Skip if FMA available [skip ci]

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

.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
@@ -18,17 +20,15 @@ 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 }}
           dev-files: true
       - run: make
         env:
-          PG_CFLAGS: -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
+          PG_CFLAGS: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
       - run: |
           export PG_CONFIG=`which pg_config`
           sudo --preserve-env=PG_CONFIG make install
@@ -40,37 +40,54 @@ jobs:
           sudo apt-get install libipc-run-perl
       - run: make prove_installcheck
   mac:
-    runs-on: macos-latest
+    runs-on: ${{ matrix.os }}
     if: ${{ !startsWith(github.ref_name, 'windows') }}
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - postgres: 16
+            os: macos-14
+          - postgres: 14
+            os: macos-12
     steps:
-      - uses: actions/checkout@v3
+      - uses: actions/checkout@v4
       - uses: ankane/setup-postgres@v1
         with:
-          postgres-version: 14
+          postgres-version: ${{ matrix.postgres }}
       - run: make
         env:
-          PG_CFLAGS: -Wall -Wextra -Werror -Wno-unused-parameter
+          PG_CFLAGS: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter
       - run: make install
       - run: make installcheck
       - if: ${{ failure() }}
         run: cat regression.diffs
+      # Homebrew Postgres does not enable TAP tests, so need to download
       - run: |
           brew install cpanm
           cpanm --notest IPC::Run
-          wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_14_5.tar.gz
-          tar xf REL_14_5.tar.gz
-      - run: make prove_installcheck PROVE_FLAGS="-I ./postgres-REL_14_5/src/test/perl" PERL5LIB="/Users/runner/perl5/lib/perl5"
-      - run: make clean && /usr/local/opt/llvm@15/bin/scan-build --status-bugs make
+          wget -q https://github.com/postgres/postgres/archive/refs/tags/$TAG.tar.gz
+          tar xf $TAG.tar.gz
+          mv postgres-$TAG postgres
+        env:
+          TAG: ${{ matrix.postgres == 16 && 'REL_16_2' || 'REL_14_11' }}
+      - run: make prove_installcheck PROVE_FLAGS="-I ./postgres/src/test/perl -I ./test/perl"
+        env:
+          PERL5LIB: /Users/runner/perl5/lib/perl5
+      - run: make clean && $(brew --prefix llvm@15)/bin/scan-build --status-bugs make
+        env:
+          PG_CFLAGS: -DUSE_ASSERT_CHECKING
   windows:
     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
       - run: |
           call "C:\Program Files\Microsoft Visual Studio\2022\Enterprise\VC\Auxiliary\Build\vcvars64.bat" && ^
+          cd %TEMP% && ^
           nmake /NOLOGO /F Makefile.win && ^
           nmake /NOLOGO /F Makefile.win install && ^
           nmake /NOLOGO /F Makefile.win installcheck && ^
@@ -81,10 +98,10 @@ jobs:
     if: ${{ !startsWith(github.ref_name, 'mac') && !startsWith(github.ref_name, 'windows') }}
     runs-on: ubuntu-latest
     container:
-      image: debian:11
+      image: debian:12
       options: --platform linux/386
     steps:
-      - run: apt-get update && apt-get install -y build-essential git libipc-run-perl postgresql-13 postgresql-server-dev-13 sudo
+      - run: apt-get update && apt-get install -y build-essential git libipc-run-perl postgresql-15 postgresql-server-dev-15 sudo
       - run: service postgresql start
       - run: |
           git clone https://github.com/${{ github.repository }}.git pgvector
@@ -97,4 +114,15 @@ jobs:
           sudo -u postgres make installcheck
           sudo -u postgres make prove_installcheck
         env:
-          PG_CFLAGS: -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
+          PG_CFLAGS: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
+  valgrind:
+    if: ${{ !startsWith(github.ref_name, 'mac') && !startsWith(github.ref_name, 'windows') }}
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: ankane/setup-postgres-valgrind@v1
+        with:
+          postgres-version: 16
+      - run: make OPTFLAGS=""
+      - run: sudo --preserve-env=PG_CONFIG make install
+      - run: make installcheck

CHANGELOG.md

@@ -1,3 +1,41 @@
+## 0.7.0 (unreleased)
+
+- Added `halfvec` type
+- Added `sparsevec` type
+- Added support for `bit` vectors to HNSW
+- Added `hamming_distance` function
+- Added `jaccard_distance` function
+- Added `quantize_binary` function
+- Added `subvector` function
+- Added CPU dispatching for distance functions on Linux x86-64
+- Updated comparison operators to support vectors with different dimensions
+
+## 0.6.2 (2024-03-18)
+
+- Reduced lock contention with parallel HNSW index builds
+
+## 0.6.1 (2024-03-04)
+
+- Fixed error with `ANALYZE` and vectors with different dimensions
+- Fixed segmentation fault with `shared_preload_libraries`
+- Fixed vector subtraction being marked as commutative
+
+## 0.6.0 (2024-01-29)
+
+If upgrading with Postgres 12 or Docker, see [these notes](https://github.com/pgvector/pgvector#060).
+
+- Added support for parallel index builds for HNSW
+- Added validation for GUC parameters
+- Changed storage for vector from `extended` to `external`
+- Improved performance of HNSW
+- Reduced memory usage for HNSW index builds
+- Reduced WAL generation for HNSW index builds
+- Fixed error with logical replication
+- Fixed `invalid memory alloc request size` error with HNSW index builds
+- Moved Docker image to `pgvector` org
+- Added Docker tags for each supported version of Postgres
+- Dropped support for Postgres 11
+
 ## 0.5.1 (2023-10-10)
 
 - Improved performance of HNSW index builds
@@ -44,7 +82,7 @@
 
 ## 0.4.0 (2023-01-11)
 
-If upgrading with Postgres < 13, see [this note](https://github.com/pgvector/pgvector#040).
+If upgrading with Postgres < 13, see [this note](https://github.com/pgvector/pgvector/blob/v0.4.0/README.md#040).
 
 - Changed text representation for vector elements to match `real`
 - Changed storage for vector from `plain` to `extended`
@@ -61,7 +99,7 @@ If upgrading with Postgres < 13, see [this note](https://github.com/pgvector/pgv
 
 ## 0.3.1 (2022-11-02)
 
-If upgrading from 0.2.7 or 0.3.0, [recreate](https://github.com/pgvector/pgvector#031) all `ivfflat` indexes after upgrading to ensure all data is indexed.
+If upgrading from 0.2.7 or 0.3.0, [recreate](https://github.com/pgvector/pgvector/blob/v0.3.1/README.md#031) all `ivfflat` indexes after upgrading to ensure all data is indexed.
 
 - Fixed issue with inserts silently corrupting `ivfflat` indexes (introduced in 0.2.7)
 - Fixed segmentation fault with index creation when lists > 6500

Dockerfile

@@ -1,4 +1,4 @@
-ARG PG_MAJOR=15
+ARG PG_MAJOR=16
 FROM postgres:$PG_MAJOR
 ARG PG_MAJOR
 

LICENSE

@@ -1,4 +1,4 @@
-Portions Copyright (c) 1996-2023, PostgreSQL Global Development Group
+Portions Copyright (c) 1996-2024, PostgreSQL Global Development Group
 
 Portions Copyright (c) 1994, The Regents of the University of California
 

META.json

@@ -2,7 +2,7 @@
 	"name": "vector",
 	"abstract": "Open-source vector similarity search for Postgres",
 	"description": "Supports L2 distance, inner product, and cosine distance",
-	"version": "0.5.1",
+	"version": "0.6.2",
 	"maintainer": [
 		"Andrew Kane <andrew@ankane.org>"
 	],
@@ -12,7 +12,7 @@
 	"prereqs": {
 		"runtime": {
 			"requires": {
-				"PostgreSQL": "11.0.0"
+				"PostgreSQL": "12.0.0"
 			}
 		}
 	},
@@ -20,7 +20,7 @@
 		"vector": {
 			"file": "sql/vector.sql",
 			"docfile": "README.md",
-			"version": "0.5.1",
+			"version": "0.6.2",
 			"abstract": "Open-source vector similarity search for Postgres"
 		}
 	},

Makefile

@@ -1,10 +1,10 @@
 EXTENSION = vector
-EXTVERSION = 0.5.1
+EXTVERSION = 0.6.2
 
 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
-HEADERS = src/vector.h
+OBJS = src/bitvector.o src/halfutils.o src/halfvec.o src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/sparsevec.o src/vector.o
+HEADERS = src/halfvec.h src/sparsevec.h src/vector.h
 
 TESTS = $(wildcard test/sql/*.sql)
 REGRESS = $(patsubst test/sql/%.sql,%,$(TESTS))
@@ -12,7 +12,7 @@ REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
 
 OPTFLAGS = -march=native
 
-# Mac ARM doesn't support -march=native
+# Mac ARM doesn't always support -march=native
 ifeq ($(shell uname -s), Darwin)
 	ifeq ($(shell uname -p), arm)
 		# no difference with -march=armv8.5-a
@@ -65,13 +65,15 @@ dist:
 	mkdir -p dist
 	git archive --format zip --prefix=$(EXTENSION)-$(EXTVERSION)/ --output dist/$(EXTENSION)-$(EXTVERSION).zip master
 
+# for Docker
+PG_MAJOR ?= 16
+
 .PHONY: docker
 
 docker:
-	docker build --pull --no-cache --platform linux/amd64 -t ankane/pgvector:latest .
+	docker build --pull --no-cache --build-arg PG_MAJOR=$(PG_MAJOR) -t pgvector/pgvector:pg$(PG_MAJOR) -t pgvector/pgvector:$(EXTVERSION)-pg$(PG_MAJOR) .
 
 .PHONY: docker-release
 
 docker-release:
-	docker buildx build --push --pull --no-cache --platform linux/amd64,linux/arm64 -t ankane/pgvector:latest .
-	docker buildx build --push --platform linux/amd64,linux/arm64 -t ankane/pgvector:v$(EXTVERSION) .
+	docker buildx build --push --pull --no-cache --platform linux/amd64,linux/arm64 --build-arg PG_MAJOR=$(PG_MAJOR) -t pgvector/pgvector:pg$(PG_MAJOR) -t pgvector/pgvector:$(EXTVERSION)-pg$(PG_MAJOR) .

Makefile.win

@@ -1,10 +1,10 @@
 EXTENSION = vector
-EXTVERSION = 0.5.1
+EXTVERSION = 0.6.2
 
-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
-HEADERS = src\vector.h
+OBJS = src\bitvector.obj src\halfutils.obj src\halfvec.obj src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\sparsevec.obj src\vector.obj
+HEADERS = src\halfvec.h src\sparsevec.h src\vector.h
 
-REGRESS = btree cast copy functions input ivfflat_cosine ivfflat_ip ivfflat_l2 ivfflat_options ivfflat_unlogged
+REGRESS = bit_functions btree cast copy halfvec_functions halfvec_input hnsw_bit_hamming hnsw_bit_jaccard hnsw_halfvec_cosine hnsw_halfvec_ip hnsw_halfvec_l2 hnsw_options hnsw_sparsevec_cosine hnsw_sparsevec_ip hnsw_sparsevec_l2 hnsw_unlogged hnsw_vector_cosine hnsw_vector_ip hnsw_vector_l2 ivfflat_options ivfflat_unlogged ivfflat_vector_cosine ivfflat_vector_ip ivfflat_vector_l2 sparsevec_functions sparsevec_input vector_functions vector_input
 REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
 
 # For /arch flags
@@ -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)

sql/vector--0.5.1--0.6.0.sql

@@ -0,0 +1,5 @@
+-- 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
+
+-- remove this single line for Postgres < 13
+ALTER TYPE vector SET (STORAGE = external);

sql/vector--0.6.0--0.6.1.sql

@@ -0,0 +1,16 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.6.1'" to load this file. \quit
+
+DROP OPERATOR - (vector, vector);
+
+CREATE OPERATOR - (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_sub
+);
+
+ALTER OPERATOR <= (vector, vector) SET (
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+ALTER OPERATOR >= (vector, vector) SET (
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);

sql/vector--0.6.1--0.6.2.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.6.2'" to load this file. \quit

sql/vector--0.6.2--0.7.0.sql

@@ -0,0 +1,283 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.7.0'" to load this file. \quit
+
+CREATE FUNCTION quantize_binary(vector) RETURNS bit
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION subvector(vector, int, int) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION hamming_distance(bit, bit) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION jaccard_distance(bit, bit) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE OPERATOR <~> (
+	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = hamming_distance,
+	COMMUTATOR = '<~>'
+);
+
+CREATE OPERATOR <%> (
+	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = jaccard_distance,
+	COMMUTATOR = '<%>'
+);
+
+CREATE OPERATOR CLASS bit_hamming_ops
+	FOR TYPE bit USING hnsw AS
+	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 hamming_distance(bit, bit);
+
+CREATE OPERATOR CLASS bit_jaccard_ops
+	FOR TYPE bit USING hnsw AS
+	OPERATOR 1 <%> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 jaccard_distance(bit, bit);
+
+CREATE TYPE halfvec;
+
+CREATE FUNCTION halfvec_in(cstring, oid, integer) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_out(halfvec) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_recv(internal, oid, integer) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_send(halfvec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE halfvec (
+	INPUT     = halfvec_in,
+	OUTPUT    = halfvec_out,
+	TYPMOD_IN = halfvec_typmod_in,
+	RECEIVE   = halfvec_recv,
+	SEND      = halfvec_send,
+	STORAGE   = external
+);
+
+CREATE FUNCTION l2_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_norm(halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION quantize_binary(halfvec) RETURNS bit
+	AS 'MODULE_PATHNAME', 'halfvec_quantize_binary' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION subvector(halfvec, int, int) RETURNS halfvec
+	AS 'MODULE_PATHNAME', 'halfvec_subvector' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_l2_squared_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_spherical_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(integer[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(real[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(double precision[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(numeric[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_to_float4(halfvec, integer, boolean) RETURNS real[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (halfvec AS halfvec)
+	WITH FUNCTION halfvec(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (halfvec AS real[])
+	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (integer[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (real[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(real[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (double precision[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(double precision[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (numeric[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(numeric[], integer, boolean) AS ASSIGNMENT;
+
+CREATE OPERATOR <-> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+CREATE OPERATOR CLASS halfvec_l2_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec),
+	FUNCTION 3 l2_distance(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_ip_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_norm(halfvec);
+
+CREATE OPERATOR CLASS halfvec_cosine_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 2 halfvec_norm(halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_norm(halfvec);
+
+CREATE OPERATOR CLASS halfvec_l2_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_ip_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_cosine_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 2 halfvec_norm(halfvec);
+
+CREATE FUNCTION halfvec_to_vector(halfvec, integer, boolean) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_to_halfvec(vector, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (halfvec AS vector)
+	WITH FUNCTION halfvec_to_vector(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (vector AS halfvec)
+	WITH FUNCTION vector_to_halfvec(vector, integer, boolean) AS IMPLICIT;
+
+CREATE TYPE sparsevec;
+
+CREATE FUNCTION sparsevec_in(cstring, oid, integer) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_out(sparsevec) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_recv(internal, oid, integer) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_send(sparsevec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE sparsevec (
+	INPUT     = sparsevec_in,
+	OUTPUT    = sparsevec_out,
+	TYPMOD_IN = sparsevec_typmod_in,
+	RECEIVE   = sparsevec_recv,
+	SEND      = sparsevec_send,
+	STORAGE   = external
+);
+
+CREATE FUNCTION l2_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_norm(sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_l2_squared_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_negative_inner_product(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec(sparsevec, integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_to_sparsevec(vector, integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (sparsevec AS sparsevec)
+	WITH FUNCTION sparsevec(sparsevec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (sparsevec AS vector)
+	WITH FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (vector AS sparsevec)
+	WITH FUNCTION vector_to_sparsevec(vector, integer, boolean) AS IMPLICIT;
+
+CREATE OPERATOR <-> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+CREATE OPERATOR CLASS sparsevec_l2_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <-> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 sparsevec_l2_squared_distance(sparsevec, sparsevec);
+
+CREATE OPERATOR CLASS sparsevec_ip_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <#> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 sparsevec_negative_inner_product(sparsevec, sparsevec);
+
+CREATE OPERATOR CLASS sparsevec_cosine_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <=> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 sparsevec_negative_inner_product(sparsevec, sparsevec),
+	FUNCTION 2 sparsevec_norm(sparsevec);

sql/vector.sql

@@ -1,7 +1,7 @@
 -- complain if script is sourced in psql, rather than via CREATE EXTENSION
 \echo Use "CREATE EXTENSION vector" to load this file. \quit
 
--- type
+-- vector type
 
 CREATE TYPE vector;
 
@@ -26,10 +26,10 @@ CREATE TYPE vector (
 	TYPMOD_IN = vector_typmod_in,
 	RECEIVE   = vector_recv,
 	SEND      = vector_send,
-	STORAGE   = extended
+	STORAGE   = external
 );
 
--- functions
+-- vector functions
 
 CREATE FUNCTION l2_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -58,7 +58,13 @@ CREATE FUNCTION vector_sub(vector, vector) RETURNS vector
 CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- private functions
+CREATE FUNCTION quantize_binary(vector) RETURNS bit
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION subvector(vector, int, int) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- vector private functions
 
 CREATE FUNCTION vector_lt(vector, vector) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -99,7 +105,7 @@ CREATE FUNCTION vector_avg(double precision[]) RETURNS vector
 CREATE FUNCTION vector_combine(double precision[], double precision[]) RETURNS double precision[]
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- aggregates
+-- vector aggregates
 
 CREATE AGGREGATE avg(vector) (
 	SFUNC = vector_accum,
@@ -117,7 +123,7 @@ CREATE AGGREGATE sum(vector) (
 	PARALLEL = SAFE
 );
 
--- cast functions
+-- vector cast functions
 
 CREATE FUNCTION vector(vector, integer, boolean) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -137,7 +143,7 @@ CREATE FUNCTION array_to_vector(numeric[], integer, boolean) RETURNS vector
 CREATE FUNCTION vector_to_float4(vector, integer, boolean) RETURNS real[]
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- casts
+-- vector casts
 
 CREATE CAST (vector AS vector)
 	WITH FUNCTION vector(vector, integer, boolean) AS IMPLICIT;
@@ -157,7 +163,7 @@ CREATE CAST (double precision[] AS vector)
 CREATE CAST (numeric[] AS vector)
 	WITH FUNCTION array_to_vector(numeric[], integer, boolean) AS ASSIGNMENT;
 
--- operators
+-- vector operators
 
 CREATE OPERATOR <-> (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = l2_distance,
@@ -180,8 +186,7 @@ CREATE OPERATOR + (
 );
 
 CREATE OPERATOR - (
-	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_sub,
-	COMMUTATOR = -
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_sub
 );
 
 CREATE OPERATOR * (
@@ -195,11 +200,10 @@ CREATE OPERATOR < (
 	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
 );
 
--- should use scalarlesel and scalarlejoinsel, but not supported in Postgres < 11
 CREATE OPERATOR <= (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_le,
 	COMMUTATOR = >= , NEGATOR = > ,
-	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
 );
 
 CREATE OPERATOR = (
@@ -214,11 +218,10 @@ CREATE OPERATOR <> (
 	RESTRICT = eqsel, JOIN = eqjoinsel
 );
 
--- should use scalargesel and scalargejoinsel, but not supported in Postgres < 11
 CREATE OPERATOR >= (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_ge,
 	COMMUTATOR = <= , NEGATOR = < ,
-	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
 );
 
 CREATE OPERATOR > (
@@ -243,7 +246,7 @@ CREATE ACCESS METHOD hnsw TYPE INDEX HANDLER hnswhandler;
 
 COMMENT ON ACCESS METHOD hnsw IS 'hnsw index access method';
 
--- opclasses
+-- vector opclasses
 
 CREATE OPERATOR CLASS vector_ops
 	DEFAULT FOR TYPE vector USING btree AS
@@ -290,3 +293,310 @@ 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);
+
+-- bit functions
+
+CREATE FUNCTION hamming_distance(bit, bit) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION jaccard_distance(bit, bit) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE OPERATOR <~> (
+	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = hamming_distance,
+	COMMUTATOR = '<~>'
+);
+
+CREATE OPERATOR <%> (
+	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = jaccard_distance,
+	COMMUTATOR = '<%>'
+);
+
+CREATE OPERATOR CLASS bit_hamming_ops
+	FOR TYPE bit USING hnsw AS
+	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 hamming_distance(bit, bit);
+
+CREATE OPERATOR CLASS bit_jaccard_ops
+	FOR TYPE bit USING hnsw AS
+	OPERATOR 1 <%> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 jaccard_distance(bit, bit);
+
+-- halfvec type
+
+CREATE TYPE halfvec;
+
+CREATE FUNCTION halfvec_in(cstring, oid, integer) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_out(halfvec) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_recv(internal, oid, integer) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_send(halfvec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE halfvec (
+	INPUT     = halfvec_in,
+	OUTPUT    = halfvec_out,
+	TYPMOD_IN = halfvec_typmod_in,
+	RECEIVE   = halfvec_recv,
+	SEND      = halfvec_send,
+	STORAGE   = external
+);
+
+-- halfvec functions
+
+CREATE FUNCTION l2_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_norm(halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION quantize_binary(halfvec) RETURNS bit
+	AS 'MODULE_PATHNAME', 'halfvec_quantize_binary' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION subvector(halfvec, int, int) RETURNS halfvec
+	AS 'MODULE_PATHNAME', 'halfvec_subvector' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- halfvec private functions
+
+CREATE FUNCTION halfvec_l2_squared_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_spherical_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- halfvec cast functions
+
+CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(integer[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(real[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(double precision[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_halfvec(numeric[], integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_to_float4(halfvec, integer, boolean) RETURNS real[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- halfvec casts
+
+CREATE CAST (halfvec AS halfvec)
+	WITH FUNCTION halfvec(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (halfvec AS real[])
+	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (integer[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (real[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(real[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (double precision[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(double precision[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (numeric[] AS halfvec)
+	WITH FUNCTION array_to_halfvec(numeric[], integer, boolean) AS ASSIGNMENT;
+
+-- halfvec operators
+
+CREATE OPERATOR <-> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+-- halfvec opclasses
+
+CREATE OPERATOR CLASS halfvec_l2_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec),
+	FUNCTION 3 l2_distance(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_ip_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_norm(halfvec);
+
+CREATE OPERATOR CLASS halfvec_cosine_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 2 halfvec_norm(halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_norm(halfvec);
+
+CREATE OPERATOR CLASS halfvec_l2_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_ip_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_cosine_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 2 halfvec_norm(halfvec);
+
+-- extension casts
+
+CREATE FUNCTION halfvec_to_vector(halfvec, integer, boolean) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_to_halfvec(vector, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (halfvec AS vector)
+	WITH FUNCTION halfvec_to_vector(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (vector AS halfvec)
+	WITH FUNCTION vector_to_halfvec(vector, integer, boolean) AS IMPLICIT;
+
+--- sparsevec type
+
+CREATE TYPE sparsevec;
+
+CREATE FUNCTION sparsevec_in(cstring, oid, integer) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_out(sparsevec) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_recv(internal, oid, integer) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_send(sparsevec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE sparsevec (
+	INPUT     = sparsevec_in,
+	OUTPUT    = sparsevec_out,
+	TYPMOD_IN = sparsevec_typmod_in,
+	RECEIVE   = sparsevec_recv,
+	SEND      = sparsevec_send,
+	STORAGE   = external
+);
+
+-- sparsevec functions
+
+CREATE FUNCTION l2_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_norm(sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- sparsevec private functions
+
+CREATE FUNCTION sparsevec_l2_squared_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_negative_inner_product(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- sparsevec cast functions
+
+CREATE FUNCTION sparsevec(sparsevec, integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_to_sparsevec(vector, integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- sparsevec casts
+
+CREATE CAST (sparsevec AS sparsevec)
+	WITH FUNCTION sparsevec(sparsevec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (sparsevec AS vector)
+	WITH FUNCTION sparsevec_to_vector(sparsevec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (vector AS sparsevec)
+	WITH FUNCTION vector_to_sparsevec(vector, integer, boolean) AS IMPLICIT;
+
+-- sparsevec operators
+
+CREATE OPERATOR <-> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+-- sparsevec opclasses
+
+CREATE OPERATOR CLASS sparsevec_l2_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <-> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 sparsevec_l2_squared_distance(sparsevec, sparsevec);
+
+CREATE OPERATOR CLASS sparsevec_ip_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <#> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 sparsevec_negative_inner_product(sparsevec, sparsevec);
+
+CREATE OPERATOR CLASS sparsevec_cosine_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <=> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 sparsevec_negative_inner_product(sparsevec, sparsevec),
+	FUNCTION 2 sparsevec_norm(sparsevec);

src/bitvector.c

@@ -0,0 +1,90 @@
+#include "postgres.h"
+
+#include "bitvector.h"
+#include "port/pg_bitutils.h"
+#include "utils/varbit.h"
+
+#if PG_VERSION_NUM >= 160000
+#include "varatt.h"
+#endif
+
+/*
+ * Allocate and initialize a new bit vector
+ */
+VarBit *
+InitBitVector(int dim)
+{
+	VarBit	   *result;
+	int			size;
+
+	size = VARBITTOTALLEN(dim);
+	result = (VarBit *) palloc0(size);
+	SET_VARSIZE(result, size);
+	VARBITLEN(result) = dim;
+
+	return result;
+}
+
+/*
+ * Ensure same dimensions
+ */
+static inline void
+CheckDims(VarBit *a, VarBit *b)
+{
+	if (VARBITLEN(a) != VARBITLEN(b))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different bit lengths %u and %u", VARBITLEN(a), VARBITLEN(b))));
+}
+
+/*
+ * Get the Hamming distance between two bit vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(hamming_distance);
+Datum
+hamming_distance(PG_FUNCTION_ARGS)
+{
+	VarBit	   *a = PG_GETARG_VARBIT_P(0);
+	VarBit	   *b = PG_GETARG_VARBIT_P(1);
+	unsigned char *ax = VARBITS(a);
+	unsigned char *bx = VARBITS(b);
+	uint64		distance = 0;
+
+	CheckDims(a, b);
+
+	/* TODO Improve performance */
+	for (uint32 i = 0; i < VARBITBYTES(a); i++)
+		distance += pg_number_of_ones[ax[i] ^ bx[i]];
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the Jaccard distance between two bit vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(jaccard_distance);
+Datum
+jaccard_distance(PG_FUNCTION_ARGS)
+{
+	VarBit	   *a = PG_GETARG_VARBIT_P(0);
+	VarBit	   *b = PG_GETARG_VARBIT_P(1);
+	unsigned char *ax = VARBITS(a);
+	unsigned char *bx = VARBITS(b);
+	uint64		ab = 0;
+	uint64		aa;
+	uint64		bb;
+
+	CheckDims(a, b);
+
+	/* TODO Improve performance */
+	for (uint32 i = 0; i < VARBITBYTES(a); i++)
+		ab += pg_number_of_ones[ax[i] & bx[i]];
+
+	if (ab == 0)
+		PG_RETURN_FLOAT8(1);
+
+	aa = pg_popcount((char *) ax, VARBITBYTES(a));
+	bb = pg_popcount((char *) bx, VARBITBYTES(b));
+
+	PG_RETURN_FLOAT8(1 - (ab / ((double) (aa + bb - ab))));
+}

src/bitvector.h

@@ -0,0 +1,8 @@
+#ifndef BITVECTOR_H
+#define BITVECTOR_H
+
+#include "utils/varbit.h"
+
+VarBit	   *InitBitVector(int dim);
+
+#endif

src/halfutils.c

@@ -0,0 +1,156 @@
+#include "postgres.h"
+
+#include "halfutils.h"
+#include "halfvec.h"
+
+#ifdef HALFVEC_DISPATCH
+#include <immintrin.h>
+
+#if defined(HAVE__GET_CPUID)
+#include <cpuid.h>
+#elif defined(HAVE__CPUID)
+#include <intrin.h>
+#endif
+
+#ifdef _MSC_VER
+#define TARGET_F16C_FMA
+#else
+#define TARGET_F16C_FMA __attribute__((target("f16c,fma")))
+#endif
+#endif
+
+float		(*HalfvecL2SquaredDistance) (int dim, half * ax, half * bx);
+float		(*HalfvecInnerProduct) (int dim, half * ax, half * bx);
+
+static float
+HalfvecL2SquaredDistanceDefault(int dim, half * ax, half * bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+
+#ifdef HALFVEC_DISPATCH
+TARGET_F16C_FMA static float
+HalfvecL2SquaredDistanceF16cFma(int dim, half * ax, half * bx)
+{
+	float		distance;
+	int			i;
+	float		s[8];
+	int			count = (dim / 8) * 8;
+	__m256		dist = _mm256_setzero_ps();
+
+	for (i = 0; i < count; i += 8)
+	{
+		__m128i		axi = _mm_loadu_si128((__m128i *) (ax + i));
+		__m128i		bxi = _mm_loadu_si128((__m128i *) (bx + i));
+		__m256		axs = _mm256_cvtph_ps(axi);
+		__m256		bxs = _mm256_cvtph_ps(bxi);
+		__m256		diff = _mm256_sub_ps(axs, bxs);
+
+		dist = _mm256_fmadd_ps(diff, diff, dist);
+	}
+
+	_mm256_storeu_ps(s, dist);
+
+	distance = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	for (; i < dim; i++)
+	{
+		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+#endif
+
+static float
+HalfvecInnerProductDefault(int dim, half * ax, half * bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	return distance;
+}
+
+#ifdef HALFVEC_DISPATCH
+TARGET_F16C_FMA static float
+HalfvecInnerProductF16cFma(int dim, half * ax, half * bx)
+{
+	float		distance;
+	int			i;
+	float		s[8];
+	int			count = (dim / 8) * 8;
+	__m256		dist = _mm256_setzero_ps();
+
+	for (i = 0; i < count; i += 8)
+	{
+		__m128i		axi = _mm_loadu_si128((__m128i *) (ax + i));
+		__m128i		bxi = _mm_loadu_si128((__m128i *) (bx + i));
+		__m256		axs = _mm256_cvtph_ps(axi);
+		__m256		bxs = _mm256_cvtph_ps(bxi);
+
+		dist = _mm256_fmadd_ps(axs, bxs, dist);
+	}
+
+	_mm256_storeu_ps(s, dist);
+
+	distance = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	for (; i < dim; i++)
+		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
+
+	return distance;
+}
+#endif
+
+#ifdef HALFVEC_DISPATCH
+#define CPU_FEATURE_FMA  (1 << 12)
+#define CPU_FEATURE_F16C (1 << 29)
+
+static bool
+SupportsCpuFeature(unsigned int feature)
+{
+	unsigned int exx[4] = {0, 0, 0, 0};
+
+#if defined(HAVE__GET_CPUID)
+	__get_cpuid(1, &exx[0], &exx[1], &exx[2], &exx[3]);
+#elif defined(HAVE__CPUID)
+	__cpuid(exx, 1);
+#endif
+
+	return (exx[2] & feature) == feature;
+}
+#endif
+
+void
+HalfvecInit(void)
+{
+	/*
+	 * Could skip pointer when single function, but no difference in
+	 * performance
+	 */
+	HalfvecL2SquaredDistance = HalfvecL2SquaredDistanceDefault;
+	HalfvecInnerProduct = HalfvecInnerProductDefault;
+
+#ifdef HALFVEC_DISPATCH
+	if (SupportsCpuFeature(CPU_FEATURE_FMA | CPU_FEATURE_F16C))
+	{
+		HalfvecL2SquaredDistance = HalfvecL2SquaredDistanceF16cFma;
+		HalfvecInnerProduct = HalfvecInnerProductF16cFma;
+	}
+#endif
+}

src/halfutils.h

@@ -0,0 +1,254 @@
+#ifndef HALFUTILS_H
+#define HALFUTILS_H
+
+#include <math.h>
+
+#include "common/shortest_dec.h"
+#include "halfvec.h"
+
+#ifdef F16C_SUPPORT
+#include <immintrin.h>
+#endif
+
+extern float (*HalfvecL2SquaredDistance) (int dim, half * ax, half * bx);
+extern float (*HalfvecInnerProduct) (int dim, half * ax, half * bx);
+
+void		HalfvecInit(void);
+
+/*
+ * Check if half is NaN
+ */
+static inline bool
+HalfIsNan(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isnan(num);
+#else
+	return (num & 0x7C00) == 0x7C00 && (num & 0x7FFF) != 0x7C00;
+#endif
+}
+
+/*
+ * Check if half is infinite
+ */
+static inline bool
+HalfIsInf(half num)
+{
+#ifdef FLT16_SUPPORT
+	return isinf(num);
+#else
+	return (num & 0x7FFF) == 0x7C00;
+#endif
+}
+
+/*
+ * Convert a half to a float4
+ */
+static inline float
+HalfToFloat4(half num)
+{
+#if defined(F16C_SUPPORT)
+	return _cvtsh_ss(num);
+#elif defined(FLT16_SUPPORT)
+	return (float) num;
+#else
+	/* TODO Improve performance */
+
+	/* Assumes same endianness for floats and integers */
+	union
+	{
+		float		f;
+		uint32		i;
+	}			swapfloat;
+
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swaphalf;
+
+	uint16		bin;
+	uint32		exponent;
+	uint32		mantissa;
+	uint32		result;
+
+	swaphalf.h = num;
+	bin = swaphalf.i;
+	exponent = (bin & 0x7C00) >> 10;
+	mantissa = bin & 0x03FF;
+
+	/* Sign */
+	result = (bin & 0x8000) << 16;
+
+	if (unlikely(exponent == 31))
+	{
+		if (mantissa == 0)
+		{
+			/* Infinite */
+			result |= 0x7F800000;
+		}
+		else
+		{
+			/* NaN */
+			result |= 0x7FC00000;
+		}
+	}
+	else if (unlikely(exponent == 0))
+	{
+		/* Subnormal */
+		if (mantissa != 0)
+		{
+			exponent = -14;
+
+			for (int i = 0; i < 10; i++)
+			{
+				mantissa <<= 1;
+				exponent -= 1;
+
+				if ((mantissa >> 10) % 2 == 1)
+				{
+					mantissa &= 0x03ff;
+					break;
+				}
+			}
+
+			result |= (exponent + 127) << 23;
+		}
+	}
+	else
+	{
+		/* Normal */
+		result |= (exponent - 15 + 127) << 23;
+	}
+
+	result |= mantissa << 13;
+
+	swapfloat.i = result;
+	return swapfloat.f;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+static inline half
+Float4ToHalfUnchecked(float num)
+{
+#if defined(F16C_SUPPORT)
+	return _cvtss_sh(num, 0);
+#elif defined(FLT16_SUPPORT)
+	return (_Float16) num;
+#else
+	/* TODO Improve performance */
+
+	/* Assumes same endianness for floats and integers */
+	union
+	{
+		float		f;
+		uint32		i;
+	}			swapfloat;
+
+	union
+	{
+		half		h;
+		uint16		i;
+	}			swaphalf;
+
+	uint32		bin;
+	int			exponent;
+	int			mantissa;
+	uint16		result;
+
+	swapfloat.f = num;
+	bin = swapfloat.i;
+	exponent = (bin & 0x7F800000) >> 23;
+	mantissa = bin & 0x007FFFFF;
+
+	/* Sign */
+	result = (bin & 0x80000000) >> 16;
+
+	if (isinf(num))
+	{
+		/* Infinite */
+		result |= 0x7C00;
+	}
+	else if (isnan(num))
+	{
+		/* NaN */
+		result |= 0x7E00;
+		result |= mantissa >> 13;
+	}
+	else if (exponent > 98)
+	{
+		int			m;
+		int			gr;
+		int			s;
+
+		exponent -= 127;
+		s = mantissa & 0x00000FFF;
+
+		/* Subnormal */
+		if (exponent < -14)
+		{
+			int			diff = -exponent - 14;
+
+			mantissa >>= diff;
+			mantissa += 1 << (23 - diff);
+			s |= mantissa & 0x00000FFF;
+		}
+
+		m = mantissa >> 13;
+
+		/* Round */
+		gr = (mantissa >> 12) % 4;
+		if (gr == 3 || (gr == 1 && s != 0))
+			m += 1;
+
+		if (m == 1024)
+		{
+			m = 0;
+			exponent += 1;
+		}
+
+		if (exponent > 15)
+		{
+			/* Infinite */
+			result |= 0x7C00;
+		}
+		else
+		{
+			if (exponent >= -14)
+				result |= (exponent + 15) << 10;
+
+			result |= m;
+		}
+	}
+
+	swaphalf.i = result;
+	return swaphalf.h;
+#endif
+}
+
+/*
+ * Convert a float4 to a half
+ */
+static inline half
+Float4ToHalf(float num)
+{
+	half		result = Float4ToHalfUnchecked(num);
+
+	if (unlikely(HalfIsInf(result)) && !isinf(num))
+	{
+		char	   *buf = palloc(FLOAT_SHORTEST_DECIMAL_LEN);
+
+		float_to_shortest_decimal_buf(num, buf);
+
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("\"%s\" is out of range for type halfvec", buf)));
+	}
+
+	return result;
+}
+
+#endif

src/halfvec.c

@@ -0,0 +1,777 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "bitvector.h"
+#include "catalog/pg_type.h"
+#include "common/shortest_dec.h"
+#include "fmgr.h"
+#include "halfutils.h"
+#include "halfvec.h"
+#include "lib/stringinfo.h"
+#include "libpq/pqformat.h"
+#include "port.h"				/* for strtof() */
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "utils/float.h"
+#include "utils/lsyscache.h"
+#include "utils/numeric.h"
+#include "vector.h"
+
+#if PG_VERSION_NUM < 130000
+#define TYPALIGN_DOUBLE 'd'
+#define TYPALIGN_INT 'i'
+#endif
+
+/*
+ * 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);
+}
+
+/*
+ * Ensure same dimensions
+ */
+static inline void
+CheckDims(HalfVector * a, HalfVector * b)
+{
+	if (a->dim != b->dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different halfvec dimensions %d and %d", a->dim, b->dim)));
+}
+
+/*
+ * Ensure expected dimensions
+ */
+static inline void
+CheckExpectedDim(int32 typmod, int dim)
+{
+	if (typmod != -1 && typmod != dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected %d dimensions, not %d", typmod, dim)));
+}
+
+/*
+ * Ensure valid dimensions
+ */
+static inline void
+CheckDim(int dim)
+{
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("halfvec must have at least 1 dimension")));
+
+	if (dim > HALFVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("halfvec cannot have more than %d dimensions", HALFVEC_MAX_DIM)));
+}
+
+/*
+ * Ensure finite element
+ */
+static inline void
+CheckElement(half value)
+{
+	if (HalfIsNan(value))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("NaN not allowed in halfvec")));
+
+	if (HalfIsInf(value))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("infinite value not allowed in halfvec")));
+}
+
+/*
+ * Allocate and initialize a new half vector
+ */
+HalfVector *
+InitHalfVector(int dim)
+{
+	HalfVector *result;
+	int			size;
+
+	size = HALFVEC_SIZE(dim);
+	result = (HalfVector *) palloc0(size);
+	SET_VARSIZE(result, size);
+	result->dim = dim;
+
+	return result;
+}
+
+/*
+ * Check for whitespace, since array_isspace() is static
+ */
+static inline bool
+halfvec_isspace(char ch)
+{
+	if (ch == ' ' ||
+		ch == '\t' ||
+		ch == '\n' ||
+		ch == '\r' ||
+		ch == '\v' ||
+		ch == '\f')
+		return true;
+	return false;
+}
+
+/*
+ * Convert textual representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_in);
+Datum
+halfvec_in(PG_FUNCTION_ARGS)
+{
+	char	   *lit = PG_GETARG_CSTRING(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	half		x[HALFVEC_MAX_DIM];
+	int			dim = 0;
+	char	   *pt = lit;
+	HalfVector *result;
+
+	while (halfvec_isspace(*pt))
+		pt++;
+
+	if (*pt != '[')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type halfvec: \"%s\"", lit),
+				 errdetail("Vector contents must start with \"[\".")));
+
+	pt++;
+
+	while (halfvec_isspace(*pt))
+		pt++;
+
+	if (*pt == ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("halfvec must have at least 1 dimension")));
+
+	for (;;)
+	{
+		float		val;
+		char	   *stringEnd;
+
+		if (dim == HALFVEC_MAX_DIM)
+			ereport(ERROR,
+					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+					 errmsg("halfvec cannot have more than %d dimensions", HALFVEC_MAX_DIM)));
+
+		while (halfvec_isspace(*pt))
+			pt++;
+
+		/* Check for empty string like float4in */
+		if (*pt == '\0')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+
+		errno = 0;
+
+		/* Postgres sets LC_NUMERIC to C on startup */
+		val = strtof(pt, &stringEnd);
+
+		if (stringEnd == pt)
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+
+		x[dim] = Float4ToHalfUnchecked(val);
+
+		/* Check for range error like float4in */
+		if ((errno == ERANGE && isinf(val)) || (HalfIsInf(x[dim]) && !isinf(val)))
+			ereport(ERROR,
+					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+					 errmsg("\"%s\" is out of range for type halfvec", pnstrdup(pt, stringEnd - pt))));
+
+		CheckElement(x[dim]);
+		dim++;
+
+		pt = stringEnd;
+
+		while (halfvec_isspace(*pt))
+			pt++;
+
+		if (*pt == ',')
+			pt++;
+		else if (*pt == ']')
+		{
+			pt++;
+			break;
+		}
+		else
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
+	}
+
+	/* Only whitespace is allowed after the closing brace */
+	while (halfvec_isspace(*pt))
+		pt++;
+
+	if (*pt != '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type halfvec: \"%s\"", lit),
+				 errdetail("Junk after closing right brace.")));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	result = InitHalfVector(dim);
+	for (int i = 0; i < dim; i++)
+		result->x[i] = x[i];
+
+	PG_RETURN_POINTER(result);
+}
+
+#define AppendChar(ptr, c) (*(ptr)++ = (c))
+#define AppendFloat(ptr, f) ((ptr) += float_to_shortest_decimal_bufn((f), (ptr)))
+
+/*
+ * Convert internal representation to textual representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_out);
+Datum
+halfvec_out(PG_FUNCTION_ARGS)
+{
+	HalfVector *vector = PG_GETARG_HALFVEC_P(0);
+	int			dim = vector->dim;
+	char	   *buf;
+	char	   *ptr;
+
+	/*
+	 * Need:
+	 *
+	 * dim * (FLOAT_SHORTEST_DECIMAL_LEN - 1) bytes for
+	 * float_to_shortest_decimal_bufn
+	 *
+	 * dim - 1 bytes for separator
+	 *
+	 * 3 bytes for [, ], and \0
+	 */
+	buf = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN * dim + 2);
+	ptr = buf;
+
+	AppendChar(ptr, '[');
+
+	for (int i = 0; i < dim; i++)
+	{
+		if (i > 0)
+			AppendChar(ptr, ',');
+
+		AppendFloat(ptr, HalfToFloat4(vector->x[i]));
+	}
+
+	AppendChar(ptr, ']');
+	*ptr = '\0';
+
+	PG_FREE_IF_COPY(vector, 0);
+	PG_RETURN_CSTRING(buf);
+}
+
+/*
+ * Convert type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_typmod_in);
+Datum
+halfvec_typmod_in(PG_FUNCTION_ARGS)
+{
+	ArrayType  *ta = PG_GETARG_ARRAYTYPE_P(0);
+	int32	   *tl;
+	int			n;
+
+	tl = ArrayGetIntegerTypmods(ta, &n);
+
+	if (n != 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("invalid type modifier")));
+
+	if (*tl < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type halfvec must be at least 1")));
+
+	if (*tl > HALFVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type halfvec cannot exceed %d", HALFVEC_MAX_DIM)));
+
+	PG_RETURN_INT32(*tl);
+}
+
+/*
+ * Convert external binary representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_recv);
+Datum
+halfvec_recv(PG_FUNCTION_ARGS)
+{
+	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	HalfVector *result;
+	int16		dim;
+	int16		unused;
+
+	dim = pq_getmsgint(buf, sizeof(int16));
+	unused = pq_getmsgint(buf, sizeof(int16));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	if (unused != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected unused to be 0, not %d", unused)));
+
+	result = InitHalfVector(dim);
+	for (int i = 0; i < dim; i++)
+	{
+		result->x[i] = pq_getmsghalf(buf);
+		CheckElement(result->x[i]);
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert internal representation to the external binary representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_send);
+Datum
+halfvec_send(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	StringInfoData buf;
+
+	pq_begintypsend(&buf);
+	pq_sendint(&buf, vec->dim, sizeof(int16));
+	pq_sendint(&buf, vec->unused, sizeof(int16));
+	for (int i = 0; i < vec->dim; i++)
+		pq_sendhalf(&buf, vec->x[i]);
+
+	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
+}
+
+/*
+ * Convert half vector to half vector
+ * This is needed to check the type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec);
+Datum
+halfvec(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+
+	CheckExpectedDim(typmod, vec->dim);
+
+	PG_RETURN_POINTER(vec);
+}
+
+/*
+ * Convert array to half vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(array_to_halfvec);
+Datum
+array_to_halfvec(PG_FUNCTION_ARGS)
+{
+	ArrayType  *array = PG_GETARG_ARRAYTYPE_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	HalfVector *result;
+	int16		typlen;
+	bool		typbyval;
+	char		typalign;
+	Datum	   *elemsp;
+	int			nelemsp;
+
+	if (ARR_NDIM(array) > 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("array must be 1-D")));
+
+	if (ARR_HASNULL(array) && array_contains_nulls(array))
+		ereport(ERROR,
+				(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
+				 errmsg("array must not contain nulls")));
+
+	get_typlenbyvalalign(ARR_ELEMTYPE(array), &typlen, &typbyval, &typalign);
+	deconstruct_array(array, ARR_ELEMTYPE(array), typlen, typbyval, typalign, &elemsp, NULL, &nelemsp);
+
+	CheckDim(nelemsp);
+	CheckExpectedDim(typmod, nelemsp);
+
+	result = InitHalfVector(nelemsp);
+
+	if (ARR_ELEMTYPE(array) == INT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetInt32(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == FLOAT8OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat8(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == FLOAT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat4(elemsp[i]));
+	}
+	else if (ARR_ELEMTYPE(array) == NUMERICOID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = Float4ToHalf(DatumGetFloat4(DirectFunctionCall1(numeric_float4, elemsp[i])));
+	}
+	else
+	{
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("unsupported array type")));
+	}
+
+	/*
+	 * Free allocation from deconstruct_array. Do not free individual elements
+	 * when pass-by-reference since they point to original array.
+	 */
+	pfree(elemsp);
+
+	/* Check elements */
+	for (int i = 0; i < result->dim; i++)
+		CheckElement(result->x[i]);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert half vector to float4[]
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_to_float4);
+Datum
+halfvec_to_float4(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	Datum	   *datums;
+	ArrayType  *result;
+
+	datums = (Datum *) palloc(sizeof(Datum) * vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		datums[i] = Float4GetDatum(HalfToFloat4(vec->x[i]));
+
+	/* Use TYPALIGN_INT for float4 */
+	result = construct_array(datums, vec->dim, FLOAT4OID, sizeof(float4), true, TYPALIGN_INT);
+
+	pfree(datums);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert vector to half vec
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_to_halfvec);
+Datum
+vector_to_halfvec(PG_FUNCTION_ARGS)
+{
+	Vector	   *vec = PG_GETARG_VECTOR_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	HalfVector *result;
+
+	CheckDim(vec->dim);
+	CheckExpectedDim(typmod, vec->dim);
+
+	result = InitHalfVector(vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		result->x[i] = Float4ToHalf(vec->x[i]);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Get the L2 distance between half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l2_distance);
+Datum
+halfvec_l2_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(sqrt((double) HalfvecL2SquaredDistance(a->dim, a->x, b->x)));
+}
+
+/*
+ * Get the L2 squared distance between half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l2_squared_distance);
+Datum
+halfvec_l2_squared_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) HalfvecL2SquaredDistance(a->dim, a->x, b->x));
+}
+
+/*
+ * Get the inner product of two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_inner_product);
+Datum
+halfvec_inner_product(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) HalfvecInnerProduct(a->dim, a->x, b->x));
+}
+
+/*
+ * Get the negative inner product of two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_negative_inner_product);
+Datum
+halfvec_negative_inner_product(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) -HalfvecInnerProduct(a->dim, a->x, b->x));
+}
+
+/*
+ * Get the cosine distance between two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_cosine_distance);
+Datum
+halfvec_cosine_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+	float		norma = 0.0;
+	float		normb = 0.0;
+	double		similarity;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		float		axi = HalfToFloat4(ax[i]);
+		float		bxi = HalfToFloat4(bx[i]);
+
+		distance += axi * bxi;
+		norma += axi * axi;
+		normb += bxi * bxi;
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	similarity = (double) distance / sqrt((double) norma * (double) normb);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	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 distance for spherical k-means
+ * Currently uses angular distance since needs to satisfy triangle inequality
+ * Assumes inputs are unit vectors (skips norm)
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_spherical_distance);
+Datum
+halfvec_spherical_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	double		distance;
+
+	CheckDims(a, b);
+
+	distance = (double) HalfvecInnerProduct(a->dim, a->x, b->x);
+
+	/* Prevent NaN with acos with loss of precision */
+	if (distance > 1)
+		distance = 1;
+	else if (distance < -1)
+		distance = -1;
+
+	PG_RETURN_FLOAT8(acos(distance) / M_PI);
+}
+
+/*
+ * Get the L1 distance between two half vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_l1_distance);
+Datum
+halfvec_l1_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	half	   *ax = a->x;
+	half	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += fabsf(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
+/*
+ * Get the L2 norm of a half vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_norm);
+Datum
+halfvec_norm(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	half	   *ax = a->x;
+	double		norm = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+	{
+		double		axi = (double) HalfToFloat4(ax[i]);
+
+		norm += axi * axi;
+	}
+
+	PG_RETURN_FLOAT8(sqrt(norm));
+}
+
+/*
+ * Quantize a half vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_quantize_binary);
+Datum
+halfvec_quantize_binary(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	half	   *ax = a->x;
+	VarBit	   *result = InitBitVector(a->dim);
+	unsigned char *rx = VARBITS(result);
+
+	for (int i = 0; i < a->dim; i++)
+		rx[i / 8] |= (HalfToFloat4(ax[i]) > 0) << (7 - (i % 8));
+
+	PG_RETURN_VARBIT_P(result);
+}
+
+/*
+ * Get a subvector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_subvector);
+Datum
+halfvec_subvector(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	int32		start = PG_GETARG_INT32(1);
+	int32		count = PG_GETARG_INT32(2);
+	int32		end = start + count;
+	half	   *ax = a->x;
+	HalfVector *result;
+	int			dim;
+
+	/* Indexing starts at 1, like substring */
+	if (start < 1)
+		start = 1;
+
+	if (end > a->dim)
+		end = a->dim + 1;
+
+	dim = end - start;
+	CheckDim(dim);
+	result = InitHalfVector(dim);
+
+	for (int i = 0; i < dim; i++)
+		result->x[i] = ax[start - 1 + i];
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Internal helper to compare half vectors
+ */
+int
+halfvec_cmp_internal(HalfVector * a, HalfVector * b)
+{
+	int			dim = Min(a->dim, b->dim);
+
+	/* Check values before dimensions to be consistent with Postgres arrays */
+	for (int i = 0; i < dim; i++)
+	{
+		if (HalfToFloat4(a->x[i]) < HalfToFloat4(b->x[i]))
+			return -1;
+
+		if (HalfToFloat4(a->x[i]) > HalfToFloat4(b->x[i]))
+			return 1;
+	}
+
+	if (a->dim < b->dim)
+		return -1;
+
+	if (a->dim > b->dim)
+		return 1;
+
+	return 0;
+}

src/halfvec.h

@@ -0,0 +1,47 @@
+#ifndef HALFVEC_H
+#define HALFVEC_H
+
+#define __STDC_WANT_IEC_60559_TYPES_EXT__
+
+#include <float.h>
+
+#include "vector.h"
+
+#if defined(__x86_64__) || defined(_M_AMD64)
+#define HALFVEC_DISPATCH
+#endif
+
+/* F16C has better performance than _Float16 (on x86-64) */
+#if defined(__F16C__)
+#define F16C_SUPPORT
+#elif defined(__FLT16_MAX__) && !defined(HALFVEC_DISPATCH)
+#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 HALFVEC_MAX_DIM VECTOR_MAX_DIM
+
+#define HALFVEC_SIZE(_dim)		(offsetof(HalfVector, x) + sizeof(half)*(_dim))
+#define DatumGetHalfVector(x)	((HalfVector *) PG_DETOAST_DATUM(x))
+#define PG_GETARG_HALFVEC_P(x)	DatumGetHalfVector(PG_GETARG_DATUM(x))
+#define PG_RETURN_HALFVEC_P(x)	PG_RETURN_POINTER(x)
+
+typedef struct HalfVector
+{
+	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int16		dim;			/* number of dimensions */
+	int16		unused;
+	half		x[FLEXIBLE_ARRAY_MEMBER];
+}			HalfVector;
+
+HalfVector *InitHalfVector(int dim);
+int			halfvec_cmp_internal(HalfVector * a, HalfVector * b);
+
+#endif

src/hnsw.c

@@ -4,24 +4,59 @@
 #include <math.h>
 
 #include "access/amapi.h"
+#include "access/reloptions.h"
+#include "commands/progress.h"
 #include "commands/vacuum.h"
 #include "hnsw.h"
+#include "miscadmin.h"
 #include "utils/guc.h"
 #include "utils/selfuncs.h"
 
-#if PG_VERSION_NUM >= 120000
-#include "commands/progress.h"
+#if PG_VERSION_NUM < 150000
+#define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
 #endif
 
 int			hnsw_ef_search;
+int			hnsw_lock_tranche_id;
 static relopt_kind hnsw_relopt_kind;
 
+/*
+ * Assign a tranche ID for our LWLocks. This only needs to be done by one
+ * backend, as the tranche ID is remembered in shared memory.
+ *
+ * This shared memory area is very small, so we just allocate it from the
+ * "slop" that PostgreSQL reserves for small allocations like this. If
+ * this grows bigger, we should use a shmem_request_hook and
+ * RequestAddinShmemSpace() to pre-reserve space for this.
+ */
+void
+HnswInitLockTranche(void)
+{
+	int		   *tranche_ids;
+	bool		found;
+
+	LWLockAcquire(AddinShmemInitLock, LW_EXCLUSIVE);
+	tranche_ids = ShmemInitStruct("hnsw LWLock ids",
+								  sizeof(int) * 1,
+								  &found);
+	if (!found)
+		tranche_ids[0] = LWLockNewTrancheId();
+	hnsw_lock_tranche_id = tranche_ids[0];
+	LWLockRelease(AddinShmemInitLock);
+
+	/* Per-backend registration of the tranche ID */
+	LWLockRegisterTranche(hnsw_lock_tranche_id, "HnswBuild");
+}
+
 /*
  * Initialize index options and variables
  */
 void
 HnswInit(void)
 {
+	if (!process_shared_preload_libraries_in_progress)
+		HnswInitLockTranche();
+
 	hnsw_relopt_kind = add_reloption_kind();
 	add_int_reloption(hnsw_relopt_kind, "m", "Max number of connections",
 					  HNSW_DEFAULT_M, HNSW_MIN_M, HNSW_MAX_M
@@ -39,12 +74,13 @@ 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);
+
+	MarkGUCPrefixReserved("hnsw");
 }
 
 /*
  * Get the name of index build phase
  */
-#if PG_VERSION_NUM >= 120000
 static char *
 hnswbuildphasename(int64 phasenum)
 {
@@ -58,7 +94,6 @@ hnswbuildphasename(int64 phasenum)
 			return NULL;
 	}
 }
-#endif
 
 /*
  * Estimate the cost of an index scan
@@ -73,9 +108,6 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	int			m;
 	int			entryLevel;
 	Relation	index;
-#if PG_VERSION_NUM < 120000
-	List	   *qinfos;
-#endif
 
 	/* Never use index without order */
 	if (path->indexorderbys == NULL)
@@ -101,12 +133,7 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	/* Account for number of tuples (or entry level), m, and ef_search */
 	costs.numIndexTuples = (entryLevel + 2) * m;
 
-#if PG_VERSION_NUM >= 120000
 	genericcostestimate(root, path, loop_count, &costs);
-#else
-	qinfos = deconstruct_indexquals(path);
-	genericcostestimate(root, path, loop_count, qinfos, &costs);
-#endif
 
 	/* Use total cost since most work happens before first tuple is returned */
 	*indexStartupCost = costs.indexTotalCost;
@@ -200,9 +227,7 @@ hnswhandler(PG_FUNCTION_ARGS)
 	amroutine->amcostestimate = hnswcostestimate;
 	amroutine->amoptions = hnswoptions;
 	amroutine->amproperty = NULL;	/* TODO AMPROP_DISTANCE_ORDERABLE */
-#if PG_VERSION_NUM >= 120000
 	amroutine->ambuildphasename = hnswbuildphasename;
-#endif
 	amroutine->amvalidate = hnswvalidate;
 #if PG_VERSION_NUM >= 140000
 	amroutine->amadjustmembers = NULL;

src/hnsw.h

@@ -3,18 +3,21 @@
 
 #include "postgres.h"
 
-#include "access/generic_xlog.h"
-#include "access/reloptions.h"
+#include "access/genam.h"
+#include "access/parallel.h"
+#include "lib/pairingheap.h"
 #include "nodes/execnodes.h"
 #include "port.h"				/* for random() */
+#include "utils/relptr.h"
 #include "utils/sampling.h"
 #include "vector.h"
 
-#if PG_VERSION_NUM < 110000
-#error "Requires PostgreSQL 11+"
+#if PG_VERSION_NUM < 120000
+#error "Requires PostgreSQL 12+"
 #endif
 
 #define HNSW_MAX_DIM 2000
+#define HNSW_MAX_NNZ 1000
 
 /* Support functions */
 #define HNSW_DISTANCE_PROC 1
@@ -53,27 +56,40 @@
 #define HNSW_UPDATE_ENTRY_GREATER 1
 #define HNSW_UPDATE_ENTRY_ALWAYS 2
 
+typedef enum HnswType
+{
+	HNSW_TYPE_VECTOR,
+	HNSW_TYPE_HALFVEC,
+	HNSW_TYPE_BIT,
+	HNSW_TYPE_SPARSEVEC
+}			HnswType;
+
 /* Build phases */
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
 #define PROGRESS_HNSW_PHASE_LOAD		2
 
 #define HNSW_MAX_SIZE (BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - sizeof(ItemIdData))
+#define HNSW_TUPLE_ALLOC_SIZE BLCKSZ
 
-#define HNSW_ELEMENT_TUPLE_SIZE(_dim)	MAXALIGN(offsetof(HnswElementTupleData, vec) + VECTOR_SIZE(_dim))
+#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 HNSW_NEIGHBOR_ARRAY_SIZE(lm)	(offsetof(HnswNeighborArray, items) + sizeof(HnswCandidate) * (lm))
+
 #define HnswPageGetOpaque(page)	((HnswPageOpaque) PageGetSpecialPointer(page))
 #define HnswPageGetMeta(page)	((HnswMetaPageData *) PageGetContents(page))
 
 #if PG_VERSION_NUM >= 150000
 #define RandomDouble() pg_prng_double(&pg_global_prng_state)
+#define SeedRandom(seed) pg_prng_seed(&pg_global_prng_state, seed)
 #else
 #define RandomDouble() (((double) random()) / MAX_RANDOM_VALUE)
+#define SeedRandom(seed) srandom(seed)
 #endif
 
 #if PG_VERSION_NUM < 130000
 #define list_delete_last(list) list_truncate(list, list_length(list) - 1)
-#define list_sort(list, cmp) list_qsort(list, cmp)
+#define list_sort(list, cmp) ((list) = list_qsort(list, cmp))
 #endif
 
 #define HnswIsElementTuple(tup) ((tup)->type == HNSW_ELEMENT_TUPLE_TYPE)
@@ -86,41 +102,74 @@
 #define HnswGetMl(m) (1 / log(m))
 
 /* Ensure fits on page and in uint8 */
-#define HnswGetMaxLevel(m) Min(((BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - offsetof(HnswNeighborTupleData, indextids) - sizeof(ItemIdData)) / (sizeof(ItemPointerData)) / m) - 2, 255)
+#define HnswGetMaxLevel(m) Min(((BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(HnswPageOpaqueData)) - offsetof(HnswNeighborTupleData, indextids) - sizeof(ItemIdData)) / (sizeof(ItemPointerData)) / (m)) - 2, 255)
+
+#define HnswGetValue(base, element) PointerGetDatum(HnswPtrAccess(base, (element)->value))
+
+#if PG_VERSION_NUM < 140005
+#define relptr_offset(rp) ((rp).relptr_off - 1)
+#endif
+
+/* Pointer macros */
+#define HnswPtrAccess(base, hp) ((base) == NULL ? (hp).ptr : relptr_access(base, (hp).relptr))
+#define HnswPtrStore(base, hp, value) ((base) == NULL ? (void) ((hp).ptr = (value)) : (void) relptr_store(base, (hp).relptr, value))
+#define HnswPtrIsNull(base, hp) ((base) == NULL ? (hp).ptr == NULL : relptr_is_null((hp).relptr))
+#define HnswPtrEqual(base, hp1, hp2) ((base) == NULL ? (hp1).ptr == (hp2).ptr : relptr_offset((hp1).relptr) == relptr_offset((hp2).relptr))
+
+/* For code paths dedicated to each type */
+#define HnswPtrPointer(hp) (hp).ptr
+#define HnswPtrOffset(hp) relptr_offset((hp).relptr)
 
 /* Variables */
 extern int	hnsw_ef_search;
+extern int	hnsw_lock_tranche_id;
 
+typedef struct HnswElementData HnswElementData;
 typedef struct HnswNeighborArray HnswNeighborArray;
 
-typedef struct HnswElementData
+#define HnswPtrDeclare(type, relptrtype, ptrtype) \
+	relptr_declare(type, relptrtype); \
+	typedef union { type *ptr; relptrtype relptr; } ptrtype;
+
+/* Pointers that can be absolute or relative */
+/* Use char for DatumPtr so works with Pointer */
+HnswPtrDeclare(HnswElementData, HnswElementRelptr, HnswElementPtr);
+HnswPtrDeclare(HnswNeighborArray, HnswNeighborArrayRelptr, HnswNeighborArrayPtr);
+HnswPtrDeclare(HnswNeighborArrayPtr, HnswNeighborsRelptr, HnswNeighborsPtr);
+HnswPtrDeclare(char, DatumRelptr, DatumPtr);
+
+struct HnswElementData
 {
-	List	   *heaptids;
+	HnswElementPtr next;
+	ItemPointerData heaptids[HNSW_HEAPTIDS];
+	uint8		heaptidsLength;
 	uint8		level;
 	uint8		deleted;
-	HnswNeighborArray *neighbors;
+	uint32		hash;
+	HnswNeighborsPtr neighbors;
 	BlockNumber blkno;
 	OffsetNumber offno;
 	OffsetNumber neighborOffno;
 	BlockNumber neighborPage;
-	Vector	   *vec;
-}			HnswElementData;
+	DatumPtr	value;
+	LWLock		lock;
+};
 
 typedef HnswElementData * HnswElement;
 
 typedef struct HnswCandidate
 {
-	HnswElement element;
+	HnswElementPtr element;
 	float		distance;
 	bool		closer;
 }			HnswCandidate;
 
-typedef struct HnswNeighborArray
+struct HnswNeighborArray
 {
 	int			length;
 	bool		closerSet;
-	HnswCandidate *items;
-}			HnswNeighborArray;
+	HnswCandidate items[FLEXIBLE_ARRAY_MEMBER];
+};
 
 typedef struct HnswPairingHeapNode
 {
@@ -136,6 +185,65 @@ typedef struct HnswOptions
 	int			efConstruction; /* size of dynamic candidate list */
 }			HnswOptions;
 
+typedef struct HnswGraph
+{
+	/* Graph state */
+	slock_t		lock;
+	HnswElementPtr head;
+	double		indtuples;
+
+	/* Entry state */
+	LWLock		entryLock;
+	LWLock		entryWaitLock;
+	HnswElementPtr entryPoint;
+
+	/* Allocations state */
+	LWLock		allocatorLock;
+	long		memoryUsed;
+	long		memoryTotal;
+
+	/* Flushed state */
+	LWLock		flushLock;
+	bool		flushed;
+}			HnswGraph;
+
+typedef struct HnswShared
+{
+	/* Immutable state */
+	Oid			heaprelid;
+	Oid			indexrelid;
+	bool		isconcurrent;
+
+	/* Worker progress */
+	ConditionVariable workersdonecv;
+
+	/* Mutex for mutable state */
+	slock_t		mutex;
+
+	/* Mutable state */
+	int			nparticipantsdone;
+	double		reltuples;
+	HnswGraph	graphData;
+}			HnswShared;
+
+#define ParallelTableScanFromHnswShared(shared) \
+	(ParallelTableScanDesc) ((char *) (shared) + BUFFERALIGN(sizeof(HnswShared)))
+
+typedef struct HnswLeader
+{
+	ParallelContext *pcxt;
+	int			nparticipanttuplesorts;
+	HnswShared *hnswshared;
+	Snapshot	snapshot;
+	char	   *hnswarea;
+}			HnswLeader;
+
+typedef struct HnswAllocator
+{
+	void	   *(*alloc) (Size size, void *state);
+	void	   *state;
+}			HnswAllocator;
+
 typedef struct HnswBuildState
 {
 	/* Info */
@@ -143,6 +251,7 @@ typedef struct HnswBuildState
 	Relation	index;
 	IndexInfo  *indexInfo;
 	ForkNumber	forkNum;
+	HnswType	type;
 
 	/* Settings */
 	int			dimensions;
@@ -159,16 +268,20 @@ typedef struct HnswBuildState
 	Oid			collation;
 
 	/* Variables */
-	List	   *elements;
-	HnswElement entryPoint;
+	HnswGraph	graphData;
+	HnswGraph  *graph;
 	double		ml;
 	int			maxLevel;
-	double		maxInMemoryElements;
-	bool		flushed;
-	Vector	   *normvec;
 
 	/* Memory */
+	MemoryContext graphCtx;
 	MemoryContext tmpCtx;
+	HnswAllocator allocator;
+
+	/* Parallel builds */
+	HnswLeader *hnswleader;
+	HnswShared *hnswshared;
+	char	   *hnswarea;
 }			HnswBuildState;
 
 typedef struct HnswMetaPageData
@@ -204,7 +317,7 @@ typedef struct HnswElementTupleData
 	ItemPointerData heaptids[HNSW_HEAPTIDS];
 	ItemPointerData neighbortid;
 	uint16		unused2;
-	Vector		vec;
+	Vector		data;
 }			HnswElementTupleData;
 
 typedef HnswElementTupleData * HnswElementTuple;
@@ -250,7 +363,7 @@ typedef struct HnswVacuumState
 	Oid			collation;
 
 	/* Variables */
-	HTAB	   *deleted;
+	struct tidhash_hash *deleted;
 	BufferAccessStrategy bas;
 	HnswNeighborTuple ntup;
 	HnswElementData highestPoint;
@@ -263,32 +376,33 @@ typedef struct HnswVacuumState
 int			HnswGetM(Relation index);
 int			HnswGetEfConstruction(Relation index);
 FmgrInfo   *HnswOptionalProcInfo(Relation index, uint16 procnum);
-bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
-void		HnswCommitBuffer(Buffer buf, GenericXLogState *state);
+HnswType	HnswGetType(Relation index);
+bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, HnswType type);
+void		HnswCheckValue(Datum value, HnswType type);
 Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
 void		HnswInitPage(Buffer buf, Page page);
-void		HnswInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state);
 void		HnswInit(void);
-List	   *HnswSearchLayer(Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement);
+List	   *HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement);
 HnswElement HnswGetEntryPoint(Relation index);
 void		HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
-HnswElement HnswInitElement(ItemPointer tid, int m, double ml, int maxLevel);
-void		HnswFreeElement(HnswElement element);
+void	   *HnswAlloc(HnswAllocator * allocator, Size size);
+HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
 HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
-void		HnswInsertElement(HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
-HnswElement HnswFindDuplicate(HnswElement e);
-HnswCandidate *HnswEntryCandidate(HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
-void		HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum);
-void		HnswSetNeighborTuple(HnswNeighborTuple ntup, HnswElement e, int m);
+void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
+HnswCandidate *HnswEntryCandidate(char *base, HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
+void		HnswUpdateMetaPage(Relation index, int updateEntry, HnswElement entryPoint, BlockNumber insertPage, ForkNumber forkNum, bool building);
+void		HnswSetNeighborTuple(char *base, HnswNeighborTuple ntup, HnswElement e, int m);
 void		HnswAddHeapTid(HnswElement element, ItemPointer heaptid);
-void		HnswInitNeighbors(HnswElement element, int m);
-bool		HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel);
-void		HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting);
+void		HnswInitNeighbors(char *base, HnswElement element, int m, HnswAllocator * alloc);
+bool		HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, bool building);
+void		HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building);
 void		HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHeaptids, bool loadVec);
 void		HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec);
-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		HnswSetElementTuple(char *base, HnswElementTuple etup, HnswElement element);
+void		HnswUpdateConnection(char *base, HnswElement element, HnswCandidate * hc, int lm, int lc, int *updateIdx, Relation index, FmgrInfo *procinfo, Oid collation);
 void		HnswLoadNeighbors(HnswElement element, Relation index, int m);
+void		HnswInitLockTranche(void);
+PGDLLEXPORT void HnswParallelBuildMain(dsm_segment *seg, shm_toc *toc);
 
 /* Index access methods */
 IndexBuildResult *hnswbuild(Relation heap, Relation index, IndexInfo *indexInfo);
@@ -306,4 +420,54 @@ void		hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys,
 bool		hnswgettuple(IndexScanDesc scan, ScanDirection dir);
 void		hnswendscan(IndexScanDesc scan);
 
+static inline HnswNeighborArray *
+HnswGetNeighbors(char *base, HnswElement element, int lc)
+{
+	HnswNeighborArrayPtr *neighborList = HnswPtrAccess(base, element->neighbors);
+
+	Assert(element->level >= lc);
+
+	return HnswPtrAccess(base, neighborList[lc]);
+}
+
+/* Hash tables */
+typedef struct TidHashEntry
+{
+	ItemPointerData tid;
+	char		status;
+}			TidHashEntry;
+
+#define SH_PREFIX tidhash
+#define SH_ELEMENT_TYPE TidHashEntry
+#define SH_KEY_TYPE ItemPointerData
+#define SH_SCOPE extern
+#define SH_DECLARE
+#include "lib/simplehash.h"
+
+typedef struct PointerHashEntry
+{
+	uintptr_t	ptr;
+	char		status;
+}			PointerHashEntry;
+
+#define SH_PREFIX pointerhash
+#define SH_ELEMENT_TYPE PointerHashEntry
+#define SH_KEY_TYPE uintptr_t
+#define SH_SCOPE extern
+#define SH_DECLARE
+#include "lib/simplehash.h"
+
+typedef struct OffsetHashEntry
+{
+	Size		offset;
+	char		status;
+}			OffsetHashEntry;
+
+#define SH_PREFIX offsethash
+#define SH_ELEMENT_TYPE OffsetHashEntry
+#define SH_KEY_TYPE Size
+#define SH_SCOPE extern
+#define SH_DECLARE
+#include "lib/simplehash.h"
+
 #endif

src/hnswinsert.c

@@ -2,9 +2,11 @@
 
 #include <math.h>
 
+#include "access/generic_xlog.h"
 #include "hnsw.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
+#include "utils/datum.h"
 #include "utils/memutils.h"
 
 /*
@@ -92,7 +94,7 @@ HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size
  * Add a new page
  */
 static void
-HnswInsertAppendPage(Relation index, Buffer *nbuf, Page *npage, GenericXLogState *state, Page page)
+HnswInsertAppendPage(Relation index, Buffer *nbuf, Page *npage, GenericXLogState *state, Page page, bool building)
 {
 	/* Add a new page */
 	LockRelationForExtension(index, ExclusiveLock);
@@ -100,7 +102,11 @@ HnswInsertAppendPage(Relation index, Buffer *nbuf, Page *npage, GenericXLogState
 	UnlockRelationForExtension(index, ExclusiveLock);
 
 	/* Init new page */
-	*npage = GenericXLogRegisterBuffer(state, *nbuf, GENERIC_XLOG_FULL_IMAGE);
+	if (building)
+		*npage = BufferGetPage(*nbuf);
+	else
+		*npage = GenericXLogRegisterBuffer(state, *nbuf, GENERIC_XLOG_FULL_IMAGE);
+
 	HnswInitPage(*nbuf, *npage);
 
 	/* Update previous buffer */
@@ -111,7 +117,7 @@ HnswInsertAppendPage(Relation index, Buffer *nbuf, Page *npage, GenericXLogState
  * Add to element and neighbor pages
  */
 static void
-WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPage, BlockNumber *updatedInsertPage)
+AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, BlockNumber *updatedInsertPage, bool building)
 {
 	Buffer		buf;
 	Page		page;
@@ -123,16 +129,16 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	Size		minCombinedSize;
 	HnswElementTuple etup;
 	BlockNumber currentPage = insertPage;
-	int			dimensions = e->vec->dim;
 	HnswNeighborTuple ntup;
 	Buffer		nbuf;
 	Page		npage;
 	OffsetNumber freeOffno = InvalidOffsetNumber;
 	OffsetNumber freeNeighborOffno = InvalidOffsetNumber;
 	BlockNumber newInsertPage = InvalidBlockNumber;
+	char	   *base = NULL;
 
 	/* Calculate sizes */
-	etupSize = HNSW_ELEMENT_TUPLE_SIZE(dimensions);
+	etupSize = HNSW_ELEMENT_TUPLE_SIZE(VARSIZE_ANY(HnswPtrAccess(base, e->value)));
 	ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(e->level, m);
 	combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
 	maxSize = HNSW_MAX_SIZE;
@@ -140,11 +146,11 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 
 	/* Prepare element tuple */
 	etup = palloc0(etupSize);
-	HnswSetElementTuple(etup, e);
+	HnswSetElementTuple(base, etup, e);
 
 	/* Prepare neighbor tuple */
 	ntup = palloc0(ntupSize);
-	HnswSetNeighborTuple(ntup, e, m);
+	HnswSetNeighborTuple(base, ntup, e, m);
 
 	/* Find a page (or two if needed) to insert the tuples */
 	for (;;)
@@ -152,8 +158,16 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 		buf = ReadBuffer(index, currentPage);
 		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
 
-		state = GenericXLogStart(index);
-		page = GenericXLogRegisterBuffer(state, buf, 0);
+		if (building)
+		{
+			state = NULL;
+			page = BufferGetPage(buf);
+		}
+		else
+		{
+			state = GenericXLogStart(index);
+			page = GenericXLogRegisterBuffer(state, buf, 0);
+		}
 
 		/* Keep track of first page where element at level 0 can fit */
 		if (!BlockNumberIsValid(newInsertPage) && PageGetFreeSpace(page) >= minCombinedSize)
@@ -173,7 +187,12 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 		if (HnswFreeOffset(index, buf, page, e, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage))
 		{
 			if (nbuf != buf)
-				npage = GenericXLogRegisterBuffer(state, nbuf, 0);
+			{
+				if (building)
+					npage = BufferGetPage(nbuf);
+				else
+					npage = GenericXLogRegisterBuffer(state, nbuf, 0);
+			}
 
 			break;
 		}
@@ -182,7 +201,7 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 		/* Skip if both tuples can fit on the same page */
 		if (combinedSize > maxSize && PageGetFreeSpace(page) >= etupSize && !BlockNumberIsValid(HnswPageGetOpaque(page)->nextblkno))
 		{
-			HnswInsertAppendPage(index, &nbuf, &npage, state, page);
+			HnswInsertAppendPage(index, &nbuf, &npage, state, page, building);
 			break;
 		}
 
@@ -191,7 +210,8 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 		if (BlockNumberIsValid(currentPage))
 		{
 			/* Move to next page */
-			GenericXLogAbort(state);
+			if (!building)
+				GenericXLogAbort(state);
 			UnlockReleaseBuffer(buf);
 		}
 		else
@@ -199,22 +219,33 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 			Buffer		newbuf;
 			Page		newpage;
 
-			HnswInsertAppendPage(index, &newbuf, &newpage, state, page);
+			HnswInsertAppendPage(index, &newbuf, &newpage, state, page, building);
 
 			/* Commit */
-			GenericXLogFinish(state);
+			if (building)
+				MarkBufferDirty(buf);
+			else
+				GenericXLogFinish(state);
 
 			/* Unlock previous buffer */
 			UnlockReleaseBuffer(buf);
 
 			/* Prepare new buffer */
-			state = GenericXLogStart(index);
 			buf = newbuf;
-			page = GenericXLogRegisterBuffer(state, buf, 0);
+			if (building)
+			{
+				state = NULL;
+				page = BufferGetPage(buf);
+			}
+			else
+			{
+				state = GenericXLogStart(index);
+				page = GenericXLogRegisterBuffer(state, buf, 0);
+			}
 
 			/* Create new page for neighbors if needed */
 			if (PageGetFreeSpace(page) < combinedSize)
-				HnswInsertAppendPage(index, &nbuf, &npage, state, page);
+				HnswInsertAppendPage(index, &nbuf, &npage, state, page, building);
 			else
 			{
 				nbuf = buf;
@@ -268,7 +299,14 @@ WriteNewElementPages(Relation index, HnswElement e, int m, BlockNumber insertPag
 	}
 
 	/* Commit */
-	GenericXLogFinish(state);
+	if (building)
+	{
+		MarkBufferDirty(buf);
+		if (nbuf != buf)
+			MarkBufferDirty(nbuf);
+	}
+	else
+		GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 	if (nbuf != buf)
 		UnlockReleaseBuffer(nbuf);
@@ -302,12 +340,14 @@ ConnectionExists(HnswElement e, HnswNeighborTuple ntup, int startIdx, int lm)
  * Update neighbors
  */
 void
-HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting)
+HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building)
 {
+	char	   *base = NULL;
+
 	for (int lc = e->level; lc >= 0; lc--)
 	{
 		int			lm = HnswGetLayerM(m, lc);
-		HnswNeighborArray *neighbors = &e->neighbors[lc];
+		HnswNeighborArray *neighbors = HnswGetNeighbors(base, e, lc);
 
 		for (int i = 0; i < neighbors->length; i++)
 		{
@@ -315,16 +355,15 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
 			Buffer		buf;
 			Page		page;
 			GenericXLogState *state;
-			ItemId		itemid;
 			HnswNeighborTuple ntup;
-			Size		ntupSize;
 			int			idx = -1;
 			int			startIdx;
-			OffsetNumber offno = hc->element->neighborOffno;
+			HnswElement neighborElement = HnswPtrAccess(base, hc->element);
+			OffsetNumber offno = neighborElement->neighborOffno;
 
 			/* Get latest neighbors since they may have changed */
 			/* Do not lock yet since selecting neighbors can take time */
-			HnswLoadNeighbors(hc->element, index, m);
+			HnswLoadNeighbors(neighborElement, index, m);
 
 			/*
 			 * Could improve performance for vacuuming by checking neighbors
@@ -334,25 +373,31 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
 			 */
 
 			/* Select neighbors */
-			HnswUpdateConnection(e, hc, lm, lc, &idx, index, procinfo, collation);
+			HnswUpdateConnection(NULL, e, hc, lm, lc, &idx, index, procinfo, collation);
 
 			/* New element was not selected as a neighbor */
 			if (idx == -1)
 				continue;
 
 			/* Register page */
-			buf = ReadBuffer(index, hc->element->neighborPage);
+			buf = ReadBuffer(index, neighborElement->neighborPage);
 			LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
-			state = GenericXLogStart(index);
-			page = GenericXLogRegisterBuffer(state, buf, 0);
+			if (building)
+			{
+				state = NULL;
+				page = BufferGetPage(buf);
+			}
+			else
+			{
+				state = GenericXLogStart(index);
+				page = GenericXLogRegisterBuffer(state, buf, 0);
+			}
 
 			/* Get tuple */
-			itemid = PageGetItemId(page, offno);
-			ntup = (HnswNeighborTuple) PageGetItem(page, itemid);
-			ntupSize = ItemIdGetLength(itemid);
+			ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, offno));
 
 			/* Calculate index for update */
-			startIdx = (hc->element->level - lc) * m;
+			startIdx = (neighborElement->level - lc) * m;
 
 			/* Check for existing connection */
 			if (checkExisting && ConnectionExists(e, ntup, startIdx, lm))
@@ -378,17 +423,16 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
 			{
 				ItemPointer indextid = &ntup->indextids[idx];
 
-				/* Update neighbor */
+				/* Update neighbor on the buffer */
 				ItemPointerSet(indextid, e->blkno, e->offno);
 
-				/* Overwrite tuple */
-				if (!PageIndexTupleOverwrite(page, offno, (Item) ntup, ntupSize))
-					elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
-
 				/* Commit */
-				GenericXLogFinish(state);
+				if (building)
+					MarkBufferDirty(buf);
+				else
+					GenericXLogFinish(state);
 			}
-			else
+			else if (!building)
 				GenericXLogAbort(state);
 
 			UnlockReleaseBuffer(buf);
@@ -400,20 +444,27 @@ HnswUpdateNeighborPages(Relation index, FmgrInfo *procinfo, Oid collation, HnswE
  * Add a heap TID to an existing element
  */
 static bool
-HnswAddDuplicate(Relation index, HnswElement element, HnswElement dup)
+AddDuplicateOnDisk(Relation index, HnswElement element, HnswElement dup, bool building)
 {
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
-	Size		etupSize = HNSW_ELEMENT_TUPLE_SIZE(dup->vec->dim);
 	HnswElementTuple etup;
 	int			i;
 
 	/* Read page */
 	buf = ReadBuffer(index, dup->blkno);
 	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
-	state = GenericXLogStart(index);
-	page = GenericXLogRegisterBuffer(state, buf, 0);
+	if (building)
+	{
+		state = NULL;
+		page = BufferGetPage(buf);
+	}
+	else
+	{
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+	}
 
 	/* Find space */
 	etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, dup->offno));
@@ -426,82 +477,93 @@ HnswAddDuplicate(Relation index, HnswElement element, HnswElement dup)
 	/* Either being deleted or we lost our chance to another backend */
 	if (i == 0 || i == HNSW_HEAPTIDS)
 	{
-		GenericXLogAbort(state);
+		if (!building)
+			GenericXLogAbort(state);
 		UnlockReleaseBuffer(buf);
 		return false;
 	}
 
-	/* Add heap TID */
-	etup->heaptids[i] = *((ItemPointer) linitial(element->heaptids));
-
-	/* Overwrite tuple */
-	if (!PageIndexTupleOverwrite(page, dup->offno, (Item) etup, etupSize))
-		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+	/* Add heap TID, modifying the tuple on the page directly */
+	etup->heaptids[i] = element->heaptids[0];
 
 	/* Commit */
-	GenericXLogFinish(state);
+	if (building)
+		MarkBufferDirty(buf);
+	else
+		GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 
 	return true;
 }
 
 /*
- * Write changes to disk
+ * Find duplicate element
+ */
+static bool
+FindDuplicateOnDisk(Relation index, HnswElement element, bool building)
+{
+	char	   *base = NULL;
+	HnswNeighborArray *neighbors = HnswGetNeighbors(base, element, 0);
+	Datum		value = HnswGetValue(base, element);
+
+	for (int i = 0; i < neighbors->length; i++)
+	{
+		HnswCandidate *neighbor = &neighbors->items[i];
+		HnswElement neighborElement = HnswPtrAccess(base, neighbor->element);
+		Datum		neighborValue = HnswGetValue(base, neighborElement);
+
+		/* Exit early since ordered by distance */
+		if (!datumIsEqual(value, neighborValue, false, -1))
+			return false;
+
+		if (AddDuplicateOnDisk(index, element, neighborElement, building))
+			return true;
+	}
+
+	return false;
+}
+
+/*
+ * Update graph on disk
  */
 static void
-WriteElement(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement dup, HnswElement entryPoint)
+UpdateGraphOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement entryPoint, bool building)
 {
 	BlockNumber newInsertPage = InvalidBlockNumber;
 
-	/* Try to add to existing page */
-	if (dup != NULL)
-	{
-		if (HnswAddDuplicate(index, element, dup))
-			return;
-	}
+	/* Look for duplicate */
+	if (FindDuplicateOnDisk(index, element, building))
+		return;
 
-	/* Write element and neighbor tuples */
-	WriteNewElementPages(index, element, m, GetInsertPage(index), &newInsertPage);
+	/* Add element */
+	AddElementOnDisk(index, element, m, GetInsertPage(index), &newInsertPage, building);
 
 	/* Update insert page if needed */
 	if (BlockNumberIsValid(newInsertPage))
-		HnswUpdateMetaPage(index, 0, NULL, newInsertPage, MAIN_FORKNUM);
+		HnswUpdateMetaPage(index, 0, NULL, newInsertPage, MAIN_FORKNUM, building);
 
 	/* Update neighbors */
-	HnswUpdateNeighborPages(index, procinfo, collation, element, m, false);
+	HnswUpdateNeighborsOnDisk(index, procinfo, collation, element, m, false, building);
 
-	/* Update metapage if needed */
+	/* Update entry point if needed */
 	if (entryPoint == NULL || element->level > entryPoint->level)
-		HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM);
+		HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM, building);
 }
 
 /*
  * Insert a tuple into the index
  */
 bool
-HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel)
+HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, bool building)
 {
-	Datum		value;
-	FmgrInfo   *normprocinfo;
 	HnswElement entryPoint;
 	HnswElement element;
 	int			m;
 	int			efConstruction = HnswGetEfConstruction(index);
 	FmgrInfo   *procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
 	Oid			collation = index->rd_indcollation[0];
-	HnswElement dup;
 	LOCKMODE	lockmode = ShareLock;
-
-	/* Detoast once for all calls */
-	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
-
-	/* Normalize if needed */
-	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
-	if (normprocinfo != NULL)
-	{
-		if (!HnswNormValue(normprocinfo, collation, &value, NULL))
-			return false;
-	}
+	char	   *base = NULL;
 
 	/*
 	 * Get a shared lock. This allows vacuum to ensure no in-flight inserts
@@ -514,8 +576,8 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
 
 	/* Create an element */
-	element = HnswInitElement(heap_tid, m, HnswGetMl(m), HnswGetMaxLevel(m));
-	element->vec = DatumGetVector(value);
+	element = HnswInitElement(base, heap_tid, m, HnswGetMl(m), HnswGetMaxLevel(m), NULL);
+	HnswPtrStore(base, element->value, DatumGetPointer(value));
 
 	/* Prevent concurrent inserts when likely updating entry point */
 	if (entryPoint == NULL || element->level > entryPoint->level)
@@ -531,14 +593,11 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 		entryPoint = HnswGetEntryPoint(index);
 	}
 
-	/* Insert element in graph */
-	HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, false);
+	/* Find neighbors for element */
+	HnswFindElementNeighbors(base, element, entryPoint, index, procinfo, collation, m, efConstruction, false);
 
-	/* Look for duplicate */
-	dup = HnswFindDuplicate(element);
-
-	/* Write to disk */
-	WriteElement(index, procinfo, collation, element, m, efConstruction, dup, entryPoint);
+	/* Update graph on disk */
+	UpdateGraphOnDisk(index, procinfo, collation, element, m, efConstruction, entryPoint, building);
 
 	/* Release lock */
 	UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
@@ -546,6 +605,34 @@ HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_ti
 	return true;
 }
 
+/*
+ * Insert a tuple into the index
+ */
+static void
+HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid)
+{
+	Datum		value;
+	FmgrInfo   *normprocinfo;
+	Oid			collation = index->rd_indcollation[0];
+	HnswType	type = HnswGetType(index);
+
+	/* Detoast once for all calls */
+	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+
+	/* Check value */
+	HnswCheckValue(value, type);
+
+	/* Normalize if needed */
+	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	if (normprocinfo != NULL)
+	{
+		if (!HnswNormValue(normprocinfo, collation, &value, type))
+			return;
+	}
+
+	HnswInsertTupleOnDisk(index, value, values, isnull, heap_tid, false);
+}
+
 /*
  * Insert a tuple into the index
  */
@@ -572,7 +659,7 @@ hnswinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid,
 	oldCtx = MemoryContextSwitchTo(insertCtx);
 
 	/* Insert tuple */
-	HnswInsertTuple(index, values, isnull, heap_tid, heap);
+	HnswInsertTuple(index, values, isnull, heap_tid);
 
 	/* Delete memory context */
 	MemoryContextSwitchTo(oldCtx);

src/hnswscan.c

@@ -21,6 +21,7 @@ GetScanItems(IndexScanDesc scan, Datum q)
 	List	   *w;
 	int			m;
 	HnswElement entryPoint;
+	char	   *base = NULL;
 
 	/* Get m and entry point */
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
@@ -28,38 +29,15 @@ GetScanItems(IndexScanDesc scan, Datum q)
 	if (entryPoint == NULL)
 		return NIL;
 
-	ep = list_make1(HnswEntryCandidate(entryPoint, q, index, procinfo, collation, false));
+	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, false));
 
 	for (int lc = entryPoint->level; lc >= 1; lc--)
 	{
-		w = HnswSearchLayer(q, ep, 1, lc, index, procinfo, collation, m, false, NULL);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, false, NULL);
 		ep = w;
 	}
 
-	return HnswSearchLayer(q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
-}
-
-/*
- * Get dimensions from metapage
- */
-static int
-GetDimensions(Relation index)
-{
-	Buffer		buf;
-	Page		page;
-	HnswMetaPage metap;
-	int			dimensions;
-
-	buf = ReadBuffer(index, HNSW_METAPAGE_BLKNO);
-	LockBuffer(buf, BUFFER_LOCK_SHARE);
-	page = BufferGetPage(buf);
-	metap = HnswPageGetMeta(page);
-
-	dimensions = metap->dimensions;
-
-	UnlockReleaseBuffer(buf);
-
-	return dimensions;
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
 }
 
 /*
@@ -72,7 +50,7 @@ GetScanValue(IndexScanDesc scan)
 	Datum		value;
 
 	if (scan->orderByData->sk_flags & SK_ISNULL)
-		value = PointerGetDatum(InitVector(GetDimensions(scan->indexRelation)));
+		value = PointerGetDatum(NULL);
 	else
 	{
 		value = scan->orderByData->sk_argument;
@@ -83,7 +61,7 @@ GetScanValue(IndexScanDesc scan)
 
 		/* Fine if normalization fails */
 		if (so->normprocinfo != NULL)
-			HnswNormValue(so->normprocinfo, so->collation, &value, NULL);
+			HnswNormValue(so->normprocinfo, so->collation, &value, HnswGetType(scan->indexRelation));
 	}
 
 	return value;
@@ -180,32 +158,32 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
 
 		so->first = false;
+
+#if defined(HNSW_MEMORY) && PG_VERSION_NUM >= 130000
+		elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(so->tmpCtx, false) / (1024 * 1024));
+#endif
 	}
 
 	while (list_length(so->w) > 0)
 	{
+		char	   *base = NULL;
 		HnswCandidate *hc = llast(so->w);
+		HnswElement element = HnswPtrAccess(base, hc->element);
 		ItemPointer heaptid;
 
 		/* Move to next element if no valid heap TIDs */
-		if (list_length(hc->element->heaptids) == 0)
+		if (element->heaptidsLength == 0)
 		{
 			so->w = list_delete_last(so->w);
 			continue;
 		}
 
-		heaptid = llast(hc->element->heaptids);
-
-		hc->element->heaptids = list_delete_last(hc->element->heaptids);
+		heaptid = &element->heaptids[--element->heaptidsLength];
 
 		MemoryContextSwitchTo(oldCtx);
 
-#if PG_VERSION_NUM >= 120000
 		scan->xs_heaptid = *heaptid;
-#else
-		scan->xs_ctup.t_self = *heaptid;
-#endif
-
+		scan->xs_recheck = false;
 		scan->xs_recheckorderby = false;
 		return true;
 	}

src/hnswvacuum.c

@@ -2,6 +2,7 @@
 
 #include <math.h>
 
+#include "access/generic_xlog.h"
 #include "commands/vacuum.h"
 #include "hnsw.h"
 #include "storage/bufmgr.h"
@@ -12,12 +13,9 @@
  * Check if deleted list contains an index TID
  */
 static bool
-DeletedContains(HTAB *deleted, ItemPointer indextid)
+DeletedContains(tidhash_hash * deleted, ItemPointer indextid)
 {
-	bool		found;
-
-	hash_search(deleted, indextid, HASH_FIND, &found);
-	return found;
+	return tidhash_lookup(deleted, *indextid) != NULL;
 }
 
 /*
@@ -93,15 +91,10 @@ RemoveHeapTids(HnswVacuumState * vacuumstate)
 
 				if (itemUpdated)
 				{
-					Size		etupSize = HNSW_ELEMENT_TUPLE_SIZE(etup->vec.dim);
-
 					/* Mark rest as invalid */
 					for (int i = idx; i < HNSW_HEAPTIDS; i++)
 						ItemPointerSetInvalid(&etup->heaptids[i]);
 
-					if (!PageIndexTupleOverwrite(page, offno, (Item) etup, etupSize))
-						elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
-
 					updated = true;
 				}
 			}
@@ -109,11 +102,13 @@ RemoveHeapTids(HnswVacuumState * vacuumstate)
 			if (!ItemPointerIsValid(&etup->heaptids[0]))
 			{
 				ItemPointerData ip;
+				bool		found;
 
 				/* Add to deleted list */
 				ItemPointerSet(&ip, blkno, offno);
 
-				(void) hash_search(vacuumstate->deleted, &ip, HASH_ENTER, NULL);
+				tidhash_insert(vacuumstate->deleted, ip, &found);
+				Assert(!found);
 			}
 			else if (etup->level > highestLevel && !(entryPoint != NULL && blkno == entryPoint->blkno && offno == entryPoint->offno))
 			{
@@ -199,21 +194,25 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	BufferAccessStrategy bas = vacuumstate->bas;
 	HnswNeighborTuple ntup = vacuumstate->ntup;
 	Size		ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(element->level, m);
+	char	   *base = NULL;
 
 	/* Skip if element is entry point */
 	if (entryPoint != NULL && element->blkno == entryPoint->blkno && element->offno == entryPoint->offno)
 		return;
 
 	/* Init fields */
-	HnswInitNeighbors(element, m);
-	element->heaptids = NIL;
+	HnswInitNeighbors(base, element, m, NULL);
+	element->heaptidsLength = 0;
 
-	/* Add element to graph, skipping itself */
-	HnswInsertElement(element, entryPoint, index, procinfo, collation, m, efConstruction, true);
+	/* Find neighbors for element, skipping itself */
+	HnswFindElementNeighbors(base, element, entryPoint, index, procinfo, collation, m, efConstruction, true);
+
+	/* Zero memory for each element */
+	MemSet(ntup, 0, HNSW_TUPLE_ALLOC_SIZE);
 
 	/* Update neighbor tuple */
 	/* Do this before getting page to minimize locking */
-	HnswSetNeighborTuple(ntup, element, m);
+	HnswSetNeighborTuple(base, ntup, element, m);
 
 	/* Get neighbor page */
 	buf = ReadBufferExtended(index, MAIN_FORKNUM, element->neighborPage, RBM_NORMAL, bas);
@@ -230,7 +229,7 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	UnlockReleaseBuffer(buf);
 
 	/* Update neighbors */
-	HnswUpdateNeighborPages(index, procinfo, collation, element, m, true);
+	HnswUpdateNeighborsOnDisk(index, procinfo, collation, element, m, true, false);
 }
 
 /*
@@ -286,7 +285,7 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 			 * point is outdated and empty, the entry point will be empty
 			 * until an element is repaired.
 			 */
-			HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_ALWAYS, highestPoint, InvalidBlockNumber, MAIN_FORKNUM);
+			HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_ALWAYS, highestPoint, InvalidBlockNumber, MAIN_FORKNUM, false);
 		}
 		else
 		{
@@ -301,7 +300,7 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 			{
 				/* Reset neighbors from previous update */
 				if (highestPoint != NULL)
-					highestPoint->neighbors = NULL;
+					HnswPtrStore((char *) NULL, highestPoint->neighbors, (HnswNeighborArrayPtr *) NULL);
 
 				RepairGraphElement(vacuumstate, entryPoint, highestPoint);
 			}
@@ -419,7 +418,7 @@ RepairGraph(HnswVacuumState * vacuumstate)
 			 * was replaced and highest point was outdated.
 			 */
 			if (entryPoint == NULL || element->level > entryPoint->level)
-				HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM);
+				HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM, false);
 
 			/* Release lock */
 			UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
@@ -479,8 +478,6 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 		{
 			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
 			HnswNeighborTuple ntup;
-			Size		etupSize;
-			Size		ntupSize;
 			Buffer		nbuf;
 			Page		npage;
 			BlockNumber neighborPage;
@@ -504,10 +501,6 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 			if (ItemPointerIsValid(&etup->heaptids[0]))
 				continue;
 
-			/* Calculate sizes */
-			etupSize = HNSW_ELEMENT_TUPLE_SIZE(etup->vec.dim);
-			ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(etup->level, vacuumstate->m);
-
 			/* Get neighbor page */
 			neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
 			neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
@@ -528,19 +521,16 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 
 			/* Overwrite element */
 			etup->deleted = 1;
-			MemSet(&etup->vec.x, 0, etup->vec.dim * sizeof(float));
+			MemSet(&etup->data, 0, VARSIZE_ANY(&etup->data));
 
 			/* Overwrite neighbors */
 			for (int i = 0; i < ntup->count; i++)
 				ItemPointerSetInvalid(&ntup->indextids[i]);
 
-			/* Overwrite element tuple */
-			if (!PageIndexTupleOverwrite(page, offno, (Item) etup, etupSize))
-				elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
-
-			/* Overwrite neighbor tuple */
-			if (!PageIndexTupleOverwrite(npage, neighborOffno, (Item) ntup, ntupSize))
-				elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+			/*
+			 * We modified the tuples in place, no need to call
+			 * PageIndexTupleOverwrite
+			 */
 
 			/* Commit */
 			GenericXLogFinish(state);
@@ -563,7 +553,7 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 	}
 
 	/* Update insert page last, after everything has been marked as deleted */
-	HnswUpdateMetaPage(index, 0, NULL, insertPage, MAIN_FORKNUM);
+	HnswUpdateMetaPage(index, 0, NULL, insertPage, MAIN_FORKNUM, false);
 }
 
 /*
@@ -573,7 +563,6 @@ static void
 InitVacuumState(HnswVacuumState * vacuumstate, IndexVacuumInfo *info, IndexBulkDeleteResult *stats, IndexBulkDeleteCallback callback, void *callback_state)
 {
 	Relation	index = info->index;
-	HASHCTL		hash_ctl;
 
 	if (stats == NULL)
 		stats = (IndexBulkDeleteResult *) palloc0(sizeof(IndexBulkDeleteResult));
@@ -586,7 +575,7 @@ InitVacuumState(HnswVacuumState * vacuumstate, IndexVacuumInfo *info, IndexBulkD
 	vacuumstate->bas = GetAccessStrategy(BAS_BULKREAD);
 	vacuumstate->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
 	vacuumstate->collation = index->rd_indcollation[0];
-	vacuumstate->ntup = palloc0(BLCKSZ);
+	vacuumstate->ntup = palloc0(HNSW_TUPLE_ALLOC_SIZE);
 	vacuumstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 												"Hnsw vacuum temporary context",
 												ALLOCSET_DEFAULT_SIZES);
@@ -595,10 +584,7 @@ InitVacuumState(HnswVacuumState * vacuumstate, IndexVacuumInfo *info, IndexBulkD
 	HnswGetMetaPageInfo(index, &vacuumstate->m, NULL);
 
 	/* Create hash table */
-	hash_ctl.keysize = sizeof(ItemPointerData);
-	hash_ctl.entrysize = sizeof(ItemPointerData);
-	hash_ctl.hcxt = CurrentMemoryContext;
-	vacuumstate->deleted = hash_create("hnswbulkdelete indextids", 256, &hash_ctl, HASH_ELEM | HASH_BLOBS | HASH_CONTEXT);
+	vacuumstate->deleted = tidhash_create(CurrentMemoryContext, 256, NULL);
 }
 
 /*
@@ -607,7 +593,7 @@ InitVacuumState(HnswVacuumState * vacuumstate, IndexVacuumInfo *info, IndexBulkD
 static void
 FreeVacuumState(HnswVacuumState * vacuumstate)
 {
-	hash_destroy(vacuumstate->deleted);
+	tidhash_destroy(vacuumstate->deleted);
 	FreeAccessStrategy(vacuumstate->bas);
 	pfree(vacuumstate->ntup);
 	MemoryContextDelete(vacuumstate->tmpCtx);

src/ivfbuild.c

@@ -2,30 +2,27 @@
 
 #include <float.h>
 
+#include "access/table.h"
+#include "access/tableam.h"
 #include "access/parallel.h"
 #include "access/xact.h"
 #include "catalog/index.h"
 #include "catalog/pg_operator_d.h"
 #include "catalog/pg_type_d.h"
+#include "commands/progress.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
+#include "optimizer/optimizer.h"
 #include "storage/bufmgr.h"
 #include "tcop/tcopprot.h"
 #include "utils/memutils.h"
+#include "vector.h"
 
 #if PG_VERSION_NUM >= 140000
 #include "utils/backend_progress.h"
-#elif PG_VERSION_NUM >= 120000
-#include "pgstat.h"
-#endif
-
-#if PG_VERSION_NUM >= 120000
-#include "access/tableam.h"
-#include "commands/progress.h"
 #else
-#define PROGRESS_CREATEIDX_SUBPHASE 0
-#define PROGRESS_CREATEIDX_TUPLES_TOTAL 0
-#define PROGRESS_CREATEIDX_TUPLES_DONE 0
+#include "pgstat.h"
 #endif
 
 #if PG_VERSION_NUM >= 130000
@@ -34,26 +31,11 @@
 #define CALLBACK_ITEM_POINTER HeapTuple hup
 #endif
 
-#if PG_VERSION_NUM >= 120000
-#define UpdateProgress(index, val) pgstat_progress_update_param(index, val)
-#else
-#define UpdateProgress(index, val) ((void)val)
-#endif
-
 #if PG_VERSION_NUM >= 140000
 #include "utils/backend_status.h"
 #include "utils/wait_event.h"
 #endif
 
-#if PG_VERSION_NUM >= 120000
-#include "access/table.h"
-#include "optimizer/optimizer.h"
-#else
-#include "access/heapam.h"
-#include "optimizer/planner.h"
-#include "pgstat.h"
-#endif
-
 #define PARALLEL_KEY_IVFFLAT_SHARED		UINT64CONST(0xA000000000000001)
 #define PARALLEL_KEY_TUPLESORT			UINT64CONST(0xA000000000000002)
 #define PARALLEL_KEY_IVFFLAT_CENTERS	UINT64CONST(0xA000000000000003)
@@ -77,13 +59,13 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 	 */
 	if (buildstate->kmeansnormprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->normvec))
+		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->type))
 			return;
 	}
 
 	if (samples->length < targsamples)
 	{
-		VectorArraySet(samples, samples->length, DatumGetVector(value));
+		VectorArraySet(samples, samples->length, DatumGetPointer(value));
 		samples->length++;
 	}
 	else
@@ -100,7 +82,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 #endif
 
 			Assert(k >= 0 && k < targsamples);
-			VectorArraySet(samples, k, DatumGetVector(value));
+			VectorArraySet(samples, k, DatumGetPointer(value));
 		}
 
 		buildstate->rowstoskip -= 1;
@@ -125,7 +107,7 @@ SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
 
 	/* Add sample */
-	AddSample(values, state);
+	AddSample(values, buildstate);
 
 	/* Reset memory context */
 	MemoryContextSwitchTo(oldCtx);
@@ -150,13 +132,8 @@ SampleRows(IvfflatBuildState * buildstate)
 	{
 		BlockNumber targblock = BlockSampler_Next(&buildstate->bs);
 
-#if PG_VERSION_NUM >= 120000
 		table_index_build_range_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
 									 false, true, false, targblock, 1, SampleCallback, (void *) buildstate, NULL);
-#else
-		IndexBuildHeapRangeScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-								false, true, targblock, 1, SampleCallback, (void *) buildstate, NULL);
-#endif
 	}
 }
 
@@ -178,7 +155,7 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState
 	/* Normalize if needed */
 	if (buildstate->normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->normvec))
+		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->type))
 			return;
 	}
 
@@ -282,16 +259,12 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 	IndexTuple	itup = NULL;	/* silence compiler warning */
 	int64		inserted = 0;
 
-#if PG_VERSION_NUM >= 120000
 	TupleTableSlot *slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsMinimalTuple);
-#else
-	TupleTableSlot *slot = MakeSingleTupleTableSlot(buildstate->tupdesc);
-#endif
 	TupleDesc	tupdesc = RelationGetDescr(index);
 
-	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_LOAD);
+	pgstat_progress_update_param(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_LOAD);
 
-	UpdateProgress(PROGRESS_CREATEIDX_TUPLES_TOTAL, buildstate->indtuples);
+	pgstat_progress_update_param(PROGRESS_CREATEIDX_TUPLES_TOTAL, buildstate->indtuples);
 
 	GetNextTuple(buildstate->sortstate, tupdesc, slot, &itup, &list);
 
@@ -327,7 +300,7 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 
 			pfree(itup);
 
-			UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++inserted);
+			pgstat_progress_update_param(PROGRESS_CREATEIDX_TUPLES_DONE, ++inserted);
 
 			GetNextTuple(buildstate->sortstate, tupdesc, slot, &itup, &list);
 		}
@@ -341,25 +314,58 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 	}
 }
 
+/*
+ * Get max dimensions
+ */
+static int
+GetMaxDimensions(IvfflatType type)
+{
+	int			maxDimensions = IVFFLAT_MAX_DIM;
+
+	if (type == IVFFLAT_TYPE_HALFVEC)
+		maxDimensions *= 2;
+
+	return maxDimensions;
+}
+
+/*
+ * Get item size
+ */
+static Size
+GetItemSize(IvfflatType type, int dimensions)
+{
+	if (type == IVFFLAT_TYPE_VECTOR)
+		return VECTOR_SIZE(dimensions);
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+		return HALFVEC_SIZE(dimensions);
+	else
+		elog(ERROR, "Unsupported type");
+}
+
 /*
  * Initialize the build state
  */
 static void
 InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, IndexInfo *indexInfo)
 {
+	int			maxDimensions;
+
 	buildstate->heap = heap;
 	buildstate->index = index;
 	buildstate->indexInfo = indexInfo;
+	buildstate->type = IvfflatGetType(index);
 
 	buildstate->lists = IvfflatGetLists(index);
 	buildstate->dimensions = TupleDescAttr(index->rd_att, 0)->atttypmod;
 
+	maxDimensions = GetMaxDimensions(buildstate->type);
+
 	/* Require column to have dimensions to be indexed */
 	if (buildstate->dimensions < 0)
 		elog(ERROR, "column does not have dimensions");
 
-	if (buildstate->dimensions > IVFFLAT_MAX_DIM)
-		elog(ERROR, "column cannot have more than %d dimensions for ivfflat index", IVFFLAT_MAX_DIM);
+	if (buildstate->dimensions > maxDimensions)
+		elog(ERROR, "column cannot have more than %d dimensions for ivfflat index", maxDimensions);
 
 	buildstate->reltuples = 0;
 	buildstate->indtuples = 0;
@@ -375,27 +381,16 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 		elog(ERROR, "dimensions must be greater than one for this opclass");
 
 	/* Create tuple description for sorting */
-#if PG_VERSION_NUM >= 120000
 	buildstate->tupdesc = CreateTemplateTupleDesc(3);
-#else
-	buildstate->tupdesc = CreateTemplateTupleDesc(3, false);
-#endif
 	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 1, "list", INT4OID, -1, 0);
 	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
 	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 3, "vector", RelationGetDescr(index)->attrs[0].atttypid, -1, 0);
 
-#if PG_VERSION_NUM >= 120000
 	buildstate->slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsVirtual);
-#else
-	buildstate->slot = MakeSingleTupleTableSlot(buildstate->tupdesc);
-#endif
 
-	buildstate->centers = VectorArrayInit(buildstate->lists, buildstate->dimensions);
+	buildstate->centers = VectorArrayInit(buildstate->lists, buildstate->dimensions, GetItemSize(buildstate->type, buildstate->dimensions));
 	buildstate->listInfo = palloc(sizeof(ListInfo) * buildstate->lists);
 
-	/* Reuse for each tuple */
-	buildstate->normvec = InitVector(buildstate->dimensions);
-
 	buildstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 											   "Ivfflat build temporary context",
 											   ALLOCSET_DEFAULT_SIZES);
@@ -417,7 +412,6 @@ FreeBuildState(IvfflatBuildState * buildstate)
 {
 	VectorArrayFree(buildstate->centers);
 	pfree(buildstate->listInfo);
-	pfree(buildstate->normvec);
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	pfree(buildstate->listSums);
@@ -435,7 +429,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 {
 	int			numSamples;
 
-	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_KMEANS);
+	pgstat_progress_update_param(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_KMEANS);
 
 	/* Target 50 samples per list, with at least 10000 samples */
 	/* The number of samples has a large effect on index build time */
@@ -449,7 +443,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 
 	/* Sample rows */
 	/* TODO Ensure within maintenance_work_mem */
-	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions);
+	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions, buildstate->centers->itemsize);
 	if (buildstate->heap != NULL)
 	{
 		SampleRows(buildstate);
@@ -464,7 +458,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 	}
 
 	/* Calculate centers */
-	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers));
+	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers, buildstate->type));
 
 	/* Free samples before we allocate more memory */
 	VectorArrayFree(buildstate->samples);
@@ -509,8 +503,8 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	Size		listSize;
 	IvfflatList list;
 
-	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(dimensions));
-	list = palloc(listSize);
+	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(centers->itemsize));
+	list = palloc0(listSize);
 
 	buf = IvfflatNewBuffer(index, forkNum);
 	IvfflatInitRegisterPage(index, &buf, &page, &state);
@@ -522,7 +516,7 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 		/* Load list */
 		list->startPage = InvalidBlockNumber;
 		list->insertPage = InvalidBlockNumber;
-		memcpy(&list->center, VectorArrayGet(centers, i), VECTOR_SIZE(dimensions));
+		memcpy(&list->center, VectorArrayGet(centers, i), centers->itemsize);
 
 		/* Ensure free space */
 		if (PageGetFreeSpace(page) < listSize)
@@ -543,10 +537,10 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	pfree(list);
 }
 
+#ifdef IVFFLAT_KMEANS_DEBUG
 /*
  * Print k-means metrics
  */
-#ifdef IVFFLAT_KMEANS_DEBUG
 static void
 PrintKmeansMetrics(IvfflatBuildState * buildstate)
 {
@@ -627,15 +621,11 @@ ParallelHeapScan(IvfflatBuildState * buildstate)
  * Perform a worker's portion of a parallel sort
  */
 static void
-IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, Sharedsort *sharedsort, Vector * ivfcenters, int sortmem, bool progress)
+IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, Sharedsort *sharedsort, char *ivfcenters, int sortmem, bool progress)
 {
 	SortCoordinate coordinate;
 	IvfflatBuildState buildstate;
-#if PG_VERSION_NUM >= 120000
 	TableScanDesc scan;
-#else
-	HeapScanDesc scan;
-#endif
 	double		reltuples;
 	IndexInfo  *indexInfo;
 
@@ -655,22 +645,15 @@ IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, S
 	indexInfo = BuildIndexInfo(ivfspool->index);
 	indexInfo->ii_Concurrent = ivfshared->isconcurrent;
 	InitBuildState(&buildstate, ivfspool->heap, ivfspool->index, indexInfo);
-	memcpy(buildstate.centers->items, ivfcenters, VECTOR_SIZE(buildstate.centers->dim) * buildstate.centers->maxlen);
+	memcpy(buildstate.centers->items, ivfcenters, buildstate.centers->itemsize * buildstate.centers->maxlen);
 	buildstate.centers->length = buildstate.centers->maxlen;
 	ivfspool->sortstate = tuplesort_begin_heap(buildstate.tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, sortmem, coordinate, false);
 	buildstate.sortstate = ivfspool->sortstate;
-#if PG_VERSION_NUM >= 120000
 	scan = table_beginscan_parallel(ivfspool->heap,
 									ParallelTableScanFromIvfflatShared(ivfshared));
 	reltuples = table_index_build_scan(ivfspool->heap, ivfspool->index, indexInfo,
 									   true, progress, BuildCallback,
 									   (void *) &buildstate, scan);
-#else
-	scan = heap_beginscan_parallel(ivfspool->heap, &ivfshared->heapdesc);
-	reltuples = IndexBuildHeapScan(ivfspool->heap, ivfspool->index, indexInfo,
-								   true, BuildCallback,
-								   (void *) &buildstate, scan);
-#endif
 
 	/* Execute this worker's part of the sort */
 	tuplesort_performsort(ivfspool->sortstate);
@@ -710,7 +693,7 @@ IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc)
 	IvfflatSpool *ivfspool;
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 	Relation	heapRel;
 	Relation	indexRel;
 	LOCKMODE	heapLockmode;
@@ -740,11 +723,7 @@ IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc)
 	}
 
 	/* Open relations within worker */
-#if PG_VERSION_NUM >= 120000
 	heapRel = table_open(ivfshared->heaprelid, heapLockmode);
-#else
-	heapRel = heap_open(ivfshared->heaprelid, heapLockmode);
-#endif
 	indexRel = index_open(ivfshared->indexrelid, indexLockmode);
 
 	/* Initialize worker's own spool */
@@ -764,11 +743,7 @@ IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc)
 
 	/* Close relations within worker */
 	index_close(indexRel, indexLockmode);
-#if PG_VERSION_NUM >= 120000
 	table_close(heapRel, heapLockmode);
-#else
-	heap_close(heapRel, heapLockmode);
-#endif
 }
 
 /*
@@ -793,19 +768,7 @@ IvfflatEndParallel(IvfflatLeader * ivfleader)
 static Size
 ParallelEstimateShared(Relation heap, Snapshot snapshot)
 {
-#if PG_VERSION_NUM >= 120000
 	return add_size(BUFFERALIGN(sizeof(IvfflatShared)), table_parallelscan_estimate(heap, snapshot));
-#else
-	if (!IsMVCCSnapshot(snapshot))
-	{
-		Assert(snapshot == SnapshotAny);
-		return sizeof(IvfflatShared);
-	}
-
-	return add_size(offsetof(IvfflatShared, heapdesc) +
-					offsetof(ParallelHeapScanDescData, phs_snapshot_data),
-					EstimateSnapshotSpace(snapshot));
-#endif
 }
 
 /*
@@ -844,7 +807,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	Size		estcenters;
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 	IvfflatLeader *ivfleader = (IvfflatLeader *) palloc0(sizeof(IvfflatLeader));
 	bool		leaderparticipates = true;
 	int			querylen;
@@ -856,11 +819,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	/* Enter parallel mode and create context */
 	EnterParallelMode();
 	Assert(request > 0);
-#if PG_VERSION_NUM >= 120000
 	pcxt = CreateParallelContext("vector", "IvfflatParallelBuildMain", request);
-#else
-	pcxt = CreateParallelContext("vector", "IvfflatParallelBuildMain", request, true);
-#endif
 
 	scantuplesortstates = leaderparticipates ? request + 1 : request;
 
@@ -875,7 +834,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	shm_toc_estimate_chunk(&pcxt->estimator, estivfshared);
 	estsort = tuplesort_estimate_shared(scantuplesortstates);
 	shm_toc_estimate_chunk(&pcxt->estimator, estsort);
-	estcenters = VECTOR_SIZE(buildstate->dimensions) * buildstate->lists;
+	estcenters = buildstate->centers->itemsize * buildstate->centers->maxlen;
 	shm_toc_estimate_chunk(&pcxt->estimator, estcenters);
 	shm_toc_estimate_keys(&pcxt->estimator, 3);
 
@@ -918,20 +877,16 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 #ifdef IVFFLAT_KMEANS_DEBUG
 	ivfshared->inertia = 0;
 #endif
-#if PG_VERSION_NUM >= 120000
 	table_parallelscan_initialize(buildstate->heap,
 								  ParallelTableScanFromIvfflatShared(ivfshared),
 								  snapshot);
-#else
-	heap_parallelscan_initialize(&ivfshared->heapdesc, buildstate->heap, snapshot);
-#endif
 
 	/* Store shared tuplesort-private state, for which we reserved space */
 	sharedsort = (Sharedsort *) shm_toc_allocate(pcxt->toc, estsort);
 	tuplesort_initialize_shared(sharedsort, scantuplesortstates,
 								pcxt->seg);
 
-	ivfcenters = (Vector *) shm_toc_allocate(pcxt->toc, estcenters);
+	ivfcenters = shm_toc_allocate(pcxt->toc, estcenters);
 	memcpy(ivfcenters, buildstate->centers->items, estcenters);
 
 	shm_toc_insert(pcxt->toc, PARALLEL_KEY_IVFFLAT_SHARED, ivfshared);
@@ -995,7 +950,7 @@ AssignTuples(IvfflatBuildState * buildstate)
 	Oid			sortCollations[] = {InvalidOid};
 	bool		nullsFirstFlags[] = {false};
 
-	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_ASSIGN);
+	pgstat_progress_update_param(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_ASSIGN);
 
 	/* Calculate parallel workers */
 	if (buildstate->heap != NULL)
@@ -1023,15 +978,8 @@ AssignTuples(IvfflatBuildState * buildstate)
 		if (buildstate->ivfleader)
 			buildstate->reltuples = ParallelHeapScan(buildstate);
 		else
-		{
-#if PG_VERSION_NUM >= 120000
 			buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
 														   true, true, BuildCallback, (void *) buildstate, NULL);
-#else
-			buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-													   true, BuildCallback, (void *) buildstate, NULL);
-#endif
-		}
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 		PrintKmeansMetrics(buildstate);

src/ivfflat.c

@@ -3,14 +3,16 @@
 #include <float.h>
 
 #include "access/amapi.h"
+#include "access/reloptions.h"
+#include "commands/progress.h"
 #include "commands/vacuum.h"
 #include "ivfflat.h"
 #include "utils/guc.h"
 #include "utils/selfuncs.h"
 #include "utils/spccache.h"
 
-#if PG_VERSION_NUM >= 120000
-#include "commands/progress.h"
+#if PG_VERSION_NUM < 150000
+#define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
 #endif
 
 int			ivfflat_probes;
@@ -33,12 +35,13 @@ IvfflatInit(void)
 	DefineCustomIntVariable("ivfflat.probes", "Sets the number of probes",
 							"Valid range is 1..lists.", &ivfflat_probes,
 							IVFFLAT_DEFAULT_PROBES, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
+
+	MarkGUCPrefixReserved("ivfflat");
 }
 
 /*
  * Get the name of index build phase
  */
-#if PG_VERSION_NUM >= 120000
 static char *
 ivfflatbuildphasename(int64 phasenum)
 {
@@ -56,7 +59,6 @@ ivfflatbuildphasename(int64 phasenum)
 			return NULL;
 	}
 }
-#endif
 
 /*
  * Estimate the cost of an index scan
@@ -72,9 +74,6 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	double		ratio;
 	double		spc_seq_page_cost;
 	Relation	index;
-#if PG_VERSION_NUM < 120000
-	List	   *qinfos;
-#endif
 
 	/* Never use index without order */
 	if (path->indexorderbys == NULL)
@@ -105,12 +104,7 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	 */
 	costs.numIndexTuples = path->indexinfo->tuples * ratio;
 
-#if PG_VERSION_NUM >= 120000
 	genericcostestimate(root, path, loop_count, &costs);
-#else
-	qinfos = deconstruct_indexquals(path);
-	genericcostestimate(root, path, loop_count, qinfos, &costs);
-#endif
 
 	get_tablespace_page_costs(path->indexinfo->reltablespace, NULL, &spc_seq_page_cost);
 
@@ -227,9 +221,7 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	amroutine->amcostestimate = ivfflatcostestimate;
 	amroutine->amoptions = ivfflatoptions;
 	amroutine->amproperty = NULL;	/* TODO AMPROP_DISTANCE_ORDERABLE */
-#if PG_VERSION_NUM >= 120000
 	amroutine->ambuildphasename = ivfflatbuildphasename;
-#endif
 	amroutine->amvalidate = ivfflatvalidate;
 #if PG_VERSION_NUM >= 140000
 	amroutine->amadjustmembers = NULL;

src/ivfflat.h

@@ -3,9 +3,10 @@
 
 #include "postgres.h"
 
+#include "access/genam.h"
 #include "access/generic_xlog.h"
 #include "access/parallel.h"
-#include "access/reloptions.h"
+#include "lib/pairingheap.h"
 #include "nodes/execnodes.h"
 #include "port.h"				/* for random() */
 #include "utils/sampling.h"
@@ -16,10 +17,6 @@
 #include "common/pg_prng.h"
 #endif
 
-#if PG_VERSION_NUM < 120000
-#include "access/relscan.h"
-#endif
-
 #ifdef IVFFLAT_BENCH
 #include "portability/instr_time.h"
 #endif
@@ -46,13 +43,19 @@
 #define IVFFLAT_MAX_LISTS		32768
 #define IVFFLAT_DEFAULT_PROBES	1
 
+typedef enum IvfflatType
+{
+	IVFFLAT_TYPE_VECTOR,
+	IVFFLAT_TYPE_HALFVEC
+}			IvfflatType;
+
 /* Build phases */
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
 #define PROGRESS_IVFFLAT_PHASE_KMEANS	2
 #define PROGRESS_IVFFLAT_PHASE_ASSIGN	3
 #define PROGRESS_IVFFLAT_PHASE_LOAD		4
 
-#define IVFFLAT_LIST_SIZE(_dim)	(offsetof(IvfflatListData, center) + VECTOR_SIZE(_dim))
+#define IVFFLAT_LIST_SIZE(size)	(offsetof(IvfflatListData, center) + size)
 
 #define IvfflatPageGetOpaque(page)	((IvfflatPageOpaque) PageGetSpecialPointer(page))
 #define IvfflatPageGetMeta(page)	((IvfflatMetaPageData *) PageGetContents(page))
@@ -88,7 +91,8 @@ typedef struct VectorArrayData
 	int			length;
 	int			maxlen;
 	int			dim;
-	Vector	   *items;
+	Size		itemsize;
+	char	   *items;
 }			VectorArrayData;
 
 typedef VectorArrayData * VectorArray;
@@ -135,16 +139,10 @@ typedef struct IvfflatShared
 #ifdef IVFFLAT_KMEANS_DEBUG
 	double		inertia;
 #endif
-
-#if PG_VERSION_NUM < 120000
-	ParallelHeapScanDescData heapdesc;	/* must come last */
-#endif
 }			IvfflatShared;
 
-#if PG_VERSION_NUM >= 120000
 #define ParallelTableScanFromIvfflatShared(shared) \
 	(ParallelTableScanDesc) ((char *) (shared) + BUFFERALIGN(sizeof(IvfflatShared)))
-#endif
 
 typedef struct IvfflatLeader
 {
@@ -153,7 +151,7 @@ typedef struct IvfflatLeader
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
 	Snapshot	snapshot;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 }			IvfflatLeader;
 
 typedef struct IvfflatBuildState
@@ -162,6 +160,7 @@ typedef struct IvfflatBuildState
 	Relation	heap;
 	Relation	index;
 	IndexInfo  *indexInfo;
+	IvfflatType type;
 
 	/* Settings */
 	int			dimensions;
@@ -181,7 +180,6 @@ typedef struct IvfflatBuildState
 	VectorArray samples;
 	VectorArray centers;
 	ListInfo   *listInfo;
-	Vector	   *normvec;
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	double		inertia;
@@ -265,18 +263,18 @@ typedef struct IvfflatScanOpaqueData
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;
 
-#define VECTOR_ARRAY_SIZE(_length, _dim) (sizeof(VectorArrayData) + (_length) * VECTOR_SIZE(_dim))
-#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * VECTOR_SIZE((_arr)->dim))
-#define VectorArrayGet(_arr, _offset) ((Vector *) VECTOR_ARRAY_OFFSET(_arr, _offset))
-#define VectorArraySet(_arr, _offset, _val) memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, VECTOR_SIZE((_arr)->dim))
+#define VECTOR_ARRAY_SIZE(_length, _size) (sizeof(VectorArrayData) + (_length) * _size)
+#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * (_arr)->itemsize)
+#define VectorArrayGet(_arr, _offset) VECTOR_ARRAY_OFFSET(_arr, _offset)
+#define VectorArraySet(_arr, _offset, _val) memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, (_arr)->itemsize)
 
 /* Methods */
-VectorArray VectorArrayInit(int maxlen, int dimensions);
+VectorArray VectorArrayInit(int maxlen, int dimensions, Size itemsize);
 void		VectorArrayFree(VectorArray arr);
-void		PrintVectorArray(char *msg, VectorArray arr);
-void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
+void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatType type);
 FmgrInfo   *IvfflatOptionalProcInfo(Relation index, uint16 procnum);
-bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+IvfflatType IvfflatGetType(Relation index);
+bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, IvfflatType type);
 int			IvfflatGetLists(Relation index);
 void		IvfflatGetMetaPageInfo(Relation index, int *lists, int *dimensions);
 void		IvfflatUpdateList(Relation index, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);

src/ivfinsert.c

@@ -2,6 +2,7 @@
 
 #include <float.h>
 
+#include "access/generic_xlog.h"
 #include "ivfflat.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
@@ -84,7 +85,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(normprocinfo, index->rd_indcollation[0], &value, NULL))
+		if (!IvfflatNormValue(normprocinfo, index->rd_indcollation[0], &value, IvfflatGetType(index)))
 			return;
 	}
 

src/ivfkmeans.c

@@ -3,8 +3,13 @@
 #include <float.h>
 #include <math.h>
 
+#include "halfutils.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
+#include "utils/datum.h"
+#include "utils/memutils.h"
+#include "vector.h"
 
 /*
  * Initialize with kmeans++
@@ -42,12 +47,12 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 
 		for (j = 0; j < numSamples; j++)
 		{
-			Vector	   *vec = VectorArrayGet(samples, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, j));
 			double		distance;
 
 			/* Only need to compute distance for new center */
 			/* TODO Use triangle inequality to reduce distance calculations */
-			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, i))));
+			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, i))));
 
 			/* Set lower bound */
 			lowerBound[j * numCenters + i] = distance;
@@ -85,15 +90,29 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
  * Apply norm to vector
  */
 static inline void
-ApplyNorm(FmgrInfo *normprocinfo, Oid collation, Vector * vec)
+ApplyNorm(FmgrInfo *normprocinfo, Oid collation, Datum value, IvfflatType type)
 {
-	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(vec)));
+	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, value));
 
 	/* TODO Handle zero norm */
 	if (norm > 0)
 	{
-		for (int i = 0; i < vec->dim; i++)
-			vec->x[i] /= norm;
+		if (type == IVFFLAT_TYPE_VECTOR)
+		{
+			Vector	   *vec = DatumGetVector(value);
+
+			for (int i = 0; i < vec->dim; i++)
+				vec->x[i] /= norm;
+		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *vec = DatumGetHalfVector(value);
+
+			for (int i = 0; i < vec->dim; i++)
+				vec->x[i] = Float4ToHalfUnchecked(HalfToFloat4(vec->x[i]) / norm);
+		}
+		else
+			elog(ERROR, "Unsupported type");
 	}
 }
 
@@ -106,11 +125,20 @@ CompareVectors(const void *a, const void *b)
 	return vector_cmp_internal((Vector *) a, (Vector *) b);
 }
 
+/*
+ * Compare half vectors
+ */
+static int
+CompareHalfVectors(const void *a, const void *b)
+{
+	return halfvec_cmp_internal((HalfVector *) a, (HalfVector *) b);
+}
+
 /*
  * Quick approach if we have little data
  */
 static void
-QuickCenters(Relation index, VectorArray samples, VectorArray centers)
+QuickCenters(Relation index, VectorArray samples, VectorArray centers, IvfflatType type)
 {
 	int			dimensions = centers->dim;
 	Oid			collation = index->rd_indcollation[0];
@@ -119,14 +147,20 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	/* Copy existing vectors while avoiding duplicates */
 	if (samples->length > 0)
 	{
-		qsort(samples->items, samples->length, VECTOR_SIZE(samples->dim), CompareVectors);
+		if (type == IVFFLAT_TYPE_VECTOR)
+			qsort(samples->items, samples->length, samples->itemsize, CompareVectors);
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+			qsort(samples->items, samples->length, samples->itemsize, CompareHalfVectors);
+		else
+			elog(ERROR, "Unsupported type");
+
 		for (int i = 0; i < samples->length; i++)
 		{
-			Vector	   *vec = VectorArrayGet(samples, i);
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, i));
 
-			if (i == 0 || CompareVectors(vec, VectorArrayGet(samples, i - 1)) != 0)
+			if (i == 0 || !datumIsEqual(vec, PointerGetDatum(VectorArrayGet(samples, i - 1)), false, -1))
 			{
-				VectorArraySet(centers, centers->length, vec);
+				VectorArraySet(centers, centers->length, DatumGetPointer(vec));
 				centers->length++;
 			}
 		}
@@ -135,22 +169,158 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	/* Fill remaining with random data */
 	while (centers->length < centers->maxlen)
 	{
-		Vector	   *vec = VectorArrayGet(centers, centers->length);
+		Datum		center = PointerGetDatum(VectorArrayGet(centers, centers->length));
 
-		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
-		vec->dim = dimensions;
+		if (type == IVFFLAT_TYPE_VECTOR)
+		{
+			Vector	   *vec = DatumGetVector(center);
 
-		for (int j = 0; j < dimensions; j++)
-			vec->x[j] = RandomDouble();
+			SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
+			vec->dim = dimensions;
+
+			for (int j = 0; j < dimensions; j++)
+				vec->x[j] = RandomDouble();
+		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *vec = DatumGetHalfVector(center);
+
+			SET_VARSIZE(vec, HALFVEC_SIZE(dimensions));
+			vec->dim = dimensions;
+
+			for (int j = 0; j < dimensions; j++)
+				vec->x[j] = Float4ToHalfUnchecked((float) RandomDouble());
+		}
+		else
+			elog(ERROR, "Unsupported type");
 
 		/* Normalize if needed (only needed for random centers) */
 		if (normprocinfo != NULL)
-			ApplyNorm(normprocinfo, collation, vec);
+			ApplyNorm(normprocinfo, collation, center, type);
 
 		centers->length++;
 	}
 }
 
+#ifdef IVFFLAT_MEMORY
+/*
+ * Show memory usage
+ */
+static void
+ShowMemoryUsage(MemoryContext context, Size estimatedSize)
+{
+#if PG_VERSION_NUM >= 130000
+	elog(INFO, "total memory: %zu MB",
+		 MemoryContextMemAllocated(context, true) / (1024 * 1024));
+#else
+	MemoryContextStats(context);
+#endif
+	elog(INFO, "estimated memory: %zu MB", estimatedSize / (1024 * 1024));
+}
+#endif
+
+/*
+ * Compute new centers
+ */
+static void
+ComputeNewCenters(VectorArray samples, VectorArray aggCenters, VectorArray newCenters, int *centerCounts, int *closestCenters, FmgrInfo *normprocinfo, Oid collation, IvfflatType type)
+{
+	int			dimensions = aggCenters->dim;
+	int			numCenters = aggCenters->maxlen;
+	int			numSamples = samples->length;
+
+	/* Reset sum and count */
+	for (int j = 0; j < numCenters; j++)
+	{
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
+		for (int k = 0; k < dimensions; k++)
+			vec->x[k] = 0.0;
+
+		centerCounts[j] = 0;
+	}
+
+	/* Increment sum of closest center */
+	if (type == IVFFLAT_TYPE_VECTOR)
+	{
+		for (int j = 0; j < numSamples; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, closestCenters[j]);
+			Vector	   *vec = (Vector *) VectorArrayGet(samples, j);
+
+			for (int k = 0; k < dimensions; k++)
+				aggCenter->x[k] += vec->x[k];
+		}
+	}
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		for (int j = 0; j < numSamples; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, closestCenters[j]);
+			HalfVector *vec = (HalfVector *) VectorArrayGet(samples, j);
+
+			for (int k = 0; k < dimensions; k++)
+				aggCenter->x[k] += HalfToFloat4(vec->x[k]);
+		}
+	}
+	else
+		elog(ERROR, "Unsupported type");
+
+	/* Increment count of closest center */
+	for (int j = 0; j < numSamples; j++)
+		centerCounts[closestCenters[j]] += 1;
+
+	/* Divide sum by count */
+	for (int j = 0; j < numCenters; j++)
+	{
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
+		if (centerCounts[j] > 0)
+		{
+			/* Double avoids overflow, but requires more memory */
+			/* TODO Update bounds */
+			for (int k = 0; k < dimensions; k++)
+			{
+				if (isinf(vec->x[k]))
+					vec->x[k] = vec->x[k] > 0 ? FLT_MAX : -FLT_MAX;
+			}
+
+			for (int k = 0; k < dimensions; k++)
+				vec->x[k] /= centerCounts[j];
+		}
+		else
+		{
+			/* TODO Handle empty centers properly */
+			for (int k = 0; k < dimensions; k++)
+				vec->x[k] = RandomDouble();
+		}
+	}
+
+	/* Set new centers if different from agg centers */
+	if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		for (int j = 0; j < numCenters; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, j);
+			HalfVector *newCenter = (HalfVector *) VectorArrayGet(newCenters, j);
+
+			for (int k = 0; k < dimensions; k++)
+				newCenter->x[k] = Float4ToHalfUnchecked(aggCenter->x[k]);
+		}
+	}
+
+	/* Normalize if needed */
+	if (normprocinfo != NULL)
+	{
+		for (int j = 0; j < numCenters; j++)
+		{
+			Datum		newCenter = PointerGetDatum(VectorArrayGet(newCenters, j));
+
+			ApplyNorm(normprocinfo, collation, newCenter, type);
+		}
+	}
+}
+
 /*
  * Use Elkan for performance. This requires distance function to satisfy triangle inequality.
  *
@@ -160,19 +330,16 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
  * https://www.aaai.org/Papers/ICML/2003/ICML03-022.pdf
  */
 static void
-ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
+ElkanKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatType type)
 {
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
 	Oid			collation;
-	Vector	   *vec;
-	Vector	   *newCenter;
-	int64		j;
-	int64		k;
 	int			dimensions = centers->dim;
 	int			numCenters = centers->maxlen;
 	int			numSamples = samples->length;
 	VectorArray newCenters;
+	VectorArray aggCenters;
 	int		   *centerCounts;
 	int		   *closestCenters;
 	float	   *lowerBound;
@@ -180,11 +347,14 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	float	   *s;
 	float	   *halfcdist;
 	float	   *newcdist;
+	MemoryContext kmeansCtx;
+	MemoryContext oldCtx;
 
 	/* Calculate allocation sizes */
-	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->dim);
-	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->dim);
-	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, dimensions);
+	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->itemsize);
+	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->itemsize);
+	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, centers->itemsize);
+	Size		aggCentersSize = type == IVFFLAT_TYPE_VECTOR ? 0 : VECTOR_ARRAY_SIZE(numCenters, VECTOR_SIZE(dimensions));
 	Size		centerCountsSize = sizeof(int) * numCenters;
 	Size		closestCentersSize = sizeof(int) * numSamples;
 	Size		lowerBoundSize = sizeof(float) * numSamples * numCenters;
@@ -194,7 +364,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	Size		newcdistSize = sizeof(float) * numCenters;
 
 	/* Calculate total size */
-	Size		totalSize = samplesSize + centersSize + newCentersSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
+	Size		totalSize = samplesSize + centersSize + newCentersSize + aggCentersSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
 
 	/* Check memory requirements */
 	/* Add one to error message to ceil */
@@ -213,6 +383,12 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
 	collation = index->rd_indcollation[0];
 
+	/* Use memory context */
+	kmeansCtx = AllocSetContextCreate(CurrentMemoryContext,
+									  "Ivfflat kmeans temporary context",
+									  ALLOCSET_DEFAULT_SIZES);
+	oldCtx = MemoryContextSwitchTo(kmeansCtx);
+
 	/* Allocate space */
 	/* Use float instead of double to save memory */
 	centerCounts = palloc(centerCountsSize);
@@ -223,25 +399,50 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	halfcdist = palloc_extended(halfcdistSize, MCXT_ALLOC_HUGE);
 	newcdist = palloc(newcdistSize);
 
-	newCenters = VectorArrayInit(numCenters, dimensions);
-	for (j = 0; j < numCenters; j++)
+	aggCenters = VectorArrayInit(numCenters, dimensions, VECTOR_SIZE(dimensions));
+	for (int j = 0; j < numCenters; j++)
 	{
-		vec = VectorArrayGet(newCenters, j);
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
 		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
 		vec->dim = dimensions;
 	}
 
+	if (type == IVFFLAT_TYPE_VECTOR)
+	{
+		/* Use same centers to save memory */
+		newCenters = aggCenters;
+	}
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		newCenters = VectorArrayInit(numCenters, dimensions, centers->itemsize);
+
+		for (int j = 0; j < numCenters; j++)
+		{
+			HalfVector *vec = (HalfVector *) VectorArrayGet(newCenters, j);
+
+			SET_VARSIZE(vec, HALFVEC_SIZE(dimensions));
+			vec->dim = dimensions;
+		}
+	}
+	else
+		elog(ERROR, "Unsupported type");
+
+#ifdef IVFFLAT_MEMORY
+	ShowMemoryUsage(oldCtx, totalSize);
+#endif
+
 	/* Pick initial centers */
 	InitCenters(index, samples, centers, lowerBound);
 
 	/* Assign each x to its closest initial center c(x) = argmin d(x,c) */
-	for (j = 0; j < numSamples; j++)
+	for (int64 j = 0; j < numSamples; j++)
 	{
 		float		minDistance = FLT_MAX;
 		int			closestCenter = 0;
 
 		/* Find closest center */
-		for (k = 0; k < numCenters; k++)
+		for (int64 k = 0; k < numCenters; k++)
 		{
 			/* TODO Use Lemma 1 in k-means++ initialization */
 			float		distance = lowerBound[j * numCenters + k];
@@ -267,13 +468,13 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		CHECK_FOR_INTERRUPTS();
 
 		/* Step 1: For all centers, compute distance */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
-			vec = VectorArrayGet(centers, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(centers, j));
 
-			for (k = j + 1; k < numCenters; k++)
+			for (int64 k = j + 1; k < numCenters; k++)
 			{
-				float		distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
+				float		distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, k))));
 
 				halfcdist[j * numCenters + k] = distance;
 				halfcdist[k * numCenters + j] = distance;
@@ -281,11 +482,11 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		}
 
 		/* For all centers c, compute s(c) */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
 			float		minDistance = FLT_MAX;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
 				float		distance;
 
@@ -302,7 +503,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 		rjreset = iteration != 0;
 
-		for (j = 0; j < numSamples; j++)
+		for (int64 j = 0; j < numSamples; j++)
 		{
 			bool		rj;
 
@@ -312,8 +513,9 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 			rj = rjreset;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
+				Datum		vec;
 				float		dxcx;
 
 				/* Step 3: For all remaining points x and centers c */
@@ -326,12 +528,12 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 				if (upperBound[j] <= halfcdist[closestCenters[j] * numCenters + k])
 					continue;
 
-				vec = VectorArrayGet(samples, j);
+				vec = PointerGetDatum(VectorArrayGet(samples, j));
 
 				/* Step 3a */
 				if (rj)
 				{
-					dxcx = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, closestCenters[j]))));
+					dxcx = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, closestCenters[j]))));
 
 					/* d(x,c(x)) computed, which is a form of d(x,c) */
 					lowerBound[j * numCenters + closestCenters[j]] = dxcx;
@@ -345,7 +547,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 				/* Step 3b */
 				if (dxcx > lowerBound[j * numCenters + k] || dxcx > halfcdist[closestCenters[j] * numCenters + k])
 				{
-					float		dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
+					float		dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, k))));
 
 					/* d(x,c) calculated */
 					lowerBound[j * numCenters + k] = dxc;
@@ -364,66 +566,15 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		}
 
 		/* Step 4: For each center c, let m(c) be mean of all points assigned */
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-			for (k = 0; k < dimensions; k++)
-				vec->x[k] = 0.0;
-
-			centerCounts[j] = 0;
-		}
-
-		for (j = 0; j < numSamples; j++)
-		{
-			int			closestCenter;
-
-			vec = VectorArrayGet(samples, j);
-			closestCenter = closestCenters[j];
-
-			/* Increment sum and count of closest center */
-			newCenter = VectorArrayGet(newCenters, closestCenter);
-			for (k = 0; k < dimensions; k++)
-				newCenter->x[k] += vec->x[k];
-
-			centerCounts[closestCenter] += 1;
-		}
-
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-
-			if (centerCounts[j] > 0)
-			{
-				/* Double avoids overflow, but requires more memory */
-				/* TODO Update bounds */
-				for (k = 0; k < dimensions; k++)
-				{
-					if (isinf(vec->x[k]))
-						vec->x[k] = vec->x[k] > 0 ? FLT_MAX : -FLT_MAX;
-				}
-
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] /= centerCounts[j];
-			}
-			else
-			{
-				/* TODO Handle empty centers properly */
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] = RandomDouble();
-			}
-
-			/* Normalize if needed */
-			if (normprocinfo != NULL)
-				ApplyNorm(normprocinfo, collation, vec);
-		}
+		ComputeNewCenters(samples, aggCenters, newCenters, centerCounts, closestCenters, normprocinfo, collation, type);
 
 		/* Step 5 */
-		for (j = 0; j < numCenters; j++)
+		for (int j = 0; j < numCenters; j++)
 			newcdist[j] = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(VectorArrayGet(centers, j)), PointerGetDatum(VectorArrayGet(newCenters, j))));
 
-		for (j = 0; j < numSamples; j++)
+		for (int64 j = 0; j < numSamples; j++)
 		{
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
 				float		distance = lowerBound[j * numCenters + k] - newcdist[k];
 
@@ -436,32 +587,26 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 		/* Step 6 */
 		/* We reset r(x) before Step 3 in the next iteration */
-		for (j = 0; j < numSamples; j++)
+		for (int j = 0; j < numSamples; j++)
 			upperBound[j] += newcdist[closestCenters[j]];
 
 		/* Step 7 */
-		for (j = 0; j < numCenters; j++)
+		for (int j = 0; j < numCenters; j++)
 			VectorArraySet(centers, j, VectorArrayGet(newCenters, j));
 
 		if (changes == 0 && iteration != 0)
 			break;
 	}
 
-	VectorArrayFree(newCenters);
-	pfree(centerCounts);
-	pfree(closestCenters);
-	pfree(lowerBound);
-	pfree(upperBound);
-	pfree(s);
-	pfree(halfcdist);
-	pfree(newcdist);
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(kmeansCtx);
 }
 
 /*
  * Detect issues with centers
  */
 static void
-CheckCenters(Relation index, VectorArray centers)
+CheckCenters(Relation index, VectorArray centers, IvfflatType type)
 {
 	FmgrInfo   *normprocinfo;
 
@@ -471,24 +616,48 @@ CheckCenters(Relation index, VectorArray centers)
 	/* Ensure no NaN or infinite values */
 	for (int i = 0; i < centers->length; i++)
 	{
-		Vector	   *vec = VectorArrayGet(centers, i);
-
-		for (int j = 0; j < vec->dim; j++)
+		if (type == IVFFLAT_TYPE_VECTOR)
 		{
-			if (isnan(vec->x[j]))
-				elog(ERROR, "NaN detected. Please report a bug.");
+			Vector	   *vec = (Vector *) VectorArrayGet(centers, i);
 
-			if (isinf(vec->x[j]))
-				elog(ERROR, "Infinite value detected. Please report a bug.");
+			for (int j = 0; j < vec->dim; j++)
+			{
+				if (isnan(vec->x[j]))
+					elog(ERROR, "NaN detected. Please report a bug.");
+
+				if (isinf(vec->x[j]))
+					elog(ERROR, "Infinite value detected. Please report a bug.");
+			}
 		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *vec = (HalfVector *) VectorArrayGet(centers, i);
+
+			for (int j = 0; j < vec->dim; j++)
+			{
+				if (HalfIsNan(vec->x[j]))
+					elog(ERROR, "NaN detected. Please report a bug.");
+
+				if (HalfIsInf(vec->x[j]))
+					elog(ERROR, "Infinite value detected. Please report a bug.");
+			}
+		}
+		else
+			elog(ERROR, "Unsupported type");
 	}
 
 	/* Ensure no duplicate centers */
 	/* Fine to sort in-place */
-	qsort(centers->items, centers->length, VECTOR_SIZE(centers->dim), CompareVectors);
+	if (type == IVFFLAT_TYPE_VECTOR)
+		qsort(centers->items, centers->length, centers->itemsize, CompareVectors);
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+		qsort(centers->items, centers->length, centers->itemsize, CompareHalfVectors);
+	else
+		elog(ERROR, "Unsupported type");
+
 	for (int i = 1; i < centers->length; i++)
 	{
-		if (CompareVectors(VectorArrayGet(centers, i), VectorArrayGet(centers, i - 1)) == 0)
+		if (datumIsEqual(PointerGetDatum(VectorArrayGet(centers, i)), PointerGetDatum(VectorArrayGet(centers, i - 1)), false, -1))
 			elog(ERROR, "Duplicate centers detected. Please report a bug.");
 	}
 
@@ -514,12 +683,12 @@ CheckCenters(Relation index, VectorArray centers)
  * We use spherical k-means for inner product and cosine
  */
 void
-IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers)
+IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatType type)
 {
 	if (samples->length <= centers->maxlen)
-		QuickCenters(index, samples, centers);
+		QuickCenters(index, samples, centers, type);
 	else
-		ElkanKmeans(index, samples, centers);
+		ElkanKmeans(index, samples, centers, type);
 
-	CheckCenters(index, centers);
+	CheckCenters(index, centers, type);
 }

src/ivfscan.c

@@ -5,6 +5,8 @@
 #include "access/relscan.h"
 #include "catalog/pg_operator_d.h"
 #include "catalog/pg_type_d.h"
+#include "halfvec.h"
+#include "lib/pairingheap.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
 #include "pgstat.h"
@@ -105,12 +107,7 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 	TupleDesc	tupdesc = RelationGetDescr(scan->indexRelation);
 	double		tuples = 0;
-
-#if PG_VERSION_NUM >= 120000
 	TupleTableSlot *slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsVirtual);
-#else
-	TupleTableSlot *slot = MakeSingleTupleTableSlot(so->tupdesc);
-#endif
 
 	/*
 	 * Reuse same set of shared buffers for scan
@@ -181,6 +178,42 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	tuplesort_performsort(so->sortstate);
 }
 
+/*
+ * Get scan value
+ */
+static Datum
+GetScanValue(IndexScanDesc scan)
+{
+	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
+	Datum		value;
+
+	if (scan->orderByData->sk_flags & SK_ISNULL)
+	{
+		IvfflatType type = IvfflatGetType(scan->indexRelation);
+
+		if (type == IVFFLAT_TYPE_VECTOR)
+			value = PointerGetDatum(InitVector(so->dimensions));
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+			value = PointerGetDatum(InitHalfVector(so->dimensions));
+		else
+			elog(ERROR, "Unsupported type");
+	}
+	else
+	{
+		value = scan->orderByData->sk_argument;
+
+		/* Value should not be compressed or toasted */
+		Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
+		Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
+
+		/* Fine if normalization fails */
+		if (so->normprocinfo != NULL)
+			IvfflatNormValue(so->normprocinfo, so->collation, &value, IvfflatGetType(scan->indexRelation));
+	}
+
+	return value;
+}
+
 /*
  * Prepare for an index scan
  */
@@ -216,22 +249,14 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	so->collation = index->rd_indcollation[0];
 
 	/* Create tuple description for sorting */
-#if PG_VERSION_NUM >= 120000
 	so->tupdesc = CreateTemplateTupleDesc(2);
-#else
-	so->tupdesc = CreateTemplateTupleDesc(2, false);
-#endif
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "heaptid", TIDOID, -1, 0);
 
 	/* Prep sort */
 	so->sortstate = tuplesort_begin_heap(so->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, work_mem, NULL, false);
 
-#if PG_VERSION_NUM >= 120000
 	so->slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsMinimalTuple);
-#else
-	so->slot = MakeSingleTupleTableSlot(so->tupdesc);
-#endif
 
 	so->listQueue = pairingheap_allocate(CompareLists, scan);
 
@@ -293,21 +318,7 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (!IsMVCCSnapshot(scan->xs_snapshot))
 			elog(ERROR, "non-MVCC snapshots are not supported with ivfflat");
 
-		if (scan->orderByData->sk_flags & SK_ISNULL)
-			value = PointerGetDatum(InitVector(so->dimensions));
-		else
-		{
-			value = scan->orderByData->sk_argument;
-
-			/* Value should not be compressed or toasted */
-			Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
-			Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
-
-			/* Fine if normalization fails */
-			if (so->normprocinfo != NULL)
-				IvfflatNormValue(so->normprocinfo, so->collation, &value, NULL);
-		}
-
+		value = GetScanValue(scan);
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
 		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;
@@ -321,12 +332,8 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 	{
 		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->slot, 2, &so->isnull));
 
-#if PG_VERSION_NUM >= 120000
 		scan->xs_heaptid = *heaptid;
-#else
-		scan->xs_ctup.t_self = *heaptid;
-#endif
-
+		scan->xs_recheck = false;
 		scan->xs_recheckorderby = false;
 		return true;
 	}

src/ivfutils.c

@@ -1,21 +1,27 @@
 #include "postgres.h"
 
+#include "access/generic_xlog.h"
+#include "catalog/pg_type.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "storage/bufmgr.h"
 #include "vector.h"
+#include "utils/syscache.h"
 
 /*
  * Allocate a vector array
  */
 VectorArray
-VectorArrayInit(int maxlen, int dimensions)
+VectorArrayInit(int maxlen, int dimensions, Size itemsize)
 {
 	VectorArray res = palloc(sizeof(VectorArrayData));
 
 	res->length = 0;
 	res->maxlen = maxlen;
 	res->dim = dimensions;
-	res->items = palloc_extended(maxlen * VECTOR_SIZE(dimensions), MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
+	res->itemsize = itemsize;
+	res->items = palloc_extended(maxlen * itemsize, MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
 	return res;
 }
 
@@ -29,16 +35,6 @@ VectorArrayFree(VectorArray arr)
 	pfree(arr);
 }
 
-/*
- * Print vector array - useful for debugging
- */
-void
-PrintVectorArray(char *msg, VectorArray arr)
-{
-	for (int i = 0; i < arr->length; i++)
-		PrintVector(msg, VectorArrayGet(arr, i));
-}
-
 /*
  * Get the number of lists in the index
  */
@@ -65,6 +61,37 @@ IvfflatOptionalProcInfo(Relation index, uint16 procnum)
 	return index_getprocinfo(index, 1, procnum);
 }
 
+/*
+ * Get type
+ */
+IvfflatType
+IvfflatGetType(Relation index)
+{
+	Oid			typid = TupleDescAttr(index->rd_att, 0)->atttypid;
+	HeapTuple	tuple;
+	Form_pg_type type;
+	IvfflatType result;
+
+	tuple = SearchSysCache1(TYPEOID, ObjectIdGetDatum(typid));
+	if (!HeapTupleIsValid(tuple))
+		elog(ERROR, "cache lookup failed for type %u", typid);
+
+	type = (Form_pg_type) GETSTRUCT(tuple);
+	if (strcmp(NameStr(type->typname), "vector") == 0)
+		result = IVFFLAT_TYPE_VECTOR;
+	else if (strcmp(NameStr(type->typname), "halfvec") == 0)
+		result = IVFFLAT_TYPE_HALFVEC;
+	else
+	{
+		ReleaseSysCache(tuple);
+		elog(ERROR, "type not supported for ivfflat index");
+	}
+
+	ReleaseSysCache(tuple);
+
+	return result;
+}
+
 /*
  * Divide by the norm
  *
@@ -74,21 +101,34 @@ IvfflatOptionalProcInfo(Relation index, uint16 procnum)
  * if it's different than the original value
  */
 bool
-IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result)
+IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, IvfflatType type)
 {
 	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
 
 	if (norm > 0)
 	{
-		Vector	   *v = DatumGetVector(*value);
+		if (type == IVFFLAT_TYPE_VECTOR)
+		{
+			Vector	   *v = DatumGetVector(*value);
+			Vector	   *result = InitVector(v->dim);
 
-		if (result == NULL)
-			result = InitVector(v->dim);
+			for (int i = 0; i < v->dim; i++)
+				result->x[i] = v->x[i] / norm;
 
-		for (int i = 0; i < v->dim; i++)
-			result->x[i] = v->x[i] / norm;
+			*value = PointerGetDatum(result);
+		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *v = DatumGetHalfVector(*value);
+			HalfVector *result = InitHalfVector(v->dim);
 
-		*value = PointerGetDatum(result);
+			for (int i = 0; i < v->dim; i++)
+				result->x[i] = Float4ToHalfUnchecked(HalfToFloat4(v->x[i]) / norm);
+
+			*value = PointerGetDatum(result);
+		}
+		else
+			elog(ERROR, "Unsupported type");
 
 		return true;
 	}

src/ivfvacuum.c

@@ -1,5 +1,6 @@
 #include "postgres.h"
 
+#include "access/generic_xlog.h"
 #include "commands/vacuum.h"
 #include "ivfflat.h"
 #include "storage/bufmgr.h"

src/sparsevec.c

@@ -0,0 +1,800 @@
+#include "postgres.h"
+
+#include <limits.h>
+#include <math.h>
+
+#include "fmgr.h"
+#include "libpq/pqformat.h"
+#include "sparsevec.h"
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "vector.h"
+
+#if PG_VERSION_NUM >= 120000
+#include "common/shortest_dec.h"
+#include "utils/float.h"
+#else
+#include <float.h>
+#include "utils/builtins.h"
+#endif
+
+/*
+ * Ensure same dimensions
+ */
+static inline void
+CheckDims(SparseVector * a, SparseVector * b)
+{
+	if (a->dim != b->dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different sparsevec dimensions %d and %d", a->dim, b->dim)));
+}
+
+/*
+ * Ensure expected dimensions
+ */
+static inline void
+CheckExpectedDim(int32 typmod, int dim)
+{
+	if (typmod != -1 && typmod != dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected %d dimensions, not %d", typmod, dim)));
+}
+
+/*
+ * Ensure valid dimensions
+ */
+static inline void
+CheckDim(int dim)
+{
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("sparsevec must have at least 1 dimension")));
+
+	if (dim > SPARSEVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("sparsevec cannot have more than %d dimensions", SPARSEVEC_MAX_DIM)));
+}
+
+/*
+ * Ensure valid nnz
+ */
+static inline void
+CheckNnz(int nnz, int dim)
+{
+	if (nnz < 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("sparsevec cannot have negative number of elements")));
+
+	if (nnz > SPARSEVEC_MAX_NNZ)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("sparsevec cannot have more than %d non-zero elements", SPARSEVEC_MAX_NNZ)));
+
+	if (nnz > dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("sparsevec cannot have more elements than dimensions")));
+}
+
+/*
+ * Ensure valid index
+ */
+static inline void
+CheckIndex(int32 *indices, int i, int dim)
+{
+	int32		index = indices[i];
+
+	if (index < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("index must be greater than zero")));
+
+	if (index > dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("index must be less than or equal to dimensions")));
+
+	if (i > 0)
+	{
+		if (index < indices[i - 1])
+			ereport(ERROR,
+					(errcode(ERRCODE_DATA_EXCEPTION),
+					 errmsg("indexes must be in ascending order")));
+
+		if (index == indices[i - 1])
+			ereport(ERROR,
+					(errcode(ERRCODE_DATA_EXCEPTION),
+					 errmsg("indexes must not contain duplicates")));
+	}
+}
+
+/*
+ * Ensure finite element
+ */
+static inline void
+CheckElement(float value)
+{
+	if (isnan(value))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("NaN not allowed in sparsevec")));
+
+	if (isinf(value))
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("infinite value not allowed in sparsevec")));
+}
+
+/*
+ * Allocate and initialize a new sparse vector
+ */
+SparseVector *
+InitSparseVector(int dim, int nnz)
+{
+	SparseVector *result;
+	int			size;
+
+	size = SPARSEVEC_SIZE(nnz);
+	result = (SparseVector *) palloc0(size);
+	SET_VARSIZE(result, size);
+	result->dim = dim;
+	result->nnz = nnz;
+
+	return result;
+}
+
+/*
+ * Check for whitespace, since array_isspace() is static
+ */
+static inline bool
+sparsevec_isspace(char ch)
+{
+	if (ch == ' ' ||
+		ch == '\t' ||
+		ch == '\n' ||
+		ch == '\r' ||
+		ch == '\v' ||
+		ch == '\f')
+		return true;
+	return false;
+}
+
+/*
+ * Convert textual representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_in);
+Datum
+sparsevec_in(PG_FUNCTION_ARGS)
+{
+	char	   *lit = PG_GETARG_CSTRING(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	int			dim;
+	char	   *pt = lit;
+	char	   *stringEnd;
+	SparseVector *result;
+	float	   *rvalues;
+	int32	   *indices;
+	float	   *values;
+	int			maxNnz;
+	int			nnz = 0;
+
+	maxNnz = 1;
+	while (*pt != '\0')
+	{
+		if (*pt == ',')
+			maxNnz++;
+
+		pt++;
+	}
+
+	if (maxNnz > SPARSEVEC_MAX_NNZ)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("sparsevec cannot have more than %d non-zero elements", SPARSEVEC_MAX_NNZ)));
+
+	indices = palloc(maxNnz * sizeof(int32));
+	values = palloc(maxNnz * sizeof(float));
+
+	pt = lit;
+
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '{')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
+				 errdetail("Vector contents must start with \"{\".")));
+
+	pt++;
+
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt == '}')
+		pt++;
+	else
+	{
+		for (;;)
+		{
+			long		index;
+			float		value;
+
+			/* TODO Better error */
+			if (nnz == maxNnz)
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("ran out of buffer: \"%s\"", lit)));
+
+			while (sparsevec_isspace(*pt))
+				pt++;
+
+			/* Check for empty string like float4in */
+			if (*pt == '\0')
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+
+			/* Use similar logic as int2vectorin */
+			errno = 0;
+			index = strtol(pt, &stringEnd, 10);
+
+			if (stringEnd == pt)
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+
+			if (errno == ERANGE || index < 1 || index > INT_MAX)
+				ereport(ERROR,
+						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+						 errmsg("index \"%ld\" is out of range for type sparsevec", index)));
+
+			pt = stringEnd;
+
+			while (sparsevec_isspace(*pt))
+				pt++;
+
+			if (*pt != ':')
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+
+			pt++;
+
+			while (sparsevec_isspace(*pt))
+				pt++;
+
+			errno = 0;
+
+			/* Use strtof like float4in to avoid a double-rounding problem */
+			/* Postgres sets LC_NUMERIC to C on startup */
+			value = strtof(pt, &stringEnd);
+
+			if (stringEnd == pt)
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+
+			/* Check for range error like float4in */
+			if (errno == ERANGE && (value == 0 || isinf(value)))
+				ereport(ERROR,
+						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+						 errmsg("\"%s\" is out of range for type sparsevec", pnstrdup(pt, stringEnd - pt))));
+
+			CheckElement(value);
+
+			/* Do not store zero values */
+			if (value != 0)
+			{
+				indices[nnz] = index;
+				values[nnz] = value;
+				nnz++;
+			}
+
+			pt = stringEnd;
+
+			while (sparsevec_isspace(*pt))
+				pt++;
+
+			if (*pt == ',')
+				pt++;
+			else if (*pt == '}')
+			{
+				pt++;
+				break;
+			}
+			else
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+		}
+	}
+
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '/')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
+				 errdetail("Unexpected end of input.")));
+
+	pt++;
+
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	/* Use similar logic as int2vectorin */
+	errno = 0;
+	dim = strtol(pt, &stringEnd, 10);
+
+	if (stringEnd == pt)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+
+	pt = stringEnd;
+
+	/* Only whitespace is allowed after the closing brace */
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
+				 errdetail("Junk after closing.")));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	result = InitSparseVector(dim, nnz);
+	rvalues = SPARSEVEC_VALUES(result);
+	for (int i = 0; i < nnz; i++)
+	{
+		result->indices[i] = indices[i];
+		rvalues[i] = values[i];
+
+		CheckIndex(result->indices, i, dim);
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+#define AppendChar(ptr, c) (*(ptr)++ = (c))
+#define AppendFloat(ptr, f) ((ptr) += float_to_shortest_decimal_bufn((f), (ptr)))
+
+#if PG_VERSION_NUM >= 140000
+#define AppendInt(ptr, i) ((ptr) += pg_ltoa((i), (ptr)))
+#else
+#define AppendInt(ptr, i) \
+	do { \
+		pg_ltoa(i, ptr); \
+		while (*ptr != '\0') \
+			ptr++; \
+	} while (0)
+#endif
+
+/*
+ * Convert internal representation to textual representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_out);
+Datum
+sparsevec_out(PG_FUNCTION_ARGS)
+{
+	SparseVector *sparsevec = PG_GETARG_SPARSEVEC_P(0);
+	float	   *values = SPARSEVEC_VALUES(sparsevec);
+	char	   *buf;
+	char	   *ptr;
+
+	/*
+	 * Need:
+	 *
+	 * nnz * 10 bytes for index (positive integer)
+	 *
+	 * nnz bytes for :
+	 *
+	 * nnz * (FLOAT_SHORTEST_DECIMAL_LEN - 1) bytes for
+	 * float_to_shortest_decimal_bufn
+	 *
+	 * nnz - 1 bytes for ,
+	 *
+	 * 10 bytes for dimensions
+	 *
+	 * 4 bytes for {, }, /, and \0
+	 */
+	buf = (char *) palloc((11 + FLOAT_SHORTEST_DECIMAL_LEN) * sparsevec->nnz + 13);
+	ptr = buf;
+
+	AppendChar(ptr, '{');
+
+	for (int i = 0; i < sparsevec->nnz; i++)
+	{
+		if (i > 0)
+			AppendChar(ptr, ',');
+
+		AppendInt(ptr, sparsevec->indices[i]);
+		AppendChar(ptr, ':');
+		AppendFloat(ptr, values[i]);
+	}
+
+	AppendChar(ptr, '}');
+	AppendChar(ptr, '/');
+	AppendInt(ptr, sparsevec->dim);
+	*ptr = '\0';
+
+	PG_FREE_IF_COPY(sparsevec, 0);
+	PG_RETURN_CSTRING(buf);
+}
+
+/*
+ * Convert type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_typmod_in);
+Datum
+sparsevec_typmod_in(PG_FUNCTION_ARGS)
+{
+	ArrayType  *ta = PG_GETARG_ARRAYTYPE_P(0);
+	int32	   *tl;
+	int			n;
+
+	tl = ArrayGetIntegerTypmods(ta, &n);
+
+	if (n != 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("invalid type modifier")));
+
+	if (*tl < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type sparsevec must be at least 1")));
+
+	if (*tl > SPARSEVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type sparsevec cannot exceed %d", SPARSEVEC_MAX_DIM)));
+
+	PG_RETURN_INT32(*tl);
+}
+
+/*
+ * Convert external binary representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_recv);
+Datum
+sparsevec_recv(PG_FUNCTION_ARGS)
+{
+	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	SparseVector *result;
+	int32		dim;
+	int32		nnz;
+	int32		unused;
+	float	   *values;
+
+	dim = pq_getmsgint(buf, sizeof(int32));
+	nnz = pq_getmsgint(buf, sizeof(int32));
+	unused = pq_getmsgint(buf, sizeof(int32));
+
+	CheckDim(dim);
+	CheckNnz(nnz, dim);
+	CheckExpectedDim(typmod, dim);
+
+	if (unused != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected unused to be 0, not %d", unused)));
+
+	result = InitSparseVector(dim, nnz);
+	values = SPARSEVEC_VALUES(result);
+
+	for (int i = 0; i < nnz; i++)
+	{
+		result->indices[i] = pq_getmsgint(buf, sizeof(int32));
+		CheckIndex(result->indices, i, dim);
+	}
+
+	for (int i = 0; i < nnz; i++)
+	{
+		values[i] = pq_getmsgfloat4(buf);
+		CheckElement(values[i]);
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert internal representation to the external binary representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_send);
+Datum
+sparsevec_send(PG_FUNCTION_ARGS)
+{
+	SparseVector *svec = PG_GETARG_SPARSEVEC_P(0);
+	float	   *values = SPARSEVEC_VALUES(svec);
+	StringInfoData buf;
+
+	pq_begintypsend(&buf);
+	pq_sendint(&buf, svec->dim, sizeof(int32));
+	pq_sendint(&buf, svec->nnz, sizeof(int32));
+	pq_sendint(&buf, svec->unused, sizeof(int32));
+	for (int i = 0; i < svec->nnz; i++)
+		pq_sendint(&buf, svec->indices[i], sizeof(int32));
+	for (int i = 0; i < svec->nnz; i++)
+		pq_sendfloat4(&buf, values[i]);
+
+	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
+}
+
+/*
+ * Convert sparse vector to sparse vector
+ * This is needed to check the type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec);
+Datum
+sparsevec(PG_FUNCTION_ARGS)
+{
+	SparseVector *svec = PG_GETARG_SPARSEVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+
+	CheckExpectedDim(typmod, svec->dim);
+
+	PG_RETURN_POINTER(svec);
+}
+
+/*
+ * Convert dense vector to sparse vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_to_sparsevec);
+Datum
+vector_to_sparsevec(PG_FUNCTION_ARGS)
+{
+	Vector	   *vec = PG_GETARG_VECTOR_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	SparseVector *result;
+	int			dim = vec->dim;
+	int			nnz = 0;
+	float	   *values;
+	int			j = 0;
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	for (int i = 0; i < dim; i++)
+	{
+		if (vec->x[i] != 0)
+			nnz++;
+	}
+
+	result = InitSparseVector(dim, nnz);
+	values = SPARSEVEC_VALUES(result);
+	for (int i = 0; i < dim; i++)
+	{
+		if (vec->x[i] != 0)
+		{
+			/* Safety check */
+			if (j == nnz)
+				elog(ERROR, "safety check failed");
+
+			result->indices[j] = i + 1;
+			values[j] = vec->x[i];
+			j++;
+		}
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Get the L2 squared distance between sparse vectors
+ */
+static double
+SparsevecL2SquaredDistance(SparseVector * a, SparseVector * b)
+{
+	float	   *ax = SPARSEVEC_VALUES(a);
+	float	   *bx = SPARSEVEC_VALUES(b);
+	double		distance = 0.0;
+	int			bpos = 0;
+
+	for (int i = 0; i < a->nnz; i++)
+	{
+		int			ai = a->indices[i];
+		int			bi = -1;
+
+		for (int j = bpos; j < b->nnz; j++)
+		{
+			bi = b->indices[j];
+
+			if (ai == bi)
+			{
+				double		diff = ax[i] - bx[j];
+
+				distance += diff * diff;
+			}
+			else if (ai > bi)
+				distance += bx[j] * bx[j];
+
+			/* Update start for next iteration */
+			if (ai >= bi)
+				bpos = j + 1;
+
+			/* Found or passed it */
+			if (bi >= ai)
+				break;
+		}
+
+		if (ai != bi)
+			distance += ax[i] * ax[i];
+	}
+
+	for (int j = bpos; j < b->nnz; j++)
+		distance += bx[j] * bx[j];
+
+	return distance;
+}
+
+/*
+ * Get the L2 distance between sparse vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_l2_distance);
+Datum
+sparsevec_l2_distance(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(sqrt(SparsevecL2SquaredDistance(a, b)));
+}
+
+/*
+ * Get the L2 squared distance between sparse vectors
+ * This saves a sqrt calculation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_l2_squared_distance);
+Datum
+sparsevec_l2_squared_distance(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(SparsevecL2SquaredDistance(a, b));
+}
+
+/*
+ * Get the inner product of two sparse vectors
+ */
+static double
+SparsevecInnerProduct(SparseVector * a, SparseVector * b)
+{
+	float	   *ax = SPARSEVEC_VALUES(a);
+	float	   *bx = SPARSEVEC_VALUES(b);
+	double		distance = 0.0;
+	int			bpos = 0;
+
+	for (int i = 0; i < a->nnz; i++)
+	{
+		int			ai = a->indices[i];
+
+		for (int j = bpos; j < b->nnz; j++)
+		{
+			int			bi = b->indices[j];
+
+			/* Only update when the same index */
+			if (ai == bi)
+				distance += ax[i] * bx[j];
+
+			/* Update start for next iteration */
+			if (ai >= bi)
+				bpos = j + 1;
+
+			/* Found or passed it */
+			if (bi >= ai)
+				break;
+		}
+	}
+
+	return distance;
+}
+
+/*
+ * Get the inner product of two sparse vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_inner_product);
+Datum
+sparsevec_inner_product(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(SparsevecInnerProduct(a, b));
+}
+
+/*
+ * Get the negative inner product of two sparse vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_negative_inner_product);
+Datum
+sparsevec_negative_inner_product(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(-SparsevecInnerProduct(a, b));
+}
+
+/*
+ * Get the cosine distance between two sparse vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_cosine_distance);
+Datum
+sparsevec_cosine_distance(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
+	float	   *ax = SPARSEVEC_VALUES(a);
+	float	   *bx = SPARSEVEC_VALUES(b);
+	float		norma = 0.0;
+	float		normb = 0.0;
+	double		similarity;
+
+	CheckDims(a, b);
+
+	similarity = SparsevecInnerProduct(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->nnz; i++)
+		norma += ax[i] * ax[i];
+
+	/* Auto-vectorized */
+	for (int i = 0; i < b->nnz; i++)
+		normb += bx[i] * bx[i];
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	similarity /= sqrt((double) norma * (double) normb);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	if (isnan(similarity))
+		PG_RETURN_FLOAT8(NAN);
+#endif
+
+	/* Keep in range */
+	if (similarity > 1)
+		similarity = 1.0;
+	else if (similarity < -1)
+		similarity = -1.0;
+
+	PG_RETURN_FLOAT8(1.0 - similarity);
+}
+
+/*
+ * Get the L2 norm of a sparse vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_norm);
+Datum
+sparsevec_norm(PG_FUNCTION_ARGS)
+{
+	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
+	float	   *ax = SPARSEVEC_VALUES(a);
+	double		norm = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->nnz; i++)
+		norm += (double) ax[i] * (double) ax[i];
+
+	PG_RETURN_FLOAT8(sqrt(norm));
+}

src/sparsevec.h

@@ -0,0 +1,25 @@
+#ifndef SPARSEVEC_H
+#define SPARSEVEC_H
+
+#define SPARSEVEC_MAX_DIM 100000
+#define SPARSEVEC_MAX_NNZ 16000
+
+/* Ensure values are aligned */
+#define SPARSEVEC_SIZE(_nnz)		(offsetof(SparseVector, indices) + MAXALIGN((_nnz) * sizeof(int32)) + (_nnz * sizeof(float)))
+#define SPARSEVEC_VALUES(x)		((float *) (((char *) (x)) + offsetof(SparseVector, indices) + MAXALIGN((x)->nnz * sizeof(int32))))
+#define DatumGetSparseVector(x)		((SparseVector *) PG_DETOAST_DATUM(x))
+#define PG_GETARG_SPARSEVEC_P(x)	DatumGetSparseVector(PG_GETARG_DATUM(x))
+#define PG_RETURN_SPARSEVEC_P(x)	PG_RETURN_POINTER(x)
+
+typedef struct SparseVector
+{
+	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int32		dim;			/* number of dimensions */
+	int32		nnz;
+	int32		unused;
+	int32		indices[FLEXIBLE_ARRAY_MEMBER];
+}			SparseVector;
+
+SparseVector *InitSparseVector(int dim, int nnz);
+
+#endif

src/vector.c

@@ -2,15 +2,21 @@
 
 #include <math.h>
 
+#include "bitvector.h"
 #include "catalog/pg_type.h"
+#include "common/shortest_dec.h"
 #include "fmgr.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "hnsw.h"
 #include "ivfflat.h"
 #include "lib/stringinfo.h"
 #include "libpq/pqformat.h"
 #include "port.h"				/* for strtof() */
+#include "sparsevec.h"
 #include "utils/array.h"
 #include "utils/builtins.h"
+#include "utils/float.h"
 #include "utils/lsyscache.h"
 #include "utils/numeric.h"
 #include "vector.h"
@@ -19,13 +25,6 @@
 #include "varatt.h"
 #endif
 
-#if PG_VERSION_NUM >= 120000
-#include "common/shortest_dec.h"
-#include "utils/float.h"
-#else
-#include <float.h>
-#endif
-
 #if PG_VERSION_NUM < 130000
 #define TYPALIGN_DOUBLE 'd'
 #define TYPALIGN_INT 'i'
@@ -34,6 +33,13 @@
 #define STATE_DIMS(x) (ARR_DIMS(x)[0] - 1)
 #define CreateStateDatums(dim) palloc(sizeof(Datum) * (dim + 1))
 
+/* target_clones requires glibc */
+#if defined(__x86_64__) && defined(__gnu_linux__) && defined(__has_attribute) && __has_attribute(target_clones) && !defined(__FMA__)
+#define VECTOR_DISPATCH __attribute__((target_clones("default", "fma")))
+#else
+#define VECTOR_DISPATCH
+#endif
+
 PG_MODULE_MAGIC;
 
 /*
@@ -43,6 +49,7 @@ PGDLLEXPORT void _PG_init(void);
 void
 _PG_init(void)
 {
+	HalfvecInit();
 	HnswInit();
 	IvfflatInit();
 }
@@ -89,7 +96,7 @@ CheckDim(int dim)
 }
 
 /*
- * Ensure finite elements
+ * Ensure finite element
  */
 static inline void
 CheckElement(float value)
@@ -177,30 +184,37 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_in);
 Datum
 vector_in(PG_FUNCTION_ARGS)
 {
-	char	   *str = PG_GETARG_CSTRING(0);
+	char	   *lit = PG_GETARG_CSTRING(0);
 	int32		typmod = PG_GETARG_INT32(2);
 	float		x[VECTOR_MAX_DIM];
 	int			dim = 0;
-	char	   *pt;
-	char	   *stringEnd;
+	char	   *pt = lit;
 	Vector	   *result;
-	char	   *lit = pstrdup(str);
 
-	while (vector_isspace(*str))
-		str++;
+	while (vector_isspace(*pt))
+		pt++;
 
-	if (*str != '[')
+	if (*pt != '[')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type vector: \"%s\"", lit),
 				 errdetail("Vector contents must start with \"[\".")));
 
-	str++;
-	pt = strtok(str, ",");
-	stringEnd = pt;
+	pt++;
 
-	while (pt != NULL && *stringEnd != ']')
+	while (vector_isspace(*pt))
+		pt++;
+
+	if (*pt == ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("vector must have at least 1 dimension")));
+
+	for (;;)
 	{
+		float		val;
+		char	   *stringEnd;
+
 		if (dim == VECTOR_MAX_DIM)
 			ereport(ERROR,
 					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
@@ -215,61 +229,55 @@ vector_in(PG_FUNCTION_ARGS)
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
 
+		errno = 0;
+
 		/* Use strtof like float4in to avoid a double-rounding problem */
-		x[dim] = strtof(pt, &stringEnd);
-		CheckElement(x[dim]);
-		dim++;
+		/* Postgres sets LC_NUMERIC to C on startup */
+		val = strtof(pt, &stringEnd);
 
 		if (stringEnd == pt)
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
 
-		while (vector_isspace(*stringEnd))
-			stringEnd++;
+		/* Check for range error like float4in */
+		if (errno == ERANGE && isinf(val))
+			ereport(ERROR,
+					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+					 errmsg("\"%s\" is out of range for type vector", pnstrdup(pt, stringEnd - pt))));
 
-		if (*stringEnd != '\0' && *stringEnd != ']')
+		CheckElement(val);
+		x[dim++] = val;
+
+		pt = stringEnd;
+
+		while (vector_isspace(*pt))
+			pt++;
+
+		if (*pt == ',')
+			pt++;
+		else if (*pt == ']')
+		{
+			pt++;
+			break;
+		}
+		else
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
-
-		pt = strtok(NULL, ",");
 	}
 
-	if (stringEnd == NULL || *stringEnd != ']')
-		ereport(ERROR,
-				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
-				 errdetail("Unexpected end of input.")));
-
-	stringEnd++;
-
 	/* Only whitespace is allowed after the closing brace */
-	while (vector_isspace(*stringEnd))
-		stringEnd++;
+	while (vector_isspace(*pt))
+		pt++;
 
-	if (*stringEnd != '\0')
+	if (*pt != '\0')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type vector: \"%s\"", lit),
 				 errdetail("Junk after closing right brace.")));
 
-	/* Ensure no consecutive delimiters since strtok skips */
-	for (pt = lit + 1; *pt != '\0'; pt++)
-	{
-		if (pt[-1] == ',' && *pt == ',')
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("malformed vector literal: \"%s\"", lit)));
-	}
-
-	if (dim < 1)
-		ereport(ERROR,
-				(errcode(ERRCODE_DATA_EXCEPTION),
-				 errmsg("vector must have at least 1 dimension")));
-
-	pfree(lit);
-
+	CheckDim(dim);
 	CheckExpectedDim(typmod, dim);
 
 	result = InitVector(dim);
@@ -279,6 +287,9 @@ vector_in(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+#define AppendChar(ptr, c) (*(ptr)++ = (c))
+#define AppendFloat(ptr, f) ((ptr) += float_to_shortest_decimal_bufn((f), (ptr)))
+
 /*
  * Convert internal representation to textual representation
  */
@@ -290,16 +301,6 @@ vector_out(PG_FUNCTION_ARGS)
 	int			dim = vector->dim;
 	char	   *buf;
 	char	   *ptr;
-	int			n;
-
-#if PG_VERSION_NUM < 120000
-	int			ndig = FLT_DIG + extra_float_digits;
-
-	if (ndig < 1)
-		ndig = 1;
-
-#define FLOAT_SHORTEST_DECIMAL_LEN (ndig + 10)
-#endif
 
 	/*
 	 * Need:
@@ -314,25 +315,17 @@ vector_out(PG_FUNCTION_ARGS)
 	buf = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN * dim + 2);
 	ptr = buf;
 
-	*ptr = '[';
-	ptr++;
+	AppendChar(ptr, '[');
+
 	for (int i = 0; i < dim; i++)
 	{
 		if (i > 0)
-		{
-			*ptr = ',';
-			ptr++;
-		}
+			AppendChar(ptr, ',');
 
-#if PG_VERSION_NUM >= 120000
-		n = float_to_shortest_decimal_bufn(vector->x[i], ptr);
-#else
-		n = sprintf(ptr, "%.*g", ndig, vector->x[i]);
-#endif
-		ptr += n;
+		AppendFloat(ptr, vector->x[i]);
 	}
-	*ptr = ']';
-	ptr++;
+
+	AppendChar(ptr, ']');
 	*ptr = '\0';
 
 	PG_FREE_IF_COPY(vector, 0);
@@ -437,17 +430,18 @@ 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 +458,6 @@ array_to_vector(PG_FUNCTION_ARGS)
 	bool		typbyval;
 	char		typalign;
 	Datum	   *elemsp;
-	bool	   *nullsp;
 	int			nelemsp;
 
 	if (ARR_NDIM(array) > 1)
@@ -478,7 +471,7 @@ 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 +505,12 @@ 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]);
@@ -543,6 +542,44 @@ vector_to_float4(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+/*
+ * Convert half vector to vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_to_vector);
+Datum
+halfvec_to_vector(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	Vector	   *result;
+
+	CheckDim(vec->dim);
+	CheckExpectedDim(typmod, vec->dim);
+
+	result = InitVector(vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		result->x[i] = HalfToFloat4(vec->x[i]);
+
+	PG_RETURN_POINTER(result);
+}
+
+VECTOR_DISPATCH static float
+VectorL2SquaredDistance(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		diff = ax[i] - bx[i];
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+
 /*
  * Get the L2 distance between vectors
  */
@@ -552,21 +589,10 @@ l2_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
-	float		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
-
-	PG_RETURN_FLOAT8(sqrt((double) distance));
+	PG_RETURN_FLOAT8(sqrt((double) VectorL2SquaredDistance(a->dim, a->x, b->x)));
 }
 
 /*
@@ -579,21 +605,22 @@ vector_l2_squared_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
-	float		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
+	PG_RETURN_FLOAT8((double) VectorL2SquaredDistance(a->dim, a->x, b->x));
+}
 
-	PG_RETURN_FLOAT8((double) distance);
+VECTOR_DISPATCH static float
+VectorInnerProduct(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += ax[i] * bx[i];
+
+	return distance;
 }
 
 /*
@@ -605,17 +632,10 @@ inner_product(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) VectorInnerProduct(a->dim, a->x, b->x));
 }
 
 /*
@@ -627,17 +647,10 @@ vector_negative_inner_product(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8((double) distance * -1);
+	PG_RETURN_FLOAT8((double) -VectorInnerProduct(a->dim, a->x, b->x));
 }
 
 /*
@@ -695,18 +708,11 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		dp = 0.0;
 	double		distance;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		dp += ax[i] * bx[i];
-
-	distance = (double) dp;
+	distance = (double) VectorInnerProduct(a->dim, a->x, b->x);
 
 	/* Prevent NaN with acos with loss of precision */
 	if (distance > 1)
@@ -718,7 +724,7 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 }
 
 /*
- * Get the L1 distance between vectors
+ * Get the L1 distance between two vectors
  */
 PGDLLEXPORT PG_FUNCTION_INFO_V1(l1_distance);
 Datum
@@ -871,15 +877,66 @@ vector_mul(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+/*
+ * Quantize a vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(quantize_binary);
+Datum
+quantize_binary(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	float	   *ax = a->x;
+	VarBit	   *result = InitBitVector(a->dim);
+	unsigned char *rx = VARBITS(result);
+
+	for (int i = 0; i < a->dim; i++)
+		rx[i / 8] |= (ax[i] > 0) << (7 - (i % 8));
+
+	PG_RETURN_VARBIT_P(result);
+}
+
+/*
+ * Get a subvector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(subvector);
+Datum
+subvector(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	int32		start = PG_GETARG_INT32(1);
+	int32		count = PG_GETARG_INT32(2);
+	int32		end = start + count;
+	float	   *ax = a->x;
+	Vector	   *result;
+	int			dim;
+
+	/* Indexing starts at 1, like substring */
+	if (start < 1)
+		start = 1;
+
+	if (end > a->dim)
+		end = a->dim + 1;
+
+	dim = end - start;
+	CheckDim(dim);
+	result = InitVector(dim);
+
+	for (int i = 0; i < dim; i++)
+		result->x[i] = ax[start - 1 + i];
+
+	PG_RETURN_POINTER(result);
+}
+
 /*
  * Internal helper to compare vectors
  */
 int
 vector_cmp_internal(Vector * a, Vector * b)
 {
-	CheckDims(a, b);
+	int			dim = Min(a->dim, b->dim);
 
-	for (int i = 0; i < a->dim; i++)
+	/* Check values before dimensions to be consistent with Postgres arrays */
+	for (int i = 0; i < dim; i++)
 	{
 		if (a->x[i] < b->x[i])
 			return -1;
@@ -887,6 +944,13 @@ vector_cmp_internal(Vector * a, Vector * b)
 		if (a->x[i] > b->x[i])
 			return 1;
 	}
+
+	if (a->dim < b->dim)
+		return -1;
+
+	if (a->dim > b->dim)
+		return 1;
+
 	return 0;
 }
 
@@ -897,8 +961,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_lt);
 Datum
 vector_lt(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) < 0);
 }
@@ -910,8 +974,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_le);
 Datum
 vector_le(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) <= 0);
 }
@@ -923,8 +987,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_eq);
 Datum
 vector_eq(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) == 0);
 }
@@ -936,8 +1000,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_ne);
 Datum
 vector_ne(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) != 0);
 }
@@ -949,8 +1013,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_ge);
 Datum
 vector_ge(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) >= 0);
 }
@@ -962,8 +1026,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_gt);
 Datum
 vector_gt(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) > 0);
 }
@@ -975,8 +1039,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_cmp);
 Datum
 vector_cmp(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_INT32(vector_cmp_internal(a, b));
 }
@@ -1145,3 +1209,26 @@ vector_avg(PG_FUNCTION_ARGS)
 
 	PG_RETURN_POINTER(result);
 }
+
+/*
+ * Convert sparse vector to dense vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_to_vector);
+Datum
+sparsevec_to_vector(PG_FUNCTION_ARGS)
+{
+	SparseVector *svec = PG_GETARG_SPARSEVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	Vector	   *result;
+	int			dim = svec->dim;
+	float	   *values = SPARSEVEC_VALUES(svec);
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	result = InitVector(dim);
+	for (int i = 0; i < svec->nnz; i++)
+		result->x[svec->indices[i] - 1] = values[i];
+
+	PG_RETURN_POINTER(result);
+}

test/expected/bit_functions.out

@@ -0,0 +1,104 @@
+SELECT hamming_distance('111', '111');
+ hamming_distance 
+------------------
+                0
+(1 row)
+
+SELECT hamming_distance('111', '110');
+ hamming_distance 
+------------------
+                1
+(1 row)
+
+SELECT hamming_distance('111', '100');
+ hamming_distance 
+------------------
+                2
+(1 row)
+
+SELECT hamming_distance('111', '000');
+ hamming_distance 
+------------------
+                3
+(1 row)
+
+SELECT hamming_distance('10101010101010101010', '01010101010101010101');
+ hamming_distance 
+------------------
+               20
+(1 row)
+
+SELECT hamming_distance('', '');
+ hamming_distance 
+------------------
+                0
+(1 row)
+
+SELECT hamming_distance('111', '00');
+ERROR:  different bit lengths 3 and 2
+SELECT hamming_distance('111', '000'::varbit(4));
+ hamming_distance 
+------------------
+                3
+(1 row)
+
+SELECT hamming_distance('111', '0000'::varbit(4));
+ERROR:  different bit lengths 3 and 4
+SELECT jaccard_distance('1111', '1111');
+ jaccard_distance 
+------------------
+                0
+(1 row)
+
+SELECT jaccard_distance('1111', '1110');
+ jaccard_distance 
+------------------
+             0.25
+(1 row)
+
+SELECT jaccard_distance('1111', '1100');
+ jaccard_distance 
+------------------
+              0.5
+(1 row)
+
+SELECT jaccard_distance('1111', '1000');
+ jaccard_distance 
+------------------
+             0.75
+(1 row)
+
+SELECT jaccard_distance('1111', '0000');
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('1100', '1000');
+ jaccard_distance 
+------------------
+              0.5
+(1 row)
+
+SELECT jaccard_distance('10101010101010101010', '01010101010101010101');
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('', '');
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('1111', '000');
+ERROR:  different bit lengths 4 and 3
+SELECT jaccard_distance('1111', '0000'::varbit(5));
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('1111', '00000'::varbit(5));
+ERROR:  different bit lengths 4 and 5

test/expected/cast.out

@@ -28,6 +28,26 @@ SELECT ARRAY[1,2,3]::numeric[]::vector;
  [1,2,3]
 (1 row)
 
+SELECT '[1,2,3]'::vector::real[];
+ float4  
+---------
+ {1,2,3}
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector(2);
+ERROR:  expected 2 dimensions, not 3
 SELECT '{NULL}'::real[]::vector;
 ERROR:  array must not contain nulls
 SELECT '{NaN}'::real[]::vector;
@@ -40,12 +60,116 @@ SELECT '{}'::real[]::vector;
 ERROR:  vector must have at least 1 dimension
 SELECT '{{1}}'::real[]::vector;
 ERROR:  array must be 1-D
-SELECT '[1,2,3]'::vector::real[];
- float4  
+SELECT '{1,2,3}'::double precision[]::vector;
+ vector  
 ---------
- {1,2,3}
+ [1,2,3]
 (1 row)
 
+SELECT '{1,2,3}'::double precision[]::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::double precision[]::vector(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{4e38,-4e38}'::double precision[]::vector;
+ERROR:  infinite value not allowed in vector
+SELECT '{1e-46,-1e-46}'::double precision[]::vector;
+ vector 
+--------
+ [0,-0]
+(1 row)
+
+SELECT '[1,2,3]'::vector::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::vector::halfvec(3);
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::vector::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '[65520]'::vector::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '[1e-8]'::vector::halfvec;
+ halfvec 
+---------
+ [0]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{1,2,3}'::real[]::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::halfvec(3);
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{65520,-65520}'::real[]::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '{1e-8,-1e-8}'::real[]::halfvec;
+ halfvec 
+---------
+ [0,-0]
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(5);
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector;
+     vector      
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(5);
+     vector      
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{}/16001'::sparsevec::vector;
+ERROR:  vector cannot have more than 16000 dimensions
 SELECT array_agg(n)::vector FROM generate_series(1, 16001) n;
 ERROR:  vector cannot have more than 16000 dimensions
 SELECT array_to_vector(array_agg(n), 16001, false) FROM generate_series(1, 16001) n;

test/expected/copy.out

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

test/expected/functions.out

@@ -1,210 +0,0 @@
-SELECT '[1,2,3]'::vector + '[4,5,6]';
- ?column? 
-----------
- [5,7,9]
-(1 row)
-
-SELECT '[3e38]'::vector + '[3e38]';
-ERROR:  value out of range: overflow
-SELECT '[1,2,3]'::vector - '[4,5,6]';
-  ?column?  
-------------
- [-3,-3,-3]
-(1 row)
-
-SELECT '[-3e38]'::vector - '[3e38]';
-ERROR:  value out of range: overflow
-SELECT '[1,2,3]'::vector * '[4,5,6]';
- ?column?  
------------
- [4,10,18]
-(1 row)
-
-SELECT '[1e37]'::vector * '[1e37]';
-ERROR:  value out of range: overflow
-SELECT '[1e-37]'::vector * '[1e-37]';
-ERROR:  value out of range: underflow
-SELECT vector_dims('[1,2,3]');
- vector_dims 
--------------
-           3
-(1 row)
-
-SELECT round(vector_norm('[1,1]')::numeric, 5);
-  round  
----------
- 1.41421
-(1 row)
-
-SELECT vector_norm('[3,4]');
- vector_norm 
--------------
-           5
-(1 row)
-
-SELECT vector_norm('[0,1]');
- vector_norm 
--------------
-           1
-(1 row)
-
-SELECT vector_norm('[3e37,4e37]')::real;
- vector_norm 
--------------
-       5e+37
-(1 row)
-
-SELECT l2_distance('[0,0]', '[3,4]');
- l2_distance 
--------------
-           5
-(1 row)
-
-SELECT l2_distance('[0,0]', '[0,1]');
- l2_distance 
--------------
-           1
-(1 row)
-
-SELECT l2_distance('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-SELECT l2_distance('[3e38]', '[-3e38]');
- l2_distance 
--------------
-    Infinity
-(1 row)
-
-SELECT inner_product('[1,2]', '[3,4]');
- inner_product 
----------------
-            11
-(1 row)
-
-SELECT inner_product('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-SELECT inner_product('[3e38]', '[3e38]');
- inner_product 
----------------
-      Infinity
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[2,4]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[0,0]');
- cosine_distance 
------------------
-             NaN
-(1 row)
-
-SELECT cosine_distance('[1,1]', '[1,1]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,0]', '[0,2]');
- cosine_distance 
------------------
-               1
-(1 row)
-
-SELECT cosine_distance('[1,1]', '[-1,-1]');
- cosine_distance 
------------------
-               2
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-SELECT cosine_distance('[1,1]', '[1.1,1.1]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
- cosine_distance 
------------------
-               2
-(1 row)
-
-SELECT cosine_distance('[3e38]', '[3e38]');
- cosine_distance 
------------------
-             NaN
-(1 row)
-
-SELECT l1_distance('[0,0]', '[3,4]');
- l1_distance 
--------------
-           7
-(1 row)
-
-SELECT l1_distance('[0,0]', '[0,1]');
- l1_distance 
--------------
-           1
-(1 row)
-
-SELECT l1_distance('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-SELECT l1_distance('[3e38]', '[-3e38]');
- l1_distance 
--------------
-    Infinity
-(1 row)
-
-SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
-    avg    
------------
- [2,3.5,5]
-(1 row)
-
-SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
-    avg    
------------
- [2,3.5,5]
-(1 row)
-
-SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
- avg 
------
- 
-(1 row)
-
-SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
-ERROR:  expected 2 dimensions, not 1
-SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
-   avg   
----------
- [3e+38]
-(1 row)
-
-SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
-ERROR:  vector cannot have more than 16000 dimensions
-SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
-   sum    
-----------
- [4,7,10]
-(1 row)
-
-SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
-   sum    
-----------
- [4,7,10]
-(1 row)
-
-SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
- sum 
------
- 
-(1 row)
-
-SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
-ERROR:  different vector dimensions 2 and 1
-SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
-ERROR:  value out of range: overflow

test/expected/halfvec_functions.out

@@ -0,0 +1,176 @@
+SELECT round(halfvec_norm('[1,1]')::numeric, 5);
+  round  
+---------
+ 1.41421
+(1 row)
+
+SELECT halfvec_norm('[3,4]');
+ halfvec_norm 
+--------------
+            5
+(1 row)
+
+SELECT halfvec_norm('[0,1]');
+ halfvec_norm 
+--------------
+            1
+(1 row)
+
+SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
+ l2_distance 
+-------------
+           1
+(1 row)
+
+SELECT l2_distance('[1,2]'::halfvec, '[3]');
+ERROR:  different halfvec dimensions 2 and 1
+SELECT l2_distance('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,1,1,1,1,1,1,4,5]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT '[0,0]'::halfvec <-> '[3,4]';
+ ?column? 
+----------
+        5
+(1 row)
+
+SELECT inner_product('[1,2]'::halfvec, '[3,4]');
+ inner_product 
+---------------
+            11
+(1 row)
+
+SELECT inner_product('[1,2]'::halfvec, '[3]');
+ERROR:  different halfvec dimensions 2 and 1
+SELECT inner_product('[65504]'::halfvec, '[65504]');
+ inner_product 
+---------------
+    4290774016
+(1 row)
+
+SELECT inner_product('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+ inner_product 
+---------------
+            45
+(1 row)
+
+SELECT '[1,2]'::halfvec <#> '[3,4]';
+ ?column? 
+----------
+      -11
+(1 row)
+
+SELECT cosine_distance('[1,2]'::halfvec, '[2,4]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,2]'::halfvec, '[0,0]');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('[1,1]'::halfvec, '[1,1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,0]'::halfvec, '[0,2]');
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
+SELECT cosine_distance('[1,1]'::halfvec, '[-1,-1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('[1,2]'::halfvec, '[3]');
+ERROR:  different halfvec dimensions 2 and 1
+SELECT cosine_distance('[1,1]'::halfvec, '[1.1,1.1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,1]'::halfvec, '[-1.1,-1.1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT '[1,2]'::halfvec <=> '[2,4]';
+ ?column? 
+----------
+        0
+(1 row)
+
+SELECT l1_distance('[0,0]'::halfvec, '[3,4]');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('[0,0]'::halfvec, '[0,1]');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('[1,2]'::halfvec, '[3]');
+ERROR:  different halfvec dimensions 2 and 1
+SELECT quantize_binary('[1,0,-1]'::halfvec);
+ quantize_binary 
+-----------------
+ 100
+(1 row)
+
+SELECT quantize_binary('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::halfvec);
+ quantize_binary 
+-----------------
+ 01001110101
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::halfvec, 1, 3);
+ subvector 
+-----------
+ [1,2,3]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::halfvec, 3, 2);
+ subvector 
+-----------
+ [3,4]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::halfvec, -1, 3);
+ subvector 
+-----------
+ [1]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::halfvec, 3, 9);
+ subvector 
+-----------
+ [3,4,5]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::halfvec, 1, 0);
+ERROR:  halfvec must have at least 1 dimension
+SELECT subvector('[1,2,3,4,5]'::halfvec, 3, -1);
+ERROR:  halfvec must have at least 1 dimension
+SELECT subvector('[1,2,3,4,5]'::halfvec, -1, 2);
+ERROR:  halfvec must have at least 1 dimension

test/expected/halfvec_input.out

@@ -0,0 +1,164 @@
+SELECT '[1,2,3]'::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[-1,-2,-3]'::halfvec;
+  halfvec   
+------------
+ [-1,-2,-3]
+(1 row)
+
+SELECT '[1.,2.,3.]'::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT ' [ 1,  2 ,    3  ] '::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1.23456]'::halfvec;
+  halfvec   
+------------
+ [1.234375]
+(1 row)
+
+SELECT '[hello,1]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[hello,1]"
+LINE 1: SELECT '[hello,1]'::halfvec;
+               ^
+SELECT '[NaN,1]'::halfvec;
+ERROR:  NaN not allowed in halfvec
+LINE 1: SELECT '[NaN,1]'::halfvec;
+               ^
+SELECT '[Infinity,1]'::halfvec;
+ERROR:  infinite value not allowed in halfvec
+LINE 1: SELECT '[Infinity,1]'::halfvec;
+               ^
+SELECT '[-Infinity,1]'::halfvec;
+ERROR:  infinite value not allowed in halfvec
+LINE 1: SELECT '[-Infinity,1]'::halfvec;
+               ^
+SELECT '[65519,-65519]'::halfvec;
+    halfvec     
+----------------
+ [65504,-65504]
+(1 row)
+
+SELECT '[65520,-65520]'::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+LINE 1: SELECT '[65520,-65520]'::halfvec;
+               ^
+SELECT '[1e-8,-1e-8]'::halfvec;
+ halfvec 
+---------
+ [0,-0]
+(1 row)
+
+SELECT '[4e38,1]'::halfvec;
+ERROR:  "4e38" is out of range for type halfvec
+LINE 1: SELECT '[4e38,1]'::halfvec;
+               ^
+SELECT '[1e-46,1]'::halfvec;
+ halfvec 
+---------
+ [0,1]
+(1 row)
+
+SELECT '[1,2,3'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1,2,3"
+LINE 1: SELECT '[1,2,3'::halfvec;
+               ^
+SELECT '[1,2,3]9'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1,2,3]9"
+LINE 1: SELECT '[1,2,3]9'::halfvec;
+               ^
+DETAIL:  Junk after closing right brace.
+SELECT '1,2,3'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "1,2,3"
+LINE 1: SELECT '1,2,3'::halfvec;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT ''::halfvec;
+ERROR:  invalid input syntax for type halfvec: ""
+LINE 1: SELECT ''::halfvec;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT '['::halfvec;
+ERROR:  invalid input syntax for type halfvec: "["
+LINE 1: SELECT '['::halfvec;
+               ^
+SELECT '[ '::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[ "
+LINE 1: SELECT '[ '::halfvec;
+               ^
+SELECT '[,'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[,"
+LINE 1: SELECT '[,'::halfvec;
+               ^
+SELECT '[]'::halfvec;
+ERROR:  halfvec must have at least 1 dimension
+LINE 1: SELECT '[]'::halfvec;
+               ^
+SELECT '[ ]'::halfvec;
+ERROR:  halfvec must have at least 1 dimension
+LINE 1: SELECT '[ ]'::halfvec;
+               ^
+SELECT '[,]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[,]"
+LINE 1: SELECT '[,]'::halfvec;
+               ^
+SELECT '[1,]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1,]"
+LINE 1: SELECT '[1,]'::halfvec;
+               ^
+SELECT '[1a]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1a]"
+LINE 1: SELECT '[1a]'::halfvec;
+               ^
+SELECT '[1,,3]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1,,3]"
+LINE 1: SELECT '[1,,3]'::halfvec;
+               ^
+SELECT '[1, ,3]'::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[1, ,3]"
+LINE 1: SELECT '[1, ,3]'::halfvec;
+               ^
+SELECT '[1,2,3]'::halfvec(3);
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::halfvec(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '[1,2,3]'::halfvec(3, 2);
+                          ^
+SELECT '[1,2,3]'::halfvec('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '[1,2,3]'::halfvec('a');
+                          ^
+SELECT '[1,2,3]'::halfvec(0);
+ERROR:  dimensions for type halfvec must be at least 1
+LINE 1: SELECT '[1,2,3]'::halfvec(0);
+                          ^
+SELECT '[1,2,3]'::halfvec(16001);
+ERROR:  dimensions for type halfvec cannot exceed 16000
+LINE 1: SELECT '[1,2,3]'::halfvec(16001);
+                          ^
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::halfvec[]);
+ unnest  
+---------
+ [1,2,3]
+ [4,5,6]
+(2 rows)
+
+SELECT '{"[1,2,3]"}'::halfvec(2)[];
+ERROR:  expected 2 dimensions, not 3

test/expected/hnsw_bit_hamming.out

@@ -0,0 +1,29 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val bit(3));
+INSERT INTO t (val) VALUES (B'000'), (B'100'), (B'111'), (NULL);
+CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
+INSERT INTO t (val) VALUES (B'110');
+SELECT * FROM t ORDER BY val <~> B'111';
+ val 
+-----
+ 111
+ 110
+ 100
+ 000
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <~> (SELECT NULL::bit)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;
+-- TODO move
+CREATE TABLE t (val varbit(3));
+CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
+ERROR:  type not supported for hnsw index
+CREATE INDEX ON t USING hnsw ((val::bit(3)) bit_hamming_ops);
+CREATE INDEX ON t USING hnsw ((val::bit(64001)) bit_hamming_ops);
+ERROR:  column cannot have more than 64000 dimensions for hnsw index
+DROP TABLE t;

test/expected/hnsw_bit_jaccard.out

@@ -0,0 +1,21 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val bit(4));
+INSERT INTO t (val) VALUES (B'0000'), (B'1100'), (B'1111'), (NULL);
+CREATE INDEX ON t USING hnsw (val bit_jaccard_ops);
+INSERT INTO t (val) VALUES (B'1110');
+SELECT * FROM t ORDER BY val <%> B'1111';
+ val  
+------
+ 1111
+ 1110
+ 1100
+ 0000
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <%> (SELECT NULL::bit)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_halfvec_cosine.out

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

test/expected/hnsw_halfvec_ip.out

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

test/expected/hnsw_halfvec_l2.out

@@ -0,0 +1,33 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val halfvec_l2_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::halfvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+SELECT COUNT(*) FROM t;
+ count 
+-------
+     5
+(1 row)
+
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+ val 
+-----
+(0 rows)
+
+DROP TABLE t;

test/expected/hnsw_sparsevec_cosine.out

@@ -0,0 +1,26 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val sparsevec(3));
+INSERT INTO t (val) VALUES ('{}/3'), ('{1:1,2:2,3:3}/3'), ('{1:1,2:1,3:1}/3'), (NULL);
+CREATE INDEX ON t USING hnsw (val sparsevec_cosine_ops);
+INSERT INTO t (val) VALUES ('{1:1,2:2,3:4}/3');
+SELECT * FROM t ORDER BY val <=> '{1:3,2:3,3:3}/3';
+       val       
+-----------------
+ {1:1,2:1,3:1}/3
+ {1:1,2:2,3:3}/3
+ {1:1,2:2,3:4}/3
+(3 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '{}/3') t2;
+ count 
+-------
+     3
+(1 row)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::sparsevec)) t2;
+ count 
+-------
+     3
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_sparsevec_ip.out

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

test/expected/hnsw_sparsevec_l2.out

@@ -0,0 +1,43 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val sparsevec(3));
+INSERT INTO t (val) VALUES ('{}/3'), ('{1:1,2:2,3:3}/3'), ('{1:1,2:1,3:1}/3'), (NULL);
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+INSERT INTO t (val) VALUES ('{1:1,2:2,3:4}/3');
+SELECT * FROM t ORDER BY val <-> '{1:3,2:3,3:3}/3';
+       val       
+-----------------
+ {1:1,2:2,3:3}/3
+ {1:1,2:2,3:4}/3
+ {1:1,2:1,3:1}/3
+ {}/3
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::sparsevec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+SELECT COUNT(*) FROM t;
+ count 
+-------
+     5
+(1 row)
+
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '{1:3,2:3,3:3}/3';
+ val 
+-----
+(0 rows)
+
+DROP TABLE t;
+-- TODO move
+CREATE TABLE t (val sparsevec(1001));
+INSERT INTO t (val) VALUES (array_fill(1, ARRAY[1001])::vector::sparsevec);
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+ERROR:  sparsevec cannot have more than 1000 non-zero elements for hnsw index
+TRUNCATE t;
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+INSERT INTO t (val) VALUES (array_fill(1, ARRAY[1001])::vector::sparsevec);
+ERROR:  sparsevec cannot have more than 1000 non-zero elements for hnsw index
+DROP TABLE t;

test/expected/hnsw_vector_l2.out

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

test/expected/ivfflat_halfvec_cosine.out

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

test/expected/ivfflat_halfvec_ip.out

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

test/expected/ivfflat_halfvec_l2.out

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

test/expected/ivfflat_vector_l2.out

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

test/expected/sparsevec_functions.out

@@ -0,0 +1,86 @@
+SELECT round(sparsevec_norm('{1:1,2:1}/2')::numeric, 5);
+  round  
+---------
+ 1.41421
+(1 row)
+
+SELECT sparsevec_norm('{1:3,2:4}/2');
+ sparsevec_norm 
+----------------
+              5
+(1 row)
+
+SELECT sparsevec_norm('{2:1}/2');
+ sparsevec_norm 
+----------------
+              1
+(1 row)
+
+SELECT sparsevec_norm('{1:3e37,2:4e37}/2')::real;
+ sparsevec_norm 
+----------------
+          5e+37
+(1 row)
+
+SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('{}/2'::sparsevec, '{2:1}/2');
+ l2_distance 
+-------------
+           1
+(1 row)
+
+SELECT '{}/2'::sparsevec <-> '{1:3,2:4}/2';
+ ?column? 
+----------
+        5
+(1 row)
+
+SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
+ inner_product 
+---------------
+            10
+(1 row)
+
+SELECT sparsevec_negative_inner_product('{1:1,2:2}/2', '{1:2,2:4}/2');
+ sparsevec_negative_inner_product 
+----------------------------------
+                              -10
+(1 row)
+
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{}/2');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1,2:-1}/2');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('{1:2}/2'::sparsevec, '{2:2}/2');
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
+SELECT cosine_distance('{}/1'::sparsevec, '{}/1');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('{1:2}/2'::sparsevec, '{1:1}/3');
+ERROR:  different sparsevec dimensions 2 and 3

test/expected/sparsevec_input.out

@@ -0,0 +1,215 @@
+SELECT '{1:1.5,3:3.5}/5'::sparsevec;
+    sparsevec    
+-----------------
+ {1:1.5,3:3.5}/5
+(1 row)
+
+SELECT '{1:-2,3:-4}/5'::sparsevec;
+   sparsevec   
+---------------
+ {1:-2,3:-4}/5
+(1 row)
+
+SELECT '{1:2.,3:4.}/5'::sparsevec;
+  sparsevec  
+-------------
+ {1:2,3:4}/5
+(1 row)
+
+SELECT ' { 1 : 1.5 ,  3  :  3.5  } / 5 '::sparsevec;
+    sparsevec    
+-----------------
+ {1:1.5,3:3.5}/5
+(1 row)
+
+SELECT '{1:1.23456}/1'::sparsevec;
+   sparsevec   
+---------------
+ {1:1.23456}/1
+(1 row)
+
+SELECT '{1:hello,2:1}/2'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:hello,2:1}/2"
+LINE 1: SELECT '{1:hello,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:NaN,2:1}/2'::sparsevec;
+ERROR:  NaN not allowed in sparsevec
+LINE 1: SELECT '{1:NaN,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:Infinity,2:1}/2'::sparsevec;
+ERROR:  infinite value not allowed in sparsevec
+LINE 1: SELECT '{1:Infinity,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:-Infinity,2:1}/2'::sparsevec;
+ERROR:  infinite value not allowed in sparsevec
+LINE 1: SELECT '{1:-Infinity,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:1.5e38,2:-1.5e38}/2'::sparsevec;
+        sparsevec         
+--------------------------
+ {1:1.5e+38,2:-1.5e+38}/2
+(1 row)
+
+SELECT '{1:1.5e+38,2:-1.5e+38}/2'::sparsevec;
+        sparsevec         
+--------------------------
+ {1:1.5e+38,2:-1.5e+38}/2
+(1 row)
+
+SELECT '{1:1.5e-38,2:-1.5e-38}/2'::sparsevec;
+        sparsevec         
+--------------------------
+ {1:1.5e-38,2:-1.5e-38}/2
+(1 row)
+
+SELECT '{1:4e38,2:1}/2'::sparsevec;
+ERROR:  "4e38" is out of range for type sparsevec
+LINE 1: SELECT '{1:4e38,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:-4e38,2:1}/2'::sparsevec;
+ERROR:  "-4e38" is out of range for type sparsevec
+LINE 1: SELECT '{1:-4e38,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:1e-46,2:1}/2'::sparsevec;
+ERROR:  "1e-46" is out of range for type sparsevec
+LINE 1: SELECT '{1:1e-46,2:1}/2'::sparsevec;
+               ^
+SELECT '{1:-1e-46,2:1}/2'::sparsevec;
+ERROR:  "-1e-46" is out of range for type sparsevec
+LINE 1: SELECT '{1:-1e-46,2:1}/2'::sparsevec;
+               ^
+SELECT ''::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: ""
+LINE 1: SELECT ''::sparsevec;
+               ^
+DETAIL:  Vector contents must start with "{".
+SELECT '{'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{"
+LINE 1: SELECT '{'::sparsevec;
+               ^
+SELECT '{ '::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{ "
+LINE 1: SELECT '{ '::sparsevec;
+               ^
+SELECT '{:'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{:"
+LINE 1: SELECT '{:'::sparsevec;
+               ^
+SELECT '{,'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{,"
+LINE 1: SELECT '{,'::sparsevec;
+               ^
+SELECT '{}'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{}"
+LINE 1: SELECT '{}'::sparsevec;
+               ^
+DETAIL:  Unexpected end of input.
+SELECT '{}/'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{}/"
+LINE 1: SELECT '{}/'::sparsevec;
+               ^
+SELECT '{}/1'::sparsevec;
+ sparsevec 
+-----------
+ {}/1
+(1 row)
+
+SELECT '{}/1a'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{}/1a"
+LINE 1: SELECT '{}/1a'::sparsevec;
+               ^
+DETAIL:  Junk after closing.
+SELECT '{ }/1'::sparsevec;
+ sparsevec 
+-----------
+ {}/1
+(1 row)
+
+SELECT '{:}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{:}/1"
+LINE 1: SELECT '{:}/1'::sparsevec;
+               ^
+SELECT '{,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{,}/1"
+LINE 1: SELECT '{,}/1'::sparsevec;
+               ^
+SELECT '{1,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1,}/1"
+LINE 1: SELECT '{1,}/1'::sparsevec;
+               ^
+SELECT '{:1}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{:1}/1"
+LINE 1: SELECT '{:1}/1'::sparsevec;
+               ^
+SELECT '{1:}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:}/1"
+LINE 1: SELECT '{1:}/1'::sparsevec;
+               ^
+SELECT '{1a:1}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1a:1}/1"
+LINE 1: SELECT '{1a:1}/1'::sparsevec;
+               ^
+SELECT '{1:1a}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:1a}/1"
+LINE 1: SELECT '{1:1a}/1'::sparsevec;
+               ^
+SELECT '{1:1,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:1,}/1"
+LINE 1: SELECT '{1:1,}/1'::sparsevec;
+               ^
+SELECT '{1:0,2:1,3:0}/3'::sparsevec;
+ sparsevec 
+-----------
+ {2:1}/3
+(1 row)
+
+SELECT '{2:1,1:1}/2'::sparsevec;
+ERROR:  indexes must be in ascending order
+LINE 1: SELECT '{2:1,1:1}/2'::sparsevec;
+               ^
+SELECT '{}/5'::sparsevec;
+ sparsevec 
+-----------
+ {}/5
+(1 row)
+
+SELECT '{}/-1'::sparsevec;
+ERROR:  sparsevec must have at least 1 dimension
+LINE 1: SELECT '{}/-1'::sparsevec;
+               ^
+SELECT '{}/100001'::sparsevec;
+ERROR:  sparsevec cannot have more than 100000 dimensions
+LINE 1: SELECT '{}/100001'::sparsevec;
+               ^
+SELECT '{0:1}/1'::sparsevec;
+ERROR:  index "0" is out of range for type sparsevec
+LINE 1: SELECT '{0:1}/1'::sparsevec;
+               ^
+SELECT '{2:1}/1'::sparsevec;
+ERROR:  index must be less than or equal to dimensions
+LINE 1: SELECT '{2:1}/1'::sparsevec;
+               ^
+SELECT '{}/3'::sparsevec(3);
+ sparsevec 
+-----------
+ {}/3
+(1 row)
+
+SELECT '{}/3'::sparsevec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{}/3'::sparsevec(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '{}/3'::sparsevec(3, 2);
+                       ^
+SELECT '{}/3'::sparsevec('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '{}/3'::sparsevec('a');
+                       ^
+SELECT '{}/3'::sparsevec(0);
+ERROR:  dimensions for type sparsevec must be at least 1
+LINE 1: SELECT '{}/3'::sparsevec(0);
+                       ^
+SELECT '{}/3'::sparsevec(100001);
+ERROR:  dimensions for type sparsevec cannot exceed 100000
+LINE 1: SELECT '{}/3'::sparsevec(100001);
+                       ^

test/expected/vector_functions.out

@@ -0,0 +1,366 @@
+SELECT '[1,2,3]'::vector + '[4,5,6]';
+ ?column? 
+----------
+ [5,7,9]
+(1 row)
+
+SELECT '[3e38]'::vector + '[3e38]';
+ERROR:  value out of range: overflow
+SELECT '[1,2,3]'::vector - '[4,5,6]';
+  ?column?  
+------------
+ [-3,-3,-3]
+(1 row)
+
+SELECT '[-3e38]'::vector - '[3e38]';
+ERROR:  value out of range: overflow
+SELECT '[1,2,3]'::vector * '[4,5,6]';
+ ?column?  
+-----------
+ [4,10,18]
+(1 row)
+
+SELECT '[1e37]'::vector * '[1e37]';
+ERROR:  value out of range: overflow
+SELECT '[1e-37]'::vector * '[1e-37]';
+ERROR:  value out of range: underflow
+SELECT '[1,2,3]'::vector < '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::vector < '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::vector <= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::vector <= '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::vector = '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::vector = '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::vector != '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::vector != '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::vector >= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::vector >= '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::vector > '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::vector > '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT vector_cmp('[1,2,3]', '[1,2,3]');
+ vector_cmp 
+------------
+          0
+(1 row)
+
+SELECT vector_cmp('[1,2,3]', '[0,0,0]');
+ vector_cmp 
+------------
+          1
+(1 row)
+
+SELECT vector_cmp('[0,0,0]', '[1,2,3]');
+ vector_cmp 
+------------
+         -1
+(1 row)
+
+SELECT vector_cmp('[1,2]', '[1,2,3]');
+ vector_cmp 
+------------
+         -1
+(1 row)
+
+SELECT vector_cmp('[1,2,3]', '[1,2]');
+ vector_cmp 
+------------
+          1
+(1 row)
+
+SELECT vector_cmp('[1,2]', '[2,3,4]');
+ vector_cmp 
+------------
+         -1
+(1 row)
+
+SELECT vector_cmp('[2,3]', '[1,2,3]');
+ vector_cmp 
+------------
+          1
+(1 row)
+
+SELECT vector_dims('[1,2,3]');
+ vector_dims 
+-------------
+           3
+(1 row)
+
+SELECT round(vector_norm('[1,1]')::numeric, 5);
+  round  
+---------
+ 1.41421
+(1 row)
+
+SELECT vector_norm('[3,4]');
+ vector_norm 
+-------------
+           5
+(1 row)
+
+SELECT vector_norm('[0,1]');
+ vector_norm 
+-------------
+           1
+(1 row)
+
+SELECT vector_norm('[3e37,4e37]')::real;
+ vector_norm 
+-------------
+       5e+37
+(1 row)
+
+SELECT l2_distance('[0,0]'::vector, '[3,4]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('[0,0]'::vector, '[0,1]');
+ l2_distance 
+-------------
+           1
+(1 row)
+
+SELECT l2_distance('[1,2]'::vector, '[3]');
+ERROR:  different vector dimensions 2 and 1
+SELECT l2_distance('[3e38]'::vector, '[-3e38]');
+ l2_distance 
+-------------
+    Infinity
+(1 row)
+
+SELECT inner_product('[1,2]'::vector, '[3,4]');
+ inner_product 
+---------------
+            11
+(1 row)
+
+SELECT inner_product('[1,2]'::vector, '[3]');
+ERROR:  different vector dimensions 2 and 1
+SELECT inner_product('[3e38]'::vector, '[3e38]');
+ inner_product 
+---------------
+      Infinity
+(1 row)
+
+SELECT cosine_distance('[1,2]'::vector, '[2,4]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,2]'::vector, '[0,0]');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('[1,1]'::vector, '[1,1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,0]'::vector, '[0,2]');
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
+SELECT cosine_distance('[1,1]'::vector, '[-1,-1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('[1,2]'::vector, '[3]');
+ERROR:  different vector dimensions 2 and 1
+SELECT cosine_distance('[1,1]'::vector, '[1.1,1.1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,1]'::vector, '[-1.1,-1.1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('[3e38]'::vector, '[3e38]');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT l1_distance('[0,0]'::vector, '[3,4]');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('[0,0]'::vector, '[0,1]');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('[1,2]'::vector, '[3]');
+ERROR:  different vector dimensions 2 and 1
+SELECT l1_distance('[3e38]'::vector, '[-3e38]');
+ l1_distance 
+-------------
+    Infinity
+(1 row)
+
+SELECT quantize_binary('[1,0,-1]'::vector);
+ quantize_binary 
+-----------------
+ 100
+(1 row)
+
+SELECT quantize_binary('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::vector);
+ quantize_binary 
+-----------------
+ 01001110101
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::vector, 1, 3);
+ subvector 
+-----------
+ [1,2,3]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::vector, 3, 2);
+ subvector 
+-----------
+ [3,4]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::vector, -1, 3);
+ subvector 
+-----------
+ [1]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::vector, 3, 9);
+ subvector 
+-----------
+ [3,4,5]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::vector, 1, 0);
+ERROR:  vector must have at least 1 dimension
+SELECT subvector('[1,2,3,4,5]'::vector, 3, -1);
+ERROR:  vector must have at least 1 dimension
+SELECT subvector('[1,2,3,4,5]'::vector, -1, 2);
+ERROR:  vector must have at least 1 dimension
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
+    avg    
+-----------
+ [2,3.5,5]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
+    avg    
+-----------
+ [2,3.5,5]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
+ avg 
+-----
+ 
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+ERROR:  expected 2 dimensions, not 1
+SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
+   avg   
+---------
+ [3e+38]
+(1 row)
+
+SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
+ERROR:  vector cannot have more than 16000 dimensions
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
+ sum 
+-----
+ 
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+ERROR:  different vector dimensions 2 and 1
+SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
+ERROR:  value out of range: overflow

test/expected/vector_input.out

@@ -63,43 +63,68 @@ SELECT '[1.5e-38,-1.5e-38]'::vector;
 (1 row)
 
 SELECT '[4e38,1]'::vector;
-ERROR:  infinite value not allowed in vector
+ERROR:  "4e38" is out of range for type vector
 LINE 1: SELECT '[4e38,1]'::vector;
                ^
+SELECT '[-4e38,1]'::vector;
+ERROR:  "-4e38" is out of range for type vector
+LINE 1: SELECT '[-4e38,1]'::vector;
+               ^
+SELECT '[1e-46,1]'::vector;
+ vector 
+--------
+ [0,1]
+(1 row)
+
+SELECT '[-1e-46,1]'::vector;
+ vector 
+--------
+ [-0,1]
+(1 row)
+
 SELECT '[1,2,3'::vector;
-ERROR:  malformed vector literal: "[1,2,3"
+ERROR:  invalid input syntax for type vector: "[1,2,3"
 LINE 1: SELECT '[1,2,3'::vector;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[1,2,3]9'::vector;
-ERROR:  malformed vector literal: "[1,2,3]9"
+ERROR:  invalid input syntax for type vector: "[1,2,3]9"
 LINE 1: SELECT '[1,2,3]9'::vector;
                ^
 DETAIL:  Junk after closing right brace.
 SELECT '1,2,3'::vector;
-ERROR:  malformed vector literal: "1,2,3"
+ERROR:  invalid input syntax for type vector: "1,2,3"
 LINE 1: SELECT '1,2,3'::vector;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT ''::vector;
-ERROR:  malformed vector literal: ""
+ERROR:  invalid input syntax for type vector: ""
 LINE 1: SELECT ''::vector;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT '['::vector;
-ERROR:  malformed vector literal: "["
+ERROR:  invalid input syntax for type vector: "["
 LINE 1: SELECT '['::vector;
                ^
-DETAIL:  Unexpected end of input.
+SELECT '[ '::vector;
+ERROR:  invalid input syntax for type vector: "[ "
+LINE 1: SELECT '[ '::vector;
+               ^
 SELECT '[,'::vector;
-ERROR:  malformed vector literal: "[,"
+ERROR:  invalid input syntax for type vector: "[,"
 LINE 1: SELECT '[,'::vector;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[]'::vector;
 ERROR:  vector must have at least 1 dimension
 LINE 1: SELECT '[]'::vector;
                ^
+SELECT '[ ]'::vector;
+ERROR:  vector must have at least 1 dimension
+LINE 1: SELECT '[ ]'::vector;
+               ^
+SELECT '[,]'::vector;
+ERROR:  invalid input syntax for type vector: "[,]"
+LINE 1: SELECT '[,]'::vector;
+               ^
 SELECT '[1,]'::vector;
 ERROR:  invalid input syntax for type vector: "[1,]"
 LINE 1: SELECT '[1,]'::vector;
@@ -109,15 +134,37 @@ ERROR:  invalid input syntax for type vector: "[1a]"
 LINE 1: SELECT '[1a]'::vector;
                ^
 SELECT '[1,,3]'::vector;
-ERROR:  malformed vector literal: "[1,,3]"
+ERROR:  invalid input syntax for type vector: "[1,,3]"
 LINE 1: SELECT '[1,,3]'::vector;
                ^
 SELECT '[1, ,3]'::vector;
 ERROR:  invalid input syntax for type vector: "[1, ,3]"
 LINE 1: SELECT '[1, ,3]'::vector;
                ^
+SELECT '[1,2,3]'::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
 SELECT '[1,2,3]'::vector(2);
 ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::vector(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '[1,2,3]'::vector(3, 2);
+                          ^
+SELECT '[1,2,3]'::vector('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '[1,2,3]'::vector('a');
+                          ^
+SELECT '[1,2,3]'::vector(0);
+ERROR:  dimensions for type vector must be at least 1
+LINE 1: SELECT '[1,2,3]'::vector(0);
+                          ^
+SELECT '[1,2,3]'::vector(16001);
+ERROR:  dimensions for type vector cannot exceed 16000
+LINE 1: SELECT '[1,2,3]'::vector(16001);
+                          ^
 SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
  unnest  
 ---------

test/sql/bit_functions.sql

@@ -0,0 +1,21 @@
+SELECT hamming_distance('111', '111');
+SELECT hamming_distance('111', '110');
+SELECT hamming_distance('111', '100');
+SELECT hamming_distance('111', '000');
+SELECT hamming_distance('10101010101010101010', '01010101010101010101');
+SELECT hamming_distance('', '');
+SELECT hamming_distance('111', '00');
+SELECT hamming_distance('111', '000'::varbit(4));
+SELECT hamming_distance('111', '0000'::varbit(4));
+
+SELECT jaccard_distance('1111', '1111');
+SELECT jaccard_distance('1111', '1110');
+SELECT jaccard_distance('1111', '1100');
+SELECT jaccard_distance('1111', '1000');
+SELECT jaccard_distance('1111', '0000');
+SELECT jaccard_distance('1100', '1000');
+SELECT jaccard_distance('10101010101010101010', '01010101010101010101');
+SELECT jaccard_distance('', '');
+SELECT jaccard_distance('1111', '000');
+SELECT jaccard_distance('1111', '0000'::varbit(5));
+SELECT jaccard_distance('1111', '00000'::varbit(5));

test/sql/cast.sql

@@ -3,13 +3,50 @@ SELECT ARRAY[1.0,2.0,3.0]::vector;
 SELECT ARRAY[1,2,3]::float4[]::vector;
 SELECT ARRAY[1,2,3]::float8[]::vector;
 SELECT ARRAY[1,2,3]::numeric[]::vector;
+
+SELECT '[1,2,3]'::vector::real[];
+
+SELECT '{1,2,3}'::real[]::vector;
+SELECT '{1,2,3}'::real[]::vector(3);
+SELECT '{1,2,3}'::real[]::vector(2);
 SELECT '{NULL}'::real[]::vector;
 SELECT '{NaN}'::real[]::vector;
 SELECT '{Infinity}'::real[]::vector;
 SELECT '{-Infinity}'::real[]::vector;
 SELECT '{}'::real[]::vector;
 SELECT '{{1}}'::real[]::vector;
-SELECT '[1,2,3]'::vector::real[];
+
+SELECT '{1,2,3}'::double precision[]::vector;
+SELECT '{1,2,3}'::double precision[]::vector(3);
+SELECT '{1,2,3}'::double precision[]::vector(2);
+SELECT '{4e38,-4e38}'::double precision[]::vector;
+SELECT '{1e-46,-1e-46}'::double precision[]::vector;
+
+SELECT '[1,2,3]'::vector::halfvec;
+SELECT '[1,2,3]'::vector::halfvec(3);
+SELECT '[1,2,3]'::vector::halfvec(2);
+SELECT '[65520]'::vector::halfvec;
+SELECT '[1e-8]'::vector::halfvec;
+
+SELECT '[1,2,3]'::halfvec::vector;
+SELECT '[1,2,3]'::halfvec::vector(3);
+SELECT '[1,2,3]'::halfvec::vector(2);
+
+SELECT '{1,2,3}'::real[]::halfvec;
+SELECT '{1,2,3}'::real[]::halfvec(3);
+SELECT '{1,2,3}'::real[]::halfvec(2);
+SELECT '{65520,-65520}'::real[]::halfvec;
+SELECT '{1e-8,-1e-8}'::real[]::halfvec;
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(5);
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(4);
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector;
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(5);
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(4);
+SELECT '{}/16001'::sparsevec::vector;
+
 SELECT array_agg(n)::vector FROM generate_series(1, 16001) n;
 SELECT array_to_vector(array_agg(n), 16001, false) FROM generate_series(1, 16001) n;
 

test/sql/copy.sql

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

test/sql/functions.sql

@@ -1,51 +0,0 @@
-SELECT '[1,2,3]'::vector + '[4,5,6]';
-SELECT '[3e38]'::vector + '[3e38]';
-SELECT '[1,2,3]'::vector - '[4,5,6]';
-SELECT '[-3e38]'::vector - '[3e38]';
-SELECT '[1,2,3]'::vector * '[4,5,6]';
-SELECT '[1e37]'::vector * '[1e37]';
-SELECT '[1e-37]'::vector * '[1e-37]';
-
-SELECT vector_dims('[1,2,3]');
-
-SELECT round(vector_norm('[1,1]')::numeric, 5);
-SELECT vector_norm('[3,4]');
-SELECT vector_norm('[0,1]');
-SELECT vector_norm('[3e37,4e37]')::real;
-
-SELECT l2_distance('[0,0]', '[3,4]');
-SELECT l2_distance('[0,0]', '[0,1]');
-SELECT l2_distance('[1,2]', '[3]');
-SELECT l2_distance('[3e38]', '[-3e38]');
-
-SELECT inner_product('[1,2]', '[3,4]');
-SELECT inner_product('[1,2]', '[3]');
-SELECT inner_product('[3e38]', '[3e38]');
-
-SELECT cosine_distance('[1,2]', '[2,4]');
-SELECT cosine_distance('[1,2]', '[0,0]');
-SELECT cosine_distance('[1,1]', '[1,1]');
-SELECT cosine_distance('[1,0]', '[0,2]');
-SELECT cosine_distance('[1,1]', '[-1,-1]');
-SELECT cosine_distance('[1,2]', '[3]');
-SELECT cosine_distance('[1,1]', '[1.1,1.1]');
-SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
-SELECT cosine_distance('[3e38]', '[3e38]');
-
-SELECT l1_distance('[0,0]', '[3,4]');
-SELECT l1_distance('[0,0]', '[0,1]');
-SELECT l1_distance('[1,2]', '[3]');
-SELECT l1_distance('[3e38]', '[-3e38]');
-
-SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
-SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
-SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
-SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
-SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
-SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
-
-SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
-SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
-SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
-SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
-SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;

test/sql/halfvec_functions.sql

@@ -0,0 +1,40 @@
+SELECT round(halfvec_norm('[1,1]')::numeric, 5);
+SELECT halfvec_norm('[3,4]');
+SELECT halfvec_norm('[0,1]');
+
+SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
+SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
+SELECT l2_distance('[1,2]'::halfvec, '[3]');
+SELECT l2_distance('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,1,1,1,1,1,1,4,5]');
+SELECT '[0,0]'::halfvec <-> '[3,4]';
+
+SELECT inner_product('[1,2]'::halfvec, '[3,4]');
+SELECT inner_product('[1,2]'::halfvec, '[3]');
+SELECT inner_product('[65504]'::halfvec, '[65504]');
+SELECT inner_product('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+SELECT '[1,2]'::halfvec <#> '[3,4]';
+
+SELECT cosine_distance('[1,2]'::halfvec, '[2,4]');
+SELECT cosine_distance('[1,2]'::halfvec, '[0,0]');
+SELECT cosine_distance('[1,1]'::halfvec, '[1,1]');
+SELECT cosine_distance('[1,0]'::halfvec, '[0,2]');
+SELECT cosine_distance('[1,1]'::halfvec, '[-1,-1]');
+SELECT cosine_distance('[1,2]'::halfvec, '[3]');
+SELECT cosine_distance('[1,1]'::halfvec, '[1.1,1.1]');
+SELECT cosine_distance('[1,1]'::halfvec, '[-1.1,-1.1]');
+SELECT '[1,2]'::halfvec <=> '[2,4]';
+
+SELECT l1_distance('[0,0]'::halfvec, '[3,4]');
+SELECT l1_distance('[0,0]'::halfvec, '[0,1]');
+SELECT l1_distance('[1,2]'::halfvec, '[3]');
+
+SELECT quantize_binary('[1,0,-1]'::halfvec);
+SELECT quantize_binary('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::halfvec);
+
+SELECT subvector('[1,2,3,4,5]'::halfvec, 1, 3);
+SELECT subvector('[1,2,3,4,5]'::halfvec, 3, 2);
+SELECT subvector('[1,2,3,4,5]'::halfvec, -1, 3);
+SELECT subvector('[1,2,3,4,5]'::halfvec, 3, 9);
+SELECT subvector('[1,2,3,4,5]'::halfvec, 1, 0);
+SELECT subvector('[1,2,3,4,5]'::halfvec, 3, -1);
+SELECT subvector('[1,2,3,4,5]'::halfvec, -1, 2);

test/sql/halfvec_input.sql

@@ -0,0 +1,38 @@
+SELECT '[1,2,3]'::halfvec;
+SELECT '[-1,-2,-3]'::halfvec;
+SELECT '[1.,2.,3.]'::halfvec;
+SELECT ' [ 1,  2 ,    3  ] '::halfvec;
+SELECT '[1.23456]'::halfvec;
+SELECT '[hello,1]'::halfvec;
+SELECT '[NaN,1]'::halfvec;
+SELECT '[Infinity,1]'::halfvec;
+SELECT '[-Infinity,1]'::halfvec;
+SELECT '[65519,-65519]'::halfvec;
+SELECT '[65520,-65520]'::halfvec;
+SELECT '[1e-8,-1e-8]'::halfvec;
+SELECT '[4e38,1]'::halfvec;
+SELECT '[1e-46,1]'::halfvec;
+SELECT '[1,2,3'::halfvec;
+SELECT '[1,2,3]9'::halfvec;
+SELECT '1,2,3'::halfvec;
+SELECT ''::halfvec;
+SELECT '['::halfvec;
+SELECT '[ '::halfvec;
+SELECT '[,'::halfvec;
+SELECT '[]'::halfvec;
+SELECT '[ ]'::halfvec;
+SELECT '[,]'::halfvec;
+SELECT '[1,]'::halfvec;
+SELECT '[1a]'::halfvec;
+SELECT '[1,,3]'::halfvec;
+SELECT '[1, ,3]'::halfvec;
+
+SELECT '[1,2,3]'::halfvec(3);
+SELECT '[1,2,3]'::halfvec(2);
+SELECT '[1,2,3]'::halfvec(3, 2);
+SELECT '[1,2,3]'::halfvec('a');
+SELECT '[1,2,3]'::halfvec(0);
+SELECT '[1,2,3]'::halfvec(16001);
+
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::halfvec[]);
+SELECT '{"[1,2,3]"}'::halfvec(2)[];

test/sql/hnsw_bit_hamming.sql

@@ -0,0 +1,19 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val bit(3));
+INSERT INTO t (val) VALUES (B'000'), (B'100'), (B'111'), (NULL);
+CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
+
+INSERT INTO t (val) VALUES (B'110');
+
+SELECT * FROM t ORDER BY val <~> B'111';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <~> (SELECT NULL::bit)) t2;
+
+DROP TABLE t;
+
+-- TODO move
+CREATE TABLE t (val varbit(3));
+CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
+CREATE INDEX ON t USING hnsw ((val::bit(3)) bit_hamming_ops);
+CREATE INDEX ON t USING hnsw ((val::bit(64001)) bit_hamming_ops);
+DROP TABLE t;

test/sql/hnsw_bit_jaccard.sql

@@ -0,0 +1,12 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val bit(4));
+INSERT INTO t (val) VALUES (B'0000'), (B'1100'), (B'1111'), (NULL);
+CREATE INDEX ON t USING hnsw (val bit_jaccard_ops);
+
+INSERT INTO t (val) VALUES (B'1110');
+
+SELECT * FROM t ORDER BY val <%> B'1111';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <%> (SELECT NULL::bit)) t2;
+
+DROP TABLE t;

test/sql/hnsw_halfvec_cosine.sql

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

test/sql/hnsw_halfvec_ip.sql

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

test/sql/hnsw_halfvec_l2.sql

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

test/sql/hnsw_sparsevec_cosine.sql

@@ -0,0 +1,13 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val sparsevec(3));
+INSERT INTO t (val) VALUES ('{}/3'), ('{1:1,2:2,3:3}/3'), ('{1:1,2:1,3:1}/3'), (NULL);
+CREATE INDEX ON t USING hnsw (val sparsevec_cosine_ops);
+
+INSERT INTO t (val) VALUES ('{1:1,2:2,3:4}/3');
+
+SELECT * FROM t ORDER BY val <=> '{1:3,2:3,3:3}/3';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '{}/3') t2;
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::sparsevec)) t2;
+
+DROP TABLE t;

test/sql/hnsw_sparsevec_ip.sql

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

test/sql/hnsw_sparsevec_l2.sql

@@ -0,0 +1,25 @@
+SET enable_seqscan = off;
+
+CREATE TABLE t (val sparsevec(3));
+INSERT INTO t (val) VALUES ('{}/3'), ('{1:1,2:2,3:3}/3'), ('{1:1,2:1,3:1}/3'), (NULL);
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+
+INSERT INTO t (val) VALUES ('{1:1,2:2,3:4}/3');
+
+SELECT * FROM t ORDER BY val <-> '{1:3,2:3,3:3}/3';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::sparsevec)) t2;
+SELECT COUNT(*) FROM t;
+
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '{1:3,2:3,3:3}/3';
+
+DROP TABLE t;
+
+-- TODO move
+CREATE TABLE t (val sparsevec(1001));
+INSERT INTO t (val) VALUES (array_fill(1, ARRAY[1001])::vector::sparsevec);
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+TRUNCATE t;
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+INSERT INTO t (val) VALUES (array_fill(1, ARRAY[1001])::vector::sparsevec);
+DROP TABLE t;

test/sql/hnsw_vector_l2.sql

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

test/sql/ivfflat_halfvec_cosine.sql

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

test/sql/ivfflat_halfvec_ip.sql

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

test/sql/ivfflat_halfvec_l2.sql

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

test/sql/ivfflat_vector_l2.sql

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

test/sql/sparsevec_functions.sql

@@ -0,0 +1,18 @@
+SELECT round(sparsevec_norm('{1:1,2:1}/2')::numeric, 5);
+SELECT sparsevec_norm('{1:3,2:4}/2');
+SELECT sparsevec_norm('{2:1}/2');
+SELECT sparsevec_norm('{1:3e37,2:4e37}/2')::real;
+
+SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+SELECT l2_distance('{}/2'::sparsevec, '{2:1}/2');
+SELECT '{}/2'::sparsevec <-> '{1:3,2:4}/2';
+
+SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
+SELECT sparsevec_negative_inner_product('{1:1,2:2}/2', '{1:2,2:4}/2');
+
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{}/2');
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1,2:-1}/2');
+SELECT cosine_distance('{1:2}/2'::sparsevec, '{2:2}/2');
+SELECT cosine_distance('{}/1'::sparsevec, '{}/1');
+SELECT cosine_distance('{1:2}/2'::sparsevec, '{1:1}/3');

test/sql/sparsevec_input.sql

@@ -0,0 +1,48 @@
+SELECT '{1:1.5,3:3.5}/5'::sparsevec;
+SELECT '{1:-2,3:-4}/5'::sparsevec;
+SELECT '{1:2.,3:4.}/5'::sparsevec;
+SELECT ' { 1 : 1.5 ,  3  :  3.5  } / 5 '::sparsevec;
+SELECT '{1:1.23456}/1'::sparsevec;
+SELECT '{1:hello,2:1}/2'::sparsevec;
+SELECT '{1:NaN,2:1}/2'::sparsevec;
+SELECT '{1:Infinity,2:1}/2'::sparsevec;
+SELECT '{1:-Infinity,2:1}/2'::sparsevec;
+SELECT '{1:1.5e38,2:-1.5e38}/2'::sparsevec;
+SELECT '{1:1.5e+38,2:-1.5e+38}/2'::sparsevec;
+SELECT '{1:1.5e-38,2:-1.5e-38}/2'::sparsevec;
+SELECT '{1:4e38,2:1}/2'::sparsevec;
+SELECT '{1:-4e38,2:1}/2'::sparsevec;
+SELECT '{1:1e-46,2:1}/2'::sparsevec;
+SELECT '{1:-1e-46,2:1}/2'::sparsevec;
+SELECT ''::sparsevec;
+SELECT '{'::sparsevec;
+SELECT '{ '::sparsevec;
+SELECT '{:'::sparsevec;
+SELECT '{,'::sparsevec;
+SELECT '{}'::sparsevec;
+SELECT '{}/'::sparsevec;
+SELECT '{}/1'::sparsevec;
+SELECT '{}/1a'::sparsevec;
+SELECT '{ }/1'::sparsevec;
+SELECT '{:}/1'::sparsevec;
+SELECT '{,}/1'::sparsevec;
+SELECT '{1,}/1'::sparsevec;
+SELECT '{:1}/1'::sparsevec;
+SELECT '{1:}/1'::sparsevec;
+SELECT '{1a:1}/1'::sparsevec;
+SELECT '{1:1a}/1'::sparsevec;
+SELECT '{1:1,}/1'::sparsevec;
+SELECT '{1:0,2:1,3:0}/3'::sparsevec;
+SELECT '{2:1,1:1}/2'::sparsevec;
+SELECT '{}/5'::sparsevec;
+SELECT '{}/-1'::sparsevec;
+SELECT '{}/100001'::sparsevec;
+SELECT '{0:1}/1'::sparsevec;
+SELECT '{2:1}/1'::sparsevec;
+
+SELECT '{}/3'::sparsevec(3);
+SELECT '{}/3'::sparsevec(2);
+SELECT '{}/3'::sparsevec(3, 2);
+SELECT '{}/3'::sparsevec('a');
+SELECT '{}/3'::sparsevec(0);
+SELECT '{}/3'::sparsevec(100001);

test/sql/vector_functions.sql

@@ -0,0 +1,83 @@
+SELECT '[1,2,3]'::vector + '[4,5,6]';
+SELECT '[3e38]'::vector + '[3e38]';
+SELECT '[1,2,3]'::vector - '[4,5,6]';
+SELECT '[-3e38]'::vector - '[3e38]';
+SELECT '[1,2,3]'::vector * '[4,5,6]';
+SELECT '[1e37]'::vector * '[1e37]';
+SELECT '[1e-37]'::vector * '[1e-37]';
+
+SELECT '[1,2,3]'::vector < '[1,2,3]';
+SELECT '[1,2,3]'::vector < '[1,2]';
+SELECT '[1,2,3]'::vector <= '[1,2,3]';
+SELECT '[1,2,3]'::vector <= '[1,2]';
+SELECT '[1,2,3]'::vector = '[1,2,3]';
+SELECT '[1,2,3]'::vector = '[1,2]';
+SELECT '[1,2,3]'::vector != '[1,2,3]';
+SELECT '[1,2,3]'::vector != '[1,2]';
+SELECT '[1,2,3]'::vector >= '[1,2,3]';
+SELECT '[1,2,3]'::vector >= '[1,2]';
+SELECT '[1,2,3]'::vector > '[1,2,3]';
+SELECT '[1,2,3]'::vector > '[1,2]';
+
+SELECT vector_cmp('[1,2,3]', '[1,2,3]');
+SELECT vector_cmp('[1,2,3]', '[0,0,0]');
+SELECT vector_cmp('[0,0,0]', '[1,2,3]');
+SELECT vector_cmp('[1,2]', '[1,2,3]');
+SELECT vector_cmp('[1,2,3]', '[1,2]');
+SELECT vector_cmp('[1,2]', '[2,3,4]');
+SELECT vector_cmp('[2,3]', '[1,2,3]');
+
+SELECT vector_dims('[1,2,3]');
+
+SELECT round(vector_norm('[1,1]')::numeric, 5);
+SELECT vector_norm('[3,4]');
+SELECT vector_norm('[0,1]');
+SELECT vector_norm('[3e37,4e37]')::real;
+
+SELECT l2_distance('[0,0]'::vector, '[3,4]');
+SELECT l2_distance('[0,0]'::vector, '[0,1]');
+SELECT l2_distance('[1,2]'::vector, '[3]');
+SELECT l2_distance('[3e38]'::vector, '[-3e38]');
+
+SELECT inner_product('[1,2]'::vector, '[3,4]');
+SELECT inner_product('[1,2]'::vector, '[3]');
+SELECT inner_product('[3e38]'::vector, '[3e38]');
+
+SELECT cosine_distance('[1,2]'::vector, '[2,4]');
+SELECT cosine_distance('[1,2]'::vector, '[0,0]');
+SELECT cosine_distance('[1,1]'::vector, '[1,1]');
+SELECT cosine_distance('[1,0]'::vector, '[0,2]');
+SELECT cosine_distance('[1,1]'::vector, '[-1,-1]');
+SELECT cosine_distance('[1,2]'::vector, '[3]');
+SELECT cosine_distance('[1,1]'::vector, '[1.1,1.1]');
+SELECT cosine_distance('[1,1]'::vector, '[-1.1,-1.1]');
+SELECT cosine_distance('[3e38]'::vector, '[3e38]');
+
+SELECT l1_distance('[0,0]'::vector, '[3,4]');
+SELECT l1_distance('[0,0]'::vector, '[0,1]');
+SELECT l1_distance('[1,2]'::vector, '[3]');
+SELECT l1_distance('[3e38]'::vector, '[-3e38]');
+
+SELECT quantize_binary('[1,0,-1]'::vector);
+SELECT quantize_binary('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::vector);
+
+SELECT subvector('[1,2,3,4,5]'::vector, 1, 3);
+SELECT subvector('[1,2,3,4,5]'::vector, 3, 2);
+SELECT subvector('[1,2,3,4,5]'::vector, -1, 3);
+SELECT subvector('[1,2,3,4,5]'::vector, 3, 9);
+SELECT subvector('[1,2,3,4,5]'::vector, 1, 0);
+SELECT subvector('[1,2,3,4,5]'::vector, 3, -1);
+SELECT subvector('[1,2,3,4,5]'::vector, -1, 2);
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
+SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
+SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
+SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
+SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;

test/sql/vector_input.sql

@@ -11,18 +11,30 @@ SELECT '[1.5e38,-1.5e38]'::vector;
 SELECT '[1.5e+38,-1.5e+38]'::vector;
 SELECT '[1.5e-38,-1.5e-38]'::vector;
 SELECT '[4e38,1]'::vector;
+SELECT '[-4e38,1]'::vector;
+SELECT '[1e-46,1]'::vector;
+SELECT '[-1e-46,1]'::vector;
 SELECT '[1,2,3'::vector;
 SELECT '[1,2,3]9'::vector;
 SELECT '1,2,3'::vector;
 SELECT ''::vector;
 SELECT '['::vector;
+SELECT '[ '::vector;
 SELECT '[,'::vector;
 SELECT '[]'::vector;
+SELECT '[ ]'::vector;
+SELECT '[,]'::vector;
 SELECT '[1,]'::vector;
 SELECT '[1a]'::vector;
 SELECT '[1,,3]'::vector;
 SELECT '[1, ,3]'::vector;
+
+SELECT '[1,2,3]'::vector(3);
 SELECT '[1,2,3]'::vector(2);
+SELECT '[1,2,3]'::vector(3, 2);
+SELECT '[1,2,3]'::vector('a');
+SELECT '[1,2,3]'::vector(0);
+SELECT '[1,2,3]'::vector(16001);
 
 SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
 SELECT '{"[1,2,3]"}'::vector(2)[];

test/t/003_ivfflat_build_recall.pl

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

test/t/012_hnsw_build_recall.pl

@@ -83,11 +83,46 @@ for my $i (0 .. $#operators)
 		push(@expected, $res);
 	}
 
-	# Add index
-	$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v $opclass);");
+	# Build index serially
+	$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);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel in memory
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		SET client_min_messages = DEBUG;
+		SET min_parallel_table_scan_size = 1;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel on disk
+	# Set parallel_workers on table to use workers with low maintenance_work_mem
+	($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		ALTER TABLE tst SET (parallel_workers = 2);
+		SET client_min_messages = DEBUG;
+		SET maintenance_work_mem = '4MB';
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+		ALTER TABLE tst RESET (parallel_workers);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+	like($stderr, qr/hnsw graph no longer fits into maintenance_work_mem/);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
 }
 
 done_testing();

test/t/013_hnsw_insert_recall.pl

@@ -98,6 +98,7 @@ for my $i (0 .. $#operators)
 		push(@expected, $res);
 	}
 
+	# Test approximate results
 	my $min = $operator eq "<#>" ? 0.80 : 0.99;
 	test_recall($min, $operator);
 

test/t/016_hnsw_vacuum_recall.pl

@@ -86,7 +86,7 @@ foreach (@queries)
 	push(@expected, $res);
 }
 
-test_recall(0.20, $limit, "before vacuum");
+test_recall(0.18, $limit, "before vacuum");
 test_recall(0.95, 100, "before vacuum");
 
 # TODO Test concurrent inserts with vacuum

test/t/018_hnsw_filtering.pl

@@ -0,0 +1,114 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $dim = 3;
+my $nc = 50;
+my $limit = 20;
+
+my $array_sql = join(",", ('random()') x $dim);
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table and index
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim), c int4, t text);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql], i % $nc, 'test ' || i FROM generate_series(1, 10000) i;"
+);
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v vector_l2_ops);");
+$node->safe_psql("postgres", "ANALYZE tst;");
+
+# Generate query
+my @r = ();
+for (1 .. $dim)
+{
+	push(@r, rand());
+}
+my $query = "[" . join(",", @r) . "]";
+my $c = int(rand() * $nc);
+
+# Test attribute filtering
+my $explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Do not use index
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with few rows removed
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c != $c ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with few rows removed comparison
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c >= 1 ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with many rows removed comparison
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c < 1 ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Do not use index
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with few rows removed like
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE t LIKE '%%test%%' ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with many rows removed like
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE t LIKE '%%other%%' ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Seq Scan/);
+
+# Test distance filtering
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1 ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test distance filtering greater than distance
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' > 1 ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Do not use index
+like($explain, qr/Index Scan using idx/);
+
+# Test distance filtering without order
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1;
+));
+like($explain, qr/Seq Scan/);
+
+# Test distance filtering without limit
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1 ORDER BY v <-> '$query';
+));
+like($explain, qr/Seq Scan/);
+
+# Test attribute index
+$node->safe_psql("postgres", "CREATE INDEX attribute_idx ON tst (c);");
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Use attribute index
+like($explain, qr/Index Scan using idx/);
+
+# Test partial index
+$node->safe_psql("postgres", "CREATE INDEX partial_idx ON tst USING hnsw (v vector_l2_ops) WHERE (c = $c);");
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using partial_idx/);
+
+done_testing();

test/t/018_ivfflat_deletes.pl

@@ -1,43 +0,0 @@
-use strict;
-use warnings;
-use PostgresNode;
-use TestLib;
-use Test::More;
-
-my $dim = 3;
-
-my $array_sql = join(",", ('random()') x $dim);
-
-# Initialize node
-my $node = get_new_node('node');
-$node->init;
-$node->start;
-
-# Create table and index
-$node->safe_psql("postgres", "CREATE EXTENSION vector;");
-$node->safe_psql("postgres", "CREATE TABLE tst (i serial, v vector($dim));");
-$node->safe_psql("postgres",
-	"INSERT INTO tst (v) SELECT ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
-);
-$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v vector_l2_ops);");
-
-# Delete data
-$node->safe_psql("postgres", "DELETE FROM tst WHERE i % 100 != 0;");
-
-my $exp = $node->safe_psql("postgres", qq(
-	SET enable_indexscan = off;
-	SELECT i FROM tst ORDER BY v <-> '[0,0,0]';
-));
-
-# Run twice to make sure correct tuples marked as dead
-for (1 .. 2)
-{
-	my $res = $node->safe_psql("postgres", qq(
-		SET enable_seqscan = off;
-		SET ivfflat.probes = 100;
-		SELECT i FROM tst ORDER BY v <-> '[0,0,0]';
-	));
-	is($res, $exp);
-}
-
-done_testing();

test/t/019_ivfflat_filtering.pl

@@ -0,0 +1,116 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $dim = 3;
+my $nc = 50;
+my $limit = 20;
+
+my $array_sql = join(",", ('random()') x $dim);
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table and index
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector($dim), c int4, t text);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql], i % $nc, 'test ' || i FROM generate_series(1, 10000) i;"
+);
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING ivfflat (v vector_l2_ops) WITH (lists = 100);");
+$node->safe_psql("postgres", "ANALYZE tst;");
+
+# Generate query
+my @r = ();
+for (1 .. $dim)
+{
+	push(@r, rand());
+}
+my $query = "[" . join(",", @r) . "]";
+my $c = int(rand() * $nc);
+
+# Test attribute filtering
+my $explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Do not use index
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with few rows removed
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c != $c ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with few rows removed comparison
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c >= 1 ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with many rows removed comparison
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c < 1 ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Do not use index
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with few rows removed like
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE t LIKE '%%test%%' ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute filtering with many rows removed like
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE t LIKE '%%other%%' ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Seq Scan/);
+
+# Test distance filtering
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1 ORDER BY v <-> '$query' LIMIT $limit;
+));
+like($explain, qr/Index Scan using idx/);
+
+# Test distance filtering greater than distance
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' > 1 ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Do not use index
+like($explain, qr/Index Scan using idx/);
+
+# Test distance filtering without order
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1;
+));
+like($explain, qr/Seq Scan/);
+
+# Test distance filtering without limit
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE v <-> '$query' < 1 ORDER BY v <-> '$query';
+));
+# TODO Do not use index
+like($explain, qr/Index Scan using idx/);
+
+# Test attribute index
+$node->safe_psql("postgres", "CREATE INDEX attribute_idx ON tst (c);");
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Use attribute index
+like($explain, qr/Index Scan using idx/);
+
+# Test partial index
+$node->safe_psql("postgres", "CREATE INDEX partial_idx ON tst USING ivfflat (v vector_l2_ops) WITH (lists = 5) WHERE (c = $c);");
+$explain = $node->safe_psql("postgres", qq(
+	EXPLAIN ANALYZE SELECT i FROM tst WHERE c = $c ORDER BY v <-> '$query' LIMIT $limit;
+));
+# TODO Use partial index
+like($explain, qr/Index Scan using idx/);
+
+done_testing();

test/t/020_hnsw_bit_build_recall.pl

@@ -0,0 +1,137 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 52;
+my $max = 2**$dim;
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 100;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator $queries[0] LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = 100;
+			SELECT i FROM tst ORDER BY v $operator $queries[$i] LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+
+		my @expected_ids = split("\n", $expected[$i]);
+		my %expected_set = map { $_ => 1 } @expected_ids;
+
+		foreach (@actual_ids)
+		{
+			if (exists($expected_set{$_}))
+			{
+				$correct++;
+			}
+		}
+
+		$total += $limit;
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v bit($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, (random() * $max)::bigint::bit($dim) FROM generate_series(1, 10000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r = int(rand() * $max);
+	push(@queries, "${r}::bigint::bit($dim)");
+}
+
+# Check each index type
+my @operators = ("<~>", "<\%>");
+my @opclasses = ("bit_hamming_ops", "bit_jaccard_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		# Handle ties
+		my $res = $node->safe_psql("postgres", qq(
+			WITH top AS (
+				SELECT v $operator $_ AS distance FROM tst ORDER BY distance LIMIT $limit
+			)
+			SELECT i FROM tst WHERE (v $operator $_) <= (SELECT MAX(distance) FROM top)
+		));
+		push(@expected, $res);
+	}
+
+	# Build index serially
+	$node->safe_psql("postgres", qq(
+		SET max_parallel_maintenance_workers = 0;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+
+	# Test approximate results
+	my $min = $operator eq "<\%>" ? 0.95 : 0.98;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel in memory
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		SET client_min_messages = DEBUG;
+		SET min_parallel_table_scan_size = 1;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel on disk
+	# Set parallel_workers on table to use workers with low maintenance_work_mem
+	($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		ALTER TABLE tst SET (parallel_workers = 2);
+		SET client_min_messages = DEBUG;
+		SET maintenance_work_mem = '4MB';
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+		ALTER TABLE tst RESET (parallel_workers);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+	like($stderr, qr/hnsw graph no longer fits into maintenance_work_mem/);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();

test/t/021_hnsw_halfvec_build_recall.pl

@@ -0,0 +1,132 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 10;
+my $array_sql = join(",", ('random()') x $dim);
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v halfvec($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 10000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
+		push(@expected, $res);
+	}
+
+	# Build index serially
+	$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 = $operator eq "<#>" ? 0.93 : 0.98;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel in memory
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		SET client_min_messages = DEBUG;
+		SET min_parallel_table_scan_size = 1;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel on disk
+	# Set parallel_workers on table to use workers with low maintenance_work_mem
+	($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		ALTER TABLE tst SET (parallel_workers = 2);
+		SET client_min_messages = DEBUG;
+		SET maintenance_work_mem = '4MB';
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+		ALTER TABLE tst RESET (parallel_workers);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+	like($stderr, qr/hnsw graph no longer fits into maintenance_work_mem/);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();