec->x[j]))
+				elog(ERROR, "NaN detected. Please report a bug.");
+
+			if (isinf(vec->x[j]))
+				elog(ERROR, "Infinite value detected. Please report a bug.");
+		}
+	}
+
 	/* Ensure no duplicate centers */
 	/* Fine to sort in-place */
 	qsort(centers->items, centers->length, VECTOR_SIZE(centers->dim), CompareVectors);
-	for (i = 1; i < centers->length; i++)
+	for (int i = 1; i < centers->length; i++)
 	{
 		if (CompareVectors(VectorArrayGet(centers, i), VectorArrayGet(centers, i - 1)) == 0)
 			elog(ERROR, "Duplicate centers detected. Please report a bug.");
@@ -483,7 +503,7 @@ CheckCenters(Relation index, VectorArray centers)
 	{
 		collation = index->rd_indcollation[0];
 
-		for (i = 0; i < centers->length; i++)
+		for (int i = 0; i < centers->length; i++)
 		{
 			norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(VectorArrayGet(centers, i))));
 			if (norm == 0)

src/ivfscan.c

@@ -3,14 +3,13 @@
 #include <float.h>
 
 #include "access/relscan.h"
+#include "catalog/pg_operator_d.h"
+#include "catalog/pg_type_d.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
 #include "pgstat.h"
 #include "storage/bufmgr.h"
 
-#include "catalog/pg_operator_d.h"
-#include "catalog/pg_type_d.h"
-
 /*
  * Compare list distances
  */
@@ -170,7 +169,8 @@ GetScanItems(IndexScanDesc scan, Datum value)
 		}
 	}
 
-	/* TODO Scan more lists */
+	FreeAccessStrategy(bas);
+
 	if (tuples < 100)
 		ereport(DEBUG1,
 				(errmsg("index scan found few tuples"),
@@ -180,6 +180,29 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	tuplesort_performsort(so->sortstate);
 }
 
+/*
+ * Get dimensions from metapage
+ */
+static int
+GetDimensions(Relation index)
+{
+	Buffer		buf;
+	Page		page;
+	IvfflatMetaPage metap;
+	int			dimensions;
+
+	buf = ReadBuffer(index, IVFFLAT_METAPAGE_BLKNO);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	metap = IvfflatPageGetMeta(page);
+
+	dimensions = metap->dimensions;
+
+	UnlockReleaseBuffer(buf);
+
+	return dimensions;
+}
+
 /*
  * Prepare for an index scan
  */
@@ -209,6 +232,7 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	/* Set support functions */
 	so->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
 	so->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
+	so->normalizeprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORMALIZE_PROC);
 	so->collation = index->rd_indcollation[0];
 
 	/* Create tuple description for sorting */
@@ -285,21 +309,18 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (scan->orderByData == NULL)
 			elog(ERROR, "cannot scan ivfflat index without order");
 
-		/* No items will match if null */
 		if (scan->orderByData->sk_flags & SK_ISNULL)
-			return false;
+			value = PointerGetDatum(InitVector(GetDimensions(scan->indexRelation)));
-
+		else
-		value = scan->orderByData->sk_argument;
-
-		/* Value should not be compressed or toasted */
-		Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
-		Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
-
-		if (so->normprocinfo != NULL)
 		{
-			/* No items will match if normalization fails */
+			value = scan->orderByData->sk_argument;
-			if (!IvfflatNormValue(so->normprocinfo, so->collation, &value, NULL))
+
-				return false;
+			/* Value should not be compressed or toasted */
+			Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
+			Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
+
+			/* Fine if normalization fails */
+			IvfflatNormValue(so->normprocinfo, so->normalizeprocinfo, so->collation, &value, NULL);
 		}
 
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));

src/ivfutils.c

@@ -35,9 +35,7 @@ VectorArrayFree(VectorArray arr)
 void
 PrintVectorArray(char *msg, VectorArray arr)
 {
-	int			i;
+	for (int i = 0; i < arr->length; i++)
-
-	for (i = 0; i < arr->length; i++)
 		PrintVector(msg, VectorArrayGet(arr, i));
 }
 
@@ -68,38 +66,39 @@ IvfflatOptionalProcInfo(Relation rel, uint16 procnum)
 }
 
 /*
- * Divide by the norm
+ * Normalize a vector
- *
- * Returns false if value should not be indexed
  *
  * The caller needs to free the pointer stored in value
  * if it's different than the original value
  */
-bool
+void
-IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result)
+IvfflatNormValue(FmgrInfo *procinfo, FmgrInfo *normalizeprocinfo, Oid collation, Datum *value, Vector * result)
 {
-	Vector	   *v;
-	int			i;
 	double		norm;
 
+	if (normalizeprocinfo != NULL)
+	{
+		*value = FunctionCall1Coll(normalizeprocinfo, collation, *value);
+		return;
+	}
+
+	if (procinfo == NULL)
+		return;
+
 	norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
 
 	if (norm > 0)
 	{
-		v = DatumGetVector(*value);
+		Vector	   *v = DatumGetVector(*value);
 
 		if (result == NULL)
 			result = InitVector(v->dim);
 
-		for (i = 0; i < v->dim; i++)
+		for (int i = 0; i < v->dim; i++)
 			result->x[i] = v->x[i] / norm;
 
 		*value = PointerGetDatum(result);
-
-		return true;
 	}
-
-	return false;
 }
 
 /*
@@ -182,12 +181,13 @@ IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **st
  * Update the start or insert page of a list
  */
 void
-IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo,
+IvfflatUpdateList(Relation index, ListInfo listInfo,
 				  BlockNumber insertPage, BlockNumber originalInsertPage,
 				  BlockNumber startPage, ForkNumber forkNum)
 {
 	Buffer		buf;
 	Page		page;
+	GenericXLogState *state;
 	IvfflatList list;
 	bool		changed = false;
 

src/ivfvacuum.c

@@ -12,34 +12,23 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 				  IndexBulkDeleteCallback callback, void *callback_state)
 {
 	Relation	index = info->index;
-	Buffer		cbuf;
+	BlockNumber blkno = IVFFLAT_HEAD_BLKNO;
-	Page		cpage;
-	Buffer		buf;
-	Page		page;
-	IvfflatList list;
-	IndexTuple	itup;
-	ItemPointer htup;
-	OffsetNumber deletable[MaxOffsetNumber];
-	int			ndeletable;
-	BlockNumber startPages[MaxOffsetNumber];
-	BlockNumber nextblkno = IVFFLAT_HEAD_BLKNO;
-	BlockNumber searchPage;
-	BlockNumber insertPage;
-	GenericXLogState *state;
-	OffsetNumber coffno;
-	OffsetNumber cmaxoffno;
-	OffsetNumber offno;
-	OffsetNumber maxoffno;
-	ListInfo	listInfo;
 	BufferAccessStrategy bas = GetAccessStrategy(BAS_BULKREAD);
 
 	if (stats == NULL)
 		stats = (IndexBulkDeleteResult *) palloc0(sizeof(IndexBulkDeleteResult));
 
 	/* Iterate over list pages */
-	while (BlockNumberIsValid(nextblkno))
+	while (BlockNumberIsValid(blkno))
 	{
-		cbuf = ReadBuffer(index, nextblkno);
+		Buffer		cbuf;
+		Page		cpage;
+		OffsetNumber coffno;
+		OffsetNumber cmaxoffno;
+		BlockNumber startPages[MaxOffsetNumber];
+		ListInfo	listInfo;
+
+		cbuf = ReadBuffer(index, blkno);
 		LockBuffer(cbuf, BUFFER_LOCK_SHARE);
 		cpage = BufferGetPage(cbuf);
 
@@ -48,23 +37,32 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 		/* Iterate over lists */
 		for (coffno = FirstOffsetNumber; coffno <= cmaxoffno; coffno = OffsetNumberNext(coffno))
 		{
-			list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, coffno));
+			IvfflatList list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, coffno));
+
 			startPages[coffno - FirstOffsetNumber] = list->startPage;
 		}
 
-		listInfo.blkno = nextblkno;
+		listInfo.blkno = blkno;
-		nextblkno = IvfflatPageGetOpaque(cpage)->nextblkno;
+		blkno = IvfflatPageGetOpaque(cpage)->nextblkno;
 
 		UnlockReleaseBuffer(cbuf);
 
 		for (coffno = FirstOffsetNumber; coffno <= cmaxoffno; coffno = OffsetNumberNext(coffno))
 		{
-			searchPage = startPages[coffno - FirstOffsetNumber];
+			BlockNumber searchPage = startPages[coffno - FirstOffsetNumber];
-			insertPage = InvalidBlockNumber;
+			BlockNumber insertPage = InvalidBlockNumber;
 
 			/* Iterate over entry pages */
 			while (BlockNumberIsValid(searchPage))
 			{
+				Buffer		buf;
+				Page		page;
+				GenericXLogState *state;
+				OffsetNumber offno;
+				OffsetNumber maxoffno;
+				OffsetNumber deletable[MaxOffsetNumber];
+				int			ndeletable;
+
 				vacuum_delay_point();
 
 				buf = ReadBufferExtended(index, MAIN_FORKNUM, searchPage, RBM_NORMAL, bas);
@@ -86,8 +84,8 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 				/* Find deleted tuples */
 				for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
 				{
-					itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offno));
+					IndexTuple	itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offno));
-					htup = &(itup->t_tid);
+					ItemPointer htup = &(itup->t_tid);
 
 					if (callback(htup, callback_state))
 					{
@@ -127,11 +125,13 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 			if (BlockNumberIsValid(insertPage))
 			{
 				listInfo.offno = coffno;
-				IvfflatUpdateList(index, state, listInfo, insertPage, InvalidBlockNumber, InvalidBlockNumber, MAIN_FORKNUM);
+				IvfflatUpdateList(index, listInfo, insertPage, InvalidBlockNumber, InvalidBlockNumber, MAIN_FORKNUM);
 			}
 		}
 	}
 
+	FreeAccessStrategy(bas);
+
 	return stats;
 }
 

src/vector.c

@@ -2,15 +2,18 @@
 
 #include <math.h>
 
-#include "vector.h"
-#include "fmgr.h"
 #include "catalog/pg_type.h"
+#include "fmgr.h"
+#include "hnsw.h"
+#include "ivfflat.h"
 #include "lib/stringinfo.h"
 #include "libpq/pqformat.h"
+#include "port.h"				/* for strtof() */
 #include "utils/array.h"
 #include "utils/builtins.h"
 #include "utils/lsyscache.h"
 #include "utils/numeric.h"
+#include "vector.h"
 
 #if PG_VERSION_NUM >= 120000
 #include "common/shortest_dec.h"
@@ -29,6 +32,16 @@
 
 PG_MODULE_MAGIC;
 
+/*
+ * Initialize index options and variables
+ */
+void
+_PG_init(void)
+{
+	HnswInit();
+	IvfflatInit();
+}
+
 /*
  * Ensure same dimensions
  */
@@ -42,7 +55,7 @@ CheckDims(Vector * a, Vector * b)
 }
 
 /*
- * Ensure expected dimension
+ * Ensure expected dimensions
  */
 static inline void
 CheckExpectedDim(int32 typmod, int dim)
@@ -53,7 +66,9 @@ CheckExpectedDim(int32 typmod, int dim)
 				 errmsg("expected %d dimensions, not %d", typmod, dim)));
 }
 
-
+/*
+ * Ensure valid dimensions
+ */
 static inline void
 CheckDim(int dim)
 {
@@ -79,13 +94,28 @@ CheckElement(float value)
 				(errcode(ERRCODE_DATA_EXCEPTION),
 				 errmsg("NaN not allowed in vector")));
 
-
 	if (isinf(value))
 		ereport(ERROR,
 				(errcode(ERRCODE_DATA_EXCEPTION),
 				 errmsg("infinite value not allowed in vector")));
 }
 
+/*
+ * Check for whitespace, since array_isspace() is static
+ */
+static inline bool
+vector_isspace(char ch)
+{
+	if (ch == ' ' ||
+		ch == '\t' ||
+		ch == '\n' ||
+		ch == '\r' ||
+		ch == '\v' ||
+		ch == '\f')
+		return true;
+	return false;
+}
+
 /*
  * Check state array
  */
@@ -108,31 +138,15 @@ float_overflow_error(void)
 			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
 			 errmsg("value out of range: overflow")));
 }
-#endif
 
-/*
+static pg_noinline void
- * Print vector - useful for debugging
+float_underflow_error(void)
- */
-void
-PrintVector(char *msg, Vector * vector)
 {
-	StringInfoData buf;
+	ereport(ERROR,
-	int			dim = vector->dim;
+			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-	int			i;
+			 errmsg("value out of range: underflow")));
-
-	initStringInfo(&buf);
-
-	appendStringInfoChar(&buf, '[');
-	for (i = 0; i < dim; i++)
-	{
-		if (i > 0)
-			appendStringInfoString(&buf, ",");
-		appendStringInfoString(&buf, float8out_internal(vector->x[i]));
-	}
-	appendStringInfoChar(&buf, ']');
-
-	elog(INFO, "%s = %s", msg, buf.data);
 }
+#endif
 
 /*
  * Convert textual representation to internal representation
@@ -143,17 +157,20 @@ vector_in(PG_FUNCTION_ARGS)
 {
 	char	   *str = PG_GETARG_CSTRING(0);
 	int32		typmod = PG_GETARG_INT32(2);
-	int			i;
 	float		x[VECTOR_MAX_DIM];
 	int			dim = 0;
 	char	   *pt;
 	char	   *stringEnd;
 	Vector	   *result;
+	char	   *lit = pstrdup(str);
+
+	while (vector_isspace(*str))
+		str++;
 
 	if (*str != '[')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", str),
+				 errmsg("malformed vector literal: \"%s\"", lit),
 				 errdetail("Vector contents must start with \"[\".")));
 
 	str++;
@@ -167,6 +184,15 @@ vector_in(PG_FUNCTION_ARGS)
 					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
 					 errmsg("vector cannot have more than %d dimensions", VECTOR_MAX_DIM)));
 
+		while (vector_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 vector: \"%s\"", lit)));
+
 		/* Use strtof like float4in to avoid a double-rounding problem */
 		x[dim] = strtof(pt, &stringEnd);
 		CheckElement(x[dim]);
@@ -175,37 +201,57 @@ vector_in(PG_FUNCTION_ARGS)
 		if (stringEnd == pt)
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type vector: \"%s\"", pt)));
+					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
+
+		while (vector_isspace(*stringEnd))
+			stringEnd++;
 
 		if (*stringEnd != '\0' && *stringEnd != ']')
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type vector: \"%s\"", pt)));
+					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
 
 		pt = strtok(NULL, ",");
 	}
 
-	if (*stringEnd != ']')
+	if (stringEnd == NULL || *stringEnd != ']')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal"),
+				 errmsg("malformed vector literal: \"%s\"", lit),
 				 errdetail("Unexpected end of input.")));
 
-	if (stringEnd[1] != '\0')
+	stringEnd++;
+
+	/* Only whitespace is allowed after the closing brace */
+	while (vector_isspace(*stringEnd))
+		stringEnd++;
+
+	if (*stringEnd != '\0')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal"),
+				 errmsg("malformed vector literal: \"%s\"", lit),
 				 errdetail("Junk after closing right brace.")));
 
+	/* Ensure no consecutive delimiters since strtok skips */
+	for (pt = lit + 1; *pt != '\0'; pt++)
+	{
+		if (pt[-1] == ',' && *pt == ',')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("malformed vector literal: \"%s\"", lit)));
+	}
+
 	if (dim < 1)
 		ereport(ERROR,
 				(errcode(ERRCODE_DATA_EXCEPTION),
 				 errmsg("vector must have at least 1 dimension")));
 
+	pfree(lit);
+
 	CheckExpectedDim(typmod, dim);
 
 	result = InitVector(dim);
-	for (i = 0; i < dim; i++)
+	for (int i = 0; i < dim; i++)
 		result->x[i] = x[i];
 
 	PG_RETURN_POINTER(result);
@@ -222,7 +268,6 @@ vector_out(PG_FUNCTION_ARGS)
 	int			dim = vector->dim;
 	char	   *buf;
 	char	   *ptr;
-	int			i;
 	int			n;
 
 #if PG_VERSION_NUM < 120000
@@ -249,7 +294,7 @@ vector_out(PG_FUNCTION_ARGS)
 
 	*ptr = '[';
 	ptr++;
-	for (i = 0; i < dim; i++)
+	for (int i = 0; i < dim; i++)
 	{
 		if (i > 0)
 		{
@@ -272,6 +317,18 @@ vector_out(PG_FUNCTION_ARGS)
 	PG_RETURN_CSTRING(buf);
 }
 
+/*
+ * Print vector - useful for debugging
+ */
+void
+PrintVector(char *msg, Vector * vector)
+{
+	char	   *out = DatumGetPointer(DirectFunctionCall1(vector_out, PointerGetDatum(vector)));
+
+	elog(INFO, "%s = %s", msg, out);
+	pfree(out);
+}
+
 /*
  * Convert type modifier
  */
@@ -315,7 +372,6 @@ vector_recv(PG_FUNCTION_ARGS)
 	Vector	   *result;
 	int16		dim;
 	int16		unused;
-	int			i;
 
 	dim = pq_getmsgint(buf, sizeof(int16));
 	unused = pq_getmsgint(buf, sizeof(int16));
@@ -329,8 +385,11 @@ vector_recv(PG_FUNCTION_ARGS)
 				 errmsg("expected unused to be 0, not %d", unused)));
 
 	result = InitVector(dim);
-	for (i = 0; i < dim; i++)
+	for (int i = 0; i < dim; i++)
+	{
 		result->x[i] = pq_getmsgfloat4(buf);
+		CheckElement(result->x[i]);
+	}
 
 	PG_RETURN_POINTER(result);
 }
@@ -344,12 +403,11 @@ vector_send(PG_FUNCTION_ARGS)
 {
 	Vector	   *vec = PG_GETARG_VECTOR_P(0);
 	StringInfoData buf;
-	int			i;
 
 	pq_begintypsend(&buf);
 	pq_sendint(&buf, vec->dim, sizeof(int16));
 	pq_sendint(&buf, vec->unused, sizeof(int16));
-	for (i = 0; i < vec->dim; i++)
+	for (int i = 0; i < vec->dim; i++)
 		pq_sendfloat4(&buf, vec->x[i]);
 
 	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
@@ -379,7 +437,6 @@ array_to_vector(PG_FUNCTION_ARGS)
 {
 	ArrayType  *array = PG_GETARG_ARRAYTYPE_P(0);
 	int32		typmod = PG_GETARG_INT32(1);
-	int			i;
 	Vector	   *result;
 	int16		typlen;
 	bool		typbyval;
@@ -393,6 +450,11 @@ array_to_vector(PG_FUNCTION_ARGS)
 				(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, &nullsp, &nelemsp);
 
@@ -400,28 +462,37 @@ array_to_vector(PG_FUNCTION_ARGS)
 	CheckExpectedDim(typmod, nelemsp);
 
 	result = InitVector(nelemsp);
-	for (i = 0; i < nelemsp; i++)
+
+	if (ARR_ELEMTYPE(array) == INT4OID)
 	{
-		if (nullsp[i])
+		for (int i = 0; i < nelemsp; i++)
-			ereport(ERROR,
-					(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
-					 errmsg("array must not containing NULLs")));
-
-		if (ARR_ELEMTYPE(array) == INT4OID)
 			result->x[i] = DatumGetInt32(elemsp[i]);
-		else if (ARR_ELEMTYPE(array) == FLOAT8OID)
-			result->x[i] = DatumGetFloat8(elemsp[i]);
-		else if (ARR_ELEMTYPE(array) == FLOAT4OID)
-			result->x[i] = DatumGetFloat4(elemsp[i]);
-		else if (ARR_ELEMTYPE(array) == NUMERICOID)
-			result->x[i] = DatumGetFloat4(DirectFunctionCall1(numeric_float4, elemsp[i]));
-		else
-			ereport(ERROR,
-					(errcode(ERRCODE_DATA_EXCEPTION),
-					 errmsg("unsupported array type")));
-
-		CheckElement(result->x[i]);
 	}
+	else if (ARR_ELEMTYPE(array) == FLOAT8OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = DatumGetFloat8(elemsp[i]);
+	}
+	else if (ARR_ELEMTYPE(array) == FLOAT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = DatumGetFloat4(elemsp[i]);
+	}
+	else if (ARR_ELEMTYPE(array) == NUMERICOID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = DatumGetFloat4(DirectFunctionCall1(numeric_float4, elemsp[i]));
+	}
+	else
+	{
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("unsupported array type")));
+	}
+
+	/* Check elements */
+	for (int i = 0; i < result->dim; i++)
+		CheckElement(result->x[i]);
 
 	PG_RETURN_POINTER(result);
 }
@@ -434,17 +505,18 @@ Datum
 vector_to_float4(PG_FUNCTION_ARGS)
 {
 	Vector	   *vec = PG_GETARG_VECTOR_P(0);
-	Datum	   *d;
+	Datum	   *datums;
 	ArrayType  *result;
-	int			i;
 
-	d = (Datum *) palloc(sizeof(Datum) * vec->dim);
+	datums = (Datum *) palloc(sizeof(Datum) * vec->dim);
 
-	for (i = 0; i < vec->dim; i++)
+	for (int i = 0; i < vec->dim; i++)
-		d[i] = Float4GetDatum(vec->x[i]);
+		datums[i] = Float4GetDatum(vec->x[i]);
 
 	/* Use TYPALIGN_INT for float4 */
-	result = construct_array(d, vec->dim, FLOAT4OID, sizeof(float4), true, TYPALIGN_INT);
+	result = construct_array(datums, vec->dim, FLOAT4OID, sizeof(float4), true, TYPALIGN_INT);
+
+	pfree(datums);
 
 	PG_RETURN_POINTER(result);
 }
@@ -460,8 +532,8 @@ l2_distance(PG_FUNCTION_ARGS)
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 	float	   *ax = a->x;
 	float	   *bx = b->x;
-	double		distance = 0.0;
+	float		distance = 0.0;
-	double		diff;
+	float		diff;
 
 	CheckDims(a, b);
 
@@ -472,7 +544,7 @@ l2_distance(PG_FUNCTION_ARGS)
 		distance += diff * diff;
 	}
 
-	PG_RETURN_FLOAT8(sqrt(distance));
+	PG_RETURN_FLOAT8(sqrt((double) distance));
 }
 
 /*
@@ -487,8 +559,8 @@ vector_l2_squared_distance(PG_FUNCTION_ARGS)
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 	float	   *ax = a->x;
 	float	   *bx = b->x;
-	double		distance = 0.0;
+	float		distance = 0.0;
-	double		diff;
+	float		diff;
 
 	CheckDims(a, b);
 
@@ -499,7 +571,7 @@ vector_l2_squared_distance(PG_FUNCTION_ARGS)
 		distance += diff * diff;
 	}
 
-	PG_RETURN_FLOAT8(distance);
+	PG_RETURN_FLOAT8((double) distance);
 }
 
 /*
@@ -513,7 +585,7 @@ inner_product(PG_FUNCTION_ARGS)
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 	float	   *ax = a->x;
 	float	   *bx = b->x;
-	double		distance = 0.0;
+	float		distance = 0.0;
 
 	CheckDims(a, b);
 
@@ -521,7 +593,7 @@ inner_product(PG_FUNCTION_ARGS)
 	for (int i = 0; i < a->dim; i++)
 		distance += ax[i] * bx[i];
 
-	PG_RETURN_FLOAT8(distance);
+	PG_RETURN_FLOAT8((double) distance);
 }
 
 /*
@@ -535,7 +607,7 @@ vector_negative_inner_product(PG_FUNCTION_ARGS)
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 	float	   *ax = a->x;
 	float	   *bx = b->x;
-	double		distance = 0.0;
+	float		distance = 0.0;
 
 	CheckDims(a, b);
 
@@ -543,7 +615,7 @@ vector_negative_inner_product(PG_FUNCTION_ARGS)
 	for (int i = 0; i < a->dim; i++)
 		distance += ax[i] * bx[i];
 
-	PG_RETURN_FLOAT8(distance * -1);
+	PG_RETURN_FLOAT8((double) distance * -1);
 }
 
 /*
@@ -557,9 +629,10 @@ cosine_distance(PG_FUNCTION_ARGS)
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 	float	   *ax = a->x;
 	float	   *bx = b->x;
-	double		distance = 0.0;
+	float		distance = 0.0;
-	double		norma = 0.0;
+	float		norma = 0.0;
-	double		normb = 0.0;
+	float		normb = 0.0;
+	double		similarity;
 
 	CheckDims(a, b);
 
@@ -572,7 +645,21 @@ cosine_distance(PG_FUNCTION_ARGS)
 	}
 
 	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
-	PG_RETURN_FLOAT8(1 - (distance / sqrt(norma * normb)));
+	similarity = (double) distance / sqrt((double) norma * (double) normb);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	if (isnan(similarity))
+		PG_RETURN_FLOAT8(NAN);
+#endif
+
+	/* Keep in range */
+	if (similarity > 1)
+		similarity = 1.0;
+	else if (similarity < -1)
+		similarity = -1.0;
+
+	PG_RETURN_FLOAT8(1.0 - similarity);
 }
 
 /*
@@ -586,13 +673,16 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	double		distance = 0.0;
+	float		dp = 0.0;
+	double		distance;
 
 	CheckDims(a, b);
 
 	/* Auto-vectorized */
 	for (int i = 0; i < a->dim; i++)
-		distance += a->x[i] * b->x[i];
+		dp += a->x[i] * b->x[i];
+
+	distance = (double) dp;
 
 	/* Prevent NaN with acos with loss of precision */
 	if (distance > 1)
@@ -603,6 +693,28 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(acos(distance) / M_PI);
 }
 
+/*
+ * Get the L1 distance between vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(l1_distance);
+Datum
+l1_distance(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
+	float	   *ax = a->x;
+	float	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += fabsf(ax[i] - bx[i]);
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
 /*
  * Get the dimensions of a vector
  */
@@ -624,13 +736,59 @@ vector_norm(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	float	   *ax = a->x;
-	double		norm = 0.0;
+	float		norm = 0.0;
 
 	/* Auto-vectorized */
 	for (int i = 0; i < a->dim; i++)
 		norm += ax[i] * ax[i];
 
-	PG_RETURN_FLOAT8(sqrt(norm));
+	PG_RETURN_FLOAT8(sqrt((double) norm));
+}
+
+/*
+ * Normalize a vector with the L2 norm
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(normalize_l2);
+Datum
+normalize_l2(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	float	   *ax = a->x;
+	double		norm = 0.0;
+#ifdef _MSC_VER
+	/* Fix precision on Windows */
+	double		normf;
+#else
+	float		normf;
+#endif
+	Vector	   *result;
+	float	   *rx;
+
+	result = InitVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		norm += (double) ax[i] * (double) ax[i];
+
+	norm = sqrt(norm);
+	normf = norm;
+
+	if (normf > 0)
+	{
+		/* Auto-vectorized */
+		for (int i = 0, imax = a->dim; i < imax; i++)
+			rx[i] = ax[i] / normf;
+
+		/* Check for overflow */
+		for (int i = 0, imax = a->dim; i < imax; i++)
+		{
+			if (isinf(rx[i]))
+				float_overflow_error();
+		}
+	}
+
+	PG_RETURN_POINTER(result);
 }
 
 /*
@@ -656,6 +814,13 @@ vector_add(PG_FUNCTION_ARGS)
 	for (int i = 0, imax = a->dim; i < imax; i++)
 		rx[i] = ax[i] + bx[i];
 
+	/* Check for overflow */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+		if (isinf(rx[i]))
+			float_overflow_error();
+	}
+
 	PG_RETURN_POINTER(result);
 }
 
@@ -682,6 +847,49 @@ vector_sub(PG_FUNCTION_ARGS)
 	for (int i = 0, imax = a->dim; i < imax; i++)
 		rx[i] = ax[i] - bx[i];
 
+	/* Check for overflow */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+		if (isinf(rx[i]))
+			float_overflow_error();
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Multiply vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_mul);
+Datum
+vector_mul(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
+	float	   *ax = a->x;
+	float	   *bx = b->x;
+	Vector	   *result;
+	float	   *rx;
+
+	CheckDims(a, b);
+
+	result = InitVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+		rx[i] = ax[i] * bx[i];
+
+	/* Check for overflow and underflow */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+		if (isinf(rx[i]))
+			float_overflow_error();
+
+		if (rx[i] == 0 && !(ax[i] == 0 || bx[i] == 0))
+			float_underflow_error();
+	}
+
 	PG_RETURN_POINTER(result);
 }
 
@@ -691,11 +899,9 @@ vector_sub(PG_FUNCTION_ARGS)
 int
 vector_cmp_internal(Vector * a, Vector * b)
 {
-	int			i;
-
 	CheckDims(a, b);
 
-	for (i = 0; i < a->dim; i++)
+	for (int i = 0; i < a->dim; i++)
 	{
 		if (a->x[i] < b->x[i])
 			return -1;
@@ -827,12 +1033,12 @@ vector_accum(PG_FUNCTION_ARGS)
 	n = statevalues[0] + 1.0;
 
 	statedatums = CreateStateDatums(dim);
-	statedatums[0] = Float8GetDatumFast(n);
+	statedatums[0] = Float8GetDatum(n);
 
 	if (newarr)
 	{
 		for (int i = 0; i < dim; i++)
-			statedatums[i + 1] = Float8GetDatumFast((double) x[i]);
+			statedatums[i + 1] = Float8GetDatum((double) x[i]);
 	}
 	else
 	{
@@ -840,10 +1046,11 @@ vector_accum(PG_FUNCTION_ARGS)
 		{
 			double		v = statevalues[i + 1] + x[i];
 
+			/* Check for overflow */
 			if (isinf(v))
 				float_overflow_error();
 
-			statedatums[i + 1] = Float8GetDatumFast(v);
+			statedatums[i + 1] = Float8GetDatum(v);
 		}
 	}
 
@@ -888,7 +1095,7 @@ vector_combine(PG_FUNCTION_ARGS)
 		dim = STATE_DIMS(statearray2);
 		statedatums = CreateStateDatums(dim);
 		for (int i = 1; i <= dim; i++)
-			statedatums[i] = Float8GetDatumFast(statevalues2[i]);
+			statedatums[i] = Float8GetDatum(statevalues2[i]);
 	}
 	else if (n2 == 0.0)
 	{
@@ -896,7 +1103,7 @@ vector_combine(PG_FUNCTION_ARGS)
 		dim = STATE_DIMS(statearray1);
 		statedatums = CreateStateDatums(dim);
 		for (int i = 1; i <= dim; i++)
-			statedatums[i] = Float8GetDatumFast(statevalues1[i]);
+			statedatums[i] = Float8GetDatum(statevalues1[i]);
 	}
 	else
 	{
@@ -908,14 +1115,15 @@ vector_combine(PG_FUNCTION_ARGS)
 		{
 			double		v = statevalues1[i] + statevalues2[i];
 
+			/* Check for overflow */
 			if (isinf(v))
 				float_overflow_error();
 
-			statedatums[i] = Float8GetDatumFast(v);
+			statedatums[i] = Float8GetDatum(v);
 		}
 	}
 
-	statedatums[0] = Float8GetDatumFast(n);
+	statedatums[0] = Float8GetDatum(n);
 
 	result = construct_array(statedatums, dim + 1,
 							 FLOAT8OID,
@@ -938,7 +1146,6 @@ vector_avg(PG_FUNCTION_ARGS)
 	float8		n;
 	uint16		dim;
 	Vector	   *result;
-	float		v;
 
 	/* Check array before using */
 	statevalues = CheckStateArray(statearray, "vector_avg");
@@ -954,9 +1161,8 @@ vector_avg(PG_FUNCTION_ARGS)
 	result = InitVector(dim);
 	for (int i = 0; i < dim; i++)
 	{
-		v = statevalues[i + 1] / n;
+		result->x[i] = statevalues[i + 1] / n;
-		CheckElement(v);
+		CheckElement(result->x[i]);
-		result->x[i] = v;
 	}
 
 	PG_RETURN_POINTER(result);

src/vector.h

@@ -14,6 +14,9 @@
 #define PG_GETARG_VECTOR_P(x)	DatumGetVector(PG_GETARG_DATUM(x))
 #define PG_RETURN_VECTOR_P(x)	PG_RETURN_POINTER(x)
 
+/* Exported functions */
+PGDLLEXPORT void _PG_init(void);
+
 typedef struct Vector
 {
 	int32		vl_len_;		/* varlena header (do not touch directly!) */

test/expected/cast.out

@@ -29,7 +29,7 @@ SELECT ARRAY[1,2,3]::numeric[]::vector;
 (1 row)
 
 SELECT '{NULL}'::real[]::vector;
-ERROR:  array must not containing NULLs
+ERROR:  array must not contain nulls
 SELECT '{NaN}'::real[]::vector;
 ERROR:  NaN not allowed in vector
 SELECT '{Infinity}'::real[]::vector;
@@ -38,6 +38,8 @@ SELECT '{-Infinity}'::real[]::vector;
 ERROR:  infinite value not allowed in vector
 SELECT '{}'::real[]::vector;
 ERROR:  vector must have at least 1 dimension
+SELECT '{{1}}'::real[]::vector;
+ERROR:  array must be 1-D
 SELECT '[1,2,3]'::vector::real[];
  float4  
 ---------

test/expected/functions.out

@@ -4,12 +4,26 @@ SELECT '[1,2,3]'::vector + '[4,5,6]';
  [5,7,9]
 (1 row)
 
+SELECT '[3e38]'::vector + '[3e38]';
+ERROR:  value out of range: overflow
 SELECT '[1,2,3]'::vector - '[4,5,6]';
   ?column?  
 ------------
  [-3,-3,-3]
 (1 row)
 
+SELECT '[-3e38]'::vector - '[3e38]';
+ERROR:  value out of range: overflow
+SELECT '[1,2,3]'::vector * '[4,5,6]';
+ ?column?  
+-----------
+ [4,10,18]
+(1 row)
+
+SELECT '[1e37]'::vector * '[1e37]';
+ERROR:  value out of range: overflow
+SELECT '[1e-37]'::vector * '[1e-37]';
+ERROR:  value out of range: underflow
 SELECT vector_dims('[1,2,3]');
  vector_dims 
 -------------
@@ -34,6 +48,36 @@ SELECT vector_norm('[0,1]');
            1
 (1 row)
 
+SELECT normalize_l2('[3,4]');
+ normalize_l2 
+--------------
+ [0.6,0.8]
+(1 row)
+
+SELECT normalize_l2('[3,0]');
+ normalize_l2 
+--------------
+ [1,0]
+(1 row)
+
+SELECT normalize_l2('[0,0.1]');
+ normalize_l2 
+--------------
+ [0,1]
+(1 row)
+
+SELECT normalize_l2('[0,0]');
+ normalize_l2 
+--------------
+ [0,0]
+(1 row)
+
+SELECT normalize_l2('[3e38]');
+ normalize_l2 
+--------------
+ [1]
+(1 row)
+
 SELECT l2_distance('[0,0]', '[3,4]');
  l2_distance 
 -------------
@@ -48,6 +92,12 @@ SELECT l2_distance('[0,0]', '[0,1]');
 
 SELECT l2_distance('[1,2]', '[3]');
 ERROR:  different vector dimensions 2 and 1
+SELECT l2_distance('[3e38]', '[-3e38]');
+ l2_distance 
+-------------
+    Infinity
+(1 row)
+
 SELECT inner_product('[1,2]', '[3,4]');
  inner_product 
 ---------------
@@ -56,6 +106,12 @@ SELECT inner_product('[1,2]', '[3,4]');
 
 SELECT inner_product('[1,2]', '[3]');
 ERROR:  different vector dimensions 2 and 1
+SELECT inner_product('[3e38]', '[3e38]');
+ inner_product 
+---------------
+      Infinity
+(1 row)
+
 SELECT cosine_distance('[1,2]', '[2,4]');
  cosine_distance 
 -----------------
@@ -82,6 +138,44 @@ SELECT cosine_distance('[1,1]', '[-1,-1]');
 
 SELECT cosine_distance('[1,2]', '[3]');
 ERROR:  different vector dimensions 2 and 1
+SELECT cosine_distance('[1,1]', '[1.1,1.1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('[3e38]', '[3e38]');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT l1_distance('[0,0]', '[3,4]');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('[0,0]', '[0,1]');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('[1,2]', '[3]');
+ERROR:  different vector dimensions 2 and 1
+SELECT l1_distance('[3e38]', '[-3e38]');
+ l1_distance 
+-------------
+    Infinity
+(1 row)
+
 SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
     avg    
 -----------
@@ -102,5 +196,33 @@ SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
 
 SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
 ERROR:  expected 2 dimensions, not 1
+SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
+   avg   
+---------
+ [3e+38]
+(1 row)
+
 SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
 ERROR:  vector cannot have more than 16000 dimensions
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
+ sum 
+-----
+ 
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+ERROR:  different vector dimensions 2 and 1
+SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
+ERROR:  value out of range: overflow

test/expected/hnsw_cosine.out

@@ -0,0 +1,27 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_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]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
+ count 
+-------
+     4
+(1 row)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_ip.out

@@ -0,0 +1,21 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_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::vector)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_l2.out

@@ -0,0 +1,30 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
+   val   
+---------
+ [0,0,0]
+ [1,1,1]
+ [1,2,3]
+ [1,2,4]
+(4 rows)
+
+SELECT COUNT(*) FROM t;
+ count 
+-------
+     5
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_options.out

@@ -0,0 +1,25 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val vector(3));
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 3);
+ERROR:  value 3 out of bounds for option "m"
+DETAIL:  Valid values are between "4" and "100".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 101);
+ERROR:  value 101 out of bounds for option "m"
+DETAIL:  Valid values are between "4" and "100".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 9);
+ERROR:  value 9 out of bounds for option "ef_construction"
+DETAIL:  Valid values are between "10" and "1000".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 1001);
+ERROR:  value 1001 out of bounds for option "ef_construction"
+DETAIL:  Valid values are between "10" and "1000".
+SHOW hnsw.ef_search;
+ hnsw.ef_search 
+----------------
+ 40
+(1 row)
+
+SET hnsw.ef_search = 9;
+ERROR:  9 is outside the valid range for parameter "hnsw.ef_search" (10 .. 1000)
+SET hnsw.ef_search = 1001;
+ERROR:  1001 is outside the valid range for parameter "hnsw.ef_search" (10 .. 1000)
+DROP TABLE t;

test/expected/hnsw_unlogged.out

@@ -0,0 +1,13 @@
+SET enable_seqscan = off;
+CREATE UNLOGGED 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);
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+DROP TABLE t;

test/expected/input.out

@@ -4,10 +4,22 @@ SELECT '[1,2,3]'::vector;
  [1,2,3]
 (1 row)
 
-SELECT '[-1,2,3]'::vector;
+SELECT '[-1,-2,-3]'::vector;
-  vector  
+   vector   
-----------
+------------
- [-1,2,3]
+ [-1,-2,-3]
+(1 row)
+
+SELECT '[1.,2.,3.]'::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT ' [ 1,  2 ,    3  ] '::vector;
+ vector  
+---------
+ [1,2,3]
 (1 row)
 
 SELECT '[1.23456]'::vector;
@@ -17,7 +29,7 @@ SELECT '[1.23456]'::vector;
 (1 row)
 
 SELECT '[hello,1]'::vector;
-ERROR:  invalid input syntax for type vector: "hello"
+ERROR:  invalid input syntax for type vector: "[hello,1]"
 LINE 1: SELECT '[hello,1]'::vector;
                ^
 SELECT '[NaN,1]'::vector;
@@ -32,13 +44,35 @@ SELECT '[-Infinity,1]'::vector;
 ERROR:  infinite value not allowed in vector
 LINE 1: SELECT '[-Infinity,1]'::vector;
                ^
+SELECT '[1.5e38,-1.5e38]'::vector;
+       vector       
+--------------------
+ [1.5e+38,-1.5e+38]
+(1 row)
+
+SELECT '[1.5e+38,-1.5e+38]'::vector;
+       vector       
+--------------------
+ [1.5e+38,-1.5e+38]
+(1 row)
+
+SELECT '[1.5e-38,-1.5e-38]'::vector;
+       vector       
+--------------------
+ [1.5e-38,-1.5e-38]
+(1 row)
+
+SELECT '[4e38,1]'::vector;
+ERROR:  infinite value not allowed in vector
+LINE 1: SELECT '[4e38,1]'::vector;
+               ^
 SELECT '[1,2,3'::vector;
-ERROR:  malformed vector literal
+ERROR:  malformed vector literal: "[1,2,3"
 LINE 1: SELECT '[1,2,3'::vector;
                ^
 DETAIL:  Unexpected end of input.
 SELECT '[1,2,3]9'::vector;
-ERROR:  malformed vector literal
+ERROR:  malformed vector literal: "[1,2,3]9"
 LINE 1: SELECT '[1,2,3]9'::vector;
                ^
 DETAIL:  Junk after closing right brace.
@@ -47,14 +81,41 @@ ERROR:  malformed vector literal: "1,2,3"
 LINE 1: SELECT '1,2,3'::vector;
                ^
 DETAIL:  Vector contents must start with "[".
+SELECT ''::vector;
+ERROR:  malformed vector literal: ""
+LINE 1: SELECT ''::vector;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT '['::vector;
+ERROR:  malformed vector literal: "["
+LINE 1: SELECT '['::vector;
+               ^
+DETAIL:  Unexpected end of input.
+SELECT '[,'::vector;
+ERROR:  malformed vector literal: "[,"
+LINE 1: SELECT '[,'::vector;
+               ^
+DETAIL:  Unexpected end of input.
 SELECT '[]'::vector;
 ERROR:  vector must have at least 1 dimension
 LINE 1: SELECT '[]'::vector;
                ^
 SELECT '[1,]'::vector;
-ERROR:  invalid input syntax for type vector: "]"
+ERROR:  invalid input syntax for type vector: "[1,]"
 LINE 1: SELECT '[1,]'::vector;
                ^
+SELECT '[1a]'::vector;
+ERROR:  invalid input syntax for type vector: "[1a]"
+LINE 1: SELECT '[1a]'::vector;
+               ^
+SELECT '[1,,3]'::vector;
+ERROR:  malformed vector literal: "[1,,3]"
+LINE 1: SELECT '[1,,3]'::vector;
+               ^
+SELECT '[1, ,3]'::vector;
+ERROR:  invalid input syntax for type vector: "[1, ,3]"
+LINE 1: SELECT '[1, ,3]'::vector;
+               ^
 SELECT '[1,2,3]'::vector(2);
 ERROR:  expected 2 dimensions, not 3
 SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);

test/expected/ivfflat_cosine.out

@@ -9,11 +9,19 @@ SELECT * FROM t ORDER BY val <=> '[3,3,3]';
  [1,1,1]
  [1,2,3]
  [1,2,4]
-(3 rows)
+ [0,0,0]
+(4 rows)
 
-SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector);
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
- val 
+ count 
------
+-------
-(0 rows)
+     4
+(1 row)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2;
+ count 
+-------
+     4
+(1 row)
 
 DROP TABLE t;

test/expected/ivfflat_ip.out

@@ -12,9 +12,10 @@ SELECT * FROM t ORDER BY val <#> '[3,3,3]';
  [0,0,0]
 (4 rows)
 
-SELECT * FROM t ORDER BY val <#> (SELECT NULL::vector);
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <#> (SELECT NULL::vector)) t2;
- val 
+ count 
------
+-------
-(0 rows)
+     4
+(1 row)
 
 DROP TABLE t;

test/expected/ivfflat_l2.out

@@ -13,9 +13,13 @@ SELECT * FROM t ORDER BY val <-> '[3,3,3]';
 (4 rows)
 
 SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
- val 
+   val   
------
+---------
-(0 rows)
+ [0,0,0]
+ [1,1,1]
+ [1,2,3]
+ [1,2,4]
+(4 rows)
 
 SELECT COUNT(*) FROM t;
  count 

test/sql/cast.sql

@@ -8,6 +8,7 @@ SELECT '{NaN}'::real[]::vector;
 SELECT '{Infinity}'::real[]::vector;
 SELECT '{-Infinity}'::real[]::vector;
 SELECT '{}'::real[]::vector;
+SELECT '{{1}}'::real[]::vector;
 SELECT '[1,2,3]'::vector::real[];
 SELECT array_agg(n)::vector FROM generate_series(1, 16001) n;
 SELECT array_to_vector(array_agg(n), 16001, false) FROM generate_series(1, 16001) n;

test/sql/functions.sql

@@ -1,5 +1,10 @@
 SELECT '[1,2,3]'::vector + '[4,5,6]';
+SELECT '[3e38]'::vector + '[3e38]';
 SELECT '[1,2,3]'::vector - '[4,5,6]';
+SELECT '[-3e38]'::vector - '[3e38]';
+SELECT '[1,2,3]'::vector * '[4,5,6]';
+SELECT '[1e37]'::vector * '[1e37]';
+SELECT '[1e-37]'::vector * '[1e-37]';
 
 SELECT vector_dims('[1,2,3]');
 
@@ -7,21 +12,44 @@ SELECT round(vector_norm('[1,1]')::numeric, 5);
 SELECT vector_norm('[3,4]');
 SELECT vector_norm('[0,1]');
 
+SELECT normalize_l2('[3,4]');
+SELECT normalize_l2('[3,0]');
+SELECT normalize_l2('[0,0.1]');
+SELECT normalize_l2('[0,0]');
+SELECT normalize_l2('[3e38]');
+
 SELECT l2_distance('[0,0]', '[3,4]');
 SELECT l2_distance('[0,0]', '[0,1]');
 SELECT l2_distance('[1,2]', '[3]');
+SELECT l2_distance('[3e38]', '[-3e38]');
 
 SELECT inner_product('[1,2]', '[3,4]');
 SELECT inner_product('[1,2]', '[3]');
+SELECT inner_product('[3e38]', '[3e38]');
 
 SELECT cosine_distance('[1,2]', '[2,4]');
 SELECT cosine_distance('[1,2]', '[0,0]');
 SELECT cosine_distance('[1,1]', '[1,1]');
 SELECT cosine_distance('[1,1]', '[-1,-1]');
 SELECT cosine_distance('[1,2]', '[3]');
+SELECT cosine_distance('[1,1]', '[1.1,1.1]');
+SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
+SELECT cosine_distance('[3e38]', '[3e38]');
+
+SELECT l1_distance('[0,0]', '[3,4]');
+SELECT l1_distance('[0,0]', '[0,1]');
+SELECT l1_distance('[1,2]', '[3]');
+SELECT l1_distance('[3e38]', '[-3e38]');
 
 SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
 SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
 SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
 SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
 SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
+SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;

test/sql/hnsw_cosine.sql

@@ -0,0 +1,13 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_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::vector)) t2;
+
+DROP TABLE t;

test/sql/hnsw_ip.sql

@@ -0,0 +1,12 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_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::vector)) t2;
+
+DROP TABLE t;

test/sql/hnsw_l2.sql

@@ -0,0 +1,13 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
+SELECT COUNT(*) FROM t;
+
+DROP TABLE t;

test/sql/hnsw_options.sql

@@ -0,0 +1,14 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val vector(3));
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 3);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 101);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 9);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 1001);
+
+SHOW hnsw.ef_search;
+
+SET hnsw.ef_search = 9;
+SET hnsw.ef_search = 1001;
+
+DROP TABLE t;

test/sql/hnsw_unlogged.sql

@@ -0,0 +1,9 @@
+SET enable_seqscan = off;
+
+CREATE UNLOGGED 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);
+
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+DROP TABLE t;

test/sql/input.sql

@@ -1,15 +1,27 @@
 SELECT '[1,2,3]'::vector;
-SELECT '[-1,2,3]'::vector;
+SELECT '[-1,-2,-3]'::vector;
+SELECT '[1.,2.,3.]'::vector;
+SELECT ' [ 1,  2 ,    3  ] '::vector;
 SELECT '[1.23456]'::vector;
 SELECT '[hello,1]'::vector;
 SELECT '[NaN,1]'::vector;
 SELECT '[Infinity,1]'::vector;
 SELECT '[-Infinity,1]'::vector;
+SELECT '[1.5e38,-1.5e38]'::vector;
+SELECT '[1.5e+38,-1.5e+38]'::vector;
+SELECT '[1.5e-38,-1.5e-38]'::vector;
+SELECT '[4e38,1]'::vector;
 SELECT '[1,2,3'::vector;
 SELECT '[1,2,3]9'::vector;
 SELECT '1,2,3'::vector;
+SELECT ''::vector;
+SELECT '['::vector;
+SELECT '[,'::vector;
 SELECT '[]'::vector;
 SELECT '[1,]'::vector;
+SELECT '[1a]'::vector;
+SELECT '[1,,3]'::vector;
+SELECT '[1, ,3]'::vector;
 SELECT '[1,2,3]'::vector(2);
 
 SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);

test/sql/ivfflat_cosine.sql

@@ -7,6 +7,7 @@ CREATE INDEX ON t USING ivfflat (val vector_cosine_ops) WITH (lists = 1);
 INSERT INTO t (val) VALUES ('[1,2,4]');
 
 SELECT * FROM t ORDER BY val <=> '[3,3,3]';
-SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector);
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2;
 
 DROP TABLE t;

test/sql/ivfflat_ip.sql

@@ -7,6 +7,6 @@ CREATE INDEX ON t USING ivfflat (val vector_ip_ops) WITH (lists = 1);
 INSERT INTO t (val) VALUES ('[1,2,4]');
 
 SELECT * FROM t ORDER BY val <#> '[3,3,3]';
-SELECT * FROM t ORDER BY val <#> (SELECT NULL::vector);
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <#> (SELECT NULL::vector)) t2;
 
 DROP TABLE t;

test/t/001_ivfflat_wal.pl

@@ -5,7 +5,7 @@ use strict;
 use warnings;
 use PostgresNode;
 use TestLib;
-use Test::More tests => 31;
+use Test::More;
 
 my $dim = 32;
 
@@ -95,3 +95,5 @@ for my $i (1 .. 10)
 	);
 	test_index_replay("insert $i");
 }
+
+done_testing();

test/t/002_ivfflat_vacuum.pl

@@ -2,7 +2,7 @@ use strict;
 use warnings;
 use PostgresNode;
 use TestLib;
-use Test::More tests => 1;
+use Test::More;
 
 my $dim = 3;
 
@@ -39,3 +39,5 @@ $node->safe_psql("postgres",
 # Check size
 my $new_size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");
 is($size, $new_size, "size does not change");
+
+done_testing();

test/t/003_ivfflat_recall.pl

@@ -0,0 +1,127 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($probes, $min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET ivfflat.probes = $probes;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx on tst/);
+
+	for my $i (0 .. $#queries) {
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET ivfflat.probes = $probes;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids) {
+			if (exists($actual_set{$_})) {
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v 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 = ("<->", "<#>", "<=>");
+
+foreach (@operators) {
+	my $operator = $_;
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries) {
+		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
+		push(@expected, $res);
+	}
+
+	my $opclass;
+	if ($operator eq "<->") {
+		$opclass = "vector_l2_ops";
+	} elsif ($operator eq "<#>") {
+		$opclass = "vector_ip_ops";
+	} else {
+		$opclass = "vector_cosine_ops";
+	}
+
+	# Build index serially
+	$node->safe_psql("postgres", qq(
+		SET max_parallel_maintenance_workers = 0;
+		CREATE INDEX idx ON tst USING ivfflat (v $opclass);
+	));
+
+	# Test approximate results
+	if ($operator ne "<#>") {
+		# TODO fix test
+		test_recall(1, 0.75, $operator);
+		test_recall(10, 0.95, $operator);
+	}
+	# Account for equal distances
+	test_recall(100, 0.995, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		SET client_min_messages = DEBUG;
+		SET min_parallel_table_scan_size = 1;
+		CREATE INDEX idx ON tst USING ivfflat (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	if ($operator ne "<#>") {
+		# TODO fix test
+		test_recall(1, 0.75, $operator);
+		test_recall(10, 0.95, $operator);
+	}
+	# Account for equal distances
+	test_recall(100, 0.995, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();

test/t/004_ivfflat_centers.pl

@@ -2,7 +2,7 @@ use strict;
 use warnings;
 use PostgresNode;
 use TestLib;
-use Test::More tests => 3;
+use Test::More;
 
 # Initialize node
 my $node = get_new_node('node');
@@ -34,3 +34,5 @@ $node->safe_psql("postgres",
 
 # Test no error for duplicate centers
 test_centers(10);
+
+done_testing();

test/t/005_ivfflat_query_recall.pl

@@ -2,7 +2,7 @@ use strict;
 use warnings;
 use PostgresNode;
 use TestLib;
-use Test::More tests => 60;
+use Test::More;
 
 # Initialize node
 my $node = get_new_node('node');
@@ -23,9 +23,9 @@ foreach (@operators) {
 
 	# Add index
 	my $opclass;
-	if ($operator == "<->") {
+	if ($operator eq "<->") {
 		$opclass = "vector_l2_ops";
-	} elsif ($operator == "<#>") {
+	} elsif ($operator eq "<#>") {
 		$opclass = "vector_ip_ops";
 	} else {
 		$opclass = "vector_cosine_ops";
@@ -43,3 +43,5 @@ foreach (@operators) {
 		is($res, $query);
 	}
 }
+
+done_testing();

test/t/006_ivfflat_lists.pl

@@ -2,7 +2,7 @@ use strict;
 use warnings;
 use PostgresNode;
 use TestLib;
-use Test::More tests => 3;
+use Test::More;
 
 # Initialize node
 my $node = get_new_node('node');
@@ -29,3 +29,5 @@ my ($ret, $stdout, $stderr) = $node->psql("postgres",
 	"CREATE INDEX lists10000 ON tst USING ivfflat (v) WITH (lists = 10000);"
 );
 like($stderr, qr/memory required is/);
+
+done_testing();

test/t/007_ivfflat_inserts.pl

@@ -2,7 +2,7 @@ use strict;
 use warnings;
 use PostgresNode;
 use TestLib;
-use Test::More tests => 7;
+use Test::More;
 
 my $dim = 768;
 
@@ -53,3 +53,5 @@ $count = $node->safe_psql("postgres", qq(
 ));
 is($count, $expected);
 is(idx_scan(), 1);
+
+done_testing();

test/t/008_aggregates.pl

@@ -0,0 +1,48 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (r1 real, r2 real, r3 real, v vector(3));");
+$node->safe_psql("postgres", qq(
+	INSERT INTO tst SELECT r1, r2, r3, ARRAY[r1, r2, r3] FROM (
+		SELECT random() + 1.01 AS r1, random() + 2.01 AS r2, random() + 3.01 AS r3 FROM generate_series(1, 1000000) t
+	) i;
+));
+
+sub test_aggregate
+{
+	my ($agg) = @_;
+
+	# Test value
+	my $res = $node->safe_psql("postgres", "SELECT $agg(v) FROM tst;");
+	like($res, qr/\[1\.5/);
+	like($res, qr/,2\.5/);
+	like($res, qr/,3\.5/);
+
+	# Test matches real for avg
+	# Cannot test sum since sum(real) varies between calls
+	if ($agg eq 'avg') {
+		my $r1 = $node->safe_psql("postgres", "SELECT $agg(r1)::float4 FROM tst;");
+		my $r2 = $node->safe_psql("postgres", "SELECT $agg(r2)::float4 FROM tst;");
+		my $r3 = $node->safe_psql("postgres", "SELECT $agg(r3)::float4 FROM tst;");
+		is($res, "[$r1,$r2,$r3]");
+	}
+
+	# Test explain
+	my $explain = $node->safe_psql("postgres", "EXPLAIN SELECT $agg(v) FROM tst;");
+	like($explain, qr/Partial Aggregate/);
+}
+
+test_aggregate('avg');
+test_aggregate('sum');
+
+done_testing();

test/t/008_avg.pl

@@ -1,35 +0,0 @@
-use strict;
-use warnings;
-use PostgresNode;
-use TestLib;
-use Test::More tests => 5;
-
-# Initialize node
-my $node = get_new_node('node');
-$node->init;
-$node->start;
-
-# Create table
-$node->safe_psql("postgres", "CREATE EXTENSION vector;");
-$node->safe_psql("postgres", "CREATE TABLE tst (r1 real, r2 real, r3 real, v vector(3));");
-$node->safe_psql("postgres", qq(
-	INSERT INTO tst SELECT r1, r2, r3, ARRAY[r1, r2, r3] FROM (
-		SELECT random() + 1.01 AS r1, random() + 2.01 AS r2, random() + 3.01 AS r3 FROM generate_series(1, 1000000) t
-	) i;
-));
-
-# Test avg
-my $avg = $node->safe_psql("postgres", "SELECT AVG(v) FROM tst;");
-like($avg, qr/\[1\.5/);
-like($avg, qr/,2\.5/);
-like($avg, qr/,3\.5/);
-
-# Test matches real
-my $r1 = $node->safe_psql("postgres", "SELECT AVG(r1)::float4 FROM tst;");
-my $r2 = $node->safe_psql("postgres", "SELECT AVG(r2)::float4 FROM tst;");
-my $r3 = $node->safe_psql("postgres", "SELECT AVG(r3)::float4 FROM tst;");
-is($avg, "[$r1,$r2,$r3]");
-
-# Test explain
-my $explain = $node->safe_psql("postgres", "EXPLAIN SELECT AVG(v) FROM tst;");
-like($explain, qr/Partial Aggregate/);

test/t/009_storage.pl

@@ -2,7 +2,7 @@ use strict;
 use warnings;
 use PostgresNode;
 use TestLib;
-use Test::More tests => 1;
+use Test::More;
 
 my $dim = 1024;
 
@@ -30,3 +30,5 @@ my ($ret, $stdout, $stderr) = $node->psql("postgres",
 	"INSERT INTO tst SELECT array_agg(n), array_agg(n), array_agg(n) FROM generate_series(1, $dim) n"
 );
 like($stderr, qr/row is too big/);
+
+done_testing();

test/t/010_hnsw_wal.pl

@@ -0,0 +1,99 @@
+# Based on postgres/contrib/bloom/t/001_wal.pl
+
+# Test generic xlog record work for hnsw index replication.
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $dim = 32;
+
+my $node_primary;
+my $node_replica;
+
+# Run few queries on both primary and replica and check their results match.
+sub test_index_replay
+{
+	my ($test_name) = @_;
+
+	# Wait for replica to catch up
+	my $applname = $node_replica->name;
+
+	my $server_version_num = $node_primary->safe_psql("postgres", "SHOW server_version_num");
+	my $caughtup_query = "SELECT pg_current_wal_lsn() <= replay_lsn FROM pg_stat_replication WHERE application_name = '$applname';";
+	$node_primary->poll_query_until('postgres', $caughtup_query)
+	  or die "Timed out while waiting for replica 1 to catch up";
+
+	my @r = ();
+	for (1 .. $dim) {
+		push(@r, rand());
+	}
+	my $sql = join(",", @r);
+
+	my $queries = qq(
+		SET enable_seqscan = off;
+		SELECT * FROM tst ORDER BY v <-> '[$sql]' LIMIT 10;
+	);
+
+	# Run test queries and compare their result
+	my $primary_result = $node_primary->safe_psql("postgres", $queries);
+	my $replica_result = $node_replica->safe_psql("postgres", $queries);
+
+	is($primary_result, $replica_result, "$test_name: query result matches");
+	return;
+}
+
+# Use ARRAY[random(), random(), random(), ...] over
+# SELECT array_agg(random()) FROM generate_series(1, $dim)
+# to generate different values for each row
+my $array_sql = join(",", ('random()') x $dim);
+
+# Initialize primary node
+$node_primary = get_new_node('primary');
+$node_primary->init(allows_streaming => 1);
+if ($dim > 32) {
+	# TODO use wal_keep_segments for Postgres < 13
+	$node_primary->append_conf('postgresql.conf', qq(wal_keep_size = 1GB));
+}
+if ($dim > 1500) {
+	$node_primary->append_conf('postgresql.conf', qq(maintenance_work_mem = 128MB));
+}
+$node_primary->start;
+my $backup_name = 'my_backup';
+
+# Take backup
+$node_primary->backup($backup_name);
+
+# Create streaming replica linking to primary
+$node_replica = get_new_node('replica');
+$node_replica->init_from_backup($node_primary, $backup_name,
+	has_streaming => 1);
+$node_replica->start;
+
+# Create hnsw index on primary
+$node_primary->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node_primary->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
+$node_primary->safe_psql("postgres",
+	"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series(1, 1000) i;"
+);
+$node_primary->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v vector_l2_ops);");
+
+# Test that queries give same result
+test_index_replay('initial');
+
+# Run 10 cycles of table modification. Run test queries after each modification.
+for my $i (1 .. 10)
+{
+	$node_primary->safe_psql("postgres", "DELETE FROM tst WHERE i = $i;");
+	test_index_replay("delete $i");
+	$node_primary->safe_psql("postgres", "VACUUM tst;");
+	test_index_replay("vacuum $i");
+	my ($start, $end) = (1001 + ($i - 1) * 100, 1000 + $i * 100);
+	$node_primary->safe_psql("postgres",
+		"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series($start, $end) i;"
+	);
+	test_index_replay("insert $i");
+}
+
+done_testing();

test/t/011_hnsw_vacuum.pl

@@ -0,0 +1,43 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+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);
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table and index
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i % 10, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
+);
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v vector_l2_ops);");
+
+# Get size
+my $size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");
+
+# Delete all, vacuum, and insert same data
+$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, 10000) i;"
+);
+
+# Check size
+my $new_size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");
+cmp_ok($new_size, "<=", $size * 1.01, "size does not increase too much");
+
+done_testing();

test/t/012_hnsw_build_recall.pl

@@ -2,7 +2,7 @@ use strict;
 use warnings;
 use PostgresNode;
 use TestLib;
-use Test::More tests => 9;
+use Test::More;
 
 my $node;
 my @queries = ();
@@ -11,14 +11,19 @@ my $limit = 20;
 
 sub test_recall
 {
-	my ($probes, $min, $operator) = @_;
+	my ($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;
-			SET ivfflat.probes = $probes;
 			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
 		));
 		my @actual_ids = split("\n", $actual);
@@ -46,7 +51,7 @@ $node->start;
 $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;"
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 10000) i;"
 );
 
 # Generate queries
@@ -72,17 +77,20 @@ foreach (@operators) {
 
 	# Add index
 	my $opclass;
-	if ($operator == "<->") {
+	if ($operator eq "<->") {
 		$opclass = "vector_l2_ops";
-	} elsif ($operator == "<#>") {
+	} elsif ($operator eq "<#>") {
 		$opclass = "vector_ip_ops";
 	} else {
 		$opclass = "vector_cosine_ops";
 	}
-	$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v $opclass);");
+	$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v $opclass);");
 
-	# Test approximate results
+	if ($operator eq "<#>") {
-	test_recall(1, 0.75, $operator);
+		test_recall(0.80, $operator);
-	test_recall(10, 0.95, $operator);
+	} else {
-	test_recall(100, 1.0, $operator);
+		test_recall(0.99, $operator);
+	}
 }
+
+done_testing();

test/t/013_hnsw_insert_recall.pl

@@ -0,0 +1,103 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries) {
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids) {
+			if (exists($actual_set{$_})) {
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector(3));");
+
+# 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 = ("<->", "<#>", "<=>");
+
+foreach (@operators) {
+	my $operator = $_;
+
+	# Add index
+	my $opclass;
+	if ($operator eq "<->") {
+		$opclass = "vector_l2_ops";
+	} elsif ($operator eq "<#>") {
+		$opclass = "vector_ip_ops";
+	} else {
+		$opclass = "vector_cosine_ops";
+	}
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v $opclass);");
+
+	$node->safe_psql("postgres",
+		"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 10000) i;"
+	);
+
+	# 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, $res);
+	}
+
+	if ($operator eq "<#>") {
+		test_recall(0.80, $operator);
+	} else {
+		test_recall(0.99, $operator);
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres", "TRUNCATE tst;");
+}
+
+done_testing();

test/t/014_hnsw_inserts.pl

@@ -0,0 +1,58 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+# Ensures elements and neighbors on both same and different pages
+my $dim = 1900;
+
+my $array_sql = join(",", ('random()') x $dim);
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table and index
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (v vector($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 100) i;"
+);
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v vector_l2_ops);");
+
+$node->pgbench(
+	"--no-vacuum --client=5 --transactions=100",
+	0,
+	[qr{actually processed}],
+	[qr{^$}],
+	"concurrent INSERTs",
+	{
+		"007_inserts" => "INSERT INTO tst SELECT ARRAY[$array_sql] FROM generate_series(1, 10) i;"
+	}
+);
+
+sub idx_scan
+{
+	# Stats do not update instantaneously
+	# https://www.postgresql.org/docs/current/monitoring-stats.html#MONITORING-STATS-VIEWS
+	sleep(1);
+	$node->safe_psql("postgres", "SELECT idx_scan FROM pg_stat_user_indexes WHERE indexrelid = 'tst_v_idx'::regclass;");
+}
+
+my $expected = 100 + 5 * 100 * 10;
+
+my $count = $node->safe_psql("postgres", "SELECT COUNT(*) FROM tst;");
+is($count, $expected);
+is(idx_scan(), 0);
+
+$count = $node->safe_psql("postgres", qq(
+	SET enable_seqscan = off;
+	SET hnsw.ef_search = 400;
+	SELECT COUNT(*) FROM (SELECT v FROM tst ORDER BY v <-> (SELECT v FROM tst LIMIT 1)) t;
+));
+is($count, 400);
+is(idx_scan(), 1);
+
+done_testing();

vector.control

@@ -1,4 +1,4 @@
 comment = 'vector data type and ivfflat access method'
-default_version = '0.4.2'
+default_version = '0.4.4'
 module_pathname = '$libdir/vector'
 relocatable = true