Removed comments [skip ci]

The HnswInitElement() allocate an element with not initialize value
filed, which may has garbage that lead HnswFreeElement() free an
invalid pointer.

.github/workflows/build.yml

@@ -8,6 +8,8 @@ jobs:
       fail-fast: false
       matrix:
         include:
+          - postgres: 17
+            os: ubuntu-22.04
           - postgres: 16
             os: ubuntu-22.04
           - postgres: 15
@@ -18,10 +20,8 @@ jobs:
             os: ubuntu-20.04
           - postgres: 12
             os: ubuntu-20.04
-          - postgres: 11
-            os: ubuntu-20.04
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - uses: ankane/setup-postgres@v1
         with:
           postgres-version: ${{ matrix.postgres }}
@@ -43,7 +43,7 @@ jobs:
     runs-on: macos-latest
     if: ${{ !startsWith(github.ref_name, 'windows') }}
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - uses: ankane/setup-postgres@v1
         with:
           postgres-version: 14
@@ -65,7 +65,7 @@ jobs:
     runs-on: windows-latest
     if: ${{ !startsWith(github.ref_name, 'mac') }}
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - uses: ankane/setup-postgres@v1
         with:
           postgres-version: 14

CHANGELOG.md

@@ -1,7 +1,11 @@
-## 0.5.1 (unreleased)
+## 0.5.2 (unreleased)
 
-- Improved performance of index scans for IVFFlat after updates and deletes
+- Added support for on-disk parallel index builds for HNSW
-- Fixed locking for index scans for HNSW
+
+## 0.5.1 (2023-10-10)
+
+- Improved performance of HNSW index builds
+- Added check for MVCC-compliant snapshot for index scans
 
 ## 0.5.0 (2023-08-28)
 

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": "0.5.0",
+	"version": "0.5.1",
 	"maintainer": [
 		"Andrew Kane <andrew@ankane.org>"
 	],
@@ -20,7 +20,7 @@
 		"vector": {
 			"file": "sql/vector.sql",
 			"docfile": "README.md",
-			"version": "0.5.0",
+			"version": "0.5.1",
 			"abstract": "Open-source vector similarity search for Postgres"
 		}
 	},

Makefile

@@ -1,10 +1,10 @@
 EXTENSION = vector
-EXTVERSION = 0.5.0
+EXTVERSION = 0.5.1
 
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
-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
+OBJS = src/half.o src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
-HEADERS = src/vector.h
+HEADERS = src/half.h src/vector.h
 
 TESTS = $(wildcard test/sql/*.sql)
 REGRESS = $(patsubst test/sql/%.sql,%,$(TESTS))

Makefile.win

@@ -1,8 +1,8 @@
 EXTENSION = vector
-EXTVERSION = 0.5.0
+EXTVERSION = 0.5.1
 
-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
+OBJS = src\half.obj src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\vector.obj
-HEADERS = src\vector.h
+HEADERS = src\half.h src\vector.h
 
 REGRESS = btree cast copy functions input ivfflat_cosine ivfflat_ip ivfflat_l2 ivfflat_options ivfflat_unlogged
 REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
@@ -56,7 +56,7 @@ install:
 	copy $(EXTENSION).control "$(SHAREDIR)\extension"
 	copy sql\$(EXTENSION)--*.sql "$(SHAREDIR)\extension"
 	mkdir "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
-	copy $(HEADERS) "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
+	for %f in ($(HEADERS)) do copy %f "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
 
 installcheck:
 	"$(BINDIR)\pg_regress" --bindir="$(BINDIR)" $(REGRESS_OPTS) $(REGRESS)

README.md

@@ -10,7 +10,7 @@ Store your vectors with the rest of your data. Supports:
 
 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)
+[![Build Status](https://github.com/pgvector/pgvector/actions/workflows/build.yml/badge.svg)](https://github.com/pgvector/pgvector/actions)
 
 ## Installation
 
@@ -18,7 +18,7 @@ Compile and install the extension (supports Postgres 11+)
 
 ```sh
 cd /tmp
-git clone --branch v0.5.0 https://github.com/pgvector/pgvector.git
+git clone --branch v0.5.1 https://github.com/pgvector/pgvector.git
 cd pgvector
 make
 make install # may need sudo
@@ -26,7 +26,7 @@ make install # may need sudo
 
 See the [installation notes](#installation-notes) if you run into issues
 
-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)
+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). There are also instructions for [GitHub Actions](https://github.com/pgvector/setup-pgvector).
 
 ## Getting Started
 
@@ -215,6 +215,23 @@ SELECT ...
 COMMIT;
 ```
 
+### Indexing Progress
+
+Check [indexing progress](https://www.postgresql.org/docs/current/progress-reporting.html#CREATE-INDEX-PROGRESS-REPORTING) with Postgres 12+
+
+```sql
+SELECT phase, round(100.0 * tuples_done / nullif(tuples_total, 0), 1) AS "%" FROM pg_stat_progress_create_index;
+```
+
+The phases for IVFFlat are:
+
+1. `initializing`
+2. `performing k-means`
+3. `assigning tuples`
+4. `loading tuples`
+
+Note: `%` is only populated during the `loading tuples` phase
+
 ## HNSW
 
 An HNSW index creates a multilayer graph. It has slower build times and uses more memory than IVFFlat, but has better query performance (in terms of speed-recall tradeoff). There’s no training step like IVFFlat, so the index can be created without any data in the table.
@@ -252,6 +269,8 @@ Specify HNSW parameters
 CREATE INDEX ON items USING hnsw (embedding vector_l2_ops) WITH (m = 16, ef_construction = 64);
 ```
 
+A higher value of `ef_construction` provides better recall at the cost of index build time / insert speed.
+
 ### Query Options
 
 Specify the size of the dynamic candidate list for search (40 by default)
@@ -271,22 +290,18 @@ SELECT ...
 COMMIT;
 ```
 
-## Indexing Progress
+### Indexing Progress
 
 Check [indexing progress](https://www.postgresql.org/docs/current/progress-reporting.html#CREATE-INDEX-PROGRESS-REPORTING) with Postgres 12+
 
 ```sql
-SELECT phase, tuples_done, tuples_total FROM pg_stat_progress_create_index;
+SELECT phase, round(100.0 * blocks_done / nullif(blocks_total, 0), 1) AS "%" FROM pg_stat_progress_create_index;
 ```
 
-The phases are:
+The phases for HNSW are:
 
 1. `initializing`
-2. `performing k-means` - IVFFlat only
+2. `loading tuples`
-3. `assigning tuples` - IVFFlat only
-4. `loading tuples`
-
-Note: `tuples_done` and `tuples_total` are only populated during the `loading tuples` phase
 
 ## Filtering
 
@@ -317,13 +332,15 @@ CREATE TABLE items (embedding vector(3), category_id int) PARTITION BY LIST(cate
 
 ## 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)).
+Use together with Postgres [full-text search](https://www.postgresql.org/docs/current/textsearch-intro.html) for hybrid search.
 
 ```sql
 SELECT id, content FROM items, plainto_tsquery('hello search') query
     WHERE textsearch @@ query ORDER BY ts_rank_cd(textsearch, query) DESC LIMIT 5;
 ```
 
+You can use [Reciprocal Rank Fusion](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search_rrf.py) or a [cross-encoder](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search.py) to combine results.
+
 ## Performance
 
 Use `EXPLAIN ANALYZE` to debug performance.
@@ -360,17 +377,21 @@ Use pgvector from any language with a Postgres client. You can even generate and
 
 Language | Libraries / Examples
 --- | ---
+C | [pgvector-c](https://github.com/pgvector/pgvector-c)
 C++ | [pgvector-cpp](https://github.com/pgvector/pgvector-cpp)
-C# | [pgvector-dotnet](https://github.com/pgvector/pgvector-dotnet)
+C#, F#, Visual Basic | [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)
-Java, Scala | [pgvector-java](https://github.com/pgvector/pgvector-java)
+Java, Kotlin, Groovy, Scala | [pgvector-java](https://github.com/pgvector/pgvector-java)
+JavaScript, TypeScript | [pgvector-node](https://github.com/pgvector/pgvector-node)
 Julia | [pgvector-julia](https://github.com/pgvector/pgvector-julia)
+Lisp | [pgvector-lisp](https://github.com/pgvector/pgvector-lisp)
 Lua | [pgvector-lua](https://github.com/pgvector/pgvector-lua)
-Node.js | [pgvector-node](https://github.com/pgvector/pgvector-node)
+Nim | [pgvector-nim](https://github.com/pgvector/pgvector-nim)
+OCaml | [pgvector-ocaml](https://github.com/pgvector/pgvector-ocaml)
 Perl | [pgvector-perl](https://github.com/pgvector/pgvector-perl)
 PHP | [pgvector-php](https://github.com/pgvector/pgvector-php)
 Python | [pgvector-python](https://github.com/pgvector/pgvector-python)
@@ -378,6 +399,7 @@ R | [pgvector-r](https://github.com/pgvector/pgvector-r)
 Ruby | [pgvector-ruby](https://github.com/pgvector/pgvector-ruby), [Neighbor](https://github.com/ankane/neighbor)
 Rust | [pgvector-rust](https://github.com/pgvector/pgvector-rust)
 Swift | [pgvector-swift](https://github.com/pgvector/pgvector-swift)
+Zig | [pgvector-zig](https://github.com/pgvector/pgvector-zig)
 
 ## Frequently Asked Questions
 
@@ -393,6 +415,63 @@ 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.
 
+#### Can I store vectors with different dimensions in the same column?
+
+You can use `vector` as the type (instead of `vector(3)`).
+
+```sql
+CREATE TABLE embeddings (model_id bigint, item_id bigint, embedding vector, PRIMARY KEY (model_id, item_id));
+```
+
+However, you can only create indexes on rows with the same number of dimensions (using [expression](https://www.postgresql.org/docs/current/indexes-expressional.html) and [partial](https://www.postgresql.org/docs/current/indexes-partial.html) indexing):
+
+```sql
+CREATE INDEX ON embeddings USING hnsw ((embedding::vector(3)) vector_l2_ops) WHERE (model_id = 123);
+```
+
+and query with:
+
+```sql
+SELECT * FROM embeddings WHERE model_id = 123 ORDER BY embedding::vector(3) <-> '[3,1,2]' LIMIT 5;
+```
+
+#### Can I store vectors with more precision?
+
+You can use the `double precision[]` or `numeric[]` type to store vectors with more precision.
+
+```sql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding double precision[]);
+
+-- use {} instead of [] for Postgres arrays
+INSERT INTO items (embedding) VALUES ('{1,2,3}'), ('{4,5,6}');
+```
+
+Optionally, add a [check constraint](https://www.postgresql.org/docs/current/ddl-constraints.html) to ensure data can be converted to the `vector` type and has the expected dimensions.
+
+```sql
+ALTER TABLE items ADD CHECK (vector_dims(embedding::vector) = 3);
+```
+
+Use [expression indexing](https://www.postgresql.org/docs/current/indexes-expressional.html) to index (at a lower precision):
+
+```sql
+CREATE INDEX ON items USING hnsw ((embedding::vector(3)) vector_l2_ops);
+```
+
+and query with:
+
+```sql
+SELECT * FROM items ORDER BY embedding::vector(3) <-> '[3,1,2]' LIMIT 5;
+```
+
+#### Do indexes need to fit into memory?
+
+No, but like other index types, you’ll likely see better performance if they do. You can get the size of an index with:
+
+```sql
+SELECT pg_size_pretty(pg_relation_size('index_name'));
+```
+
 ## Troubleshooting
 
 #### Why isn’t a query using an index?
@@ -406,6 +485,8 @@ SELECT ...
 COMMIT;
 ```
 
+Also, if the table is small, a table scan may be faster.
+
 #### 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:
@@ -509,7 +590,7 @@ Then use `nmake` to build:
 
 ```cmd
 set "PGROOT=C:\Program Files\PostgreSQL\15"
-git clone --branch v0.5.0 https://github.com/pgvector/pgvector.git
+git clone --branch v0.5.1 https://github.com/pgvector/pgvector.git
 cd pgvector
 nmake /F Makefile.win
 nmake /F Makefile.win install
@@ -530,7 +611,7 @@ This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (r
 You can also build the image manually:
 
 ```sh
-git clone --branch v0.5.0 https://github.com/pgvector/pgvector.git
+git clone --branch v0.5.1 https://github.com/pgvector/pgvector.git
 cd pgvector
 docker build --build-arg PG_MAJOR=15 -t myuser/pgvector .
 ```
@@ -595,7 +676,7 @@ pgvector is available on [these providers](https://github.com/pgvector/pgvector/
 
 ## Upgrading
 
-Install the latest version. Then in each database you want to upgrade, run:
+[Install](#installation) the latest version (use the same method as the original installation). Then in each database you want to upgrade, run:
 
 ```sql
 ALTER EXTENSION vector UPDATE;

sql/vector--0.5.0--0.5.1.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.5.1'" to load this file. \quit

sql/vector--0.5.1--0.6.0.sql

@@ -0,0 +1,101 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.6.0'" to load this file. \quit
+
+CREATE TYPE half;
+
+CREATE FUNCTION half_in(cstring, oid, integer) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_out(half) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_recv(internal, oid, integer) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_send(half) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE half (
+	INPUT     = half_in,
+	OUTPUT    = half_out,
+	RECEIVE   = half_recv,
+	SEND      = half_send,
+	INTERNALLENGTH = 2,
+	PASSEDBYVALUE,
+	ALIGNMENT = int2
+);
+
+CREATE FUNCTION l2_distance(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME', 'half_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME', 'half_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME', 'half_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME', 'half_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_l2_squared_distance(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_negative_inner_product(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION float4_to_half(real, integer, boolean) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_to_float4(half, integer, boolean) RETURNS real
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION float8_to_half(float8, integer, boolean) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_to_float8(half, integer, boolean) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION integer_to_half(integer, integer, boolean) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION numeric_to_half(numeric, integer, boolean) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_to_numeric(half, integer, boolean) RETURNS numeric
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (real AS half)
+	WITH FUNCTION float4_to_half(real, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (half AS real)
+	WITH FUNCTION half_to_float4(half, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (float8 AS half)
+	WITH FUNCTION float8_to_half(float8, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (half AS float8)
+	WITH FUNCTION half_to_float8(half, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (integer AS half)
+	WITH FUNCTION integer_to_half(integer, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (numeric AS half)
+	WITH FUNCTION numeric_to_half(numeric, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (half AS numeric)
+	WITH FUNCTION half_to_numeric(half, integer, boolean) AS IMPLICIT;
+
+CREATE OPERATOR <-> (
+	LEFTARG = half[], RIGHTARG = half[], PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = half[], RIGHTARG = half[], PROCEDURE = half_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = half[], RIGHTARG = half[], PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);

sql/vector.sql

@@ -290,3 +290,114 @@ CREATE OPERATOR CLASS vector_cosine_ops
 	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
 	FUNCTION 2 vector_norm(vector);
+
+-- half type
+
+CREATE TYPE half;
+
+CREATE FUNCTION half_in(cstring, oid, integer) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_out(half) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_recv(internal, oid, integer) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_send(half) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE half (
+	INPUT     = half_in,
+	OUTPUT    = half_out,
+	RECEIVE   = half_recv,
+	SEND      = half_send,
+	INTERNALLENGTH = 2,
+	PASSEDBYVALUE,
+	ALIGNMENT = int2
+);
+
+-- half functions
+
+CREATE FUNCTION l2_distance(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME', 'half_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME', 'half_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME', 'half_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME', 'half_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- half private functions
+
+CREATE FUNCTION half_l2_squared_distance(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_negative_inner_product(half[], half[]) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- half cast functions
+
+CREATE FUNCTION float4_to_half(real, integer, boolean) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_to_float4(half, integer, boolean) RETURNS real
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION float8_to_half(float8, integer, boolean) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_to_float8(half, integer, boolean) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION integer_to_half(integer, integer, boolean) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION numeric_to_half(numeric, integer, boolean) RETURNS half
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION half_to_numeric(half, integer, boolean) RETURNS numeric
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- half casts
+
+CREATE CAST (real AS half)
+	WITH FUNCTION float4_to_half(real, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (half AS real)
+	WITH FUNCTION half_to_float4(half, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (float8 AS half)
+	WITH FUNCTION float8_to_half(float8, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (half AS float8)
+	WITH FUNCTION half_to_float8(half, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (integer AS half)
+	WITH FUNCTION integer_to_half(integer, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (numeric AS half)
+	WITH FUNCTION numeric_to_half(numeric, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (half AS numeric)
+	WITH FUNCTION half_to_numeric(half, integer, boolean) AS IMPLICIT;
+
+-- half operators
+
+CREATE OPERATOR <-> (
+	LEFTARG = half[], RIGHTARG = half[], PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = half[], RIGHTARG = half[], PROCEDURE = half_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = half[], RIGHTARG = half[], PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);

src/half.c

@@ -0,0 +1,694 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "common/shortest_dec.h"
+#include "fmgr.h"
+#include "half.h"
+#include "lib/stringinfo.h"
+#include "libpq/pqformat.h"
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "utils/float.h"
+#include "utils/numeric.h"
+
+#if PG_VERSION_NUM < 120003
+static pg_noinline void
+float_overflow_error(void)
+{
+	ereport(ERROR,
+			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+			 errmsg("value out of range: overflow")));
+}
+
+static pg_noinline void
+float_underflow_error(void)
+{
+	ereport(ERROR,
+			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+			 errmsg("value out of range: underflow")));
+}
+#endif
+
+/*
+ * Check if array is a vector
+ */
+static void
+CheckArrayIsVector(ArrayType *array)
+{
+	if (ARR_NDIM(array) > 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("array must be 1-D")));
+
+	if (ARR_HASNULL(array) && array_contains_nulls(array))
+		ereport(ERROR,
+				(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
+				 errmsg("array must not contain nulls")));
+}
+
+/*
+ * Check if dimensions are the same
+ */
+static int
+CheckDims(ArrayType *a, ArrayType *b)
+{
+	int			dima;
+	int			dimb;
+
+	CheckArrayIsVector(a);
+	CheckArrayIsVector(b);
+
+	dima = ARR_DIMS(a)[0];
+	dimb = ARR_DIMS(b)[0];
+
+	if (dima != dimb)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different dimensions %d and %d", dima, dimb)));
+
+	return dima;
+}
+
+/*
+ * Return the datum representation for a half
+ */
+static inline Datum
+HalfGetDatum(half X)
+{
+	union
+	{
+		half		value;
+		int16		retval;
+	}			myunion;
+
+	myunion.value = X;
+	return Int16GetDatum(myunion.retval);
+}
+
+/*
+ * Return the half value of a datum
+ */
+static inline half
+DatumGetHalf(Datum X)
+{
+	union
+	{
+		int16		value;
+		half		retval;
+	}			myunion;
+
+	myunion.value = DatumGetInt16(X);
+	return myunion.retval;
+}
+
+/*
+ * Get a half from a message buffer
+ */
+static half
+pq_getmsghalf(StringInfo msg)
+{
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swap;
+
+	swap.i = pq_getmsgint(msg, 2);
+	return swap.h;
+}
+
+/*
+ * Append a half to a StringInfo buffer
+ */
+static void
+pq_sendhalf(StringInfo buf, half h)
+{
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swap;
+
+	swap.h = h;
+	pq_sendint16(buf, swap.i);
+}
+
+/*
+ * Convert a half to a float4
+ */
+static float
+HalfToFloat4(half num)
+{
+#ifdef FLT16_SUPPORT
+	return (float) num;
+#else
+	/* TODO Improve performance */
+	/* TODO Check endianness */
+	uint16		bin = *((uint16 *) &num);
+	uint32		exponent = (bin & 0x7C00) >> 10;
+	uint32		mantissa = bin & 0x03FF;
+
+	/* Sign */
+	uint32		result = (bin & 0x8000) << 16;
+
+	if (exponent == 31)
+	{
+		if (mantissa == 0)
+		{
+			/* Infinite */
+			result |= 0x7F800000;
+		}
+		else
+		{
+			/* NaN */
+			result |= 0x7FC00000;
+			result |= mantissa << 13;
+		}
+	}
+	else if (exponent == 0)
+	{
+		/* Subnormal */
+		if (mantissa != 0)
+		{
+			exponent = -14;
+
+			for (int i = 0; i < 10; i++)
+			{
+				mantissa <<= 1;
+				exponent -= 1;
+
+				if ((mantissa >> 10) % 2 == 1)
+				{
+					mantissa &= 0x03ff;
+					break;
+				}
+			}
+
+			result |= (exponent + 127) << 23;
+			result |= mantissa << 13;
+		}
+	}
+	else
+	{
+		/* Normal */
+		result |= (exponent - 15 + 127) << 23;
+		result |= mantissa << 13;
+	}
+
+	return *((float *) &result);
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+static half
+Float4ToHalfUnchecked(float num)
+{
+#ifdef FLT16_SUPPORT
+	return (_Float16) num;
+#else
+	/* TODO Improve performance */
+	/* TODO Check endianness */
+	uint32		bin = *((uint32 *) &num);
+	int			exponent = (bin & 0x7F800000) >> 23;
+	int			mantissa = bin & 0x007FFFFF;
+
+	/* Sign */
+	uint16		result = (bin & 0x80000000) >> 16;
+
+	if (isinf(num))
+	{
+		/* Infinite */
+		result |= 0x7C00;
+	}
+	else if (isnan(num))
+	{
+		/* NaN */
+		result |= 0x7E00;
+		result |= mantissa >> 13;
+	}
+	else if (exponent > 98)
+	{
+		int			m;
+		int			gr;
+		int			s;
+
+		exponent -= 127;
+		s = mantissa & 0x00000FFF;
+
+		/* Subnormal */
+		if (exponent < -14)
+		{
+			int			diff = -exponent - 14;
+
+			mantissa >>= diff;
+			mantissa += 1 << (23 - diff);
+			s |= mantissa & 0x00000FFF;
+		}
+
+		m = mantissa >> 13;
+
+		/* Round */
+		gr = (mantissa >> 12) % 4;
+		if (gr == 3 || (gr == 1 && s != 0))
+			m += 1;
+
+		if (m == 1024)
+		{
+			m = 0;
+			exponent += 1;
+		}
+
+		if (exponent > 15)
+		{
+			/* Infinite */
+			result |= 0x7C00;
+		}
+		else
+		{
+			if (exponent >= -14)
+				result |= (exponent + 15) << 10;
+
+			result |= m;
+		}
+	}
+
+	return *((half *) & result);
+#endif
+}
+
+/*
+ * Check if half is infinite
+ */
+static inline bool
+HalfIsInf(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isinf(num);
+#else
+	return (num << 1) == 0xF800;
+#endif
+}
+
+/*
+ * Check if half is zero
+ */
+static inline bool
+HalfIsZero(half num)
+{
+#ifdef FLT16_SUPPORT
+	return num == 0;
+#else
+	return (num << 1) == 0x0000;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+static half
+Float4ToHalf(float num)
+{
+	half		result = Float4ToHalfUnchecked(num);
+
+	if (unlikely(HalfIsInf(result)) && !isinf(num))
+		float_overflow_error();
+	if (unlikely(HalfIsZero(result)) && num != 0.0)
+		float_underflow_error();
+
+	return result;
+}
+
+/*
+ * Convert a float8 to a half
+ */
+static half
+Float8ToHalf(double num)
+{
+	/* TODO Convert directly for greater accuracy */
+	half		result = Float4ToHalfUnchecked((float) num);
+
+	if (unlikely(HalfIsInf(result)) && !isinf(num))
+		float_overflow_error();
+	if (unlikely(HalfIsZero(result)) && num != 0.0)
+		float_underflow_error();
+
+	return result;
+}
+
+/*
+ * Convert textual representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_in);
+Datum
+half_in(PG_FUNCTION_ARGS)
+{
+	char	   *num = PG_GETARG_CSTRING(0);
+	char	   *orig_num;
+	float		val;
+	char	   *endptr;
+
+	orig_num = num;
+
+	/* Skip leading whitespace */
+	while (*num != '\0' && isspace((unsigned char) *num))
+		num++;
+
+	/*
+	 * Check for an empty-string input to begin with, to avoid the vagaries of
+	 * strtof() on different platforms.
+	 */
+	if (*num == '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type %s: \"%s\"",
+						"half", orig_num)));
+
+	val = strtof(num, &endptr);
+
+	if (val < -HALF_MAX || val > HALF_MAX)
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("\"%s\" is out of range for type %s",
+						orig_num, "half")));
+
+	/* Skip trailing whitespace */
+	while (*endptr != '\0' && isspace((unsigned char) *endptr))
+		endptr++;
+
+	/* If there is any junk left at the end of the string, bail out */
+	if (*endptr != '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type %s: \"%s\"",
+						"half", orig_num)));
+
+	PG_RETURN_HALF(Float4ToHalf(val));
+}
+
+/*
+ * Convert internal representation to textual representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_out);
+Datum
+half_out(PG_FUNCTION_ARGS)
+{
+	float		num = HalfToFloat4(PG_GETARG_HALF(0));
+	char	   *ascii = (char *) palloc(32);
+	int			ndig = FLT_DIG + extra_float_digits;
+
+	if (extra_float_digits > 0)
+	{
+		float_to_shortest_decimal_buf(num, ascii);
+		PG_RETURN_CSTRING(ascii);
+	}
+
+	(void) pg_strfromd(ascii, 32, ndig, num);
+	PG_RETURN_CSTRING(ascii);
+}
+
+/*
+ * Convert external binary representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_recv);
+Datum
+half_recv(PG_FUNCTION_ARGS)
+{
+	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
+
+	PG_RETURN_HALF(pq_getmsghalf(buf));
+}
+
+/*
+ * Convert internal representation to the external binary representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_send);
+Datum
+half_send(PG_FUNCTION_ARGS)
+{
+	half		arg1 = PG_GETARG_HALF(0);
+	StringInfoData buf;
+
+	pq_begintypsend(&buf);
+	pq_sendhalf(&buf, arg1);
+	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
+}
+
+/*
+ * Convert integer to half
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(integer_to_half);
+Datum
+integer_to_half(PG_FUNCTION_ARGS)
+{
+	int32		i = PG_GETARG_INT32(0);
+
+	/* TODO Figure out correct error */
+	float		f = (float) i;
+	half		h = Float4ToHalf(f);
+
+	PG_RETURN_HALF(h);
+}
+
+/*
+ * Convert numeric to half
+ *
+ * TODO Improve error message if out of range
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(numeric_to_half);
+Datum
+numeric_to_half(PG_FUNCTION_ARGS)
+{
+	Numeric		num = PG_GETARG_NUMERIC(0);
+	float		f = DatumGetFloat4(DirectFunctionCall1(numeric_float4, NumericGetDatum(num)));
+	half		h = Float4ToHalf(f);
+
+	PG_RETURN_HALF(h);
+}
+
+/*
+ * Convert half to numeric
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_to_numeric);
+Datum
+half_to_numeric(PG_FUNCTION_ARGS)
+{
+	half		h = PG_GETARG_HALF(0);
+	float		f = HalfToFloat4(h);
+	Numeric		num = DatumGetNumeric(DirectFunctionCall1(float4_numeric, Float4GetDatum(f)));
+
+	PG_RETURN_NUMERIC(num);
+}
+
+/*
+ * Convert float4 to half
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(float4_to_half);
+Datum
+float4_to_half(PG_FUNCTION_ARGS)
+{
+	float		f = PG_GETARG_FLOAT4(0);
+	half		h = Float4ToHalf(f);
+
+	PG_RETURN_HALF(h);
+}
+
+/*
+ * Convert half to float4
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_to_float4);
+Datum
+half_to_float4(PG_FUNCTION_ARGS)
+{
+	half		h = PG_GETARG_HALF(0);
+	float		f = HalfToFloat4(h);
+
+	PG_RETURN_FLOAT4(f);
+}
+
+/*
+ * Convert float8 to half
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(float8_to_half);
+Datum
+float8_to_half(PG_FUNCTION_ARGS)
+{
+	float8		d = PG_GETARG_FLOAT8(0);
+	half		h = Float8ToHalf(d);
+
+	PG_RETURN_HALF(h);
+}
+
+/*
+ * Convert half to float8
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_to_float8);
+Datum
+half_to_float8(PG_FUNCTION_ARGS)
+{
+	half		h = PG_GETARG_HALF(0);
+	float		f = HalfToFloat4(h);
+
+	PG_RETURN_FLOAT8((double) f);
+}
+
+/*
+ * Get the L2 distance between half arrays
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_l2_distance);
+Datum
+half_l2_distance(PG_FUNCTION_ARGS)
+{
+	ArrayType  *a = PG_GETARG_ARRAYTYPE_P(0);
+	ArrayType  *b = PG_GETARG_ARRAYTYPE_P(1);
+	half	   *ax = (half *) ARR_DATA_PTR(a);
+	half	   *bx = (half *) ARR_DATA_PTR(b);
+	float		distance = 0.0;
+	int			dim = CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	PG_RETURN_FLOAT8(sqrt((double) distance));
+}
+
+/*
+ * Get the L2 squared distance between half arrays
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_l2_squared_distance);
+Datum
+half_l2_squared_distance(PG_FUNCTION_ARGS)
+{
+	ArrayType  *a = PG_GETARG_ARRAYTYPE_P(0);
+	ArrayType  *b = PG_GETARG_ARRAYTYPE_P(1);
+	half	   *ax = (half *) ARR_DATA_PTR(a);
+	half	   *bx = (half *) ARR_DATA_PTR(b);
+	float		distance = 0.0;
+	int			dim = CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the inner product of two half arrays
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_inner_product);
+Datum
+half_inner_product(PG_FUNCTION_ARGS)
+{
+	ArrayType  *a = PG_GETARG_ARRAYTYPE_P(0);
+	ArrayType  *b = PG_GETARG_ARRAYTYPE_P(1);
+	half	   *ax = (half *) ARR_DATA_PTR(a);
+	half	   *bx = (half *) ARR_DATA_PTR(b);
+	float		distance = 0.0;
+	int			dim = CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the negative inner product of two half arrays
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_negative_inner_product);
+Datum
+half_negative_inner_product(PG_FUNCTION_ARGS)
+{
+	ArrayType  *a = PG_GETARG_ARRAYTYPE_P(0);
+	ArrayType  *b = PG_GETARG_ARRAYTYPE_P(1);
+	half	   *ax = (half *) ARR_DATA_PTR(a);
+	half	   *bx = (half *) ARR_DATA_PTR(b);
+	float		distance = 0.0;
+	int			dim = CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	PG_RETURN_FLOAT8((double) distance * -1);
+}
+
+/*
+ * Get the cosine distance between two half arrays
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_cosine_distance);
+Datum
+half_cosine_distance(PG_FUNCTION_ARGS)
+{
+	ArrayType  *a = PG_GETARG_ARRAYTYPE_P(0);
+	ArrayType  *b = PG_GETARG_ARRAYTYPE_P(1);
+	half	   *ax = (half *) ARR_DATA_PTR(a);
+	half	   *bx = (half *) ARR_DATA_PTR(b);
+	float		distance = 0.0;
+	float		norma = 0.0;
+	float		normb = 0.0;
+	double		similarity;
+	int			dim = CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		axi = HalfToFloat4(ax[i]);
+		float		bxi = HalfToFloat4(bx[i]);
+
+		distance += axi * bxi;
+		norma += axi * axi;
+		normb += bxi * bxi;
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	similarity = (double) distance / sqrt((double) norma * (double) normb);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	if (isnan(similarity))
+		PG_RETURN_FLOAT8(NAN);
+#endif
+
+	/* Keep in range */
+	if (similarity > 1)
+		similarity = 1;
+	else if (similarity < -1)
+		similarity = -1;
+
+	PG_RETURN_FLOAT8(1 - similarity);
+}
+
+/*
+ * Get the L1 distance between two half arrays
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(half_l1_distance);
+Datum
+half_l1_distance(PG_FUNCTION_ARGS)
+{
+	ArrayType  *a = PG_GETARG_ARRAYTYPE_P(0);
+	ArrayType  *b = PG_GETARG_ARRAYTYPE_P(1);
+	half	   *ax = (half *) ARR_DATA_PTR(a);
+	half	   *bx = (half *) ARR_DATA_PTR(b);
+	float		distance = 0.0;
+	int			dim = CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += fabsf(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+
+	PG_RETURN_FLOAT8((double) distance);
+}

src/half.h

@@ -0,0 +1,23 @@
+#ifndef HALF_H
+#define HALF_H
+
+#define __STDC_WANT_IEC_60559_TYPES_EXT__
+
+#include <float.h>
+
+#ifdef __FLT16_MAX__
+#define FLT16_SUPPORT
+#endif
+
+#ifdef FLT16_SUPPORT
+#define half _Float16
+#define HALF_MAX FLT16_MAX
+#else
+#define half uint16
+#define HALF_MAX 65504
+#endif
+
+#define PG_GETARG_HALF(n)  DatumGetHalf(PG_GETARG_DATUM(n))
+#define PG_RETURN_HALF(x)  return HalfGetDatum(x)
+
+#endif

src/hnsw.c

@@ -14,6 +14,7 @@
 #endif
 
 int			hnsw_ef_search;
+bool		hnsw_enable_parallel_build;
 static relopt_kind hnsw_relopt_kind;
 
 /*
@@ -39,6 +40,11 @@ HnswInit(void)
 	DefineCustomIntVariable("hnsw.ef_search", "Sets the size of the dynamic candidate list for search",
 							"Valid range is 1..1000.", &hnsw_ef_search,
 							HNSW_DEFAULT_EF_SEARCH, HNSW_MIN_EF_SEARCH, HNSW_MAX_EF_SEARCH, PGC_USERSET, 0, NULL, NULL, NULL);
+
+	/* Behind a variable for now since can be slower than building in memory */
+	DefineCustomBoolVariable("hnsw.enable_parallel_build", "Enables or disables building indexes in parallel",
+							 NULL, &hnsw_enable_parallel_build,
+							 false, PGC_USERSET, 0, NULL, NULL, NULL);
 }
 
 /*

src/hnsw.h

@@ -4,6 +4,7 @@
 #include "postgres.h"
 
 #include "access/generic_xlog.h"
+#include "access/parallel.h"
 #include "access/reloptions.h"
 #include "nodes/execnodes.h"
 #include "port.h"				/* for random() */
@@ -14,6 +15,10 @@
 #error "Requires PostgreSQL 11+"
 #endif
 
+#if PG_VERSION_NUM < 120000
+#include "access/relscan.h"
+#endif
+
 #define HNSW_MAX_DIM 2000
 
 /* Support functions */
@@ -57,7 +62,9 @@
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
 #define PROGRESS_HNSW_PHASE_LOAD		2
 
-#define HNSW_ELEMENT_TUPLE_SIZE(_datum)	MAXALIGN(offsetof(HnswElementTupleData, value) + VARSIZE_ANY(_datum))
+#define HNSW_MAX_SIZE (BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - sizeof(ItemIdData))
+
+#define HNSW_ELEMENT_TUPLE_SIZE(size)	MAXALIGN(offsetof(HnswElementTupleData, data) + (size))
 #define HNSW_NEIGHBOR_TUPLE_SIZE(level, m)	MAXALIGN(offsetof(HnswNeighborTupleData, indextids) + ((level) + 2) * (m) * sizeof(ItemPointerData))
 
 #define HnswPageGetOpaque(page)	((HnswPageOpaque) PageGetSpecialPointer(page))
@@ -88,6 +95,7 @@
 
 /* Variables */
 extern int	hnsw_ef_search;
+extern bool hnsw_enable_parallel_build;
 
 typedef struct HnswNeighborArray HnswNeighborArray;
 
@@ -96,7 +104,6 @@ typedef struct HnswElementData
 	List	   *heaptids;
 	uint8		level;
 	uint8		deleted;
-	bool		loaded;
 	HnswNeighborArray *neighbors;
 	BlockNumber blkno;
 	OffsetNumber offno;
@@ -111,11 +118,13 @@ typedef struct HnswCandidate
 {
 	HnswElement element;
 	float		distance;
+	bool		closer;
 }			HnswCandidate;
 
 typedef struct HnswNeighborArray
 {
 	int			length;
+	bool		closerSet;
 	HnswCandidate *items;
 }			HnswNeighborArray;
 
@@ -133,6 +142,49 @@ typedef struct HnswOptions
 	int			efConstruction; /* size of dynamic candidate list */
 }			HnswOptions;
 
+typedef struct HnswSpool
+{
+	Relation	heap;
+	Relation	index;
+}			HnswSpool;
+
+typedef struct HnswShared
+{
+	/* 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;
+
+#if PG_VERSION_NUM < 120000
+	ParallelHeapScanDescData heapdesc;	/* must come last */
+#endif
+}			HnswShared;
+
+#if PG_VERSION_NUM >= 120000
+#define ParallelTableScanFromHnswShared(shared) \
+	(ParallelTableScanDesc) ((char *) (shared) + BUFFERALIGN(sizeof(HnswShared)))
+#endif
+
+typedef struct HnswLeader
+{
+	ParallelContext *pcxt;
+	int			nparticipanttuplesorts;
+	HnswShared *hnswshared;
+	Snapshot	snapshot;
+}			HnswLeader;
+
 typedef struct HnswBuildState
 {
 	/* Info */
@@ -160,12 +212,16 @@ typedef struct HnswBuildState
 	HnswElement entryPoint;
 	double		ml;
 	int			maxLevel;
-	double		maxInMemoryElements;
+	long		memoryLeft;
 	bool		flushed;
 	Vector	   *normvec;
 
 	/* Memory */
 	MemoryContext tmpCtx;
+
+	/* Parallel builds */
+	HnswLeader *hnswleader;
+	HnswShared *hnswshared;
 }			HnswBuildState;
 
 typedef struct HnswMetaPageData
@@ -201,7 +257,7 @@ typedef struct HnswElementTupleData
 	ItemPointerData heaptids[HNSW_HEAPTIDS];
 	ItemPointerData neighbortid;
 	uint16		unused2;
-	char		value[FLEXIBLE_ARRAY_MEMBER];
+	Vector		data;
 }			HnswElementTupleData;
 
 typedef HnswElementTupleData * HnswElementTuple;
@@ -286,6 +342,7 @@ void		HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation i
 void		HnswSetElementTuple(HnswElementTuple etup, HnswElement element);
 void		HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation);
 void		HnswLoadNeighbors(HnswElement element, Relation index, int m);
+PGDLLEXPORT void HnswParallelBuildMain(dsm_segment *seg, shm_toc *toc);
 
 /* Index access methods */
 IndexBuildResult *hnswbuild(Relation heap, Relation index, IndexInfo *indexInfo);

src/hnswbuild.c

@@ -2,12 +2,15 @@
 
 #include <math.h>
 
+#include "access/parallel.h"
+#include "access/xact.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 "tcop/tcopprot.h"
 #include "utils/datum.h"
 #include "utils/memutils.h"
 
@@ -36,6 +39,23 @@
 #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_HNSW_SHARED		UINT64CONST(0xA000000000000001)
+#define PARALLEL_KEY_QUERY_TEXT			UINT64CONST(0xA000000000000002)
+
 /*
  * Create the metapage
  */
@@ -82,7 +102,6 @@ HnswBuildAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **
 	HnswPageGetOpaque(*page)->nextblkno = BufferGetBlockNumber(newbuf);
 
 	/* Commit */
-	MarkBufferDirty(*buf);
 	GenericXLogFinish(*state);
 	UnlockReleaseBuffer(*buf);
 
@@ -107,6 +126,7 @@ CreateElementPages(HnswBuildState * buildstate)
 {
 	Relation	index = buildstate->index;
 	ForkNumber	forkNum = buildstate->forkNum;
+	Size		etupAllocSize;
 	Size		maxSize;
 	HnswElementTuple etup;
 	HnswNeighborTuple ntup;
@@ -117,11 +137,12 @@ CreateElementPages(HnswBuildState * buildstate)
 	ListCell   *lc;
 
 	/* Calculate sizes */
-	maxSize = BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData));
+	etupAllocSize = BLCKSZ;
+	maxSize = HNSW_MAX_SIZE;
 
 	/* Allocate once */
-	etup = palloc0(maxSize);
+	etup = palloc0(etupAllocSize);
-	ntup = palloc0(maxSize);
+	ntup = palloc0(BLCKSZ);
 
 	/* Prepare first page */
 	buf = HnswNewBuffer(index, forkNum);
@@ -136,13 +157,20 @@ CreateElementPages(HnswBuildState * buildstate)
 		Size		ntupSize;
 		Size		combinedSize;
 
-		HnswSetElementTuple(etup, element);
+		/* Zero memory for each element */
+		MemSet(etup, 0, etupAllocSize);
 
 		/* Calculate sizes */
-		etupSize = HNSW_ELEMENT_TUPLE_SIZE(element->value);
+		etupSize = HNSW_ELEMENT_TUPLE_SIZE(VARSIZE_ANY(DatumGetPointer(element->value)));
 		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(element->level, buildstate->m);
 		combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
 
+		/* Initial size check */
+		if (etupSize > etupAllocSize)
+			elog(ERROR, "index tuple too large");
+
+		HnswSetElementTuple(etup, element);
+
 		/* 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);
@@ -179,7 +207,6 @@ CreateElementPages(HnswBuildState * buildstate)
 	insertPage = BufferGetBlockNumber(buf);
 
 	/* Commit */
-	MarkBufferDirty(buf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 
@@ -227,7 +254,6 @@ CreateNeighborPages(HnswBuildState * buildstate)
 			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
 		/* Commit */
-		MarkBufferDirty(buf);
 		GenericXLogFinish(state);
 		UnlockReleaseBuffer(buf);
 	}
@@ -267,24 +293,30 @@ FlushPages(HnswBuildState * buildstate)
  * Insert tuple
  */
 static bool
-InsertTuple(Relation index, Datum *values, HnswElement element, HnswBuildState * buildstate, HnswElement * dup)
+InsertTuple(Relation index, Datum *values, HnswElement element, HnswBuildState * buildstate, HnswElement * dup, MemoryContext outerCtx)
 {
 	FmgrInfo   *procinfo = buildstate->procinfo;
 	Oid			collation = buildstate->collation;
 	HnswElement entryPoint = buildstate->entryPoint;
 	int			efConstruction = buildstate->efConstruction;
 	int			m = buildstate->m;
+	MemoryContext oldCtx;
 
 	/* Detoast once for all calls */
-	element->value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
 
 	/* Normalize if needed */
 	if (buildstate->normprocinfo != NULL)
 	{
-		if (!HnswNormValue(buildstate->normprocinfo, collation, &element->value, buildstate->normvec))
+		if (!HnswNormValue(buildstate->normprocinfo, collation, &value, buildstate->normvec))
 			return false;
 	}
 
+	/* Copy value to element so accessible outside of memory context */
+	oldCtx = MemoryContextSwitchTo(outerCtx);
+	element->value = datumCopy(value, false, -1);
+	MemoryContextSwitchTo(oldCtx);
+
 	/* Insert element in graph */
 	HnswInsertElement(element, entryPoint, NULL, procinfo, collation, m, efConstruction, false);
 
@@ -313,6 +345,21 @@ InsertTuple(Relation index, Datum *values, HnswElement element, HnswBuildState *
 	return *dup == NULL;
 }
 
+/*
+ * Get the memory used by an element
+ */
+static long
+HnswElementMemory(HnswElement e, int m)
+{
+	long		elementSize = sizeof(HnswElementData);
+
+	elementSize += sizeof(HnswNeighborArray) * (e->level + 1);
+	elementSize += sizeof(HnswCandidate) * (m * (e->level + 2));
+	elementSize += sizeof(ItemPointerData);
+	elementSize += VARSIZE_ANY(DatumGetPointer(e->value));
+	return elementSize;
+}
+
 /*
  * Callback for table_index_build_scan
  */
@@ -334,7 +381,7 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	if (isnull[0])
 		return;
 
-	if (buildstate->indtuples >= buildstate->maxInMemoryElements)
+	if (buildstate->memoryLeft <= 0)
 	{
 		if (!buildstate->flushed)
 		{
@@ -349,7 +396,18 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 		oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
 
 		if (HnswInsertTuple(buildstate->index, values, isnull, tid, buildstate->heap))
-			UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++buildstate->indtuples);
+		{
+			if (buildstate->hnswshared)
+			{
+				HnswShared *hnswshared = buildstate->hnswshared;
+
+				SpinLockAcquire(&hnswshared->mutex);
+				UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++hnswshared->indtuples);
+				SpinLockRelease(&hnswshared->mutex);
+			}
+			else
+				UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++buildstate->indtuples);
+		}
 
 		/* Reset memory context */
 		MemoryContextSwitchTo(oldCtx);
@@ -365,43 +423,27 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
 
 	/* Insert tuple */
-	inserted = InsertTuple(index, values, element, buildstate, &dup);
+	inserted = InsertTuple(index, values, element, buildstate, &dup, oldCtx);
 
-	/* Switch memory context */
+	/* Reset memory context */
 	MemoryContextSwitchTo(oldCtx);
+	MemoryContextReset(buildstate->tmpCtx);
 
 	/* Add outside memory context */
 	if (dup != NULL)
+	{
 		HnswAddHeapTid(dup, tid);
+		buildstate->memoryLeft -= sizeof(ItemPointerData);
+	}
 
 	/* Add to buildstate or free */
 	if (inserted)
 	{
-		element->value = datumCopy(element->value, false, -1);
-		element->loaded = true;
 		buildstate->elements = lappend(buildstate->elements, element);
+		buildstate->memoryLeft -= HnswElementMemory(element, buildstate->m);
 	}
 	else
 		HnswFreeElement(element);
-
-	/* Reset memory context */
-	MemoryContextReset(buildstate->tmpCtx);
-}
-
-/*
- * 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;
 }
 
 /*
@@ -441,7 +483,7 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	buildstate->entryPoint = NULL;
 	buildstate->ml = HnswGetMl(buildstate->m);
 	buildstate->maxLevel = HnswGetMaxLevel(buildstate->m);
-	buildstate->maxInMemoryElements = HnswGetMaxInMemoryElements(buildstate->m, buildstate->ml, buildstate->dimensions);
+	buildstate->memoryLeft = maintenance_work_mem * 1024L;
 	buildstate->flushed = false;
 
 	/* Reuse for each tuple */
@@ -450,6 +492,9 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	buildstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 											   "Hnsw build temporary context",
 											   ALLOCSET_DEFAULT_SIZES);
+
+	buildstate->hnswleader = NULL;
+	buildstate->hnswshared = NULL;
 }
 
 /*
@@ -462,21 +507,374 @@ FreeBuildState(HnswBuildState * buildstate)
 	MemoryContextDelete(buildstate->tmpCtx);
 }
 
+/*
+ * Within leader, wait for end of heap scan
+ */
+static double
+ParallelHeapScan(HnswBuildState * buildstate)
+{
+	HnswShared *hnswshared = buildstate->hnswleader->hnswshared;
+	int			nparticipanttuplesorts;
+	double		reltuples;
+
+	nparticipanttuplesorts = buildstate->hnswleader->nparticipanttuplesorts;
+	for (;;)
+	{
+		SpinLockAcquire(&hnswshared->mutex);
+		if (hnswshared->nparticipantsdone == nparticipanttuplesorts)
+		{
+			buildstate->indtuples = hnswshared->indtuples;
+			reltuples = hnswshared->reltuples;
+			SpinLockRelease(&hnswshared->mutex);
+			break;
+		}
+		SpinLockRelease(&hnswshared->mutex);
+
+		ConditionVariableSleep(&hnswshared->workersdonecv,
+							   WAIT_EVENT_PARALLEL_CREATE_INDEX_SCAN);
+	}
+
+	ConditionVariableCancelSleep();
+
+	return reltuples;
+}
+
+/*
+ * Perform a worker's portion of a parallel insert
+ */
+static void
+HnswParallelScanAndInsert(HnswSpool * hnswspool, HnswShared * hnswshared, bool progress)
+{
+	HnswBuildState buildstate;
+#if PG_VERSION_NUM >= 120000
+	TableScanDesc scan;
+#else
+	HeapScanDesc scan;
+#endif
+	double		reltuples;
+	IndexInfo  *indexInfo;
+
+	/* Join parallel scan */
+	indexInfo = BuildIndexInfo(hnswspool->index);
+	indexInfo->ii_Concurrent = hnswshared->isconcurrent;
+	InitBuildState(&buildstate, hnswspool->heap, hnswspool->index, indexInfo, MAIN_FORKNUM);
+	/* TODO Support in-memory builds */
+	buildstate.memoryLeft = 0;
+	buildstate.flushed = true;
+	buildstate.hnswshared = hnswshared;
+#if PG_VERSION_NUM >= 120000
+	scan = table_beginscan_parallel(hnswspool->heap,
+									ParallelTableScanFromHnswShared(hnswshared));
+	reltuples = table_index_build_scan(hnswspool->heap, hnswspool->index, indexInfo,
+									   true, progress, BuildCallback,
+									   (void *) &buildstate, scan);
+#else
+	scan = heap_beginscan_parallel(hnswspool->heap, &hnswshared->heapdesc);
+	reltuples = IndexBuildHeapScan(hnswspool->heap, hnswspool->index, indexInfo,
+								   true, BuildCallback,
+								   (void *) &buildstate, scan);
+#endif
+
+	/* Record statistics */
+	SpinLockAcquire(&hnswshared->mutex);
+	hnswshared->nparticipantsdone++;
+	hnswshared->reltuples += reltuples;
+	SpinLockRelease(&hnswshared->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(&hnswshared->workersdonecv);
+
+	FreeBuildState(&buildstate);
+}
+
+/*
+ * Perform work within a launched parallel process
+ */
+void
+HnswParallelBuildMain(dsm_segment *seg, shm_toc *toc)
+{
+	char	   *sharedquery;
+	HnswSpool  *hnswspool;
+	HnswShared *hnswshared;
+	Relation	heapRel;
+	Relation	indexRel;
+	LOCKMODE	heapLockmode;
+	LOCKMODE	indexLockmode;
+
+	/* 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 */
+	hnswshared = shm_toc_lookup(toc, PARALLEL_KEY_HNSW_SHARED, false);
+
+	/* Open relations using lock modes known to be obtained by index.c */
+	if (!hnswshared->isconcurrent)
+	{
+		heapLockmode = ShareLock;
+		indexLockmode = AccessExclusiveLock;
+	}
+	else
+	{
+		heapLockmode = ShareUpdateExclusiveLock;
+		indexLockmode = RowExclusiveLock;
+	}
+
+	/* Open relations within worker */
+#if PG_VERSION_NUM >= 120000
+	heapRel = table_open(hnswshared->heaprelid, heapLockmode);
+#else
+	heapRel = heap_open(hnswshared->heaprelid, heapLockmode);
+#endif
+	indexRel = index_open(hnswshared->indexrelid, indexLockmode);
+
+	/* Initialize worker's own spool */
+	hnswspool = (HnswSpool *) palloc0(sizeof(HnswSpool));
+	hnswspool->heap = heapRel;
+	hnswspool->index = indexRel;
+
+	/* Perform inserts */
+	HnswParallelScanAndInsert(hnswspool, hnswshared, 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
+HnswEndParallel(HnswLeader * hnswleader)
+{
+	/* Shutdown worker processes */
+	WaitForParallelWorkersToFinish(hnswleader->pcxt);
+
+	/* Free last reference to MVCC snapshot, if one was used */
+	if (IsMVCCSnapshot(hnswleader->snapshot))
+		UnregisterSnapshot(hnswleader->snapshot);
+	DestroyParallelContext(hnswleader->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(HnswShared)), table_parallelscan_estimate(heap, snapshot));
+#else
+	if (!IsMVCCSnapshot(snapshot))
+	{
+		Assert(snapshot == SnapshotAny);
+		return sizeof(HnswShared);
+	}
+
+	return add_size(offsetof(HnswShared, heapdesc) +
+					offsetof(ParallelHeapScanDescData, phs_snapshot_data),
+					EstimateSnapshotSpace(snapshot));
+#endif
+}
+
+/*
+ * Within leader, participate as a parallel worker
+ */
+static void
+HnswLeaderParticipateAsWorker(HnswBuildState * buildstate)
+{
+	HnswLeader *hnswleader = buildstate->hnswleader;
+	HnswSpool  *leaderworker;
+
+	/* Allocate memory and initialize private spool */
+	leaderworker = (HnswSpool *) palloc0(sizeof(HnswSpool));
+	leaderworker->heap = buildstate->heap;
+	leaderworker->index = buildstate->index;
+
+	/* Perform work common to all participants */
+	HnswParallelScanAndInsert(leaderworker, hnswleader->hnswshared, true);
+}
+
+/*
+ * Begin parallel build
+ */
+static void
+HnswBeginParallel(HnswBuildState * buildstate, bool isconcurrent, int request)
+{
+	ParallelContext *pcxt;
+	int			scantuplesortstates;
+	Snapshot	snapshot;
+	Size		esthnswshared;
+	HnswShared *hnswshared;
+	HnswLeader *hnswleader = (HnswLeader *) palloc0(sizeof(HnswLeader));
+	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", "HnswParallelBuildMain", request);
+#else
+	pcxt = CreateParallelContext("vector", "HnswParallelBuildMain", 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 */
+	esthnswshared = ParallelEstimateShared(buildstate->heap, snapshot);
+	shm_toc_estimate_chunk(&pcxt->estimator, esthnswshared);
+	shm_toc_estimate_keys(&pcxt->estimator, 1);
+
+	/* 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 */
+	hnswshared = (HnswShared *) shm_toc_allocate(pcxt->toc, esthnswshared);
+	/* Initialize immutable state */
+	hnswshared->heaprelid = RelationGetRelid(buildstate->heap);
+	hnswshared->indexrelid = RelationGetRelid(buildstate->index);
+	hnswshared->isconcurrent = isconcurrent;
+	hnswshared->scantuplesortstates = scantuplesortstates;
+	ConditionVariableInit(&hnswshared->workersdonecv);
+	SpinLockInit(&hnswshared->mutex);
+	/* Initialize mutable state */
+	hnswshared->nparticipantsdone = 0;
+	hnswshared->reltuples = 0;
+	hnswshared->indtuples = 0;
+#if PG_VERSION_NUM >= 120000
+	table_parallelscan_initialize(buildstate->heap,
+								  ParallelTableScanFromHnswShared(hnswshared),
+								  snapshot);
+#else
+	heap_parallelscan_initialize(&hnswshared->heapdesc, buildstate->heap, snapshot);
+#endif
+
+	shm_toc_insert(pcxt->toc, PARALLEL_KEY_HNSW_SHARED, hnswshared);
+
+	/* 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);
+	hnswleader->pcxt = pcxt;
+	hnswleader->nparticipanttuplesorts = pcxt->nworkers_launched;
+	if (leaderparticipates)
+		hnswleader->nparticipanttuplesorts++;
+	hnswleader->hnswshared = hnswshared;
+	hnswleader->snapshot = snapshot;
+
+	/* If no workers were successfully launched, back out (do serial build) */
+	if (pcxt->nworkers_launched == 0)
+	{
+		HnswEndParallel(hnswleader);
+		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->hnswleader = hnswleader;
+
+	/* Join heap scan ourselves */
+	if (leaderparticipates)
+		HnswLeaderParticipateAsWorker(buildstate);
+
+	/* Wait for all launched workers */
+	WaitForParallelWorkersToAttach(pcxt);
+}
+
 /*
  * Build graph
  */
 static void
 BuildGraph(HnswBuildState * buildstate, ForkNumber forkNum)
 {
+	int			parallel_workers = 0;
+
 	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_HNSW_PHASE_LOAD);
 
+	/* Calculate parallel workers */
+	if (hnsw_enable_parallel_build)
+		parallel_workers = plan_create_index_workers(RelationGetRelid(buildstate->heap), RelationGetRelid(buildstate->index));
+
+	/* Attempt to launch parallel worker scan when required */
+	if (parallel_workers > 0)
+	{
+		/* TODO Support in-memory builds */
+		FlushPages(buildstate);
+		HnswBeginParallel(buildstate, buildstate->indexInfo->ii_Concurrent, parallel_workers);
+	}
+
+	/* Add tuples to sort */
+	if (buildstate->hnswleader)
+		buildstate->reltuples = ParallelHeapScan(buildstate);
+	else
+	{
 #if PG_VERSION_NUM >= 120000
-	buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+		buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-												   true, true, BuildCallback, (void *) buildstate, NULL);
+													   true, true, BuildCallback, (void *) buildstate, NULL);
 #else
-	buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+		buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-											   true, BuildCallback, (void *) buildstate, NULL);
+												   true, BuildCallback, (void *) buildstate, NULL);
 #endif
+	}
+
+	/* End parallel build */
+	if (buildstate->hnswleader)
+		HnswEndParallel(buildstate->hnswleader);
 }
 
 /*

src/hnswinsert.c

@@ -131,10 +131,10 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	BlockNumber newInsertPage = InvalidBlockNumber;
 
 	/* Calculate sizes */
-	etupSize = HNSW_ELEMENT_TUPLE_SIZE(e->value);
+	etupSize = HNSW_ELEMENT_TUPLE_SIZE(VARSIZE_ANY(DatumGetPointer(e->value)));
 	ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(e->level, m);
 	combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
-	maxSize = BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData));
+	maxSize = HNSW_MAX_SIZE;
 	minCombinedSize = etupSize + HNSW_NEIGHBOR_TUPLE_SIZE(0, m) + sizeof(ItemIdData);
 
 	/* Prepare element tuple */
@@ -201,8 +201,6 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 			HnswInsertAppendPage(index, &newbuf, &newpage, state, page);
 
 			/* Commit */
-			MarkBufferDirty(newbuf);
-			MarkBufferDirty(buf);
 			GenericXLogFinish(state);
 
 			/* Unlock previous buffer */
@@ -269,9 +267,6 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	}
 
 	/* Commit */
-	MarkBufferDirty(buf);
-	if (nbuf != buf)
-		MarkBufferDirty(nbuf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 	if (nbuf != buf)
@@ -390,7 +385,6 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
 					elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
 				/* Commit */
-				MarkBufferDirty(buf);
 				GenericXLogFinish(state);
 			}
 			else
@@ -410,8 +404,9 @@ HnswAddDuplicate(Relation index, HnswElement element, HnswElement dup)
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
-	Size		etupSize = HNSW_ELEMENT_TUPLE_SIZE(dup->value);
+	ItemId		itemid;
 	HnswElementTuple etup;
+	Size		etupSize;
 	int			i;
 
 	/* Read page */
@@ -421,7 +416,9 @@ HnswAddDuplicate(Relation index, HnswElement element, HnswElement dup)
 	page = GenericXLogRegisterBuffer(state, buf, 0);
 
 	/* Find space */
-	etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, dup->offno));
+	itemid = PageGetItemId(page, dup->offno);
+	etup = (HnswElementTuple) PageGetItem(page, itemid);
+	etupSize = ItemIdGetLength(itemid);
 	for (i = 0; i < HNSW_HEAPTIDS; i++)
 	{
 		if (!ItemPointerIsValid(&etup->heaptids[i]))
@@ -444,7 +441,6 @@ HnswAddDuplicate(Relation index, HnswElement element, HnswElement dup)
 		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
 	/* Commit */
-	MarkBufferDirty(buf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 

src/hnswscan.c

@@ -113,12 +113,6 @@ hnswbeginscan(Relation index, int nkeys, int norderbys)
 
 	scan->opaque = so;
 
-	/*
-	 * Get a shared lock. This allows vacuum to ensure no in-flight scans
-	 * before marking tuples as deleted.
-	 */
-	LockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
-
 	return scan;
 }
 
@@ -166,11 +160,25 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (scan->orderByData == NULL)
 			elog(ERROR, "cannot scan hnsw index without order");
 
+		/* Requires MVCC-compliant snapshot as not able to maintain a pin */
+		/* https://www.postgresql.org/docs/current/index-locking.html */
+		if (!IsMVCCSnapshot(scan->xs_snapshot))
+			elog(ERROR, "non-MVCC snapshots are not supported with hnsw");
+
 		/* Get scan value */
 		value = GetScanValue(scan);
 
+		/*
+		 * Get a shared lock. This allows vacuum to ensure no in-flight scans
+		 * before marking tuples as deleted.
+		 */
+		LockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
 		so->w = GetScanItems(scan, value);
 
+		/* Release shared lock */
+		UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
 		so->first = false;
 	}
 
@@ -198,15 +206,6 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		scan->xs_ctup.t_self = *heaptid;
 #endif
 
-		/*
-		 * Typically, an index scan must maintain a pin on the index page
-		 * holding the item last returned by amgettuple. However, this is not
-		 * needed with the current vacuum strategy, which ensures scans do not
-		 * visit tuples in danger of being marked as deleted.
-		 *
-		 * https://www.postgresql.org/docs/current/index-locking.html
-		 */
-
 		scan->xs_recheckorderby = false;
 		return true;
 	}
@@ -223,9 +222,6 @@ hnswendscan(IndexScanDesc scan)
 {
 	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
 
-	/* Release shared lock */
-	UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
-
 	MemoryContextDelete(so->tmpCtx);
 
 	pfree(so);

src/hnswutils.c

@@ -118,7 +118,6 @@ HnswInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogState *
 void
 HnswCommitBuffer(Buffer buf, GenericXLogState *state)
 {
-	MarkBufferDirty(buf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 }
@@ -141,6 +140,7 @@ HnswInitNeighbors(HnswElement element, int m)
 		a = &element->neighbors[lc];
 		a->length = 0;
 		a->items = palloc(sizeof(HnswCandidate) * lm);
+		a->closerSet = false;
 	}
 }
 
@@ -177,6 +177,8 @@ HnswInitElement(ItemPointer heaptid, int m, double ml, int maxLevel)
 
 	HnswInitNeighbors(element, m);
 
+	element->value = PointerGetDatum(NULL);
+
 	return element;
 }
 
@@ -188,7 +190,7 @@ HnswFreeElement(HnswElement element)
 {
 	HnswFreeNeighbors(element);
 	list_free_deep(element->heaptids);
-	if (element->loaded)
+	if (DatumGetPointer(element->value))
 		pfree(DatumGetPointer(element->value));
 	pfree(element);
 }
@@ -216,7 +218,7 @@ HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno)
 	element->blkno = blkno;
 	element->offno = offno;
 	element->neighbors = NULL;
-	element->loaded = false;
+	element->value = PointerGetDatum(NULL);
 	return element;
 }
 
@@ -326,7 +328,7 @@ HnswSetElementTuple(HnswElementTuple etup, HnswElement element)
 		else
 			ItemPointerSetInvalid(&etup->heaptids[i]);
 	}
-	memcpy(&etup->value, DatumGetPointer(element->value), VARSIZE_ANY(element->value));
+	memcpy(&etup->data, DatumGetPointer(element->value), VARSIZE_ANY(DatumGetPointer(element->value)));
 }
 
 /*
@@ -448,12 +450,7 @@ HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHe
 	}
 
 	if (loadVec)
-	{
+		element->value = datumCopy(PointerGetDatum(&etup->data), false, -1);
-		Datum		value = PointerGetDatum(&etup->value);
-
-		element->value = datumCopy(value, false, -1);
-		element->loaded = true;
-	}
 }
 
 /*
@@ -480,7 +477,7 @@ HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index,
 
 	/* Calculate distance */
 	if (distance != NULL)
-		*distance = (float) DatumGetFloat8(FunctionCall2Coll(procinfo, collation, *q, PointerGetDatum(&etup->value)));
+		*distance = (float) DatumGetFloat8(FunctionCall2Coll(procinfo, collation, *q, PointerGetDatum(&etup->data)));
 
 	UnlockReleaseBuffer(buf);
 }
@@ -697,6 +694,34 @@ HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *pro
 	return w;
 }
 
+/*
+ * 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;
+
+	if (hca->element < hcb->element)
+		return 1;
+
+	if (hca->element > hcb->element)
+		return -1;
+
+	return 0;
+}
+
 /*
  * Calculate the distance between elements
  */
@@ -753,33 +778,77 @@ CheckElementCloser(HnswCandidate * e, List *r, int lc, FmgrInfo *procinfo, Oid c
  * Algorithm 4 from paper
  */
 static List *
-SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswCandidate * *pruned)
+SelectNeighbors(List *c, int m, int lc, FmgrInfo *procinfo, Oid collation, HnswElement e2, HnswCandidate * newCandidate, HnswCandidate * *pruned, bool sortCandidates)
 {
 	List	   *r = NIL;
 	List	   *w = list_copy(c);
 	pairingheap *wd;
+	bool		mustCalculate = !e2->neighbors[lc].closerSet;
+	List	   *added = NIL;
+	bool		removedAny = false;
 
 	if (list_length(w) <= m)
 		return w;
 
 	wd = pairingheap_allocate(CompareNearestCandidates, NULL);
 
+	/* Ensure order of candidates is deterministic for closer caching */
+	if (sortCandidates)
+		list_sort(w, CompareCandidateDistances);
+
 	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);
+		/* Use previous state of r and wd to skip work when possible */
+		if (mustCalculate)
+			e->closer = CheckElementCloser(e, r, lc, procinfo, collation);
+		else if (list_length(added) > 0)
+		{
+			/*
+			 * If the current candidate was closer, we only need to compare it
+			 * with the other candidates that we have added.
+			 */
+			if (e->closer)
+			{
+				e->closer = CheckElementCloser(e, added, lc, procinfo, collation);
 
-		if (closer)
+				if (!e->closer)
+					removedAny = true;
+			}
+			else
+			{
+				/*
+				 * If we have removed any candidates from closer, a candidate
+				 * that was not closer earlier might now be.
+				 */
+				if (removedAny)
+				{
+					e->closer = CheckElementCloser(e, r, lc, procinfo, collation);
+					if (e->closer)
+						added = lappend(added, e);
+				}
+			}
+		}
+		else if (e == newCandidate)
+		{
+			e->closer = CheckElementCloser(e, r, lc, procinfo, collation);
+			if (e->closer)
+				added = lappend(added, e);
+		}
+
+		if (e->closer)
 			r = lappend(r, e);
 		else
 			pairingheap_add(wd, &(CreatePairingHeapNode(e)->ph_node));
 	}
 
+	/* Cached value can only be used in future if sorted deterministically */
+	e2->neighbors[lc].closerSet = sortCandidates;
+
 	/* Keep pruned connections */
 	while (!pairingheap_is_empty(wd) && list_length(r) < m)
 		r = lappend(r, ((HnswPairingHeapNode *) pairingheap_remove_first(wd))->inner);
@@ -833,28 +902,6 @@ AddConnections(HnswElement element, List *neighbors, int m, int lc)
 		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;
-}
-
 /*
  * Update connections
  */
@@ -890,7 +937,7 @@ HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int
 			{
 				HnswCandidate *hc3 = &currentNeighbors->items[i];
 
-				if (!hc3->element->loaded)
+				if (DatumGetPointer(hc3->element->value) == NULL)
 					HnswLoadElement(hc3->element, &hc3->distance, &q, index, procinfo, collation, true);
 				else
 					hc3->distance = GetCandidateDistance(hc3, q, procinfo, collation);
@@ -908,13 +955,12 @@ HnswUpdateConnection(HnswElement element, HnswCandidate * hc, int m, int lc, int
 		{
 			List	   *c = NIL;
 
-			/* Add and sort candidates */
+			/* Add 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);
+			SelectNeighbors(c, m, lc, procinfo, collation, hc->element, &hc2, &pruned, true);
 
 			/* Should not happen */
 			if (pruned == NULL)
@@ -1013,7 +1059,12 @@ HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, F
 		else
 			lw = w;
 
-		neighbors = SelectNeighbors(lw, lm, lc, procinfo, collation, NULL);
+		/*
+		 * Candidates are sorted, but not deterministically. Could set
+		 * sortCandidates to true for in-memory builds to enable closer
+		 * caching, but there does not seem to be a difference in performance.
+		 */
+		neighbors = SelectNeighbors(lw, lm, lc, procinfo, collation, element, NULL, NULL, false);
 
 		AddConnections(element, neighbors, lm, lc);
 

src/hnswvacuum.c

@@ -62,7 +62,8 @@ RemoveHeapTids(HnswVacuumState * vacuumstate)
 		/* Iterate over nodes */
 		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
 		{
-			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+			ItemId		itemid = PageGetItemId(page, offno);
+			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, itemid);
 			int			idx = 0;
 			bool		itemUpdated = false;
 
@@ -93,7 +94,7 @@ RemoveHeapTids(HnswVacuumState * vacuumstate)
 
 				if (itemUpdated)
 				{
-					Size		etupSize = HNSW_ELEMENT_TUPLE_SIZE(PointerGetDatum(&etup->value));
+					Size		etupSize = ItemIdGetLength(itemid);
 
 					/* Mark rest as invalid */
 					for (int i = idx; i < HNSW_HEAPTIDS; i++)
@@ -128,10 +129,7 @@ RemoveHeapTids(HnswVacuumState * vacuumstate)
 		blkno = HnswPageGetOpaque(page)->nextblkno;
 
 		if (updated)
-		{
-			MarkBufferDirty(buf);
 			GenericXLogFinish(state);
-		}
 		else
 			GenericXLogAbort(state);
 
@@ -229,7 +227,6 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
 	/* Commit */
-	MarkBufferDirty(buf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 
@@ -481,11 +478,11 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 		/* Update element and neighbors together */
 		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
 		{
-			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+			ItemId		itemid = PageGetItemId(page, offno);
+			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, itemid);
 			HnswNeighborTuple ntup;
 			Size		etupSize;
 			Size		ntupSize;
-			Datum		value;
 			Buffer		nbuf;
 			Page		npage;
 			BlockNumber neighborPage;
@@ -509,11 +506,8 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 			if (ItemPointerIsValid(&etup->heaptids[0]))
 				continue;
 
-			/* Get datum */
-			value = PointerGetDatum(&etup->value);
-
 			/* Calculate sizes */
-			etupSize = HNSW_ELEMENT_TUPLE_SIZE(value);
+			etupSize = ItemIdGetLength(itemid);
 			ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(etup->level, vacuumstate->m);
 
 			/* Get neighbor page */
@@ -536,7 +530,7 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 
 			/* Overwrite element */
 			etup->deleted = 1;
-			MemSet(&etup->value, 0, VARSIZE_ANY(value));
+			MemSet(&etup->data, 0, VARSIZE_ANY(&etup->data));
 
 			/* Overwrite neighbors */
 			for (int i = 0; i < ntup->count; i++)
@@ -551,9 +545,6 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 				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);

src/ivfbuild.c

@@ -506,9 +506,11 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
+	Size		listSize;
 	IvfflatList list;
 
-	list = palloc0(BLCKSZ);
+	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(dimensions));
+	list = palloc(listSize);
 
 	buf = IvfflatNewBuffer(index, forkNum);
 	IvfflatInitRegisterPage(index, &buf, &page, &state);
@@ -516,13 +518,11 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	for (int i = 0; i < lists; i++)
 	{
 		OffsetNumber offno;
-		Datum		center = PointerGetDatum(VectorArrayGet(centers, i));
-		Size		listSize = MAXALIGN(IVFFLAT_LIST_SIZE(center));
 
 		/* Load list */
 		list->startPage = InvalidBlockNumber;
 		list->insertPage = InvalidBlockNumber;
-		memcpy(&list->center, DatumGetPointer(center), VARSIZE_ANY(center));
+		memcpy(&list->center, VectorArrayGet(centers, i), VECTOR_SIZE(dimensions));
 
 		/* Ensure free space */
 		if (PageGetFreeSpace(page) < listSize)

src/ivfflat.h

@@ -52,7 +52,7 @@
 #define PROGRESS_IVFFLAT_PHASE_ASSIGN	3
 #define PROGRESS_IVFFLAT_PHASE_LOAD		4
 
-#define IVFFLAT_LIST_SIZE(_datum)	(offsetof(IvfflatListData, center) + VARSIZE_ANY(_datum))
+#define IVFFLAT_LIST_SIZE(_dim)	(offsetof(IvfflatListData, center) + VECTOR_SIZE(_dim))
 
 #define IvfflatPageGetOpaque(page)	((IvfflatPageOpaque) PageGetSpecialPointer(page))
 #define IvfflatPageGetMeta(page)	((IvfflatMetaPageData *) PageGetContents(page))
@@ -229,7 +229,7 @@ typedef struct IvfflatListData
 {
 	BlockNumber startPage;
 	BlockNumber insertPage;
-	char		center[FLEXIBLE_ARRAY_MEMBER];
+	Vector		center;
 }			IvfflatListData;
 
 typedef IvfflatListData * IvfflatList;
@@ -246,8 +246,6 @@ typedef struct IvfflatScanOpaqueData
 	int			probes;
 	int			dimensions;
 	bool		first;
-	Buffer		buf;
-	ItemPointerData heaptid;
 
 	/* Sorting */
 	Tuplesortstate *sortstate;

src/ivfinsert.c

@@ -99,7 +99,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 
 	/* Get tuple size */
 	itemsz = MAXALIGN(IndexTupleSize(itup));
-	Assert(itemsz <= BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(IvfflatPageOpaqueData)));
+	Assert(itemsz <= BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(IvfflatPageOpaqueData)) - sizeof(ItemIdData));
 
 	/* Find a page to insert the item */
 	for (;;)
@@ -142,8 +142,6 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 			IvfflatPageGetOpaque(page)->nextblkno = insertPage;
 
 			/* Commit */
-			MarkBufferDirty(newbuf);
-			MarkBufferDirty(buf);
 			GenericXLogFinish(state);
 
 			/* Unlock previous buffer */

src/ivfscan.c

@@ -143,10 +143,6 @@ GetScanItems(IndexScanDesc scan, Datum value)
 				bool		isnull;
 				ItemId		itemid = PageGetItemId(page, offno);
 
-				/* Skip dead tuples */
-				if (scan->ignore_killed_tuples && ItemIdIsDead(itemid))
-					continue;
-
 				itup = (IndexTuple) PageGetItem(page, itemid);
 				datum = index_getattr(itup, 1, tupdesc, &isnull);
 
@@ -161,8 +157,6 @@ GetScanItems(IndexScanDesc scan, Datum value)
 				slot->tts_isnull[0] = false;
 				slot->tts_values[1] = PointerGetDatum(&itup->t_tid);
 				slot->tts_isnull[1] = false;
-				slot->tts_values[2] = Int32GetDatum((int) searchPage);
-				slot->tts_isnull[2] = false;
 				ExecStoreVirtualTuple(slot);
 
 				tuplesort_puttupleslot(so->sortstate, slot);
@@ -187,55 +181,6 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	tuplesort_performsort(so->sortstate);
 }
 
-/*
- * Mark prior tuple as dead
- */
-static void
-MarkPriorTupleDead(IndexScanDesc scan)
-{
-	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
-	Buffer		buf = so->buf;
-	Page		page;
-	OffsetNumber maxoffno;
-
-	/* Safety check */
-	if (!BufferIsValid(so->buf) || !ItemPointerIsValid(&so->heaptid))
-		return;
-
-	/* Only a shared locked is needed for ItemIdMarkDead */
-	LockBuffer(buf, BUFFER_LOCK_SHARE);
-	page = BufferGetPage(buf);
-	maxoffno = PageGetMaxOffsetNumber(page);
-
-	for (OffsetNumber offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
-	{
-		ItemId		itemid = PageGetItemId(page, offno);
-		IndexTuple	itup = (IndexTuple) PageGetItem(page, itemid);
-
-		/*
-		 * Find tuple. Since buffer has been pinned, tuple cannot have been
-		 * vacuumed (and heap TID reused).
-		 */
-		if (ItemPointerEquals(&itup->t_tid, &so->heaptid))
-		{
-			/*
-			 * Make sure tuple has not already been marked dead to avoid extra
-			 * WAL if wal_log_hints or data checksums enabled
-			 */
-			if (!ItemIdIsDead(itemid))
-			{
-				ItemIdMarkDead(itemid);
-				MarkBufferDirtyHint(buf, true);
-			}
-
-			break;
-		}
-	}
-
-	/* Unlock buffer */
-	LockBuffer(buf, BUFFER_LOCK_UNLOCK);
-}
-
 /*
  * Prepare for an index scan
  */
@@ -261,9 +206,7 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 		probes = lists;
 
 	so = (IvfflatScanOpaque) palloc(offsetof(IvfflatScanOpaqueData, lists) + probes * sizeof(IvfflatScanList));
-	so->buf = InvalidBuffer;
 	so->first = true;
-	ItemPointerSetInvalid(&so->heaptid);
 	so->probes = probes;
 	so->dimensions = dimensions;
 
@@ -274,13 +217,12 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 
 	/* Create tuple description for sorting */
 #if PG_VERSION_NUM >= 120000
-	so->tupdesc = CreateTemplateTupleDesc(3);
+	so->tupdesc = CreateTemplateTupleDesc(2);
 #else
-	so->tupdesc = CreateTemplateTupleDesc(3, false);
+	so->tupdesc = CreateTemplateTupleDesc(2, false);
 #endif
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "heaptid", TIDOID, -1, 0);
-	TupleDescInitEntry(so->tupdesc, (AttrNumber) 3, "indexblkno", INT4OID, -1, 0);
 
 	/* Prep sort */
 	so->sortstate = tuplesort_begin_heap(so->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, work_mem, NULL, false);
@@ -312,7 +254,6 @@ ivfflatrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int
 #endif
 
 	so->first = true;
-	ItemPointerSetInvalid(&so->heaptid);
 	pairingheap_reset(so->listQueue);
 
 	if (keys && scan->numberOfKeys > 0)
@@ -347,6 +288,11 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (scan->orderByData == NULL)
 			elog(ERROR, "cannot scan ivfflat index without order");
 
+		/* Requires MVCC-compliant snapshot as not able to pin during sorting */
+		/* https://www.postgresql.org/docs/current/index-locking.html */
+		if (!IsMVCCSnapshot(scan->xs_snapshot))
+			elog(ERROR, "non-MVCC snapshots are not supported with ivfflat");
+
 		if (scan->orderByData->sk_flags & SK_ISNULL)
 			value = PointerGetDatum(InitVector(so->dimensions));
 		else
@@ -370,17 +316,10 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (value != scan->orderByData->sk_argument)
 			pfree(DatumGetPointer(value));
 	}
-	else
-	{
-		/* Mark prior tuple as dead */
-		if (scan->kill_prior_tuple)
-			MarkPriorTupleDead(scan);
-	}
 
 	if (tuplesort_gettupleslot(so->sortstate, true, false, so->slot, NULL))
 	{
 		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->slot, 2, &so->isnull));
-		BlockNumber indexblkno = DatumGetInt32(slot_getattr(so->slot, 3, &so->isnull));
 
 #if PG_VERSION_NUM >= 120000
 		scan->xs_heaptid = *heaptid;
@@ -388,21 +327,6 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		scan->xs_ctup.t_self = *heaptid;
 #endif
 
-		/* Keep track of info needed to mark tuple as dead */
-		so->heaptid = *heaptid;
-
-		/* Unpin buffer */
-		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;
 	}
@@ -418,10 +342,6 @@ ivfflatendscan(IndexScanDesc scan)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 
-	/* Release pin */
-	if (BufferIsValid(so->buf))
-		ReleaseBuffer(so->buf);
-
 	pairingheap_free(so->listQueue);
 	tuplesort_end(so->sortstate);
 

src/ivfutils.c

@@ -136,7 +136,6 @@ IvfflatInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogStat
 void
 IvfflatCommitBuffer(Buffer buf, GenericXLogState *state)
 {
-	MarkBufferDirty(buf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 }
@@ -160,8 +159,6 @@ IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **st
 	IvfflatInitPage(newbuf, newpage);
 
 	/* Commit */
-	MarkBufferDirty(*buf);
-	MarkBufferDirty(newbuf);
 	GenericXLogFinish(*state);
 
 	/* Unlock */

src/ivfvacuum.c

@@ -107,7 +107,6 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 				{
 					/* Delete tuples */
 					PageIndexMultiDelete(page, deletable, ndeletable);
-					MarkBufferDirty(buf);
 					GenericXLogFinish(state);
 				}
 				else

src/vector.c

@@ -89,7 +89,7 @@ CheckDim(int dim)
 }
 
 /*
- * Ensure finite elements
+ * Ensure finite element
  */
 static inline void
 CheckElement(float value)
@@ -437,17 +437,18 @@ vector_send(PG_FUNCTION_ARGS)
 
 /*
  * Convert vector to vector
+ * This is needed to check the type modifier
  */
 PGDLLEXPORT PG_FUNCTION_INFO_V1(vector);
 Datum
 vector(PG_FUNCTION_ARGS)
 {
-	Vector	   *arg = PG_GETARG_VECTOR_P(0);
+	Vector	   *vec = PG_GETARG_VECTOR_P(0);
 	int32		typmod = PG_GETARG_INT32(1);
 
-	CheckExpectedDim(typmod, arg->dim);
+	CheckExpectedDim(typmod, vec->dim);
 
-	PG_RETURN_POINTER(arg);
+	PG_RETURN_POINTER(vec);
 }
 
 /*
@@ -464,7 +465,6 @@ array_to_vector(PG_FUNCTION_ARGS)
 	bool		typbyval;
 	char		typalign;
 	Datum	   *elemsp;
-	bool	   *nullsp;
 	int			nelemsp;
 
 	if (ARR_NDIM(array) > 1)
@@ -478,7 +478,7 @@ array_to_vector(PG_FUNCTION_ARGS)
 				 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);
+	deconstruct_array(array, ARR_ELEMTYPE(array), typlen, typbyval, typalign, &elemsp, NULL, &nelemsp);
 
 	CheckDim(nelemsp);
 	CheckExpectedDim(typmod, nelemsp);
@@ -512,6 +512,12 @@ array_to_vector(PG_FUNCTION_ARGS)
 				 errmsg("unsupported array type")));
 	}
 
+	/*
+	 * Free allocation from deconstruct_array. Do not free individual elements
+	 * when pass-by-reference since they point to original array.
+	 */
+	pfree(elemsp);
+
 	/* Check elements */
 	for (int i = 0; i < result->dim; i++)
 		CheckElement(result->x[i]);

test/expected/copy.out

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

test/expected/functions.out

@@ -54,105 +54,105 @@ SELECT vector_norm('[3e37,4e37]')::real;
        5e+37
 (1 row)
 
-SELECT l2_distance('[0,0]', '[3,4]');
+SELECT l2_distance('[0,0]'::vector, '[3,4]');
  l2_distance 
 -------------
            5
 (1 row)
 
-SELECT l2_distance('[0,0]', '[0,1]');
+SELECT l2_distance('[0,0]'::vector, '[0,1]');
  l2_distance 
 -------------
            1
 (1 row)
 
-SELECT l2_distance('[1,2]', '[3]');
+SELECT l2_distance('[1,2]'::vector, '[3]');
 ERROR:  different vector dimensions 2 and 1
-SELECT l2_distance('[3e38]', '[-3e38]');
+SELECT l2_distance('[3e38]'::vector, '[-3e38]');
  l2_distance 
 -------------
     Infinity
 (1 row)
 
-SELECT inner_product('[1,2]', '[3,4]');
+SELECT inner_product('[1,2]'::vector, '[3,4]');
  inner_product 
 ---------------
             11
 (1 row)
 
-SELECT inner_product('[1,2]', '[3]');
+SELECT inner_product('[1,2]'::vector, '[3]');
 ERROR:  different vector dimensions 2 and 1
-SELECT inner_product('[3e38]', '[3e38]');
+SELECT inner_product('[3e38]'::vector, '[3e38]');
  inner_product 
 ---------------
       Infinity
 (1 row)
 
-SELECT cosine_distance('[1,2]', '[2,4]');
+SELECT cosine_distance('[1,2]'::vector, '[2,4]');
  cosine_distance 
 -----------------
                0
 (1 row)
 
-SELECT cosine_distance('[1,2]', '[0,0]');
+SELECT cosine_distance('[1,2]'::vector, '[0,0]');
  cosine_distance 
 -----------------
              NaN
 (1 row)
 
-SELECT cosine_distance('[1,1]', '[1,1]');
+SELECT cosine_distance('[1,1]'::vector, '[1,1]');
  cosine_distance 
 -----------------
                0
 (1 row)
 
-SELECT cosine_distance('[1,0]', '[0,2]');
+SELECT cosine_distance('[1,0]'::vector, '[0,2]');
  cosine_distance 
 -----------------
                1
 (1 row)
 
-SELECT cosine_distance('[1,1]', '[-1,-1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1,-1]');
  cosine_distance 
 -----------------
                2
 (1 row)
 
-SELECT cosine_distance('[1,2]', '[3]');
+SELECT cosine_distance('[1,2]'::vector, '[3]');
 ERROR:  different vector dimensions 2 and 1
-SELECT cosine_distance('[1,1]', '[1.1,1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[1.1,1.1]');
  cosine_distance 
 -----------------
                0
 (1 row)
 
-SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1.1,-1.1]');
  cosine_distance 
 -----------------
                2
 (1 row)
 
-SELECT cosine_distance('[3e38]', '[3e38]');
+SELECT cosine_distance('[3e38]'::vector, '[3e38]');
  cosine_distance 
 -----------------
              NaN
 (1 row)
 
-SELECT l1_distance('[0,0]', '[3,4]');
+SELECT l1_distance('[0,0]'::vector, '[3,4]');
  l1_distance 
 -------------
            7
 (1 row)
 
-SELECT l1_distance('[0,0]', '[0,1]');
+SELECT l1_distance('[0,0]'::vector, '[0,1]');
  l1_distance 
 -------------
            1
 (1 row)
 
-SELECT l1_distance('[1,2]', '[3]');
+SELECT l1_distance('[1,2]'::vector, '[3]');
 ERROR:  different vector dimensions 2 and 1
-SELECT l1_distance('[3e38]', '[-3e38]');
+SELECT l1_distance('[3e38]'::vector, '[-3e38]');
  l1_distance 
 -------------
     Infinity

test/expected/half.out

@@ -0,0 +1,226 @@
+SELECT '1.5'::half;
+ half 
+------
+ 1.5
+(1 row)
+
+SELECT '65504'::half;
+ half  
+-------
+ 65504
+(1 row)
+
+SELECT '65505'::half;
+ERROR:  "65505" is out of range for type half
+LINE 1: SELECT '65505'::half;
+               ^
+SELECT '-65504'::half;
+  half  
+--------
+ -65504
+(1 row)
+
+SELECT '-65505'::half;
+ERROR:  "-65505" is out of range for type half
+LINE 1: SELECT '-65505'::half;
+               ^
+SELECT ''::half;
+ERROR:  invalid input syntax for type half: ""
+LINE 1: SELECT ''::half;
+               ^
+SELECT ' '::half;
+ERROR:  invalid input syntax for type half: " "
+LINE 1: SELECT ' '::half;
+               ^
+SELECT '-'::half;
+ERROR:  invalid input syntax for type half: "-"
+LINE 1: SELECT '-'::half;
+               ^
+SELECT ' 1.5'::half;
+ half 
+------
+ 1.5
+(1 row)
+
+SELECT '1.5 '::half;
+ half 
+------
+ 1.5
+(1 row)
+
+SELECT '1.5a'::half;
+ERROR:  invalid input syntax for type half: "1.5a"
+LINE 1: SELECT '1.5a'::half;
+               ^
+SELECT '{1,2,3}'::half[];
+  half   
+---------
+ {1,2,3}
+(1 row)
+
+SELECT '{1,2,3}'::half[]::real[];
+ float4  
+---------
+ {1,2,3}
+(1 row)
+
+SELECT '65505'::integer::half;
+ half  
+-------
+ 65504
+(1 row)
+
+SELECT 'NaN'::real::half;
+ half 
+------
+ NaN
+(1 row)
+
+SELECT 'Infinity'::real::half;
+   half   
+----------
+ Infinity
+(1 row)
+
+SELECT '1e-38'::real::half;
+ERROR:  value out of range: underflow
+SELECT '1.5'::half::real;
+ float4 
+--------
+    1.5
+(1 row)
+
+SELECT '1.5'::real::half;
+ half 
+------
+ 1.5
+(1 row)
+
+SELECT '1.5'::half::double precision;
+ float8 
+--------
+    1.5
+(1 row)
+
+SELECT '1.5'::double precision::half;
+ half 
+------
+ 1.5
+(1 row)
+
+SELECT '1.5'::half::numeric;
+ numeric 
+---------
+     1.5
+(1 row)
+
+SELECT '1.5'::numeric::half;
+ half 
+------
+ 1.5
+(1 row)
+
+SELECT l2_distance('{0,0}'::half[], '{3,4}'::half[]);
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('{0,0}'::half[], '{0,1}'::half[]);
+ l2_distance 
+-------------
+           1
+(1 row)
+
+SELECT l2_distance('{1,2}'::half[], '{3}'::half[]);
+ERROR:  different dimensions 2 and 1
+SELECT '{0,0}'::half[] <-> '{3,4}'::half[];
+ ?column? 
+----------
+        5
+(1 row)
+
+SELECT inner_product('{1,2}'::half[], '{3,4}'::half[]);
+ inner_product 
+---------------
+            11
+(1 row)
+
+SELECT inner_product('{1,2}'::half[], '{3}'::half[]);
+ERROR:  different dimensions 2 and 1
+SELECT inner_product('{65504}'::half[], '{65504}'::half[]);
+ inner_product 
+---------------
+    4290774016
+(1 row)
+
+SELECT '{1,2}'::half[] <#> '{3,4}'::half[];
+ ?column? 
+----------
+      -11
+(1 row)
+
+SELECT cosine_distance('{1,2}'::half[], '{2,4}'::half[]);
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('{1,2}'::half[], '{0,0}'::half[]);
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('{1,1}'::half[], '{1,1}'::half[]);
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('{1,0}'::half[], '{0,2}'::half[]);
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
+SELECT cosine_distance('{1,1}'::half[], '{-1,-1}'::half[]);
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('{1,2}'::half[], '{3}'::half[]);
+ERROR:  different dimensions 2 and 1
+SELECT cosine_distance('{1,1}'::half[], '{1.1,1.1}'::half[]);
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('{1,1}'::half[], '{-1.1,-1.1}'::half[]);
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT '{1,2}'::half[] <=> '{2,4}'::half[];
+ ?column? 
+----------
+        0
+(1 row)
+
+SELECT l1_distance('{0,0}'::half[], '{3,4}');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('{0,0}'::half[], '{0,1}');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('{1,2}'::half[], '{3}');
+ERROR:  different dimensions 2 and 1

test/sql/copy.sql

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

test/sql/functions.sql

@@ -13,29 +13,29 @@ SELECT vector_norm('[3,4]');
 SELECT vector_norm('[0,1]');
 SELECT vector_norm('[3e37,4e37]')::real;
 
-SELECT l2_distance('[0,0]', '[3,4]');
+SELECT l2_distance('[0,0]'::vector, '[3,4]');
-SELECT l2_distance('[0,0]', '[0,1]');
+SELECT l2_distance('[0,0]'::vector, '[0,1]');
-SELECT l2_distance('[1,2]', '[3]');
+SELECT l2_distance('[1,2]'::vector, '[3]');
-SELECT l2_distance('[3e38]', '[-3e38]');
+SELECT l2_distance('[3e38]'::vector, '[-3e38]');
 
-SELECT inner_product('[1,2]', '[3,4]');
+SELECT inner_product('[1,2]'::vector, '[3,4]');
-SELECT inner_product('[1,2]', '[3]');
+SELECT inner_product('[1,2]'::vector, '[3]');
-SELECT inner_product('[3e38]', '[3e38]');
+SELECT inner_product('[3e38]'::vector, '[3e38]');
 
-SELECT cosine_distance('[1,2]', '[2,4]');
+SELECT cosine_distance('[1,2]'::vector, '[2,4]');
-SELECT cosine_distance('[1,2]', '[0,0]');
+SELECT cosine_distance('[1,2]'::vector, '[0,0]');
-SELECT cosine_distance('[1,1]', '[1,1]');
+SELECT cosine_distance('[1,1]'::vector, '[1,1]');
-SELECT cosine_distance('[1,0]', '[0,2]');
+SELECT cosine_distance('[1,0]'::vector, '[0,2]');
-SELECT cosine_distance('[1,1]', '[-1,-1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1,-1]');
-SELECT cosine_distance('[1,2]', '[3]');
+SELECT cosine_distance('[1,2]'::vector, '[3]');
-SELECT cosine_distance('[1,1]', '[1.1,1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[1.1,1.1]');
-SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1.1,-1.1]');
-SELECT cosine_distance('[3e38]', '[3e38]');
+SELECT cosine_distance('[3e38]'::vector, '[3e38]');
 
-SELECT l1_distance('[0,0]', '[3,4]');
+SELECT l1_distance('[0,0]'::vector, '[3,4]');
-SELECT l1_distance('[0,0]', '[0,1]');
+SELECT l1_distance('[0,0]'::vector, '[0,1]');
-SELECT l1_distance('[1,2]', '[3]');
+SELECT l1_distance('[1,2]'::vector, '[3]');
-SELECT l1_distance('[3e38]', '[-3e38]');
+SELECT l1_distance('[3e38]'::vector, '[-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;

test/sql/half.sql

@@ -0,0 +1,53 @@
+SELECT '1.5'::half;
+SELECT '65504'::half;
+SELECT '65505'::half;
+SELECT '-65504'::half;
+SELECT '-65505'::half;
+
+SELECT ''::half;
+SELECT ' '::half;
+SELECT '-'::half;
+SELECT ' 1.5'::half;
+SELECT '1.5 '::half;
+SELECT '1.5a'::half;
+
+SELECT '{1,2,3}'::half[];
+SELECT '{1,2,3}'::half[]::real[];
+
+SELECT '65505'::integer::half;
+SELECT 'NaN'::real::half;
+SELECT 'Infinity'::real::half;
+SELECT '1e-38'::real::half;
+
+SELECT '1.5'::half::real;
+SELECT '1.5'::real::half;
+
+SELECT '1.5'::half::double precision;
+SELECT '1.5'::double precision::half;
+
+SELECT '1.5'::half::numeric;
+SELECT '1.5'::numeric::half;
+
+SELECT l2_distance('{0,0}'::half[], '{3,4}'::half[]);
+SELECT l2_distance('{0,0}'::half[], '{0,1}'::half[]);
+SELECT l2_distance('{1,2}'::half[], '{3}'::half[]);
+SELECT '{0,0}'::half[] <-> '{3,4}'::half[];
+
+SELECT inner_product('{1,2}'::half[], '{3,4}'::half[]);
+SELECT inner_product('{1,2}'::half[], '{3}'::half[]);
+SELECT inner_product('{65504}'::half[], '{65504}'::half[]);
+SELECT '{1,2}'::half[] <#> '{3,4}'::half[];
+
+SELECT cosine_distance('{1,2}'::half[], '{2,4}'::half[]);
+SELECT cosine_distance('{1,2}'::half[], '{0,0}'::half[]);
+SELECT cosine_distance('{1,1}'::half[], '{1,1}'::half[]);
+SELECT cosine_distance('{1,0}'::half[], '{0,2}'::half[]);
+SELECT cosine_distance('{1,1}'::half[], '{-1,-1}'::half[]);
+SELECT cosine_distance('{1,2}'::half[], '{3}'::half[]);
+SELECT cosine_distance('{1,1}'::half[], '{1.1,1.1}'::half[]);
+SELECT cosine_distance('{1,1}'::half[], '{-1.1,-1.1}'::half[]);
+SELECT '{1,2}'::half[] <=> '{2,4}'::half[];
+
+SELECT l1_distance('{0,0}'::half[], '{3,4}');
+SELECT l1_distance('{0,0}'::half[], '{0,1}');
+SELECT l1_distance('{1,2}'::half[], '{3}');

test/t/012_hnsw_build_recall.pl

@@ -83,11 +83,32 @@ for my $i (0 .. $#operators)
 		push(@expected, $res);
 	}
 
-	# Add index
+	# Build index serially
-	$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v $opclass);");
+	$node->safe_psql("postgres", qq(
+		SET max_parallel_maintenance_workers = 0;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
 
+	# Test approximate results
 	my $min = $operator eq "<#>" ? 0.80 : 0.99;
 	test_recall($min, $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;
+		SET hnsw.enable_parallel_build = on;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
 }
 
 done_testing();

vector.control

@@ -1,4 +1,4 @@
 comment = 'vector data type and ivfflat and hnsw access methods'
-default_version = '0.5.0'
+default_version = '0.5.1'
 module_pathname = '$libdir/vector'
 relocatable = true