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: ${{ failure() }}
         run: cat regression.diffs
+      # Homebrew Postgres does not enable TAP tests, so need to download
       - run: |
           brew install cpanm
           cpanm --notest IPC::Run
-          wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_14_5.tar.gz
+          wget -q https://github.com/postgres/postgres/archive/refs/tags/$TAG.tar.gz
-          tar xf REL_14_5.tar.gz
+          tar xf $TAG.tar.gz
-      - run: make prove_installcheck PROVE_FLAGS="-I ./postgres-REL_14_5/src/test/perl" PERL5LIB="/Users/runner/perl5/lib/perl5"
+          mv postgres-$TAG postgres
-      - run: make clean && /usr/local/opt/llvm@15/bin/scan-build --status-bugs make
+        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 && ^
@@ -78,21 +95,34 @@ jobs:
           nmake /NOLOGO /F Makefile.win uninstall
         shell: cmd
   i386:
+    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
           cd pgvector
-          git checkout ${{ github.ref }}
+          git fetch origin ${{ github.ref }}
+          git reset --hard FETCH_HEAD
           make
           make install
           chown -R postgres .
           sudo -u postgres make installcheck
           sudo -u postgres make prove_installcheck
         env:
-          PG_CFLAGS: -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
+          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 +1,57 @@
+## 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
+- Added check for MVCC-compliant snapshot for index scans
+
+## 0.5.0 (2023-08-28)
+
+- Added HNSW index type
+- Added support for parallel index builds for IVFFlat
+- Added `l1_distance` function
+- Added element-wise multiplication for vectors
+- Added `sum` aggregate
+- Improved performance of distance functions
+- Fixed out of range results for cosine distance
+- Fixed results for NULL and NaN distances for IVFFlat
+
 ## 0.4.4 (2023-06-12)
 
 - Improved error message for malformed vector literal
@@ -28,7 +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`
@@ -45,7 +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

@@ -1,10 +1,11 @@
-ARG PG_MAJOR=15
+ARG PG_MAJOR=16
 FROM postgres:$PG_MAJOR
 ARG PG_MAJOR
 
 COPY . /tmp/pgvector
 
 RUN apt-get update && \
+		apt-mark hold locales && \
 		apt-get install -y --no-install-recommends build-essential postgresql-server-dev-$PG_MAJOR && \
 		cd /tmp/pgvector && \
 		make clean && \
@@ -15,4 +16,5 @@ RUN apt-get update && \
 		rm -r /tmp/pgvector && \
 		apt-get remove -y build-essential postgresql-server-dev-$PG_MAJOR && \
 		apt-get autoremove -y && \
+		apt-mark unhold locales && \
 		rm -rf /var/lib/apt/lists/*

LICENSE

@@ -1,4 +1,4 @@
-Portions Copyright (c) 1996-2023, 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": "0.4.4",
+	"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": "0.4.4",
+			"version": "0.6.2",
 			"abstract": "Open-source vector similarity search for Postgres"
 		}
 	},

Makefile

@@ -1,17 +1,18 @@
 EXTENSION = vector
-EXTVERSION = 0.4.4
+EXTVERSION = 0.6.2
 
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
-OBJS = src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
+OBJS = src/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))
-REGRESS_OPTS = --inputdir=test --load-extension=vector
+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
@@ -64,13 +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 --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) .
-	docker buildx build --push --platform linux/amd64,linux/arm64 -t ankane/pgvector:v$(EXTVERSION) .

Makefile.win

@@ -1,10 +1,11 @@
 EXTENSION = vector
-EXTVERSION = 0.4.4
+EXTVERSION = 0.6.2
 
-OBJS = src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\vector.obj
+OBJS = src\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=vector
+REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
 
 # For /arch flags
 # https://learn.microsoft.com/en-us/cpp/build/reference/arch-minimum-cpu-architecture
@@ -54,6 +55,8 @@ install:
 	copy $(SHLIB) "$(PKGLIBDIR)"
 	copy $(EXTENSION).control "$(SHAREDIR)\extension"
 	copy sql\$(EXTENSION)--*.sql "$(SHAREDIR)\extension"
+	mkdir "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
+	for %f in ($(HEADERS)) do copy %f "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
 
 installcheck:
 	"$(BINDIR)\pg_regress" --bindir="$(BINDIR)" $(REGRESS_OPTS) $(REGRESS)
@@ -61,7 +64,9 @@ installcheck:
 uninstall:
 	del /f "$(PKGLIBDIR)\$(SHLIB)"
 	del /f "$(SHAREDIR)\extension\$(EXTENSION).control"
-	del /f "$(SHAREDIR)\extension\vector--*.sql"
+	del /f "$(SHAREDIR)\extension\$(EXTENSION)--*.sql"
+	del /f "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)\*.h"
+	rmdir "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
 
 clean:
 	del /f $(SHLIB) $(EXTENSION).lib $(EXTENSION).exp

sql/vector--0.4.4--0.5.0.sql

@@ -0,0 +1,43 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.5.0'" to load this file. \quit
+
+CREATE FUNCTION l1_distance(vector, vector) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE OPERATOR * (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_mul,
+	COMMUTATOR = *
+);
+
+CREATE AGGREGATE sum(vector) (
+	SFUNC = vector_add,
+	STYPE = vector,
+	COMBINEFUNC = vector_add,
+	PARALLEL = SAFE
+);
+
+CREATE FUNCTION hnswhandler(internal) RETURNS index_am_handler
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE ACCESS METHOD hnsw TYPE INDEX HANDLER hnswhandler;
+
+COMMENT ON ACCESS METHOD hnsw IS 'hnsw index access method';
+
+CREATE OPERATOR CLASS vector_l2_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <-> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_l2_squared_distance(vector, vector);
+
+CREATE OPERATOR CLASS vector_ip_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <#> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_negative_inner_product(vector, vector);
+
+CREATE OPERATOR CLASS vector_cosine_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_negative_inner_product(vector, vector),
+	FUNCTION 2 vector_norm(vector);

sql/vector--0.5.0--0.5.1.sql

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

sql/vector--0.5.1--0.6.0.sql

@@ -0,0 +1,5 @@
+-- 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;
@@ -40,6 +40,9 @@ CREATE FUNCTION inner_product(vector, vector) RETURNS float8
 CREATE FUNCTION cosine_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION l1_distance(vector, vector) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE FUNCTION vector_dims(vector) RETURNS integer
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
@@ -52,7 +55,16 @@ CREATE FUNCTION vector_add(vector, vector) RETURNS vector
 CREATE FUNCTION vector_sub(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- private functions
+CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+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;
@@ -93,7 +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,
@@ -104,7 +116,14 @@ CREATE AGGREGATE avg(vector) (
 	PARALLEL = SAFE
 );
 
--- cast functions
+CREATE AGGREGATE sum(vector) (
+	SFUNC = vector_add,
+	STYPE = vector,
+	COMBINEFUNC = vector_add,
+	PARALLEL = SAFE
+);
+
+-- vector cast functions
 
 CREATE FUNCTION vector(vector, integer, boolean) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -124,7 +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;
@@ -144,7 +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,
@@ -167,8 +186,12 @@ CREATE OPERATOR + (
 );
 
 CREATE OPERATOR - (
-	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_sub,
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_sub
-	COMMUTATOR = -
+);
+
+CREATE OPERATOR * (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_mul,
+	COMMUTATOR = *
 );
 
 CREATE OPERATOR < (
@@ -177,11 +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 = (
@@ -196,11 +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 > (
@@ -209,7 +230,7 @@ CREATE OPERATOR > (
 	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
 );
 
--- access method
+-- access methods
 
 CREATE FUNCTION ivfflathandler(internal) RETURNS index_am_handler
 	AS 'MODULE_PATHNAME' LANGUAGE C;
@@ -218,7 +239,14 @@ CREATE ACCESS METHOD ivfflat TYPE INDEX HANDLER ivfflathandler;
 
 COMMENT ON ACCESS METHOD ivfflat IS 'ivfflat index access method';
 
--- opclasses
+CREATE FUNCTION hnswhandler(internal) RETURNS index_am_handler
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE ACCESS METHOD hnsw TYPE INDEX HANDLER hnswhandler;
+
+COMMENT ON ACCESS METHOD hnsw IS 'hnsw index access method';
+
+-- vector opclasses
 
 CREATE OPERATOR CLASS vector_ops
 	DEFAULT FOR TYPE vector USING btree AS
@@ -249,3 +277,326 @@ CREATE OPERATOR CLASS vector_cosine_ops
 	FUNCTION 2 vector_norm(vector),
 	FUNCTION 3 vector_spherical_distance(vector, vector),
 	FUNCTION 4 vector_norm(vector);
+
+CREATE OPERATOR CLASS vector_l2_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <-> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_l2_squared_distance(vector, vector);
+
+CREATE OPERATOR CLASS vector_ip_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <#> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_negative_inner_product(vector, vector);
+
+CREATE OPERATOR CLASS vector_cosine_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 vector_negative_inner_product(vector, vector),
+	FUNCTION 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

@@ -0,0 +1,249 @@
+#include "postgres.h"
+
+#include <float.h>
+#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 < 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
+#if PG_VERSION_NUM >= 130000
+					  ,AccessExclusiveLock
+#endif
+		);
+	add_int_reloption(hnsw_relopt_kind, "ef_construction", "Size of the dynamic candidate list for construction",
+					  HNSW_DEFAULT_EF_CONSTRUCTION, HNSW_MIN_EF_CONSTRUCTION, HNSW_MAX_EF_CONSTRUCTION
+#if PG_VERSION_NUM >= 130000
+					  ,AccessExclusiveLock
+#endif
+		);
+
+	DefineCustomIntVariable("hnsw.ef_search", "Sets the size of the dynamic candidate list for search",
+							"Valid range is 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
+ */
+static char *
+hnswbuildphasename(int64 phasenum)
+{
+	switch (phasenum)
+	{
+		case PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE:
+			return "initializing";
+		case PROGRESS_HNSW_PHASE_LOAD:
+			return "loading tuples";
+		default:
+			return NULL;
+	}
+}
+
+/*
+ * Estimate the cost of an index scan
+ */
+static void
+hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
+				 Cost *indexStartupCost, Cost *indexTotalCost,
+				 Selectivity *indexSelectivity, double *indexCorrelation,
+				 double *indexPages)
+{
+	GenericCosts costs;
+	int			m;
+	int			entryLevel;
+	Relation	index;
+
+	/* Never use index without order */
+	if (path->indexorderbys == NULL)
+	{
+		*indexStartupCost = DBL_MAX;
+		*indexTotalCost = DBL_MAX;
+		*indexSelectivity = 0;
+		*indexCorrelation = 0;
+		*indexPages = 0;
+		return;
+	}
+
+	MemSet(&costs, 0, sizeof(costs));
+
+	index = index_open(path->indexinfo->indexoid, NoLock);
+	HnswGetMetaPageInfo(index, &m, NULL);
+	index_close(index, NoLock);
+
+	/* Approximate entry level */
+	entryLevel = (int) -log(1.0 / path->indexinfo->tuples) * HnswGetMl(m);
+
+	/* TODO Improve estimate of visited tuples (currently underestimates) */
+	/* Account for number of tuples (or entry level), m, and ef_search */
+	costs.numIndexTuples = (entryLevel + 2) * m;
+
+	genericcostestimate(root, path, loop_count, &costs);
+
+	/* Use total cost since most work happens before first tuple is returned */
+	*indexStartupCost = costs.indexTotalCost;
+	*indexTotalCost = costs.indexTotalCost;
+	*indexSelectivity = costs.indexSelectivity;
+	*indexCorrelation = costs.indexCorrelation;
+	*indexPages = costs.numIndexPages;
+}
+
+/*
+ * Parse and validate the reloptions
+ */
+static bytea *
+hnswoptions(Datum reloptions, bool validate)
+{
+	static const relopt_parse_elt tab[] = {
+		{"m", RELOPT_TYPE_INT, offsetof(HnswOptions, m)},
+		{"ef_construction", RELOPT_TYPE_INT, offsetof(HnswOptions, efConstruction)},
+	};
+
+#if PG_VERSION_NUM >= 130000
+	return (bytea *) build_reloptions(reloptions, validate,
+									  hnsw_relopt_kind,
+									  sizeof(HnswOptions),
+									  tab, lengthof(tab));
+#else
+	relopt_value *options;
+	int			numoptions;
+	HnswOptions *rdopts;
+
+	options = parseRelOptions(reloptions, validate, hnsw_relopt_kind, &numoptions);
+	rdopts = allocateReloptStruct(sizeof(HnswOptions), options, numoptions);
+	fillRelOptions((void *) rdopts, sizeof(HnswOptions), options, numoptions,
+				   validate, tab, lengthof(tab));
+
+	return (bytea *) rdopts;
+#endif
+}
+
+/*
+ * Validate catalog entries for the specified operator class
+ */
+static bool
+hnswvalidate(Oid opclassoid)
+{
+	return true;
+}
+
+/*
+ * Define index handler
+ *
+ * See https://www.postgresql.org/docs/current/index-api.html
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(hnswhandler);
+Datum
+hnswhandler(PG_FUNCTION_ARGS)
+{
+	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);
+
+	amroutine->amstrategies = 0;
+	amroutine->amsupport = 2;
+#if PG_VERSION_NUM >= 130000
+	amroutine->amoptsprocnum = 0;
+#endif
+	amroutine->amcanorder = false;
+	amroutine->amcanorderbyop = true;
+	amroutine->amcanbackward = false;	/* can change direction mid-scan */
+	amroutine->amcanunique = false;
+	amroutine->amcanmulticol = false;
+	amroutine->amoptionalkey = true;
+	amroutine->amsearcharray = false;
+	amroutine->amsearchnulls = false;
+	amroutine->amstorage = false;
+	amroutine->amclusterable = false;
+	amroutine->ampredlocks = false;
+	amroutine->amcanparallel = false;
+	amroutine->amcaninclude = false;
+#if PG_VERSION_NUM >= 130000
+	amroutine->amusemaintenanceworkmem = false; /* not used during VACUUM */
+	amroutine->amparallelvacuumoptions = VACUUM_OPTION_PARALLEL_BULKDEL;
+#endif
+	amroutine->amkeytype = InvalidOid;
+
+	/* Interface functions */
+	amroutine->ambuild = hnswbuild;
+	amroutine->ambuildempty = hnswbuildempty;
+	amroutine->aminsert = hnswinsert;
+	amroutine->ambulkdelete = hnswbulkdelete;
+	amroutine->amvacuumcleanup = hnswvacuumcleanup;
+	amroutine->amcanreturn = NULL;
+	amroutine->amcostestimate = hnswcostestimate;
+	amroutine->amoptions = hnswoptions;
+	amroutine->amproperty = NULL;	/* TODO AMPROP_DISTANCE_ORDERABLE */
+	amroutine->ambuildphasename = hnswbuildphasename;
+	amroutine->amvalidate = hnswvalidate;
+#if PG_VERSION_NUM >= 140000
+	amroutine->amadjustmembers = NULL;
+#endif
+	amroutine->ambeginscan = hnswbeginscan;
+	amroutine->amrescan = hnswrescan;
+	amroutine->amgettuple = hnswgettuple;
+	amroutine->amgetbitmap = NULL;
+	amroutine->amendscan = hnswendscan;
+	amroutine->ammarkpos = NULL;
+	amroutine->amrestrpos = NULL;
+
+	/* Interface functions to support parallel index scans */
+	amroutine->amestimateparallelscan = NULL;
+	amroutine->aminitparallelscan = NULL;
+	amroutine->amparallelrescan = NULL;
+
+	PG_RETURN_POINTER(amroutine);
+}

src/hnsw.h

@@ -0,0 +1,473 @@
+#ifndef HNSW_H
+#define HNSW_H
+
+#include "postgres.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 < 120000
+#error "Requires PostgreSQL 12+"
+#endif
+
+#define HNSW_MAX_DIM 2000
+#define HNSW_MAX_NNZ 1000
+
+/* Support functions */
+#define HNSW_DISTANCE_PROC 1
+#define HNSW_NORM_PROC 2
+
+#define HNSW_VERSION	1
+#define HNSW_MAGIC_NUMBER 0xA953A953
+#define HNSW_PAGE_ID	0xFF90
+
+/* Preserved page numbers */
+#define HNSW_METAPAGE_BLKNO	0
+#define HNSW_HEAD_BLKNO		1	/* first element page */
+
+/* Must correspond to page numbers since page lock is used */
+#define HNSW_UPDATE_LOCK 	0
+#define HNSW_SCAN_LOCK		1
+
+/* HNSW parameters */
+#define HNSW_DEFAULT_M	16
+#define HNSW_MIN_M	2
+#define HNSW_MAX_M		100
+#define HNSW_DEFAULT_EF_CONSTRUCTION	64
+#define HNSW_MIN_EF_CONSTRUCTION	4
+#define HNSW_MAX_EF_CONSTRUCTION		1000
+#define HNSW_DEFAULT_EF_SEARCH	40
+#define HNSW_MIN_EF_SEARCH		1
+#define HNSW_MAX_EF_SEARCH		1000
+
+/* Tuple types */
+#define HNSW_ELEMENT_TUPLE_TYPE  1
+#define HNSW_NEIGHBOR_TUPLE_TYPE 2
+
+/* Make graph robust against non-HOT updates */
+#define HNSW_HEAPTIDS 10
+
+#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(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) = list_qsort(list, cmp))
+#endif
+
+#define HnswIsElementTuple(tup) ((tup)->type == HNSW_ELEMENT_TUPLE_TYPE)
+#define HnswIsNeighborTuple(tup) ((tup)->type == HNSW_NEIGHBOR_TUPLE_TYPE)
+
+/* 2 * M connections for ground layer */
+#define HnswGetLayerM(m, layer) (layer == 0 ? (m) * 2 : (m))
+
+/* Optimal ML from paper */
+#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 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;
+
+#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
+{
+	HnswElementPtr next;
+	ItemPointerData heaptids[HNSW_HEAPTIDS];
+	uint8		heaptidsLength;
+	uint8		level;
+	uint8		deleted;
+	uint32		hash;
+	HnswNeighborsPtr neighbors;
+	BlockNumber blkno;
+	OffsetNumber offno;
+	OffsetNumber neighborOffno;
+	BlockNumber neighborPage;
+	DatumPtr	value;
+	LWLock		lock;
+};
+
+typedef HnswElementData * HnswElement;
+
+typedef struct HnswCandidate
+{
+	HnswElementPtr element;
+	float		distance;
+	bool		closer;
+}			HnswCandidate;
+
+struct HnswNeighborArray
+{
+	int			length;
+	bool		closerSet;
+	HnswCandidate items[FLEXIBLE_ARRAY_MEMBER];
+};
+
+typedef struct HnswPairingHeapNode
+{
+	pairingheap_node ph_node;
+	HnswCandidate *inner;
+}			HnswPairingHeapNode;
+
+/* HNSW index options */
+typedef struct HnswOptions
+{
+	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int			m;				/* number of connections */
+	int			efConstruction; /* size of dynamic candidate list */
+}			HnswOptions;
+
+typedef struct 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 */
+	Relation	heap;
+	Relation	index;
+	IndexInfo  *indexInfo;
+	ForkNumber	forkNum;
+	HnswType	type;
+
+	/* Settings */
+	int			dimensions;
+	int			m;
+	int			efConstruction;
+
+	/* Statistics */
+	double		indtuples;
+	double		reltuples;
+
+	/* Support functions */
+	FmgrInfo   *procinfo;
+	FmgrInfo   *normprocinfo;
+	Oid			collation;
+
+	/* Variables */
+	HnswGraph	graphData;
+	HnswGraph  *graph;
+	double		ml;
+	int			maxLevel;
+
+	/* Memory */
+	MemoryContext graphCtx;
+	MemoryContext tmpCtx;
+	HnswAllocator allocator;
+
+	/* Parallel builds */
+	HnswLeader *hnswleader;
+	HnswShared *hnswshared;
+	char	   *hnswarea;
+}			HnswBuildState;
+
+typedef struct HnswMetaPageData
+{
+	uint32		magicNumber;
+	uint32		version;
+	uint32		dimensions;
+	uint16		m;
+	uint16		efConstruction;
+	BlockNumber entryBlkno;
+	OffsetNumber entryOffno;
+	int16		entryLevel;
+	BlockNumber insertPage;
+}			HnswMetaPageData;
+
+typedef HnswMetaPageData * HnswMetaPage;
+
+typedef struct HnswPageOpaqueData
+{
+	BlockNumber nextblkno;
+	uint16		unused;
+	uint16		page_id;		/* for identification of HNSW indexes */
+}			HnswPageOpaqueData;
+
+typedef HnswPageOpaqueData * HnswPageOpaque;
+
+typedef struct HnswElementTupleData
+{
+	uint8		type;
+	uint8		level;
+	uint8		deleted;
+	uint8		unused;
+	ItemPointerData heaptids[HNSW_HEAPTIDS];
+	ItemPointerData neighbortid;
+	uint16		unused2;
+	Vector		data;
+}			HnswElementTupleData;
+
+typedef HnswElementTupleData * HnswElementTuple;
+
+typedef struct HnswNeighborTupleData
+{
+	uint8		type;
+	uint8		unused;
+	uint16		count;
+	ItemPointerData indextids[FLEXIBLE_ARRAY_MEMBER];
+}			HnswNeighborTupleData;
+
+typedef HnswNeighborTupleData * HnswNeighborTuple;
+
+typedef struct HnswScanOpaqueData
+{
+	bool		first;
+	List	   *w;
+	MemoryContext tmpCtx;
+
+	/* Support functions */
+	FmgrInfo   *procinfo;
+	FmgrInfo   *normprocinfo;
+	Oid			collation;
+}			HnswScanOpaqueData;
+
+typedef HnswScanOpaqueData * HnswScanOpaque;
+
+typedef struct HnswVacuumState
+{
+	/* Info */
+	Relation	index;
+	IndexBulkDeleteResult *stats;
+	IndexBulkDeleteCallback callback;
+	void	   *callback_state;
+
+	/* Settings */
+	int			m;
+	int			efConstruction;
+
+	/* Support functions */
+	FmgrInfo   *procinfo;
+	Oid			collation;
+
+	/* Variables */
+	struct tidhash_hash *deleted;
+	BufferAccessStrategy bas;
+	HnswNeighborTuple ntup;
+	HnswElementData highestPoint;
+
+	/* Memory */
+	MemoryContext tmpCtx;
+}			HnswVacuumState;
+
+/* Methods */
+int			HnswGetM(Relation index);
+int			HnswGetEfConstruction(Relation index);
+FmgrInfo   *HnswOptionalProcInfo(Relation index, uint16 procnum);
+HnswType	HnswGetType(Relation index);
+bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, HnswType type);
+void		HnswCheckValue(Datum value, HnswType type);
+Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
+void		HnswInitPage(Buffer buf, Page page);
+void		HnswInit(void);
+List	   *HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement);
+HnswElement HnswGetEntryPoint(Relation index);
+void		HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
+void	   *HnswAlloc(HnswAllocator * allocator, Size size);
+HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
+HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
+void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
+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(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(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);
+void		hnswbuildempty(Relation index);
+bool		hnswinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heap, IndexUniqueCheck checkUnique
+#if PG_VERSION_NUM >= 140000
+					   ,bool indexUnchanged
+#endif
+					   ,IndexInfo *indexInfo
+);
+IndexBulkDeleteResult *hnswbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats, IndexBulkDeleteCallback callback, void *callback_state);
+IndexBulkDeleteResult *hnswvacuumcleanup(IndexVacuumInfo *info, IndexBulkDeleteResult *stats);
+IndexScanDesc hnswbeginscan(Relation index, int nkeys, int norderbys);
+void		hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int norderbys);
+bool		hnswgettuple(IndexScanDesc scan, ScanDirection dir);
+void		hnswendscan(IndexScanDesc scan);
+
+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

@@ -0,0 +1,669 @@
+#include "postgres.h"
+
+#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"
+
+/*
+ * Get the insert page
+ */
+static BlockNumber
+GetInsertPage(Relation index)
+{
+	Buffer		buf;
+	Page		page;
+	HnswMetaPage metap;
+	BlockNumber insertPage;
+
+	buf = ReadBuffer(index, HNSW_METAPAGE_BLKNO);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	metap = HnswPageGetMeta(page);
+
+	insertPage = metap->insertPage;
+
+	UnlockReleaseBuffer(buf);
+
+	return insertPage;
+}
+
+/*
+ * Check for a free offset
+ */
+static bool
+HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *newInsertPage)
+{
+	OffsetNumber offno;
+	OffsetNumber maxoffno = PageGetMaxOffsetNumber(page);
+
+	for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+	{
+		HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+
+		/* Skip neighbor tuples */
+		if (!HnswIsElementTuple(etup))
+			continue;
+
+		if (etup->deleted)
+		{
+			BlockNumber elementPage = BufferGetBlockNumber(buf);
+			BlockNumber neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
+			OffsetNumber neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
+			ItemId		itemid;
+
+			if (!BlockNumberIsValid(*newInsertPage))
+				*newInsertPage = elementPage;
+
+			if (neighborPage == elementPage)
+			{
+				*nbuf = buf;
+				*npage = page;
+			}
+			else
+			{
+				*nbuf = ReadBuffer(index, neighborPage);
+				LockBuffer(*nbuf, BUFFER_LOCK_EXCLUSIVE);
+
+				/* Skip WAL for now */
+				*npage = BufferGetPage(*nbuf);
+			}
+
+			itemid = PageGetItemId(*npage, neighborOffno);
+
+			/* Check for space on neighbor tuple page */
+			if (PageGetFreeSpace(*npage) + ItemIdGetLength(itemid) - sizeof(ItemIdData) >= ntupSize)
+			{
+				*freeOffno = offno;
+				*freeNeighborOffno = neighborOffno;
+				return true;
+			}
+			else if (*nbuf != buf)
+				UnlockReleaseBuffer(*nbuf);
+		}
+	}
+
+	return false;
+}
+
+/*
+ * Add a new page
+ */
+static void
+HnswInsertAppendPage(Relation index, Buffer *nbuf, Page *npage, GenericXLogState *state, Page page, bool building)
+{
+	/* Add a new page */
+	LockRelationForExtension(index, ExclusiveLock);
+	*nbuf = HnswNewBuffer(index, MAIN_FORKNUM);
+	UnlockRelationForExtension(index, ExclusiveLock);
+
+	/* Init new page */
+	if (building)
+		*npage = BufferGetPage(*nbuf);
+	else
+		*npage = GenericXLogRegisterBuffer(state, *nbuf, GENERIC_XLOG_FULL_IMAGE);
+
+	HnswInitPage(*nbuf, *npage);
+
+	/* Update previous buffer */
+	HnswPageGetOpaque(page)->nextblkno = BufferGetBlockNumber(*nbuf);
+}
+
+/*
+ * Add to element and neighbor pages
+ */
+static void
+AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, BlockNumber *updatedInsertPage, bool building)
+{
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	Size		etupSize;
+	Size		ntupSize;
+	Size		combinedSize;
+	Size		maxSize;
+	Size		minCombinedSize;
+	HnswElementTuple etup;
+	BlockNumber currentPage = insertPage;
+	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(VARSIZE_ANY(HnswPtrAccess(base, e->value)));
+	ntupSize = HNSW_NEIGHBOR_TUPLE_SIZE(e->level, m);
+	combinedSize = etupSize + ntupSize + sizeof(ItemIdData);
+	maxSize = HNSW_MAX_SIZE;
+	minCombinedSize = etupSize + HNSW_NEIGHBOR_TUPLE_SIZE(0, m) + sizeof(ItemIdData);
+
+	/* Prepare element tuple */
+	etup = palloc0(etupSize);
+	HnswSetElementTuple(base, etup, e);
+
+	/* Prepare neighbor tuple */
+	ntup = palloc0(ntupSize);
+	HnswSetNeighborTuple(base, ntup, e, m);
+
+	/* Find a page (or two if needed) to insert the tuples */
+	for (;;)
+	{
+		buf = ReadBuffer(index, currentPage);
+		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+
+		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)
+			newInsertPage = currentPage;
+
+		/* First, try the fastest path */
+		/* Space for both tuples on the current page */
+		/* This can split existing tuples in rare cases */
+		if (PageGetFreeSpace(page) >= combinedSize)
+		{
+			nbuf = buf;
+			npage = page;
+			break;
+		}
+
+		/* Next, try space from a deleted element */
+		if (HnswFreeOffset(index, buf, page, e, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage))
+		{
+			if (nbuf != buf)
+			{
+				if (building)
+					npage = BufferGetPage(nbuf);
+				else
+					npage = GenericXLogRegisterBuffer(state, nbuf, 0);
+			}
+
+			break;
+		}
+
+		/* Finally, try space for element only if last page */
+		/* 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, building);
+			break;
+		}
+
+		currentPage = HnswPageGetOpaque(page)->nextblkno;
+
+		if (BlockNumberIsValid(currentPage))
+		{
+			/* Move to next page */
+			if (!building)
+				GenericXLogAbort(state);
+			UnlockReleaseBuffer(buf);
+		}
+		else
+		{
+			Buffer		newbuf;
+			Page		newpage;
+
+			HnswInsertAppendPage(index, &newbuf, &newpage, state, page, building);
+
+			/* Commit */
+			if (building)
+				MarkBufferDirty(buf);
+			else
+				GenericXLogFinish(state);
+
+			/* Unlock previous buffer */
+			UnlockReleaseBuffer(buf);
+
+			/* Prepare new buffer */
+			buf = newbuf;
+			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, building);
+			else
+			{
+				nbuf = buf;
+				npage = page;
+			}
+
+			break;
+		}
+	}
+
+	e->blkno = BufferGetBlockNumber(buf);
+	e->neighborPage = BufferGetBlockNumber(nbuf);
+
+	/* Added tuple to new page if newInsertPage is not set */
+	/* So can set to neighbor page instead of element page */
+	if (!BlockNumberIsValid(newInsertPage))
+		newInsertPage = e->neighborPage;
+
+	if (OffsetNumberIsValid(freeOffno))
+	{
+		e->offno = freeOffno;
+		e->neighborOffno = freeNeighborOffno;
+	}
+	else
+	{
+		e->offno = OffsetNumberNext(PageGetMaxOffsetNumber(page));
+		if (nbuf == buf)
+			e->neighborOffno = OffsetNumberNext(e->offno);
+		else
+			e->neighborOffno = FirstOffsetNumber;
+	}
+
+	ItemPointerSet(&etup->neighbortid, e->neighborPage, e->neighborOffno);
+
+	/* Add element and neighbors */
+	if (OffsetNumberIsValid(freeOffno))
+	{
+		if (!PageIndexTupleOverwrite(page, e->offno, (Item) etup, etupSize))
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+		if (!PageIndexTupleOverwrite(npage, e->neighborOffno, (Item) ntup, ntupSize))
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+	}
+	else
+	{
+		if (PageAddItem(page, (Item) etup, etupSize, InvalidOffsetNumber, false, false) != e->offno)
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+		if (PageAddItem(npage, (Item) ntup, ntupSize, InvalidOffsetNumber, false, false) != e->neighborOffno)
+			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+	}
+
+	/* Commit */
+	if (building)
+	{
+		MarkBufferDirty(buf);
+		if (nbuf != buf)
+			MarkBufferDirty(nbuf);
+	}
+	else
+		GenericXLogFinish(state);
+	UnlockReleaseBuffer(buf);
+	if (nbuf != buf)
+		UnlockReleaseBuffer(nbuf);
+
+	/* Update the insert page */
+	if (BlockNumberIsValid(newInsertPage) && newInsertPage != insertPage)
+		*updatedInsertPage = newInsertPage;
+}
+
+/*
+ * Check if connection already exists
+ */
+static bool
+ConnectionExists(HnswElement e, HnswNeighborTuple ntup, int startIdx, int lm)
+{
+	for (int i = 0; i < lm; i++)
+	{
+		ItemPointer indextid = &ntup->indextids[startIdx + i];
+
+		if (!ItemPointerIsValid(indextid))
+			break;
+
+		if (ItemPointerGetBlockNumber(indextid) == e->blkno && ItemPointerGetOffsetNumber(indextid) == e->offno)
+			return true;
+	}
+
+	return false;
+}
+
+/*
+ * Update neighbors
+ */
+void
+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 = HnswGetNeighbors(base, e, lc);
+
+		for (int i = 0; i < neighbors->length; i++)
+		{
+			HnswCandidate *hc = &neighbors->items[i];
+			Buffer		buf;
+			Page		page;
+			GenericXLogState *state;
+			HnswNeighborTuple ntup;
+			int			idx = -1;
+			int			startIdx;
+			HnswElement neighborElement = HnswPtrAccess(base, hc->element);
+			OffsetNumber offno = neighborElement->neighborOffno;
+
+			/* Get latest neighbors since they may have changed */
+			/* Do not lock yet since selecting neighbors can take time */
+			HnswLoadNeighbors(neighborElement, index, m);
+
+			/*
+			 * Could improve performance for vacuuming by checking neighbors
+			 * against list of elements being deleted to find index. It's
+			 * important to exclude already deleted elements for this since
+			 * they can be replaced at any time.
+			 */
+
+			/* Select neighbors */
+			HnswUpdateConnection(NULL, e, hc, lm, lc, &idx, index, procinfo, collation);
+
+			/* New element was not selected as a neighbor */
+			if (idx == -1)
+				continue;
+
+			/* Register page */
+			buf = ReadBuffer(index, neighborElement->neighborPage);
+			LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+			if (building)
+			{
+				state = NULL;
+				page = BufferGetPage(buf);
+			}
+			else
+			{
+				state = GenericXLogStart(index);
+				page = GenericXLogRegisterBuffer(state, buf, 0);
+			}
+
+			/* Get tuple */
+			ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, offno));
+
+			/* Calculate index for update */
+			startIdx = (neighborElement->level - lc) * m;
+
+			/* Check for existing connection */
+			if (checkExisting && ConnectionExists(e, ntup, startIdx, lm))
+				idx = -1;
+			else if (idx == -2)
+			{
+				/* Find free offset if still exists */
+				/* TODO Retry updating connections if not */
+				for (int j = 0; j < lm; j++)
+				{
+					if (!ItemPointerIsValid(&ntup->indextids[startIdx + j]))
+					{
+						idx = startIdx + j;
+						break;
+					}
+				}
+			}
+			else
+				idx += startIdx;
+
+			/* Make robust to issues */
+			if (idx >= 0 && idx < ntup->count)
+			{
+				ItemPointer indextid = &ntup->indextids[idx];
+
+				/* Update neighbor on the buffer */
+				ItemPointerSet(indextid, e->blkno, e->offno);
+
+				/* Commit */
+				if (building)
+					MarkBufferDirty(buf);
+				else
+					GenericXLogFinish(state);
+			}
+			else if (!building)
+				GenericXLogAbort(state);
+
+			UnlockReleaseBuffer(buf);
+		}
+	}
+}
+
+/*
+ * Add a heap TID to an existing element
+ */
+static bool
+AddDuplicateOnDisk(Relation index, HnswElement element, HnswElement dup, bool building)
+{
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	HnswElementTuple etup;
+	int			i;
+
+	/* Read page */
+	buf = ReadBuffer(index, dup->blkno);
+	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+	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));
+	for (i = 0; i < HNSW_HEAPTIDS; i++)
+	{
+		if (!ItemPointerIsValid(&etup->heaptids[i]))
+			break;
+	}
+
+	/* Either being deleted or we lost our chance to another backend */
+	if (i == 0 || i == HNSW_HEAPTIDS)
+	{
+		if (!building)
+			GenericXLogAbort(state);
+		UnlockReleaseBuffer(buf);
+		return false;
+	}
+
+	/* Add heap TID, modifying the tuple on the page directly */
+	etup->heaptids[i] = element->heaptids[0];
+
+	/* Commit */
+	if (building)
+		MarkBufferDirty(buf);
+	else
+		GenericXLogFinish(state);
+	UnlockReleaseBuffer(buf);
+
+	return true;
+}
+
+/*
+ * 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
+UpdateGraphOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement entryPoint, bool building)
+{
+	BlockNumber newInsertPage = InvalidBlockNumber;
+
+	/* Look for duplicate */
+	if (FindDuplicateOnDisk(index, element, building))
+		return;
+
+	/* 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, building);
+
+	/* Update neighbors */
+	HnswUpdateNeighborsOnDisk(index, procinfo, collation, element, m, false, building);
+
+	/* Update entry point if needed */
+	if (entryPoint == NULL || element->level > entryPoint->level)
+		HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM, building);
+}
+
+/*
+ * Insert a tuple into the index
+ */
+bool
+HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, bool building)
+{
+	HnswElement entryPoint;
+	HnswElement element;
+	int			m;
+	int			efConstruction = HnswGetEfConstruction(index);
+	FmgrInfo   *procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
+	Oid			collation = index->rd_indcollation[0];
+	LOCKMODE	lockmode = ShareLock;
+	char	   *base = NULL;
+
+	/*
+	 * Get a shared lock. This allows vacuum to ensure no in-flight inserts
+	 * before repairing graph. Use a page lock so it does not interfere with
+	 * buffer lock (or reads when vacuuming).
+	 */
+	LockPage(index, HNSW_UPDATE_LOCK, lockmode);
+
+	/* Get m and entry point */
+	HnswGetMetaPageInfo(index, &m, &entryPoint);
+
+	/* Create an element */
+	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)
+	{
+		/* Release shared lock */
+		UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
+
+		/* Get exclusive lock */
+		lockmode = ExclusiveLock;
+		LockPage(index, HNSW_UPDATE_LOCK, lockmode);
+
+		/* Get latest entry point after lock is acquired */
+		entryPoint = HnswGetEntryPoint(index);
+	}
+
+	/* Find neighbors for element */
+	HnswFindElementNeighbors(base, element, entryPoint, index, procinfo, collation, m, efConstruction, false);
+
+	/* Update graph on disk */
+	UpdateGraphOnDisk(index, procinfo, collation, element, m, efConstruction, entryPoint, building);
+
+	/* Release lock */
+	UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
+
+	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
+ */
+bool
+hnswinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid,
+		   Relation heap, IndexUniqueCheck checkUnique
+#if PG_VERSION_NUM >= 140000
+		   ,bool indexUnchanged
+#endif
+		   ,IndexInfo *indexInfo
+)
+{
+	MemoryContext oldCtx;
+	MemoryContext insertCtx;
+
+	/* Skip nulls */
+	if (isnull[0])
+		return false;
+
+	/* Create memory context */
+	insertCtx = AllocSetContextCreate(CurrentMemoryContext,
+									  "Hnsw insert temporary context",
+									  ALLOCSET_DEFAULT_SIZES);
+	oldCtx = MemoryContextSwitchTo(insertCtx);
+
+	/* Insert tuple */
+	HnswInsertTuple(index, values, isnull, heap_tid);
+
+	/* Delete memory context */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(insertCtx);
+
+	return false;
+}

src/hnswscan.c

@@ -0,0 +1,207 @@
+#include "postgres.h"
+
+#include "access/relscan.h"
+#include "hnsw.h"
+#include "pgstat.h"
+#include "storage/bufmgr.h"
+#include "storage/lmgr.h"
+#include "utils/memutils.h"
+
+/*
+ * Algorithm 5 from paper
+ */
+static List *
+GetScanItems(IndexScanDesc scan, Datum q)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	Relation	index = scan->indexRelation;
+	FmgrInfo   *procinfo = so->procinfo;
+	Oid			collation = so->collation;
+	List	   *ep;
+	List	   *w;
+	int			m;
+	HnswElement entryPoint;
+	char	   *base = NULL;
+
+	/* Get m and entry point */
+	HnswGetMetaPageInfo(index, &m, &entryPoint);
+
+	if (entryPoint == NULL)
+		return NIL;
+
+	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, false));
+
+	for (int lc = entryPoint->level; lc >= 1; lc--)
+	{
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, false, NULL);
+		ep = w;
+	}
+
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
+}
+
+/*
+ * Get scan value
+ */
+static Datum
+GetScanValue(IndexScanDesc scan)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	Datum		value;
+
+	if (scan->orderByData->sk_flags & SK_ISNULL)
+		value = PointerGetDatum(NULL);
+	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)
+			HnswNormValue(so->normprocinfo, so->collation, &value, HnswGetType(scan->indexRelation));
+	}
+
+	return value;
+}
+
+/*
+ * Prepare for an index scan
+ */
+IndexScanDesc
+hnswbeginscan(Relation index, int nkeys, int norderbys)
+{
+	IndexScanDesc scan;
+	HnswScanOpaque so;
+
+	scan = RelationGetIndexScan(index, nkeys, norderbys);
+
+	so = (HnswScanOpaque) palloc(sizeof(HnswScanOpaqueData));
+	so->first = true;
+	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+									   "Hnsw scan temporary context",
+									   ALLOCSET_DEFAULT_SIZES);
+
+	/* Set support functions */
+	so->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
+	so->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	so->collation = index->rd_indcollation[0];
+
+	scan->opaque = so;
+
+	return scan;
+}
+
+/*
+ * Start or restart an index scan
+ */
+void
+hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int norderbys)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+
+	so->first = true;
+	MemoryContextReset(so->tmpCtx);
+
+	if (keys && scan->numberOfKeys > 0)
+		memmove(scan->keyData, keys, scan->numberOfKeys * sizeof(ScanKeyData));
+
+	if (orderbys && scan->numberOfOrderBys > 0)
+		memmove(scan->orderByData, orderbys, scan->numberOfOrderBys * sizeof(ScanKeyData));
+}
+
+/*
+ * Fetch the next tuple in the given scan
+ */
+bool
+hnswgettuple(IndexScanDesc scan, ScanDirection dir)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	MemoryContext oldCtx = MemoryContextSwitchTo(so->tmpCtx);
+
+	/*
+	 * Index can be used to scan backward, but Postgres doesn't support
+	 * backward scan on operators
+	 */
+	Assert(ScanDirectionIsForward(dir));
+
+	if (so->first)
+	{
+		Datum		value;
+
+		/* Count index scan for stats */
+		pgstat_count_index_scan(scan->indexRelation);
+
+		/* Safety check */
+		if (scan->orderByData == NULL)
+			elog(ERROR, "cannot scan hnsw index without order");
+
+		/* Requires MVCC-compliant snapshot as not able to maintain a pin */
+		/* https://www.postgresql.org/docs/current/index-locking.html */
+		if (!IsMVCCSnapshot(scan->xs_snapshot))
+			elog(ERROR, "non-MVCC snapshots are not supported with hnsw");
+
+		/* Get scan value */
+		value = GetScanValue(scan);
+
+		/*
+		 * Get a shared lock. This allows vacuum to ensure no in-flight scans
+		 * before marking tuples as deleted.
+		 */
+		LockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+		so->w = GetScanItems(scan, value);
+
+		/* Release shared lock */
+		UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+		so->first = false;
+
+#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 (element->heaptidsLength == 0)
+		{
+			so->w = list_delete_last(so->w);
+			continue;
+		}
+
+		heaptid = &element->heaptids[--element->heaptidsLength];
+
+		MemoryContextSwitchTo(oldCtx);
+
+		scan->xs_heaptid = *heaptid;
+		scan->xs_recheck = false;
+		scan->xs_recheckorderby = false;
+		return true;
+	}
+
+	MemoryContextSwitchTo(oldCtx);
+	return false;
+}
+
+/*
+ * End a scan and release resources
+ */
+void
+hnswendscan(IndexScanDesc scan)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+
+	MemoryContextDelete(so->tmpCtx);
+
+	pfree(so);
+	scan->opaque = NULL;
+}

src/hnswvacuum.c

@@ -0,0 +1,646 @@
+#include "postgres.h"
+
+#include <math.h>
+
+#include "access/generic_xlog.h"
+#include "commands/vacuum.h"
+#include "hnsw.h"
+#include "storage/bufmgr.h"
+#include "storage/lmgr.h"
+#include "utils/memutils.h"
+
+/*
+ * Check if deleted list contains an index TID
+ */
+static bool
+DeletedContains(tidhash_hash * deleted, ItemPointer indextid)
+{
+	return tidhash_lookup(deleted, *indextid) != NULL;
+}
+
+/*
+ * Remove deleted heap TIDs
+ *
+ * OK to remove for entry point, since always considered for searches and inserts
+ */
+static void
+RemoveHeapTids(HnswVacuumState * vacuumstate)
+{
+	BlockNumber blkno = HNSW_HEAD_BLKNO;
+	HnswElement highestPoint = &vacuumstate->highestPoint;
+	Relation	index = vacuumstate->index;
+	BufferAccessStrategy bas = vacuumstate->bas;
+	HnswElement entryPoint = HnswGetEntryPoint(vacuumstate->index);
+	IndexBulkDeleteResult *stats = vacuumstate->stats;
+
+	/* Store separately since highestPoint.level is uint8 */
+	int			highestLevel = -1;
+
+	/* Initialize highest point */
+	highestPoint->blkno = InvalidBlockNumber;
+	highestPoint->offno = InvalidOffsetNumber;
+
+	while (BlockNumberIsValid(blkno))
+	{
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		OffsetNumber offno;
+		OffsetNumber maxoffno;
+		bool		updated = false;
+
+		vacuum_delay_point();
+
+		buf = ReadBufferExtended(index, MAIN_FORKNUM, blkno, RBM_NORMAL, bas);
+		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+		maxoffno = PageGetMaxOffsetNumber(page);
+
+		/* Iterate over nodes */
+		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+		{
+			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+			int			idx = 0;
+			bool		itemUpdated = false;
+
+			/* Skip neighbor tuples */
+			if (!HnswIsElementTuple(etup))
+				continue;
+
+			if (ItemPointerIsValid(&etup->heaptids[0]))
+			{
+				for (int i = 0; i < HNSW_HEAPTIDS; i++)
+				{
+					/* Stop at first unused */
+					if (!ItemPointerIsValid(&etup->heaptids[i]))
+						break;
+
+					if (vacuumstate->callback(&etup->heaptids[i], vacuumstate->callback_state))
+					{
+						itemUpdated = true;
+						stats->tuples_removed++;
+					}
+					else
+					{
+						/* Move to front of list */
+						etup->heaptids[idx++] = etup->heaptids[i];
+						stats->num_index_tuples++;
+					}
+				}
+
+				if (itemUpdated)
+				{
+					/* Mark rest as invalid */
+					for (int i = idx; i < HNSW_HEAPTIDS; i++)
+						ItemPointerSetInvalid(&etup->heaptids[i]);
+
+					updated = true;
+				}
+			}
+
+			if (!ItemPointerIsValid(&etup->heaptids[0]))
+			{
+				ItemPointerData ip;
+				bool		found;
+
+				/* Add to deleted list */
+				ItemPointerSet(&ip, blkno, offno);
+
+				tidhash_insert(vacuumstate->deleted, ip, &found);
+				Assert(!found);
+			}
+			else if (etup->level > highestLevel && !(entryPoint != NULL && blkno == entryPoint->blkno && offno == entryPoint->offno))
+			{
+				/* Keep track of highest non-entry point */
+				highestPoint->blkno = blkno;
+				highestPoint->offno = offno;
+				highestPoint->level = etup->level;
+				highestLevel = etup->level;
+			}
+		}
+
+		blkno = HnswPageGetOpaque(page)->nextblkno;
+
+		if (updated)
+			GenericXLogFinish(state);
+		else
+			GenericXLogAbort(state);
+
+		UnlockReleaseBuffer(buf);
+	}
+}
+
+/*
+ * Check for deleted neighbors
+ */
+static bool
+NeedsUpdated(HnswVacuumState * vacuumstate, HnswElement element)
+{
+	Relation	index = vacuumstate->index;
+	BufferAccessStrategy bas = vacuumstate->bas;
+	Buffer		buf;
+	Page		page;
+	HnswNeighborTuple ntup;
+	bool		needsUpdated = false;
+
+	buf = ReadBufferExtended(index, MAIN_FORKNUM, element->neighborPage, RBM_NORMAL, bas);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	ntup = (HnswNeighborTuple) PageGetItem(page, PageGetItemId(page, element->neighborOffno));
+
+	Assert(HnswIsNeighborTuple(ntup));
+
+	/* Check neighbors */
+	for (int i = 0; i < ntup->count; i++)
+	{
+		ItemPointer indextid = &ntup->indextids[i];
+
+		if (!ItemPointerIsValid(indextid))
+			continue;
+
+		/* Check if in deleted list */
+		if (DeletedContains(vacuumstate->deleted, indextid))
+		{
+			needsUpdated = true;
+			break;
+		}
+	}
+
+	/* Also update if layer 0 is not full */
+	/* This could indicate too many candidates being deleted during insert */
+	if (!needsUpdated)
+		needsUpdated = !ItemPointerIsValid(&ntup->indextids[ntup->count - 1]);
+
+	UnlockReleaseBuffer(buf);
+
+	return needsUpdated;
+}
+
+/*
+ * Repair graph for a single element
+ */
+static void
+RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswElement entryPoint)
+{
+	Relation	index = vacuumstate->index;
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	int			m = vacuumstate->m;
+	int			efConstruction = vacuumstate->efConstruction;
+	FmgrInfo   *procinfo = vacuumstate->procinfo;
+	Oid			collation = vacuumstate->collation;
+	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(base, element, m, NULL);
+	element->heaptidsLength = 0;
+
+	/* 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(base, ntup, element, m);
+
+	/* Get neighbor page */
+	buf = ReadBufferExtended(index, MAIN_FORKNUM, element->neighborPage, RBM_NORMAL, bas);
+	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
+	state = GenericXLogStart(index);
+	page = GenericXLogRegisterBuffer(state, buf, 0);
+
+	/* Overwrite tuple */
+	if (!PageIndexTupleOverwrite(page, element->neighborOffno, (Item) ntup, ntupSize))
+		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
+
+	/* Commit */
+	GenericXLogFinish(state);
+	UnlockReleaseBuffer(buf);
+
+	/* Update neighbors */
+	HnswUpdateNeighborsOnDisk(index, procinfo, collation, element, m, true, false);
+}
+
+/*
+ * Repair graph entry point
+ */
+static void
+RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
+{
+	Relation	index = vacuumstate->index;
+	HnswElement highestPoint = &vacuumstate->highestPoint;
+	HnswElement entryPoint;
+	MemoryContext oldCtx = MemoryContextSwitchTo(vacuumstate->tmpCtx);
+
+	if (!BlockNumberIsValid(highestPoint->blkno))
+		highestPoint = NULL;
+
+	/*
+	 * Repair graph for highest non-entry point. Highest point may be outdated
+	 * due to inserts that happen during and after RemoveHeapTids.
+	 */
+	if (highestPoint != NULL)
+	{
+		/* Get a shared lock */
+		LockPage(index, HNSW_UPDATE_LOCK, ShareLock);
+
+		/* Load element */
+		HnswLoadElement(highestPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true);
+
+		/* Repair if needed */
+		if (NeedsUpdated(vacuumstate, highestPoint))
+			RepairGraphElement(vacuumstate, highestPoint, HnswGetEntryPoint(index));
+
+		/* Release lock */
+		UnlockPage(index, HNSW_UPDATE_LOCK, ShareLock);
+	}
+
+	/* Prevent concurrent inserts when possibly updating entry point */
+	LockPage(index, HNSW_UPDATE_LOCK, ExclusiveLock);
+
+	/* Get latest entry point */
+	entryPoint = HnswGetEntryPoint(index);
+
+	if (entryPoint != NULL)
+	{
+		ItemPointerData epData;
+
+		ItemPointerSet(&epData, entryPoint->blkno, entryPoint->offno);
+
+		if (DeletedContains(vacuumstate->deleted, &epData))
+		{
+			/*
+			 * Replace the entry point with the highest point. If highest
+			 * 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, false);
+		}
+		else
+		{
+			/*
+			 * Repair the entry point with the highest point. If highest point
+			 * is outdated, this can remove connections at higher levels in
+			 * the graph until they are repaired, but this should be fine.
+			 */
+			HnswLoadElement(entryPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true);
+
+			if (NeedsUpdated(vacuumstate, entryPoint))
+			{
+				/* Reset neighbors from previous update */
+				if (highestPoint != NULL)
+					HnswPtrStore((char *) NULL, highestPoint->neighbors, (HnswNeighborArrayPtr *) NULL);
+
+				RepairGraphElement(vacuumstate, entryPoint, highestPoint);
+			}
+		}
+	}
+
+	/* Release lock */
+	UnlockPage(index, HNSW_UPDATE_LOCK, ExclusiveLock);
+
+	/* Reset memory context */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextReset(vacuumstate->tmpCtx);
+}
+
+/*
+ * Repair graph for all elements
+ */
+static void
+RepairGraph(HnswVacuumState * vacuumstate)
+{
+	Relation	index = vacuumstate->index;
+	BufferAccessStrategy bas = vacuumstate->bas;
+	BlockNumber blkno = HNSW_HEAD_BLKNO;
+
+	/*
+	 * Wait for inserts to complete. Inserts before this point may have
+	 * neighbors about to be deleted. Inserts after this point will not.
+	 */
+	LockPage(index, HNSW_UPDATE_LOCK, ExclusiveLock);
+	UnlockPage(index, HNSW_UPDATE_LOCK, ExclusiveLock);
+
+	/* Repair entry point first */
+	RepairGraphEntryPoint(vacuumstate);
+
+	while (BlockNumberIsValid(blkno))
+	{
+		Buffer		buf;
+		Page		page;
+		OffsetNumber offno;
+		OffsetNumber maxoffno;
+		List	   *elements = NIL;
+		ListCell   *lc2;
+		MemoryContext oldCtx;
+
+		vacuum_delay_point();
+
+		oldCtx = MemoryContextSwitchTo(vacuumstate->tmpCtx);
+
+		buf = ReadBufferExtended(index, MAIN_FORKNUM, blkno, RBM_NORMAL, bas);
+		LockBuffer(buf, BUFFER_LOCK_SHARE);
+		page = BufferGetPage(buf);
+		maxoffno = PageGetMaxOffsetNumber(page);
+
+		/* Load items into memory to minimize locking */
+		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+		{
+			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+			HnswElement element;
+
+			/* Skip neighbor tuples */
+			if (!HnswIsElementTuple(etup))
+				continue;
+
+			/* Skip updating neighbors if being deleted */
+			if (!ItemPointerIsValid(&etup->heaptids[0]))
+				continue;
+
+			/* Create an element */
+			element = HnswInitElementFromBlock(blkno, offno);
+			HnswLoadElementFromTuple(element, etup, false, true);
+
+			elements = lappend(elements, element);
+		}
+
+		blkno = HnswPageGetOpaque(page)->nextblkno;
+
+		UnlockReleaseBuffer(buf);
+
+		/* Update neighbor pages */
+		foreach(lc2, elements)
+		{
+			HnswElement element = (HnswElement) lfirst(lc2);
+			HnswElement entryPoint;
+			LOCKMODE	lockmode = ShareLock;
+
+			/* Check if any neighbors point to deleted values */
+			if (!NeedsUpdated(vacuumstate, element))
+				continue;
+
+			/* Get a shared lock */
+			LockPage(index, HNSW_UPDATE_LOCK, lockmode);
+
+			/* Refresh entry point for each element */
+			entryPoint = HnswGetEntryPoint(index);
+
+			/* Prevent concurrent inserts when likely updating entry point */
+			if (entryPoint == NULL || element->level > entryPoint->level)
+			{
+				/* Release shared lock */
+				UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
+
+				/* Get exclusive lock */
+				lockmode = ExclusiveLock;
+				LockPage(index, HNSW_UPDATE_LOCK, lockmode);
+
+				/* Get latest entry point after lock is acquired */
+				entryPoint = HnswGetEntryPoint(index);
+			}
+
+			/* Repair connections */
+			RepairGraphElement(vacuumstate, element, entryPoint);
+
+			/*
+			 * Update metapage if needed. Should only happen if entry point
+			 * was replaced and highest point was outdated.
+			 */
+			if (entryPoint == NULL || element->level > entryPoint->level)
+				HnswUpdateMetaPage(index, HNSW_UPDATE_ENTRY_GREATER, element, InvalidBlockNumber, MAIN_FORKNUM, false);
+
+			/* Release lock */
+			UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
+		}
+
+		/* Reset memory context */
+		MemoryContextSwitchTo(oldCtx);
+		MemoryContextReset(vacuumstate->tmpCtx);
+	}
+}
+
+/*
+ * Mark items as deleted
+ */
+static void
+MarkDeleted(HnswVacuumState * vacuumstate)
+{
+	BlockNumber blkno = HNSW_HEAD_BLKNO;
+	BlockNumber insertPage = InvalidBlockNumber;
+	Relation	index = vacuumstate->index;
+	BufferAccessStrategy bas = vacuumstate->bas;
+
+	/*
+	 * Wait for index scans to complete. Scans before this point may contain
+	 * tuples about to be deleted. Scans after this point will not, since the
+	 * graph has been repaired.
+	 */
+	LockPage(index, HNSW_SCAN_LOCK, ExclusiveLock);
+	UnlockPage(index, HNSW_SCAN_LOCK, ExclusiveLock);
+
+	while (BlockNumberIsValid(blkno))
+	{
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		OffsetNumber offno;
+		OffsetNumber maxoffno;
+
+		vacuum_delay_point();
+
+		buf = ReadBufferExtended(index, MAIN_FORKNUM, blkno, RBM_NORMAL, bas);
+
+		/*
+		 * ambulkdelete cannot delete entries from pages that are pinned by
+		 * other backends
+		 *
+		 * https://www.postgresql.org/docs/current/index-locking.html
+		 */
+		LockBufferForCleanup(buf);
+
+		state = GenericXLogStart(index);
+		page = GenericXLogRegisterBuffer(state, buf, 0);
+		maxoffno = PageGetMaxOffsetNumber(page);
+
+		/* Update element and neighbors together */
+		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+		{
+			HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+			HnswNeighborTuple ntup;
+			Buffer		nbuf;
+			Page		npage;
+			BlockNumber neighborPage;
+			OffsetNumber neighborOffno;
+
+			/* Skip neighbor tuples */
+			if (!HnswIsElementTuple(etup))
+				continue;
+
+			/* Skip deleted tuples */
+			if (etup->deleted)
+			{
+				/* Set to first free page */
+				if (!BlockNumberIsValid(insertPage))
+					insertPage = blkno;
+
+				continue;
+			}
+
+			/* Skip live tuples */
+			if (ItemPointerIsValid(&etup->heaptids[0]))
+				continue;
+
+			/* Get neighbor page */
+			neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
+			neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
+
+			if (neighborPage == blkno)
+			{
+				nbuf = buf;
+				npage = page;
+			}
+			else
+			{
+				nbuf = ReadBufferExtended(index, MAIN_FORKNUM, neighborPage, RBM_NORMAL, bas);
+				LockBuffer(nbuf, BUFFER_LOCK_EXCLUSIVE);
+				npage = GenericXLogRegisterBuffer(state, nbuf, 0);
+			}
+
+			ntup = (HnswNeighborTuple) PageGetItem(npage, PageGetItemId(npage, neighborOffno));
+
+			/* Overwrite element */
+			etup->deleted = 1;
+			MemSet(&etup->data, 0, VARSIZE_ANY(&etup->data));
+
+			/* Overwrite neighbors */
+			for (int i = 0; i < ntup->count; i++)
+				ItemPointerSetInvalid(&ntup->indextids[i]);
+
+			/*
+			 * We modified the tuples in place, no need to call
+			 * PageIndexTupleOverwrite
+			 */
+
+			/* Commit */
+			GenericXLogFinish(state);
+			if (nbuf != buf)
+				UnlockReleaseBuffer(nbuf);
+
+			/* Set to first free page */
+			if (!BlockNumberIsValid(insertPage))
+				insertPage = blkno;
+
+			/* Prepare new xlog */
+			state = GenericXLogStart(index);
+			page = GenericXLogRegisterBuffer(state, buf, 0);
+		}
+
+		blkno = HnswPageGetOpaque(page)->nextblkno;
+
+		GenericXLogAbort(state);
+		UnlockReleaseBuffer(buf);
+	}
+
+	/* Update insert page last, after everything has been marked as deleted */
+	HnswUpdateMetaPage(index, 0, NULL, insertPage, MAIN_FORKNUM, false);
+}
+
+/*
+ * Initialize the vacuum state
+ */
+static void
+InitVacuumState(HnswVacuumState * vacuumstate, IndexVacuumInfo *info, IndexBulkDeleteResult *stats, IndexBulkDeleteCallback callback, void *callback_state)
+{
+	Relation	index = info->index;
+
+	if (stats == NULL)
+		stats = (IndexBulkDeleteResult *) palloc0(sizeof(IndexBulkDeleteResult));
+
+	vacuumstate->index = index;
+	vacuumstate->stats = stats;
+	vacuumstate->callback = callback;
+	vacuumstate->callback_state = callback_state;
+	vacuumstate->efConstruction = HnswGetEfConstruction(index);
+	vacuumstate->bas = GetAccessStrategy(BAS_BULKREAD);
+	vacuumstate->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
+	vacuumstate->collation = index->rd_indcollation[0];
+	vacuumstate->ntup = palloc0(HNSW_TUPLE_ALLOC_SIZE);
+	vacuumstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+												"Hnsw vacuum temporary context",
+												ALLOCSET_DEFAULT_SIZES);
+
+	/* Get m from metapage */
+	HnswGetMetaPageInfo(index, &vacuumstate->m, NULL);
+
+	/* Create hash table */
+	vacuumstate->deleted = tidhash_create(CurrentMemoryContext, 256, NULL);
+}
+
+/*
+ * Free resources
+ */
+static void
+FreeVacuumState(HnswVacuumState * vacuumstate)
+{
+	tidhash_destroy(vacuumstate->deleted);
+	FreeAccessStrategy(vacuumstate->bas);
+	pfree(vacuumstate->ntup);
+	MemoryContextDelete(vacuumstate->tmpCtx);
+}
+
+/*
+ * Bulk delete tuples from the index
+ */
+IndexBulkDeleteResult *
+hnswbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
+			   IndexBulkDeleteCallback callback, void *callback_state)
+{
+	HnswVacuumState vacuumstate;
+
+	InitVacuumState(&vacuumstate, info, stats, callback, callback_state);
+
+	/* Pass 1: Remove heap TIDs */
+	RemoveHeapTids(&vacuumstate);
+
+	/* Pass 2: Repair graph */
+	RepairGraph(&vacuumstate);
+
+	/* Pass 3: Mark as deleted */
+	MarkDeleted(&vacuumstate);
+
+	FreeVacuumState(&vacuumstate);
+
+	return vacuumstate.stats;
+}
+
+/*
+ * Clean up after a VACUUM operation
+ */
+IndexBulkDeleteResult *
+hnswvacuumcleanup(IndexVacuumInfo *info, IndexBulkDeleteResult *stats)
+{
+	Relation	rel = info->index;
+
+	if (info->analyze_only)
+		return stats;
+
+	/* stats is NULL if ambulkdelete not called */
+	/* OK to return NULL if index not changed */
+	if (stats == NULL)
+		return NULL;
+
+	stats->num_pages = RelationGetNumberOfBlocks(rel);
+
+	return stats;
+}

src/ivfbuild.c

@@ -2,42 +2,45 @@
 
 #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
+#else
 #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
-#endif
-
-#include "catalog/pg_operator_d.h"
-#include "catalog/pg_type_d.h"
-
 #if PG_VERSION_NUM >= 130000
 #define CALLBACK_ITEM_POINTER ItemPointer tid
 #else
 #define CALLBACK_ITEM_POINTER HeapTuple hup
 #endif
 
-#if PG_VERSION_NUM >= 120000
+#if PG_VERSION_NUM >= 140000
-#define UpdateProgress(index, val) pgstat_progress_update_param(index, val)
+#include "utils/backend_status.h"
-#else
+#include "utils/wait_event.h"
-#define UpdateProgress(index, val) ((void)val)
 #endif
 
+#define PARALLEL_KEY_IVFFLAT_SHARED		UINT64CONST(0xA000000000000001)
+#define PARALLEL_KEY_TUPLESORT			UINT64CONST(0xA000000000000002)
+#define PARALLEL_KEY_IVFFLAT_CENTERS	UINT64CONST(0xA000000000000003)
+#define PARALLEL_KEY_QUERY_TEXT			UINT64CONST(0xA000000000000004)
+
 /*
  * Add sample
  */
@@ -56,13 +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
@@ -79,7 +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;
@@ -104,7 +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);
@@ -129,13 +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
 	}
 }
 
@@ -150,7 +148,6 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState
 	int			closestCenter = 0;
 	VectorArray centers = buildstate->centers;
 	TupleTableSlot *slot = buildstate->slot;
-	int			i;
 
 	/* Detoast once for all calls */
 	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
@@ -158,12 +155,12 @@ 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;
 	}
 
 	/* Find the list that minimizes the distance */
-	for (i = 0; i < centers->length; i++)
+	for (int i = 0; i < centers->length; i++)
 	{
 		distance = DatumGetFloat8(FunctionCall2Coll(buildstate->procinfo, buildstate->collation, value, PointerGetDatum(VectorArrayGet(centers, i))));
 
@@ -258,32 +255,27 @@ GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot,
 static void
 InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 {
-	Buffer		buf;
-	Page		page;
-	GenericXLogState *state;
 	int			list;
 	IndexTuple	itup = NULL;	/* silence compiler warning */
-	BlockNumber startPage;
-	BlockNumber insertPage;
-	Size		itemsz;
-	int			i;
 	int64		inserted = 0;
 
-#if PG_VERSION_NUM >= 120000
 	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);
 
-	for (i = 0; i < buildstate->centers->length; i++)
+	for (int i = 0; i < buildstate->centers->length; i++)
 	{
+		Buffer		buf;
+		Page		page;
+		GenericXLogState *state;
+		BlockNumber startPage;
+		BlockNumber insertPage;
+
 		/* Can take a while, so ensure we can interrupt */
 		/* Needs to be called when no buffer locks are held */
 		CHECK_FOR_INTERRUPTS();
@@ -297,7 +289,8 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 		while (list == i)
 		{
 			/* Check for free space */
-			itemsz = MAXALIGN(IndexTupleSize(itup));
+			Size		itemsz = MAXALIGN(IndexTupleSize(itup));
+
 			if (PageGetFreeSpace(page) < itemsz)
 				IvfflatAppendPage(index, &buf, &page, &state, forkNum);
 
@@ -307,7 +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);
 		}
@@ -317,29 +310,62 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 		IvfflatCommitBuffer(buf, state);
 
 		/* Set the start and insert pages */
-		IvfflatUpdateList(index, state, buildstate->listInfo[i], insertPage, InvalidBlockNumber, startPage, forkNum);
+		IvfflatUpdateList(index, buildstate->listInfo[i], insertPage, InvalidBlockNumber, startPage, forkNum);
 	}
 }
 
+/*
+ * 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)
+	if (buildstate->dimensions > maxDimensions)
-		elog(ERROR, "column cannot have more than %d dimensions for ivfflat index", IVFFLAT_MAX_DIM);
+		elog(ERROR, "column cannot have more than %d dimensions for ivfflat index", maxDimensions);
 
 	buildstate->reltuples = 0;
 	buildstate->indtuples = 0;
@@ -351,33 +377,20 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->collation = index->rd_indcollation[0];
 
 	/* Require more than one dimension for spherical k-means */
-	/* Lists check for backwards compatibility */
+	if (buildstate->kmeansnormprocinfo != NULL && buildstate->dimensions == 1)
-	/* TODO Remove lists check in 0.3.0 */
-	if (buildstate->kmeansnormprocinfo != NULL && buildstate->dimensions == 1 && buildstate->lists > 1)
 		elog(ERROR, "dimensions must be greater than one for this opclass");
 
 	/* Create tuple description for sorting */
-#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);
@@ -387,6 +400,8 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->listSums = palloc0(sizeof(double) * buildstate->lists);
 	buildstate->listCounts = palloc0(sizeof(int) * buildstate->lists);
 #endif
+
+	buildstate->ivfleader = NULL;
 }
 
 /*
@@ -397,7 +412,6 @@ FreeBuildState(IvfflatBuildState * buildstate)
 {
 	VectorArrayFree(buildstate->centers);
 	pfree(buildstate->listInfo);
-	pfree(buildstate->normvec);
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	pfree(buildstate->listSums);
@@ -415,7 +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 */
@@ -429,7 +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);
@@ -444,7 +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);
@@ -483,33 +497,33 @@ static void
 CreateListPages(Relation index, VectorArray centers, int dimensions,
 				int lists, ForkNumber forkNum, ListInfo * *listInfo)
 {
-	int			i;
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
-	OffsetNumber offno;
+	Size		listSize;
-	Size		itemsz;
 	IvfflatList list;
 
-	itemsz = MAXALIGN(IVFFLAT_LIST_SIZE(dimensions));
+	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(centers->itemsize));
-	list = palloc(itemsz);
+	list = palloc0(listSize);
 
 	buf = IvfflatNewBuffer(index, forkNum);
 	IvfflatInitRegisterPage(index, &buf, &page, &state);
 
-	for (i = 0; i < lists; i++)
+	for (int i = 0; i < lists; i++)
 	{
+		OffsetNumber offno;
+
 		/* 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) < itemsz)
+		if (PageGetFreeSpace(page) < listSize)
 			IvfflatAppendPage(index, &buf, &page, &state, forkNum);
 
 		/* Add the item */
-		offno = PageAddItem(page, (Item) list, itemsz, InvalidOffsetNumber, false, false);
+		offno = PageAddItem(page, (Item) list, listSize, InvalidOffsetNumber, false, false);
 		if (offno == InvalidOffsetNumber)
 			elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
@@ -523,17 +537,17 @@ 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)
 {
 	elog(INFO, "inertia: %.3e", buildstate->inertia);
 
 	/* Calculate Davies-Bouldin index */
-	if (buildstate->lists > 1)
+	if (buildstate->lists > 1 && !buildstate->ivfleader)
 	{
 		double		db = 0.0;
 
@@ -568,19 +582,409 @@ PrintKmeansMetrics(IvfflatBuildState * buildstate)
 }
 #endif
 
+/*
+ * Within leader, wait for end of heap scan
+ */
+static double
+ParallelHeapScan(IvfflatBuildState * buildstate)
+{
+	IvfflatShared *ivfshared = buildstate->ivfleader->ivfshared;
+	int			nparticipanttuplesorts;
+	double		reltuples;
+
+	nparticipanttuplesorts = buildstate->ivfleader->nparticipanttuplesorts;
+	for (;;)
+	{
+		SpinLockAcquire(&ivfshared->mutex);
+		if (ivfshared->nparticipantsdone == nparticipanttuplesorts)
+		{
+			buildstate->indtuples = ivfshared->indtuples;
+			reltuples = ivfshared->reltuples;
+#ifdef IVFFLAT_KMEANS_DEBUG
+			buildstate->inertia = ivfshared->inertia;
+#endif
+			SpinLockRelease(&ivfshared->mutex);
+			break;
+		}
+		SpinLockRelease(&ivfshared->mutex);
+
+		ConditionVariableSleep(&ivfshared->workersdonecv,
+							   WAIT_EVENT_PARALLEL_CREATE_INDEX_SCAN);
+	}
+
+	ConditionVariableCancelSleep();
+
+	return reltuples;
+}
+
+/*
+ * Perform a worker's portion of a parallel sort
+ */
+static void
+IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, Sharedsort *sharedsort, char *ivfcenters, int sortmem, bool progress)
+{
+	SortCoordinate coordinate;
+	IvfflatBuildState buildstate;
+	TableScanDesc scan;
+	double		reltuples;
+	IndexInfo  *indexInfo;
+
+	/* Sort options, which must match AssignTuples */
+	AttrNumber	attNums[] = {1};
+	Oid			sortOperators[] = {Int4LessOperator};
+	Oid			sortCollations[] = {InvalidOid};
+	bool		nullsFirstFlags[] = {false};
+
+	/* Initialize local tuplesort coordination state */
+	coordinate = palloc0(sizeof(SortCoordinateData));
+	coordinate->isWorker = true;
+	coordinate->nParticipants = -1;
+	coordinate->sharedsort = sharedsort;
+
+	/* Join parallel scan */
+	indexInfo = BuildIndexInfo(ivfspool->index);
+	indexInfo->ii_Concurrent = ivfshared->isconcurrent;
+	InitBuildState(&buildstate, ivfspool->heap, ivfspool->index, indexInfo);
+	memcpy(buildstate.centers->items, ivfcenters, 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;
+	scan = table_beginscan_parallel(ivfspool->heap,
+									ParallelTableScanFromIvfflatShared(ivfshared));
+	reltuples = table_index_build_scan(ivfspool->heap, ivfspool->index, indexInfo,
+									   true, progress, BuildCallback,
+									   (void *) &buildstate, scan);
+
+	/* Execute this worker's part of the sort */
+	tuplesort_performsort(ivfspool->sortstate);
+
+	/* Record statistics */
+	SpinLockAcquire(&ivfshared->mutex);
+	ivfshared->nparticipantsdone++;
+	ivfshared->reltuples += reltuples;
+	ivfshared->indtuples += buildstate.indtuples;
+#ifdef IVFFLAT_KMEANS_DEBUG
+	ivfshared->inertia += buildstate.inertia;
+#endif
+	SpinLockRelease(&ivfshared->mutex);
+
+	/* Log statistics */
+	if (progress)
+		ereport(DEBUG1, (errmsg("leader processed " INT64_FORMAT " tuples", (int64) reltuples)));
+	else
+		ereport(DEBUG1, (errmsg("worker processed " INT64_FORMAT " tuples", (int64) reltuples)));
+
+	/* Notify leader */
+	ConditionVariableSignal(&ivfshared->workersdonecv);
+
+	/* We can end tuplesorts immediately */
+	tuplesort_end(ivfspool->sortstate);
+
+	FreeBuildState(&buildstate);
+}
+
+/*
+ * Perform work within a launched parallel process
+ */
+void
+IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc)
+{
+	char	   *sharedquery;
+	IvfflatSpool *ivfspool;
+	IvfflatShared *ivfshared;
+	Sharedsort *sharedsort;
+	char	   *ivfcenters;
+	Relation	heapRel;
+	Relation	indexRel;
+	LOCKMODE	heapLockmode;
+	LOCKMODE	indexLockmode;
+	int			sortmem;
+
+	/* Set debug_query_string for individual workers first */
+	sharedquery = shm_toc_lookup(toc, PARALLEL_KEY_QUERY_TEXT, true);
+	debug_query_string = sharedquery;
+
+	/* Report the query string from leader */
+	pgstat_report_activity(STATE_RUNNING, debug_query_string);
+
+	/* Look up shared state */
+	ivfshared = shm_toc_lookup(toc, PARALLEL_KEY_IVFFLAT_SHARED, false);
+
+	/* Open relations using lock modes known to be obtained by index.c */
+	if (!ivfshared->isconcurrent)
+	{
+		heapLockmode = ShareLock;
+		indexLockmode = AccessExclusiveLock;
+	}
+	else
+	{
+		heapLockmode = ShareUpdateExclusiveLock;
+		indexLockmode = RowExclusiveLock;
+	}
+
+	/* Open relations within worker */
+	heapRel = table_open(ivfshared->heaprelid, heapLockmode);
+	indexRel = index_open(ivfshared->indexrelid, indexLockmode);
+
+	/* Initialize worker's own spool */
+	ivfspool = (IvfflatSpool *) palloc0(sizeof(IvfflatSpool));
+	ivfspool->heap = heapRel;
+	ivfspool->index = indexRel;
+
+	/* Look up shared state private to tuplesort.c */
+	sharedsort = shm_toc_lookup(toc, PARALLEL_KEY_TUPLESORT, false);
+	tuplesort_attach_shared(sharedsort, seg);
+
+	ivfcenters = shm_toc_lookup(toc, PARALLEL_KEY_IVFFLAT_CENTERS, false);
+
+	/* Perform sorting */
+	sortmem = maintenance_work_mem / ivfshared->scantuplesortstates;
+	IvfflatParallelScanAndSort(ivfspool, ivfshared, sharedsort, ivfcenters, sortmem, false);
+
+	/* Close relations within worker */
+	index_close(indexRel, indexLockmode);
+	table_close(heapRel, heapLockmode);
+}
+
+/*
+ * End parallel build
+ */
+static void
+IvfflatEndParallel(IvfflatLeader * ivfleader)
+{
+	/* Shutdown worker processes */
+	WaitForParallelWorkersToFinish(ivfleader->pcxt);
+
+	/* Free last reference to MVCC snapshot, if one was used */
+	if (IsMVCCSnapshot(ivfleader->snapshot))
+		UnregisterSnapshot(ivfleader->snapshot);
+	DestroyParallelContext(ivfleader->pcxt);
+	ExitParallelMode();
+}
+
+/*
+ * Return size of shared memory required for parallel index build
+ */
+static Size
+ParallelEstimateShared(Relation heap, Snapshot snapshot)
+{
+	return add_size(BUFFERALIGN(sizeof(IvfflatShared)), table_parallelscan_estimate(heap, snapshot));
+}
+
+/*
+ * Within leader, participate as a parallel worker
+ */
+static void
+IvfflatLeaderParticipateAsWorker(IvfflatBuildState * buildstate)
+{
+	IvfflatLeader *ivfleader = buildstate->ivfleader;
+	IvfflatSpool *leaderworker;
+	int			sortmem;
+
+	/* Allocate memory and initialize private spool */
+	leaderworker = (IvfflatSpool *) palloc0(sizeof(IvfflatSpool));
+	leaderworker->heap = buildstate->heap;
+	leaderworker->index = buildstate->index;
+
+	/* Perform work common to all participants */
+	sortmem = maintenance_work_mem / ivfleader->nparticipanttuplesorts;
+	IvfflatParallelScanAndSort(leaderworker, ivfleader->ivfshared,
+							   ivfleader->sharedsort, ivfleader->ivfcenters,
+							   sortmem, true);
+}
+
+/*
+ * Begin parallel build
+ */
+static void
+IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int request)
+{
+	ParallelContext *pcxt;
+	int			scantuplesortstates;
+	Snapshot	snapshot;
+	Size		estivfshared;
+	Size		estsort;
+	Size		estcenters;
+	IvfflatShared *ivfshared;
+	Sharedsort *sharedsort;
+	char	   *ivfcenters;
+	IvfflatLeader *ivfleader = (IvfflatLeader *) palloc0(sizeof(IvfflatLeader));
+	bool		leaderparticipates = true;
+	int			querylen;
+
+#ifdef DISABLE_LEADER_PARTICIPATION
+	leaderparticipates = false;
+#endif
+
+	/* Enter parallel mode and create context */
+	EnterParallelMode();
+	Assert(request > 0);
+	pcxt = CreateParallelContext("vector", "IvfflatParallelBuildMain", request);
+
+	scantuplesortstates = leaderparticipates ? request + 1 : request;
+
+	/* Get snapshot for table scan */
+	if (!isconcurrent)
+		snapshot = SnapshotAny;
+	else
+		snapshot = RegisterSnapshot(GetTransactionSnapshot());
+
+	/* Estimate size of workspaces */
+	estivfshared = ParallelEstimateShared(buildstate->heap, snapshot);
+	shm_toc_estimate_chunk(&pcxt->estimator, estivfshared);
+	estsort = tuplesort_estimate_shared(scantuplesortstates);
+	shm_toc_estimate_chunk(&pcxt->estimator, estsort);
+	estcenters = buildstate->centers->itemsize * buildstate->centers->maxlen;
+	shm_toc_estimate_chunk(&pcxt->estimator, estcenters);
+	shm_toc_estimate_keys(&pcxt->estimator, 3);
+
+	/* Finally, estimate PARALLEL_KEY_QUERY_TEXT space */
+	if (debug_query_string)
+	{
+		querylen = strlen(debug_query_string);
+		shm_toc_estimate_chunk(&pcxt->estimator, querylen + 1);
+		shm_toc_estimate_keys(&pcxt->estimator, 1);
+	}
+	else
+		querylen = 0;			/* keep compiler quiet */
+
+	/* Everyone's had a chance to ask for space, so now create the DSM */
+	InitializeParallelDSM(pcxt);
+
+	/* If no DSM segment was available, back out (do serial build) */
+	if (pcxt->seg == NULL)
+	{
+		if (IsMVCCSnapshot(snapshot))
+			UnregisterSnapshot(snapshot);
+		DestroyParallelContext(pcxt);
+		ExitParallelMode();
+		return;
+	}
+
+	/* Store shared build state, for which we reserved space */
+	ivfshared = (IvfflatShared *) shm_toc_allocate(pcxt->toc, estivfshared);
+	/* Initialize immutable state */
+	ivfshared->heaprelid = RelationGetRelid(buildstate->heap);
+	ivfshared->indexrelid = RelationGetRelid(buildstate->index);
+	ivfshared->isconcurrent = isconcurrent;
+	ivfshared->scantuplesortstates = scantuplesortstates;
+	ConditionVariableInit(&ivfshared->workersdonecv);
+	SpinLockInit(&ivfshared->mutex);
+	/* Initialize mutable state */
+	ivfshared->nparticipantsdone = 0;
+	ivfshared->reltuples = 0;
+	ivfshared->indtuples = 0;
+#ifdef IVFFLAT_KMEANS_DEBUG
+	ivfshared->inertia = 0;
+#endif
+	table_parallelscan_initialize(buildstate->heap,
+								  ParallelTableScanFromIvfflatShared(ivfshared),
+								  snapshot);
+
+	/* 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 = shm_toc_allocate(pcxt->toc, estcenters);
+	memcpy(ivfcenters, buildstate->centers->items, estcenters);
+
+	shm_toc_insert(pcxt->toc, PARALLEL_KEY_IVFFLAT_SHARED, ivfshared);
+	shm_toc_insert(pcxt->toc, PARALLEL_KEY_TUPLESORT, sharedsort);
+	shm_toc_insert(pcxt->toc, PARALLEL_KEY_IVFFLAT_CENTERS, ivfcenters);
+
+	/* Store query string for workers */
+	if (debug_query_string)
+	{
+		char	   *sharedquery;
+
+		sharedquery = (char *) shm_toc_allocate(pcxt->toc, querylen + 1);
+		memcpy(sharedquery, debug_query_string, querylen + 1);
+		shm_toc_insert(pcxt->toc, PARALLEL_KEY_QUERY_TEXT, sharedquery);
+	}
+
+	/* Launch workers, saving status for leader/caller */
+	LaunchParallelWorkers(pcxt);
+	ivfleader->pcxt = pcxt;
+	ivfleader->nparticipanttuplesorts = pcxt->nworkers_launched;
+	if (leaderparticipates)
+		ivfleader->nparticipanttuplesorts++;
+	ivfleader->ivfshared = ivfshared;
+	ivfleader->sharedsort = sharedsort;
+	ivfleader->snapshot = snapshot;
+	ivfleader->ivfcenters = ivfcenters;
+
+	/* If no workers were successfully launched, back out (do serial build) */
+	if (pcxt->nworkers_launched == 0)
+	{
+		IvfflatEndParallel(ivfleader);
+		return;
+	}
+
+	/* Log participants */
+	ereport(DEBUG1, (errmsg("using %d parallel workers", pcxt->nworkers_launched)));
+
+	/* Save leader state now that it's clear build will be parallel */
+	buildstate->ivfleader = ivfleader;
+
+	/* Join heap scan ourselves */
+	if (leaderparticipates)
+		IvfflatLeaderParticipateAsWorker(buildstate);
+
+	/* Wait for all launched workers */
+	WaitForParallelWorkersToAttach(pcxt);
+}
+
 /*
  * Scan table for tuples to index
  */
 static void
-ScanTable(IvfflatBuildState * buildstate)
+AssignTuples(IvfflatBuildState * buildstate)
 {
-#if PG_VERSION_NUM >= 120000
+	int			parallel_workers = 0;
-	buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+	SortCoordinate coordinate = NULL;
-												   true, true, BuildCallback, (void *) buildstate, NULL);
+
-#else
+	/* Sort options, which must match IvfflatParallelScanAndSort */
-	buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+	AttrNumber	attNums[] = {1};
-											   true, BuildCallback, (void *) buildstate, NULL);
+	Oid			sortOperators[] = {Int4LessOperator};
+	Oid			sortCollations[] = {InvalidOid};
+	bool		nullsFirstFlags[] = {false};
+
+	pgstat_progress_update_param(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_ASSIGN);
+
+	/* Calculate parallel workers */
+	if (buildstate->heap != NULL)
+		parallel_workers = plan_create_index_workers(RelationGetRelid(buildstate->heap), RelationGetRelid(buildstate->index));
+
+	/* Attempt to launch parallel worker scan when required */
+	if (parallel_workers > 0)
+		IvfflatBeginParallel(buildstate, buildstate->indexInfo->ii_Concurrent, parallel_workers);
+
+	/* Set up coordination state if at least one worker launched */
+	if (buildstate->ivfleader)
+	{
+		coordinate = (SortCoordinate) palloc0(sizeof(SortCoordinateData));
+		coordinate->isWorker = false;
+		coordinate->nParticipants = buildstate->ivfleader->nparticipanttuplesorts;
+		coordinate->sharedsort = buildstate->ivfleader->sharedsort;
+	}
+
+	/* Begin serial/leader tuplesort */
+	buildstate->sortstate = tuplesort_begin_heap(buildstate->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, maintenance_work_mem, coordinate, false);
+
+	/* Add tuples to sort */
+	if (buildstate->heap != NULL)
+	{
+		if (buildstate->ivfleader)
+			buildstate->reltuples = ParallelHeapScan(buildstate);
+		else
+			buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+														   true, true, BuildCallback, (void *) buildstate, NULL);
+
+#ifdef IVFFLAT_KMEANS_DEBUG
+		PrintKmeansMetrics(buildstate);
 #endif
+	}
 }
 
 /*
@@ -589,29 +993,21 @@ ScanTable(IvfflatBuildState * buildstate)
 static void
 CreateEntryPages(IvfflatBuildState * buildstate, ForkNumber forkNum)
 {
-	AttrNumber	attNums[] = {1};
+	/* Assign */
-	Oid			sortOperators[] = {Int4LessOperator};
+	IvfflatBench("assign tuples", AssignTuples(buildstate));
-	Oid			sortCollations[] = {InvalidOid};
-	bool		nullsFirstFlags[] = {false};
-
-	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_SORT);
-
-	buildstate->sortstate = tuplesort_begin_heap(buildstate->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, maintenance_work_mem, NULL, false);
-
-	/* Add tuples to sort */
-	if (buildstate->heap != NULL)
-		IvfflatBench("assign tuples", ScanTable(buildstate));
 
 	/* Sort */
 	IvfflatBench("sort tuples", tuplesort_performsort(buildstate->sortstate));
 
-#ifdef IVFFLAT_KMEANS_DEBUG
+	/* Load */
-	PrintKmeansMetrics(buildstate);
-#endif
-
-	/* Insert */
 	IvfflatBench("load tuples", InsertTuples(buildstate->index, buildstate, forkNum));
+
+	/* End sort */
 	tuplesort_end(buildstate->sortstate);
+
+	/* End parallel build */
+	if (buildstate->ivfleader)
+		IvfflatEndParallel(buildstate->ivfleader);
 }
 
 /*

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
+#if PG_VERSION_NUM < 150000
-#include "commands/progress.h"
+#define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
 #endif
 
 int			ivfflat_probes;
@@ -20,11 +22,11 @@ static relopt_kind ivfflat_relopt_kind;
  * Initialize index options and variables
  */
 void
-_PG_init(void)
+IvfflatInit(void)
 {
 	ivfflat_relopt_kind = add_reloption_kind();
 	add_int_reloption(ivfflat_relopt_kind, "lists", "Number of inverted lists",
-					  IVFFLAT_DEFAULT_LISTS, 1, IVFFLAT_MAX_LISTS
+					  IVFFLAT_DEFAULT_LISTS, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS
 #if PG_VERSION_NUM >= 130000
 					  ,AccessExclusiveLock
 #endif
@@ -32,13 +34,14 @@ _PG_init(void)
 
 	DefineCustomIntVariable("ivfflat.probes", "Sets the number of probes",
 							"Valid range is 1..lists.", &ivfflat_probes,
-							1, 1, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
+							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)
 {
@@ -48,15 +51,14 @@ ivfflatbuildphasename(int64 phasenum)
 			return "initializing";
 		case PROGRESS_IVFFLAT_PHASE_KMEANS:
 			return "performing k-means";
-		case PROGRESS_IVFFLAT_PHASE_SORT:
+		case PROGRESS_IVFFLAT_PHASE_ASSIGN:
-			return "sorting tuples";
+			return "assigning tuples";
 		case PROGRESS_IVFFLAT_PHASE_LOAD:
 			return "loading tuples";
 		default:
 			return NULL;
 	}
 }
-#endif
 
 /*
  * Estimate the cost of an index scan
@@ -71,10 +73,7 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	int			lists;
 	double		ratio;
 	double		spc_seq_page_cost;
-	Relation	indexRel;
+	Relation	index;
-#if PG_VERSION_NUM < 120000
-	List	   *qinfos;
-#endif
 
 	/* Never use index without order */
 	if (path->indexorderbys == NULL)
@@ -89,9 +88,9 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 
 	MemSet(&costs, 0, sizeof(costs));
 
-	indexRel = index_open(path->indexinfo->indexoid, NoLock);
+	index = index_open(path->indexinfo->indexoid, NoLock);
-	lists = IvfflatGetLists(indexRel);
+	IvfflatGetMetaPageInfo(index, &lists, NULL);
-	index_close(indexRel, NoLock);
+	index_close(index, NoLock);
 
 	/* Get the ratio of lists that we need to visit */
 	ratio = ((double) ivfflat_probes) / lists;
@@ -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

@@ -3,14 +3,12 @@
 
 #include "postgres.h"
 
-#if PG_VERSION_NUM < 110000
+#include "access/genam.h"
-#error "Requires PostgreSQL 11+"
-#endif
-
 #include "access/generic_xlog.h"
-#include "access/reloptions.h"
+#include "access/parallel.h"
+#include "lib/pairingheap.h"
 #include "nodes/execnodes.h"
-#include "port.h"				/* for strtof() and random() */
+#include "port.h"				/* for random() */
 #include "utils/sampling.h"
 #include "utils/tuplesort.h"
 #include "vector.h"
@@ -39,16 +37,25 @@
 #define IVFFLAT_METAPAGE_BLKNO	0
 #define IVFFLAT_HEAD_BLKNO		1	/* first list page */
 
+/* IVFFlat parameters */
 #define IVFFLAT_DEFAULT_LISTS	100
+#define IVFFLAT_MIN_LISTS		1
 #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_SORT		3
+#define PROGRESS_IVFFLAT_PHASE_ASSIGN	3
 #define PROGRESS_IVFFLAT_PHASE_LOAD		4
 
-#define IVFFLAT_LIST_SIZE(_dim)	(offsetof(IvfflatListData, center) + VECTOR_SIZE(_dim))
+#define IVFFLAT_LIST_SIZE(size)	(offsetof(IvfflatListData, center) + size)
 
 #define IvfflatPageGetOpaque(page)	((IvfflatPageOpaque) PageGetSpecialPointer(page))
 #define IvfflatPageGetMeta(page)	((IvfflatMetaPageData *) PageGetContents(page))
@@ -79,15 +86,13 @@
 /* Variables */
 extern int	ivfflat_probes;
 
-/* Exported functions */
-PGDLLEXPORT void _PG_init(void);
-
 typedef struct VectorArrayData
 {
 	int			length;
 	int			maxlen;
 	int			dim;
-	Vector	   *items;
+	Size		itemsize;
+	char	   *items;
 }			VectorArrayData;
 
 typedef VectorArrayData * VectorArray;
@@ -105,12 +110,57 @@ typedef struct IvfflatOptions
 	int			lists;			/* number of lists */
 }			IvfflatOptions;
 
+typedef struct IvfflatSpool
+{
+	Tuplesortstate *sortstate;
+	Relation	heap;
+	Relation	index;
+}			IvfflatSpool;
+
+typedef struct IvfflatShared
+{
+	/* Immutable state */
+	Oid			heaprelid;
+	Oid			indexrelid;
+	bool		isconcurrent;
+	int			scantuplesortstates;
+
+	/* Worker progress */
+	ConditionVariable workersdonecv;
+
+	/* Mutex for mutable state */
+	slock_t		mutex;
+
+	/* Mutable state */
+	int			nparticipantsdone;
+	double		reltuples;
+	double		indtuples;
+
+#ifdef IVFFLAT_KMEANS_DEBUG
+	double		inertia;
+#endif
+}			IvfflatShared;
+
+#define ParallelTableScanFromIvfflatShared(shared) \
+	(ParallelTableScanDesc) ((char *) (shared) + BUFFERALIGN(sizeof(IvfflatShared)))
+
+typedef struct IvfflatLeader
+{
+	ParallelContext *pcxt;
+	int			nparticipanttuplesorts;
+	IvfflatShared *ivfshared;
+	Sharedsort *sharedsort;
+	Snapshot	snapshot;
+	char	   *ivfcenters;
+}			IvfflatLeader;
+
 typedef struct IvfflatBuildState
 {
 	/* Info */
 	Relation	heap;
 	Relation	index;
 	IndexInfo  *indexInfo;
+	IvfflatType type;
 
 	/* Settings */
 	int			dimensions;
@@ -130,7 +180,6 @@ typedef struct IvfflatBuildState
 	VectorArray samples;
 	VectorArray centers;
 	ListInfo   *listInfo;
-	Vector	   *normvec;
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	double		inertia;
@@ -150,6 +199,9 @@ typedef struct IvfflatBuildState
 
 	/* Memory */
 	MemoryContext tmpCtx;
+
+	/* Parallel builds */
+	IvfflatLeader *ivfleader;
 }			IvfflatBuildState;
 
 typedef struct IvfflatMetaPageData
@@ -190,8 +242,8 @@ typedef struct IvfflatScanList
 typedef struct IvfflatScanOpaqueData
 {
 	int			probes;
+	int			dimensions;
 	bool		first;
-	Buffer		buf;
 
 	/* Sorting */
 	Tuplesortstate *sortstate;
@@ -211,25 +263,28 @@ typedef struct IvfflatScanOpaqueData
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;
 
-#define VECTOR_ARRAY_SIZE(_length, _dim) (sizeof(VectorArrayData) + (_length) * VECTOR_SIZE(_dim))
+#define VECTOR_ARRAY_SIZE(_length, _size) (sizeof(VectorArrayData) + (_length) * _size)
-#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * VECTOR_SIZE((_arr)->dim))
+#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * (_arr)->itemsize)
-#define VectorArrayGet(_arr, _offset) ((Vector *) VECTOR_ARRAY_OFFSET(_arr, _offset))
+#define VectorArrayGet(_arr, _offset) VECTOR_ARRAY_OFFSET(_arr, _offset)
-#define VectorArraySet(_arr, _offset, _val) memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, VECTOR_SIZE((_arr)->dim))
+#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, IvfflatType type);
-void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
+FmgrInfo   *IvfflatOptionalProcInfo(Relation index, uint16 procnum);
-FmgrInfo   *IvfflatOptionalProcInfo(Relation rel, uint16 procnum);
+IvfflatType IvfflatGetType(Relation index);
-bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, IvfflatType type);
 int			IvfflatGetLists(Relation index);
-void		IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);
+void		IvfflatGetMetaPageInfo(Relation index, int *lists, int *dimensions);
+void		IvfflatUpdateList(Relation index, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);
 void		IvfflatCommitBuffer(Buffer buf, GenericXLogState *state);
 void		IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state, ForkNumber forkNum);
 Buffer		IvfflatNewBuffer(Relation index, ForkNumber forkNum);
 void		IvfflatInitPage(Buffer buf, Page page);
 void		IvfflatInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state);
+void		IvfflatInit(void);
+PGDLLEXPORT void IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc);
 
 /* Index access methods */
 IndexBuildResult *ivfflatbuild(Relation heap, Relation index, IndexInfo *indexInfo);

src/ivfinsert.c

@@ -2,44 +2,47 @@
 
 #include <float.h>
 
+#include "access/generic_xlog.h"
 #include "ivfflat.h"
 #include "storage/bufmgr.h"
+#include "storage/lmgr.h"
 #include "utils/memutils.h"
 
 /*
  * Find the list that minimizes the distance function
  */
 static void
-FindInsertPage(Relation rel, Datum *values, BlockNumber *insertPage, ListInfo * listInfo)
+FindInsertPage(Relation index, Datum *values, BlockNumber *insertPage, ListInfo * listInfo)
 {
-	Buffer		cbuf;
-	Page		cpage;
-	IvfflatList list;
-	double		distance;
 	double		minDistance = DBL_MAX;
 	BlockNumber nextblkno = IVFFLAT_HEAD_BLKNO;
 	FmgrInfo   *procinfo;
 	Oid			collation;
-	OffsetNumber offno;
-	OffsetNumber maxoffno;
 
 	/* Avoid compiler warning */
 	listInfo->blkno = nextblkno;
 	listInfo->offno = FirstOffsetNumber;
 
-	procinfo = index_getprocinfo(rel, 1, IVFFLAT_DISTANCE_PROC);
+	procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
-	collation = rel->rd_indcollation[0];
+	collation = index->rd_indcollation[0];
 
 	/* Search all list pages */
 	while (BlockNumberIsValid(nextblkno))
 	{
-		cbuf = ReadBuffer(rel, nextblkno);
+		Buffer		cbuf;
+		Page		cpage;
+		OffsetNumber maxoffno;
+
+		cbuf = ReadBuffer(index, nextblkno);
 		LockBuffer(cbuf, BUFFER_LOCK_SHARE);
 		cpage = BufferGetPage(cbuf);
 		maxoffno = PageGetMaxOffsetNumber(cpage);
 
-		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+		for (OffsetNumber offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
 		{
+			IvfflatList list;
+			double		distance;
+
 			list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, offno));
 			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, values[0], PointerGetDatum(&list->center)));
 
@@ -62,7 +65,7 @@ FindInsertPage(Relation rel, Datum *values, BlockNumber *insertPage, ListInfo *
  * Insert a tuple into the index
  */
 static void
-InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel)
+InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel)
 {
 	IndexTuple	itup;
 	Datum		value;
@@ -79,33 +82,33 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
 
 	/* Normalize if needed */
-	normprocinfo = IvfflatOptionalProcInfo(rel, IVFFLAT_NORM_PROC);
+	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(normprocinfo, rel->rd_indcollation[0], &value, NULL))
+		if (!IvfflatNormValue(normprocinfo, index->rd_indcollation[0], &value, IvfflatGetType(index)))
 			return;
 	}
 
 	/* Find the insert page - sets the page and list info */
-	FindInsertPage(rel, values, &insertPage, &listInfo);
+	FindInsertPage(index, values, &insertPage, &listInfo);
 	Assert(BlockNumberIsValid(insertPage));
 	originalInsertPage = insertPage;
 
 	/* Form tuple */
-	itup = index_form_tuple(RelationGetDescr(rel), &value, isnull);
+	itup = index_form_tuple(RelationGetDescr(index), &value, isnull);
 	itup->t_tid = *heap_tid;
 
 	/* Get tuple size */
 	itemsz = MAXALIGN(IndexTupleSize(itup));
-	Assert(itemsz <= BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(IvfflatPageOpaqueData)));
+	Assert(itemsz <= BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(IvfflatPageOpaqueData)) - sizeof(ItemIdData));
 
 	/* Find a page to insert the item */
 	for (;;)
 	{
-		buf = ReadBuffer(rel, insertPage);
+		buf = ReadBuffer(index, insertPage);
 		LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
 
-		state = GenericXLogStart(rel);
+		state = GenericXLogStart(index);
 		page = GenericXLogRegisterBuffer(state, buf, 0);
 
 		if (PageGetFreeSpace(page) >= itemsz)
@@ -121,23 +124,16 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 		}
 		else
 		{
-			Buffer		metabuf;
 			Buffer		newbuf;
 			Page		newpage;
 
-			/*
-			 * From ReadBufferExtended: Caller is responsible for ensuring
-			 * that only one backend tries to extend a relation at the same
-			 * time!
-			 */
-			metabuf = ReadBuffer(rel, IVFFLAT_METAPAGE_BLKNO);
-			LockBuffer(metabuf, BUFFER_LOCK_EXCLUSIVE);
-
 			/* Add a new page */
-			newbuf = IvfflatNewBuffer(rel, MAIN_FORKNUM);
+			LockRelationForExtension(index, ExclusiveLock);
-			newpage = GenericXLogRegisterBuffer(state, newbuf, GENERIC_XLOG_FULL_IMAGE);
+			newbuf = IvfflatNewBuffer(index, MAIN_FORKNUM);
+			UnlockRelationForExtension(index, ExclusiveLock);
 
 			/* Init new page */
+			newpage = GenericXLogRegisterBuffer(state, newbuf, GENERIC_XLOG_FULL_IMAGE);
 			IvfflatInitPage(newbuf, newpage);
 
 			/* Update insert page */
@@ -147,18 +143,13 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 			IvfflatPageGetOpaque(page)->nextblkno = insertPage;
 
 			/* Commit */
-			MarkBufferDirty(newbuf);
-			MarkBufferDirty(buf);
 			GenericXLogFinish(state);
 
-			/* Unlock extend relation lock as early as possible */
-			UnlockReleaseBuffer(metabuf);
-
 			/* Unlock previous buffer */
 			UnlockReleaseBuffer(buf);
 
 			/* Prepare new buffer */
-			state = GenericXLogStart(rel);
+			state = GenericXLogStart(index);
 			buf = newbuf;
 			page = GenericXLogRegisterBuffer(state, buf, 0);
 			break;
@@ -167,13 +158,13 @@ InsertTuple(Relation rel, Datum *values, bool *isnull, ItemPointer heap_tid, Rel
 
 	/* Add to next offset */
 	if (PageAddItem(page, (Item) itup, itemsz, InvalidOffsetNumber, false, false) == InvalidOffsetNumber)
-		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(rel));
+		elog(ERROR, "failed to add index item to \"%s\"", RelationGetRelationName(index));
 
 	IvfflatCommitBuffer(buf, state);
 
 	/* Update the insert page */
 	if (insertPage != originalInsertPage)
-		IvfflatUpdateList(rel, state, listInfo, insertPage, originalInsertPage, InvalidBlockNumber, MAIN_FORKNUM);
+		IvfflatUpdateList(index, listInfo, insertPage, originalInsertPage, InvalidBlockNumber, MAIN_FORKNUM);
 }
 
 /*

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++
@@ -16,12 +21,7 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 {
 	FmgrInfo   *procinfo;
 	Oid			collation;
-	int			i;
 	int64		j;
-	double		distance;
-	double		sum;
-	double		choice;
-	Vector	   *vec;
 	float	   *weight = palloc(samples->length * sizeof(float));
 	int			numCenters = centers->maxlen;
 	int			numSamples = samples->length;
@@ -34,21 +34,25 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 	centers->length++;
 
 	for (j = 0; j < numSamples; j++)
-		weight[j] = DBL_MAX;
+		weight[j] = FLT_MAX;
 
-	for (i = 0; i < numCenters; i++)
+	for (int i = 0; i < numCenters; i++)
 	{
+		double		sum;
+		double		choice;
+
 		CHECK_FOR_INTERRUPTS();
 
 		sum = 0.0;
 
 		for (j = 0; j < numSamples; j++)
 		{
-			vec = VectorArrayGet(samples, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, j));
+			double		distance;
 
 			/* Only need to compute distance for new center */
 			/* TODO Use triangle inequality to reduce distance calculations */
-			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, i))));
+			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, i))));
 
 			/* Set lower bound */
 			lowerBound[j * numCenters + i] = distance;
@@ -86,16 +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)
 {
-	int			i;
+	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, value));
-	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(vec)));
 
 	/* TODO Handle zero norm */
 	if (norm > 0)
 	{
-		for (i = 0; i < vec->dim; i++)
+		if (type == IVFFLAT_TYPE_VECTOR)
-			vec->x[i] /= norm;
+		{
+			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");
 	}
 }
 
@@ -108,15 +125,21 @@ 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			i;
-	int			j;
-	Vector	   *vec;
 	int			dimensions = centers->dim;
 	Oid			collation = index->rd_indcollation[0];
 	FmgrInfo   *normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
@@ -124,14 +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)
-		for (i = 0; i < samples->length; i++)
+			qsort(samples->items, samples->length, samples->itemsize, CompareVectors);
-		{
+		else if (type == IVFFLAT_TYPE_HALFVEC)
-			vec = VectorArrayGet(samples, i);
+			qsort(samples->items, samples->length, samples->itemsize, CompareHalfVectors);
+		else
+			elog(ERROR, "Unsupported type");
 
-			if (i == 0 || CompareVectors(vec, VectorArrayGet(samples, i - 1)) != 0)
+		for (int i = 0; i < samples->length; i++)
+		{
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, i));
+
+			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++;
 			}
 		}
@@ -140,22 +169,158 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	/* Fill remaining with random data */
 	while (centers->length < centers->maxlen)
 	{
-		vec = VectorArrayGet(centers, centers->length);
+		Datum		center = PointerGetDatum(VectorArrayGet(centers, centers->length));
 
-		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
+		if (type == IVFFLAT_TYPE_VECTOR)
-		vec->dim = dimensions;
+		{
+			Vector	   *vec = DatumGetVector(center);
 
-		for (j = 0; j < dimensions; j++)
+			SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
-			vec->x[j] = RandomDouble();
+			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.
  *
@@ -165,20 +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;
-	int			iteration;
-	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;
@@ -186,19 +347,14 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	float	   *s;
 	float	   *halfcdist;
 	float	   *newcdist;
-	int			changes;
+	MemoryContext kmeansCtx;
-	double		minDistance;
+	MemoryContext oldCtx;
-	int			closestCenter;
-	double		distance;
-	bool		rj;
-	bool		rjreset;
-	double		dxcx;
-	double		dxc;
 
 	/* Calculate allocation sizes */
-	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->dim);
+	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->itemsize);
-	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->dim);
+	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->itemsize);
-	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, dimensions);
+	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;
@@ -208,7 +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 */
@@ -227,6 +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);
@@ -237,28 +399,53 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	halfcdist = palloc_extended(halfcdistSize, MCXT_ALLOC_HUGE);
 	newcdist = palloc(newcdistSize);
 
-	newCenters = VectorArrayInit(numCenters, dimensions);
+	aggCenters = VectorArrayInit(numCenters, dimensions, VECTOR_SIZE(dimensions));
-	for (j = 0; j < numCenters; j++)
+	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++)
 	{
-		minDistance = DBL_MAX;
+		float		minDistance = FLT_MAX;
-		closestCenter = 0;
+		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 */
-			distance = lowerBound[j * numCenters + k];
+			float		distance = lowerBound[j * numCenters + k];
 
 			if (distance < minDistance)
 			{
@@ -272,33 +459,37 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	}
 
 	/* Give 500 iterations to converge */
-	for (iteration = 0; iteration < 500; iteration++)
+	for (int iteration = 0; iteration < 500; iteration++)
 	{
+		int			changes = 0;
+		bool		rjreset;
+
 		/* Can take a while, so ensure we can interrupt */
 		CHECK_FOR_INTERRUPTS();
 
-		changes = 0;
-
 		/* 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++)
 			{
-				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;
 			}
 		}
 
 		/* For all centers c, compute s(c) */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
-			minDistance = DBL_MAX;
+			float		minDistance = FLT_MAX;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
+				float		distance;
+
 				if (j == k)
 					continue;
 
@@ -312,16 +503,21 @@ 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;
+
 			/* Step 2: Identify all points x such that u(x) <= s(c(x)) */
 			if (upperBound[j] <= s[closestCenters[j]])
 				continue;
 
 			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 */
 				if (k == closestCenters[j])
 					continue;
@@ -332,12 +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;
@@ -351,7 +547,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 				/* Step 3b */
 				if (dxcx > lowerBound[j * numCenters + k] || dxcx > halfcdist[closestCenters[j] * numCenters + k])
 				{
-					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;
@@ -365,72 +561,22 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 						changes++;
 					}
-
 				}
 			}
 		}
 
 		/* Step 4: For each center c, let m(c) be mean of all points assigned */
-		for (j = 0; j < numCenters; j++)
+		ComputeNewCenters(samples, aggCenters, newCenters, centerCounts, closestCenters, normprocinfo, collation, type);
-		{
-			vec = VectorArrayGet(newCenters, j);
-			for (k = 0; k < dimensions; k++)
-				vec->x[k] = 0.0;
-
-			centerCounts[j] = 0;
-		}
-
-		for (j = 0; j < numSamples; j++)
-		{
-			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);
-		}
 
 		/* 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++)
 			{
-				distance = lowerBound[j * numCenters + k] - newcdist[k];
+				float		distance = lowerBound[j * numCenters + k] - newcdist[k];
 
 				if (distance < 0)
 					distance = 0;
@@ -441,64 +587,77 @@ 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++)
-			memcpy(VectorArrayGet(centers, j), VectorArrayGet(newCenters, j), VECTOR_SIZE(dimensions));
+			VectorArraySet(centers, j, VectorArrayGet(newCenters, j));
 
 		if (changes == 0 && iteration != 0)
 			break;
 	}
 
-	VectorArrayFree(newCenters);
+	MemoryContextSwitchTo(oldCtx);
-	pfree(centerCounts);
+	MemoryContextDelete(kmeansCtx);
-	pfree(closestCenters);
-	pfree(lowerBound);
-	pfree(upperBound);
-	pfree(s);
-	pfree(halfcdist);
-	pfree(newcdist);
 }
 
 /*
  * Detect issues with centers
  */
 static void
-CheckCenters(Relation index, VectorArray centers)
+CheckCenters(Relation index, VectorArray centers, IvfflatType type)
 {
 	FmgrInfo   *normprocinfo;
-	Oid			collation;
-	Vector	   *vec;
-	int			i;
-	int			j;
-	double		norm;
 
 	if (centers->length != centers->maxlen)
 		elog(ERROR, "Not enough centers. Please report a bug.");
 
 	/* Ensure no NaN or infinite values */
-	for (i = 0; i < centers->length; i++)
+	for (int i = 0; i < centers->length; i++)
 	{
-		vec = VectorArrayGet(centers, i);
+		if (type == IVFFLAT_TYPE_VECTOR)
-
-		for (j = 0; j < vec->dim; j++)
 		{
-			if (isnan(vec->x[j]))
+			Vector	   *vec = (Vector *) VectorArrayGet(centers, i);
-				elog(ERROR, "NaN detected. Please report a bug.");
 
-			if (isinf(vec->x[j]))
+			for (int j = 0; j < vec->dim; j++)
-				elog(ERROR, "Infinite value detected. Please report a bug.");
+			{
+				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)
-	for (i = 1; i < centers->length; i++)
+		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.");
 	}
 
@@ -507,11 +666,12 @@ CheckCenters(Relation index, VectorArray centers)
 	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		collation = index->rd_indcollation[0];
+		Oid			collation = index->rd_indcollation[0];
 
-		for (i = 0; i < centers->length; i++)
+		for (int i = 0; i < centers->length; i++)
 		{
-			norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(VectorArrayGet(centers, i))));
+			double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(VectorArrayGet(centers, i))));
+
 			if (norm == 0)
 				elog(ERROR, "Zero norm detected. Please report a bug.");
 		}
@@ -523,12 +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

@@ -3,14 +3,15 @@
 #include <float.h>
 
 #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"
 #include "storage/bufmgr.h"
 
-#include "catalog/pg_operator_d.h"
-#include "catalog/pg_type_d.h"
-
 /*
  * Compare list distances
  */
@@ -32,36 +33,36 @@ CompareLists(const pairingheap_node *a, const pairingheap_node *b, void *arg)
 static void
 GetScanLists(IndexScanDesc scan, Datum value)
 {
-	Buffer		cbuf;
+	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
-	Page		cpage;
-	IvfflatList list;
-	OffsetNumber offno;
-	OffsetNumber maxoffno;
 	BlockNumber nextblkno = IVFFLAT_HEAD_BLKNO;
 	int			listCount = 0;
-	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
-	double		distance;
-	IvfflatScanList *scanlist;
 	double		maxDistance = DBL_MAX;
 
 	/* Search all list pages */
 	while (BlockNumberIsValid(nextblkno))
 	{
+		Buffer		cbuf;
+		Page		cpage;
+		OffsetNumber maxoffno;
+
 		cbuf = ReadBuffer(scan->indexRelation, nextblkno);
 		LockBuffer(cbuf, BUFFER_LOCK_SHARE);
 		cpage = BufferGetPage(cbuf);
 
 		maxoffno = PageGetMaxOffsetNumber(cpage);
 
-		for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+		for (OffsetNumber offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
 		{
-			list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, offno));
+			IvfflatList list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, offno));
+			double		distance;
 
 			/* Use procinfo from the index instead of scan key for performance */
 			distance = DatumGetFloat8(FunctionCall2Coll(so->procinfo, so->collation, PointerGetDatum(&list->center), value));
 
 			if (listCount < so->probes)
 			{
+				IvfflatScanList *scanlist;
+
 				scanlist = &so->lists[listCount];
 				scanlist->startPage = list->startPage;
 				scanlist->distance = distance;
@@ -76,6 +77,8 @@ GetScanLists(IndexScanDesc scan, Datum value)
 			}
 			else if (distance < maxDistance)
 			{
+				IvfflatScanList *scanlist;
+
 				/* Remove */
 				scanlist = (IvfflatScanList *) pairingheap_remove_first(so->listQueue);
 
@@ -102,22 +105,9 @@ static void
 GetScanItems(IndexScanDesc scan, Datum value)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
-	Buffer		buf;
-	Page		page;
-	IndexTuple	itup;
-	BlockNumber searchPage;
-	OffsetNumber offno;
-	OffsetNumber maxoffno;
-	Datum		datum;
-	bool		isnull;
 	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
@@ -129,19 +119,28 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	/* Search closest probes lists */
 	while (!pairingheap_is_empty(so->listQueue))
 	{
-		searchPage = ((IvfflatScanList *) pairingheap_remove_first(so->listQueue))->startPage;
+		BlockNumber searchPage = ((IvfflatScanList *) pairingheap_remove_first(so->listQueue))->startPage;
 
 		/* Search all entry pages for list */
 		while (BlockNumberIsValid(searchPage))
 		{
+			Buffer		buf;
+			Page		page;
+			OffsetNumber maxoffno;
+
 			buf = ReadBufferExtended(scan->indexRelation, MAIN_FORKNUM, searchPage, RBM_NORMAL, bas);
 			LockBuffer(buf, BUFFER_LOCK_SHARE);
 			page = BufferGetPage(buf);
 			maxoffno = PageGetMaxOffsetNumber(page);
 
-			for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+			for (OffsetNumber offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
 			{
-				itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offno));
+				IndexTuple	itup;
+				Datum		datum;
+				bool		isnull;
+				ItemId		itemid = PageGetItemId(page, offno);
+
+				itup = (IndexTuple) PageGetItem(page, itemid);
 				datum = index_getattr(itup, 1, tupdesc, &isnull);
 
 				/*
@@ -155,8 +154,6 @@ GetScanItems(IndexScanDesc scan, Datum value)
 				slot->tts_isnull[0] = false;
 				slot->tts_values[1] = PointerGetDatum(&itup->t_tid);
 				slot->tts_isnull[1] = false;
-				slot->tts_values[2] = Int32GetDatum((int) searchPage);
-				slot->tts_isnull[2] = false;
 				ExecStoreVirtualTuple(slot);
 
 				tuplesort_puttupleslot(so->sortstate, slot);
@@ -172,7 +169,6 @@ GetScanItems(IndexScanDesc scan, Datum value)
 
 	FreeAccessStrategy(bas);
 
-	/* TODO Scan more lists */
 	if (tuples < 100)
 		ereport(DEBUG1,
 				(errmsg("index scan found few tuples"),
@@ -182,6 +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
  */
@@ -191,6 +223,7 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	IndexScanDesc scan;
 	IvfflatScanOpaque so;
 	int			lists;
+	int			dimensions;
 	AttrNumber	attNums[] = {1};
 	Oid			sortOperators[] = {Float8LessOperator};
 	Oid			sortCollations[] = {InvalidOid};
@@ -198,15 +231,17 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	int			probes = ivfflat_probes;
 
 	scan = RelationGetIndexScan(index, nkeys, norderbys);
-	lists = IvfflatGetLists(scan->indexRelation);
+
+	/* Get lists and dimensions from metapage */
+	IvfflatGetMetaPageInfo(index, &lists, &dimensions);
 
 	if (probes > lists)
 		probes = lists;
 
 	so = (IvfflatScanOpaque) palloc(offsetof(IvfflatScanOpaqueData, lists) + probes * sizeof(IvfflatScanList));
-	so->buf = InvalidBuffer;
 	so->first = true;
 	so->probes = probes;
+	so->dimensions = dimensions;
 
 	/* Set support functions */
 	so->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
@@ -214,23 +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);
-	so->tupdesc = CreateTemplateTupleDesc(3);
-#else
-	so->tupdesc = CreateTemplateTupleDesc(3, false);
-#endif
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
-	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
+	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "heaptid", TIDOID, -1, 0);
-	TupleDescInitEntry(so->tupdesc, (AttrNumber) 3, "indexblkno", INT4OID, -1, 0);
 
 	/* Prep sort */
 	so->sortstate = tuplesort_begin_heap(so->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, work_mem, NULL, false);
 
-#if PG_VERSION_NUM >= 120000
 	so->slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsMinimalTuple);
-#else
-	so->slot = MakeSingleTupleTableSlot(so->tupdesc);
-#endif
 
 	so->listQueue = pairingheap_allocate(CompareLists, scan);
 
@@ -287,23 +313,12 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (scan->orderByData == NULL)
 			elog(ERROR, "cannot scan ivfflat index without order");
 
-		/* No items will match if null */
+		/* Requires MVCC-compliant snapshot as not able to pin during sorting */
-		if (scan->orderByData->sk_flags & SK_ISNULL)
+		/* https://www.postgresql.org/docs/current/index-locking.html */
-			return false;
+		if (!IsMVCCSnapshot(scan->xs_snapshot))
-
+			elog(ERROR, "non-MVCC snapshots are not supported with ivfflat");
-		value = scan->orderByData->sk_argument;
-
-		/* Value should not be compressed or toasted */
-		Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
-		Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
-
-		if (so->normprocinfo != NULL)
-		{
-			/* No items will match if normalization fails */
-			if (!IvfflatNormValue(so->normprocinfo, so->collation, &value, NULL))
-				return false;
-		}
 
+		value = GetScanValue(scan);
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
 		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;
@@ -315,26 +330,10 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 
 	if (tuplesort_gettupleslot(so->sortstate, true, false, so->slot, NULL))
 	{
-		ItemPointer tid = (ItemPointer) DatumGetPointer(slot_getattr(so->slot, 2, &so->isnull));
+		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->slot, 2, &so->isnull));
-		BlockNumber indexblkno = DatumGetInt32(slot_getattr(so->slot, 3, &so->isnull));
-
-#if PG_VERSION_NUM >= 120000
-		scan->xs_heaptid = *tid;
-#else
-		scan->xs_ctup.t_self = *tid;
-#endif
-
-		if (BufferIsValid(so->buf))
-			ReleaseBuffer(so->buf);
-
-		/*
-		 * An index scan must maintain a pin on the index page holding the
-		 * item last returned by amgettuple
-		 *
-		 * https://www.postgresql.org/docs/current/index-locking.html
-		 */
-		so->buf = ReadBuffer(scan->indexRelation, indexblkno);
 
+		scan->xs_heaptid = *heaptid;
+		scan->xs_recheck = false;
 		scan->xs_recheckorderby = false;
 		return true;
 	}
@@ -350,10 +349,6 @@ ivfflatendscan(IndexScanDesc scan)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 
-	/* Release pin */
-	if (BufferIsValid(so->buf))
-		ReleaseBuffer(so->buf);
-
 	pairingheap_free(so->listQueue);
 	tuplesort_end(so->sortstate);
 

src/ivfutils.c

@@ -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;
 }
 
@@ -29,18 +35,6 @@ VectorArrayFree(VectorArray arr)
 	pfree(arr);
 }
 
-/*
- * Print vector array - useful for debugging
- */
-void
-PrintVectorArray(char *msg, VectorArray arr)
-{
-	int			i;
-
-	for (i = 0; i < arr->length; i++)
-		PrintVector(msg, VectorArrayGet(arr, i));
-}
-
 /*
  * Get the number of lists in the index
  */
@@ -59,12 +53,43 @@ IvfflatGetLists(Relation index)
  * Get proc
  */
 FmgrInfo *
-IvfflatOptionalProcInfo(Relation rel, uint16 procnum)
+IvfflatOptionalProcInfo(Relation index, uint16 procnum)
 {
-	if (!OidIsValid(index_getprocid(rel, 1, procnum)))
+	if (!OidIsValid(index_getprocid(index, 1, procnum)))
 		return NULL;
 
-	return index_getprocinfo(rel, 1, 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;
 }
 
 /*
@@ -76,25 +101,34 @@ IvfflatOptionalProcInfo(Relation rel, 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)
 {
-	Vector	   *v;
+	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
-	int			i;
-	double		norm;
-
-	norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
 
 	if (norm > 0)
 	{
-		v = DatumGetVector(*value);
+		if (type == IVFFLAT_TYPE_VECTOR)
+		{
+			Vector	   *v = DatumGetVector(*value);
+			Vector	   *result = InitVector(v->dim);
 
-		if (result == NULL)
+			for (int i = 0; i < v->dim; i++)
-			result = InitVector(v->dim);
+				result->x[i] = v->x[i] / norm;
 
-		for (i = 0; i < v->dim; i++)
+			*value = PointerGetDatum(result);
-			result->x[i] = v->x[i] / norm;
+		}
+		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;
 	}
@@ -142,7 +176,6 @@ IvfflatInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogStat
 void
 IvfflatCommitBuffer(Buffer buf, GenericXLogState *state)
 {
-	MarkBufferDirty(buf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 }
@@ -166,8 +199,6 @@ IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **st
 	IvfflatInitPage(newbuf, newpage);
 
 	/* Commit */
-	MarkBufferDirty(*buf);
-	MarkBufferDirty(newbuf);
 	GenericXLogFinish(*state);
 
 	/* Unlock */
@@ -178,16 +209,40 @@ IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **st
 	*buf = newbuf;
 }
 
+/*
+ * Get the metapage info
+ */
+void
+IvfflatGetMetaPageInfo(Relation index, int *lists, int *dimensions)
+{
+	Buffer		buf;
+	Page		page;
+	IvfflatMetaPage metap;
+
+	buf = ReadBuffer(index, IVFFLAT_METAPAGE_BLKNO);
+	LockBuffer(buf, BUFFER_LOCK_SHARE);
+	page = BufferGetPage(buf);
+	metap = IvfflatPageGetMeta(page);
+
+	*lists = metap->lists;
+
+	if (dimensions != NULL)
+		*dimensions = metap->dimensions;
+
+	UnlockReleaseBuffer(buf);
+}
+
 /*
  * Update the start or insert page of a list
  */
 void
-IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo,
+IvfflatUpdateList(Relation index, ListInfo listInfo,
 				  BlockNumber insertPage, BlockNumber originalInsertPage,
 				  BlockNumber startPage, ForkNumber forkNum)
 {
 	Buffer		buf;
 	Page		page;
+	GenericXLogState *state;
 	IvfflatList list;
 	bool		changed = false;
 

src/ivfvacuum.c

@@ -1,5 +1,6 @@
 #include "postgres.h"
 
+#include "access/generic_xlog.h"
 #include "commands/vacuum.h"
 #include "ivfflat.h"
 #include "storage/bufmgr.h"
@@ -12,34 +13,23 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 				  IndexBulkDeleteCallback callback, void *callback_state)
 {
 	Relation	index = info->index;
-	Buffer		cbuf;
+	BlockNumber blkno = IVFFLAT_HEAD_BLKNO;
-	Page		cpage;
-	Buffer		buf;
-	Page		page;
-	IvfflatList list;
-	IndexTuple	itup;
-	ItemPointer htup;
-	OffsetNumber deletable[MaxOffsetNumber];
-	int			ndeletable;
-	BlockNumber startPages[MaxOffsetNumber];
-	BlockNumber nextblkno = IVFFLAT_HEAD_BLKNO;
-	BlockNumber searchPage;
-	BlockNumber insertPage;
-	GenericXLogState *state;
-	OffsetNumber coffno;
-	OffsetNumber cmaxoffno;
-	OffsetNumber offno;
-	OffsetNumber maxoffno;
-	ListInfo	listInfo;
 	BufferAccessStrategy bas = GetAccessStrategy(BAS_BULKREAD);
 
 	if (stats == NULL)
 		stats = (IndexBulkDeleteResult *) palloc0(sizeof(IndexBulkDeleteResult));
 
 	/* Iterate over list pages */
-	while (BlockNumberIsValid(nextblkno))
+	while (BlockNumberIsValid(blkno))
 	{
-		cbuf = ReadBuffer(index, nextblkno);
+		Buffer		cbuf;
+		Page		cpage;
+		OffsetNumber coffno;
+		OffsetNumber cmaxoffno;
+		BlockNumber startPages[MaxOffsetNumber];
+		ListInfo	listInfo;
+
+		cbuf = ReadBuffer(index, blkno);
 		LockBuffer(cbuf, BUFFER_LOCK_SHARE);
 		cpage = BufferGetPage(cbuf);
 
@@ -48,23 +38,32 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 		/* Iterate over lists */
 		for (coffno = FirstOffsetNumber; coffno <= cmaxoffno; coffno = OffsetNumberNext(coffno))
 		{
-			list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, coffno));
+			IvfflatList list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, coffno));
+
 			startPages[coffno - FirstOffsetNumber] = list->startPage;
 		}
 
-		listInfo.blkno = nextblkno;
+		listInfo.blkno = blkno;
-		nextblkno = IvfflatPageGetOpaque(cpage)->nextblkno;
+		blkno = IvfflatPageGetOpaque(cpage)->nextblkno;
 
 		UnlockReleaseBuffer(cbuf);
 
 		for (coffno = FirstOffsetNumber; coffno <= cmaxoffno; coffno = OffsetNumberNext(coffno))
 		{
-			searchPage = startPages[coffno - FirstOffsetNumber];
+			BlockNumber searchPage = startPages[coffno - FirstOffsetNumber];
-			insertPage = InvalidBlockNumber;
+			BlockNumber insertPage = InvalidBlockNumber;
 
 			/* Iterate over entry pages */
 			while (BlockNumberIsValid(searchPage))
 			{
+				Buffer		buf;
+				Page		page;
+				GenericXLogState *state;
+				OffsetNumber offno;
+				OffsetNumber maxoffno;
+				OffsetNumber deletable[MaxOffsetNumber];
+				int			ndeletable;
+
 				vacuum_delay_point();
 
 				buf = ReadBufferExtended(index, MAIN_FORKNUM, searchPage, RBM_NORMAL, bas);
@@ -86,8 +85,8 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 				/* Find deleted tuples */
 				for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
 				{
-					itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offno));
+					IndexTuple	itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offno));
-					htup = &(itup->t_tid);
+					ItemPointer htup = &(itup->t_tid);
 
 					if (callback(htup, callback_state))
 					{
@@ -109,7 +108,6 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 				{
 					/* Delete tuples */
 					PageIndexMultiDelete(page, deletable, ndeletable);
-					MarkBufferDirty(buf);
 					GenericXLogFinish(state);
 				}
 				else
@@ -127,7 +125,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 			if (BlockNumberIsValid(insertPage))
 			{
 				listInfo.offno = coffno;
-				IvfflatUpdateList(index, state, listInfo, insertPage, InvalidBlockNumber, InvalidBlockNumber, MAIN_FORKNUM);
+				IvfflatUpdateList(index, listInfo, insertPage, InvalidBlockNumber, InvalidBlockNumber, MAIN_FORKNUM);
 			}
 		}
 	}

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

@@ -2,21 +2,27 @@
 
 #include <math.h>
 
-#include "vector.h"
+#include "bitvector.h"
-#include "fmgr.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"
 
-#if PG_VERSION_NUM >= 120000
+#if PG_VERSION_NUM >= 160000
-#include "common/shortest_dec.h"
+#include "varatt.h"
-#include "utils/float.h"
-#else
-#include <float.h>
 #endif
 
 #if PG_VERSION_NUM < 130000
@@ -27,8 +33,27 @@
 #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;
 
+/*
+ * Initialize index options and variables
+ */
+PGDLLEXPORT void _PG_init(void);
+void
+_PG_init(void)
+{
+	HalfvecInit();
+	HnswInit();
+	IvfflatInit();
+}
+
 /*
  * Ensure same dimensions
  */
@@ -71,7 +96,7 @@ CheckDim(int dim)
 }
 
 /*
- * Ensure finite elements
+ * Ensure finite element
  */
 static inline void
 CheckElement(float value)
@@ -87,6 +112,23 @@ CheckElement(float value)
 				 errmsg("infinite value not allowed in vector")));
 }
 
+/*
+ * Allocate and initialize a new vector
+ */
+Vector *
+InitVector(int dim)
+{
+	Vector	   *result;
+	int			size;
+
+	size = VECTOR_SIZE(dim);
+	result = (Vector *) palloc0(size);
+	SET_VARSIZE(result, size);
+	result->dim = dim;
+
+	return result;
+}
+
 /*
  * Check for whitespace, since array_isspace() is static
  */
@@ -125,6 +167,14 @@ float_overflow_error(void)
 			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
 			 errmsg("value out of range: overflow")));
 }
+
+static pg_noinline void
+float_underflow_error(void)
+{
+	ereport(ERROR,
+			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+			 errmsg("value out of range: underflow")));
+}
 #endif
 
 /*
@@ -134,31 +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);
-	int			i;
 	float		x[VECTOR_MAX_DIM];
 	int			dim = 0;
-	char	   *pt;
+	char	   *pt = lit;
-	char	   *stringEnd;
 	Vector	   *result;
-	char	   *lit = pstrdup(str);
 
-	while (vector_isspace(*str))
+	while (vector_isspace(*pt))
-		str++;
+		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++;
-	pt = strtok(str, ",");
-	stringEnd = 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),
@@ -173,70 +229,67 @@ 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);
+		/* Postgres sets LC_NUMERIC to C on startup */
-		CheckElement(x[dim]);
+		val = strtof(pt, &stringEnd);
-		dim++;
 
 		if (stringEnd == pt)
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
 
-		while (vector_isspace(*stringEnd))
+		/* Check for range error like float4in */
-			stringEnd++;
+		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))
+	while (vector_isspace(*pt))
-		stringEnd++;
+		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 */
+	CheckDim(dim);
-	for (pt = lit + 1; *pt != '\0'; pt++)
-	{
-		if (pt[-1] == ',' && *pt == ',')
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("malformed vector literal: \"%s\"", lit)));
-	}
-
-	if (dim < 1)
-		ereport(ERROR,
-				(errcode(ERRCODE_DATA_EXCEPTION),
-				 errmsg("vector must have at least 1 dimension")));
-
-	pfree(lit);
-
 	CheckExpectedDim(typmod, dim);
 
 	result = InitVector(dim);
-	for (i = 0; i < dim; i++)
+	for (int i = 0; i < dim; i++)
 		result->x[i] = x[i];
 
 	PG_RETURN_POINTER(result);
 }
 
+#define AppendChar(ptr, c) (*(ptr)++ = (c))
+#define AppendFloat(ptr, f) ((ptr) += float_to_shortest_decimal_bufn((f), (ptr)))
+
 /*
  * Convert internal representation to textual representation
  */
@@ -248,17 +301,6 @@ vector_out(PG_FUNCTION_ARGS)
 	int			dim = vector->dim;
 	char	   *buf;
 	char	   *ptr;
-	int			i;
-	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:
@@ -273,25 +315,17 @@ vector_out(PG_FUNCTION_ARGS)
 	buf = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN * dim + 2);
 	ptr = buf;
 
-	*ptr = '[';
+	AppendChar(ptr, '[');
-	ptr++;
+
-	for (i = 0; i < dim; i++)
+	for (int i = 0; i < dim; i++)
 	{
 		if (i > 0)
-		{
+			AppendChar(ptr, ',');
-			*ptr = ',';
-			ptr++;
-		}
 
-#if PG_VERSION_NUM >= 120000
+		AppendFloat(ptr, vector->x[i]);
-		n = float_to_shortest_decimal_bufn(vector->x[i], ptr);
-#else
-		n = sprintf(ptr, "%.*g", ndig, vector->x[i]);
-#endif
-		ptr += n;
 	}
-	*ptr = ']';
+
-	ptr++;
+	AppendChar(ptr, ']');
 	*ptr = '\0';
 
 	PG_FREE_IF_COPY(vector, 0);
@@ -353,7 +387,6 @@ vector_recv(PG_FUNCTION_ARGS)
 	Vector	   *result;
 	int16		dim;
 	int16		unused;
-	int			i;
 
 	dim = pq_getmsgint(buf, sizeof(int16));
 	unused = pq_getmsgint(buf, sizeof(int16));
@@ -367,7 +400,7 @@ vector_recv(PG_FUNCTION_ARGS)
 				 errmsg("expected unused to be 0, not %d", unused)));
 
 	result = InitVector(dim);
-	for (i = 0; i < dim; i++)
+	for (int i = 0; i < dim; i++)
 	{
 		result->x[i] = pq_getmsgfloat4(buf);
 		CheckElement(result->x[i]);
@@ -385,12 +418,11 @@ vector_send(PG_FUNCTION_ARGS)
 {
 	Vector	   *vec = PG_GETARG_VECTOR_P(0);
 	StringInfoData buf;
-	int			i;
 
 	pq_begintypsend(&buf);
 	pq_sendint(&buf, vec->dim, sizeof(int16));
 	pq_sendint(&buf, vec->unused, sizeof(int16));
-	for (i = 0; i < vec->dim; i++)
+	for (int i = 0; i < vec->dim; i++)
 		pq_sendfloat4(&buf, vec->x[i]);
 
 	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
@@ -398,17 +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);
 }
 
 /*
@@ -420,13 +453,11 @@ array_to_vector(PG_FUNCTION_ARGS)
 {
 	ArrayType  *array = PG_GETARG_ARRAYTYPE_P(0);
 	int32		typmod = PG_GETARG_INT32(1);
-	int			i;
 	Vector	   *result;
 	int16		typlen;
 	bool		typbyval;
 	char		typalign;
 	Datum	   *elemsp;
-	bool	   *nullsp;
 	int			nelemsp;
 
 	if (ARR_NDIM(array) > 1)
@@ -434,36 +465,55 @@ array_to_vector(PG_FUNCTION_ARGS)
 				(errcode(ERRCODE_DATA_EXCEPTION),
 				 errmsg("array must be 1-D")));
 
+	if (ARR_HASNULL(array) && array_contains_nulls(array))
+		ereport(ERROR,
+				(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
+				 errmsg("array must not contain nulls")));
+
 	get_typlenbyvalalign(ARR_ELEMTYPE(array), &typlen, &typbyval, &typalign);
-	deconstruct_array(array, ARR_ELEMTYPE(array), typlen, typbyval, typalign, &elemsp, &nullsp, &nelemsp);
+	deconstruct_array(array, ARR_ELEMTYPE(array), typlen, typbyval, typalign, &elemsp, NULL, &nelemsp);
 
 	CheckDim(nelemsp);
 	CheckExpectedDim(typmod, nelemsp);
 
 	result = InitVector(nelemsp);
-	for (i = 0; i < nelemsp; i++)
+
+	if (ARR_ELEMTYPE(array) == INT4OID)
 	{
-		if (nullsp[i])
+		for (int i = 0; i < nelemsp; i++)
-			ereport(ERROR,
-					(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
-					 errmsg("array must not containing NULLs")));
-
-		/* TODO Move outside loop in 0.5.0 */
-		if (ARR_ELEMTYPE(array) == INT4OID)
 			result->x[i] = DatumGetInt32(elemsp[i]);
-		else if (ARR_ELEMTYPE(array) == FLOAT8OID)
-			result->x[i] = DatumGetFloat8(elemsp[i]);
-		else if (ARR_ELEMTYPE(array) == FLOAT4OID)
-			result->x[i] = DatumGetFloat4(elemsp[i]);
-		else if (ARR_ELEMTYPE(array) == NUMERICOID)
-			result->x[i] = DatumGetFloat4(DirectFunctionCall1(numeric_float4, elemsp[i]));
-		else
-			ereport(ERROR,
-					(errcode(ERRCODE_DATA_EXCEPTION),
-					 errmsg("unsupported array type")));
-
-		CheckElement(result->x[i]);
 	}
+	else if (ARR_ELEMTYPE(array) == FLOAT8OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = DatumGetFloat8(elemsp[i]);
+	}
+	else if (ARR_ELEMTYPE(array) == FLOAT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = DatumGetFloat4(elemsp[i]);
+	}
+	else if (ARR_ELEMTYPE(array) == NUMERICOID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+			result->x[i] = DatumGetFloat4(DirectFunctionCall1(numeric_float4, elemsp[i]));
+	}
+	else
+	{
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("unsupported array type")));
+	}
+
+	/*
+	 * 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);
 }
@@ -478,11 +528,10 @@ vector_to_float4(PG_FUNCTION_ARGS)
 	Vector	   *vec = PG_GETARG_VECTOR_P(0);
 	Datum	   *datums;
 	ArrayType  *result;
-	int			i;
 
 	datums = (Datum *) palloc(sizeof(Datum) * vec->dim);
 
-	for (i = 0; i < vec->dim; i++)
+	for (int i = 0; i < vec->dim; i++)
 		datums[i] = Float4GetDatum(vec->x[i]);
 
 	/* Use TYPALIGN_INT for float4 */
@@ -493,6 +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
  */
@@ -502,21 +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;
-	double		distance = 0.0;
-	double		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
+	PG_RETURN_FLOAT8(sqrt((double) VectorL2SquaredDistance(a->dim, a->x, b->x)));
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
-
-	PG_RETURN_FLOAT8(sqrt(distance));
 }
 
 /*
@@ -529,21 +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;
-	double		distance = 0.0;
-	double		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
+	PG_RETURN_FLOAT8((double) VectorL2SquaredDistance(a->dim, a->x, b->x));
-	for (int i = 0; i < a->dim; i++)
+}
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
 
-	PG_RETURN_FLOAT8(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;
 }
 
 /*
@@ -555,17 +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;
-	double		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
+	PG_RETURN_FLOAT8((double) VectorInnerProduct(a->dim, a->x, b->x));
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8(distance);
 }
 
 /*
@@ -577,17 +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;
-	double		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
+	PG_RETURN_FLOAT8((double) -VectorInnerProduct(a->dim, a->x, b->x));
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8(distance * -1);
 }
 
 /*
@@ -601,9 +664,10 @@ cosine_distance(PG_FUNCTION_ARGS)
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 	float	   *ax = a->x;
 	float	   *bx = b->x;
-	double		distance = 0.0;
+	float		distance = 0.0;
-	double		norma = 0.0;
+	float		norma = 0.0;
-	double		normb = 0.0;
+	float		normb = 0.0;
+	double		similarity;
 
 	CheckDims(a, b);
 
@@ -616,7 +680,21 @@ cosine_distance(PG_FUNCTION_ARGS)
 	}
 
 	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
-	PG_RETURN_FLOAT8(1 - (distance / sqrt(norma * normb)));
+	similarity = (double) distance / sqrt((double) norma * (double) normb);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	if (isnan(similarity))
+		PG_RETURN_FLOAT8(NAN);
+#endif
+
+	/* Keep in range */
+	if (similarity > 1)
+		similarity = 1.0;
+	else if (similarity < -1)
+		similarity = -1.0;
+
+	PG_RETURN_FLOAT8(1.0 - similarity);
 }
 
 /*
@@ -630,13 +708,11 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	double		distance = 0.0;
+	double		distance;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
+	distance = (double) VectorInnerProduct(a->dim, a->x, b->x);
-	for (int i = 0; i < a->dim; i++)
-		distance += a->x[i] * b->x[i];
 
 	/* Prevent NaN with acos with loss of precision */
 	if (distance > 1)
@@ -647,6 +723,28 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(acos(distance) / M_PI);
 }
 
+/*
+ * Get the L1 distance between two vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(l1_distance);
+Datum
+l1_distance(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
+	float	   *ax = a->x;
+	float	   *bx = b->x;
+	float		distance = 0.0;
+
+	CheckDims(a, b);
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		distance += fabsf(ax[i] - bx[i]);
+
+	PG_RETURN_FLOAT8((double) distance);
+}
+
 /*
  * Get the dimensions of a vector
  */
@@ -672,7 +770,7 @@ vector_norm(PG_FUNCTION_ARGS)
 
 	/* Auto-vectorized */
 	for (int i = 0; i < a->dim; i++)
-		norm += ax[i] * ax[i];
+		norm += (double) ax[i] * (double) ax[i];
 
 	PG_RETURN_FLOAT8(sqrt(norm));
 }
@@ -743,17 +841,102 @@ vector_sub(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+/*
+ * Multiply vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_mul);
+Datum
+vector_mul(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
+	float	   *ax = a->x;
+	float	   *bx = b->x;
+	Vector	   *result;
+	float	   *rx;
+
+	CheckDims(a, b);
+
+	result = InitVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+		rx[i] = ax[i] * bx[i];
+
+	/* Check for overflow and underflow */
+	for (int i = 0, imax = a->dim; i < imax; i++)
+	{
+		if (isinf(rx[i]))
+			float_overflow_error();
+
+		if (rx[i] == 0 && !(ax[i] == 0 || bx[i] == 0))
+			float_underflow_error();
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * 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)
 {
-	int			i;
+	int			dim = Min(a->dim, b->dim);
 
-	CheckDims(a, b);
+	/* Check values before dimensions to be consistent with Postgres arrays */
-
+	for (int i = 0; i < dim; i++)
-	for (i = 0; i < a->dim; i++)
 	{
 		if (a->x[i] < b->x[i])
 			return -1;
@@ -761,6 +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;
 }
 
@@ -771,8 +961,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_lt);
 Datum
 vector_lt(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) < 0);
 }
@@ -784,8 +974,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_le);
 Datum
 vector_le(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) <= 0);
 }
@@ -797,8 +987,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_eq);
 Datum
 vector_eq(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) == 0);
 }
@@ -810,8 +1000,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_ne);
 Datum
 vector_ne(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) != 0);
 }
@@ -823,8 +1013,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_ge);
 Datum
 vector_ge(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) >= 0);
 }
@@ -836,8 +1026,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_gt);
 Datum
 vector_gt(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) > 0);
 }
@@ -849,8 +1039,8 @@ PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_cmp);
 Datum
 vector_cmp(PG_FUNCTION_ARGS)
 {
-	Vector	   *a = (Vector *) PG_GETARG_VECTOR_P(0);
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = (Vector *) PG_GETARG_VECTOR_P(1);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
 	PG_RETURN_INT32(vector_cmp_internal(a, b));
 }
@@ -1019,3 +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);
+}

src/vector.h

@@ -1,12 +1,6 @@
 #ifndef VECTOR_H
 #define VECTOR_H
 
-#include "postgres.h"
-
-#if PG_VERSION_NUM >= 160000
-#include "varatt.h"
-#endif
-
 #define VECTOR_MAX_DIM 16000
 
 #define VECTOR_SIZE(_dim)		(offsetof(Vector, x) + sizeof(float)*(_dim))
@@ -22,24 +16,8 @@ typedef struct Vector
 	float		x[FLEXIBLE_ARRAY_MEMBER];
 }			Vector;
 
+Vector	   *InitVector(int dim);
 void		PrintVector(char *msg, Vector * vector);
 int			vector_cmp_internal(Vector * a, Vector * b);
 
-/*
- * Allocate and initialize a new vector
- */
-static inline Vector *
-InitVector(int dim)
-{
-	Vector	   *result;
-	int			size;
-
-	size = VECTOR_SIZE(dim);
-	result = (Vector *) palloc0(size);
-	SET_VARSIZE(result, size);
-	result->dim = dim;
-
-	return result;
-}
-
 #endif

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

@@ -28,8 +28,28 @@ 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 containing NULLs
+ERROR:  array must not contain nulls
 SELECT '{NaN}'::real[]::vector;
 ERROR:  NaN not allowed in vector
 SELECT '{Infinity}'::real[]::vector;
@@ -38,12 +58,118 @@ SELECT '{-Infinity}'::real[]::vector;
 ERROR:  infinite value not allowed in vector
 SELECT '{}'::real[]::vector;
 ERROR:  vector must have at least 1 dimension
-SELECT '[1,2,3]'::vector::real[];
+SELECT '{{1}}'::real[]::vector;
- float4  
+ERROR:  array must be 1-D
+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));
+CREATE TABLE t (val vector(3), val2 halfvec(3), val3 sparsevec(3));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+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)
 SELECT * FROM t2 ORDER BY val;
-   val   
+   val   |  val2   |      val3       
----------
+---------+---------+-----------------
- [0,0,0]
+ [0,0,0] | [0,0,0] | {}/3
- [1,1,1]
+ [1,1,1] | [1,1,1] | {1:1,2:1,3:1}/3
- [1,2,3]
+ [1,2,3] | [1,2,3] | {1:1,2:2,3:3}/3
- 
+         |         | 
 (4 rows)
 
 DROP TABLE t;

test/expected/functions.out

@@ -1,110 +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 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 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 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 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('[1,1]', '[-1,-1]');
- cosine_distance 
------------------
-               2
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-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 vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
-ERROR:  vector cannot have more than 16000 dimensions

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_options.out

@@ -0,0 +1,26 @@
+CREATE TABLE t (val vector(3));
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 1);
+ERROR:  value 1 out of bounds for option "m"
+DETAIL:  Valid values are between "2" and "100".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 101);
+ERROR:  value 101 out of bounds for option "m"
+DETAIL:  Valid values are between "2" and "100".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 3);
+ERROR:  value 3 out of bounds for option "ef_construction"
+DETAIL:  Valid values are between "4" and "1000".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 1001);
+ERROR:  value 1001 out of bounds for option "ef_construction"
+DETAIL:  Valid values are between "4" and "1000".
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 16, ef_construction = 31);
+ERROR:  ef_construction must be greater than or equal to 2 * m
+SHOW hnsw.ef_search;
+ hnsw.ef_search 
+----------------
+ 40
+(1 row)
+
+SET hnsw.ef_search = 0;
+ERROR:  0 is outside the valid range for parameter "hnsw.ef_search" (1 .. 1000)
+SET hnsw.ef_search = 1001;
+ERROR:  1001 is outside the valid range for parameter "hnsw.ef_search" (1 .. 1000)
+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_unlogged.out

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

test/expected/hnsw_vector_cosine.out

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

test/expected/hnsw_vector_ip.out

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

test/expected/hnsw_vector_l2.out

@@ -1,7 +1,7 @@
 SET enable_seqscan = off;
 CREATE TABLE t (val vector(3));
 INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE INDEX ON t USING ivfflat (val) WITH (lists = 1);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops);
 INSERT INTO t (val) VALUES ('[1,2,4]');
 SELECT * FROM t ORDER BY val <-> '[3,3,3]';
    val   
@@ -12,10 +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);
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector)) t2;
- val 
+ count 
------
+-------
-(0 rows)
+     4
+(1 row)
 
 SELECT COUNT(*) FROM t;
  count 
@@ -23,4 +24,10 @@ SELECT COUNT(*) FROM t;
      5
 (1 row)
 
+TRUNCATE t;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+ val 
+-----
+(0 rows)
+
 DROP TABLE t;

test/expected/ivfflat_halfvec_cosine.out

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

test/expected/ivfflat_halfvec_ip.out

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

test/expected/ivfflat_halfvec_l2.out

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

test/expected/ivfflat_options.out

@@ -1,9 +1,8 @@
-SET enable_seqscan = off;
 CREATE TABLE t (val vector(3));
-CREATE INDEX ON t USING ivfflat (val) WITH (lists = 0);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 0);
 ERROR:  value 0 out of bounds for option "lists"
 DETAIL:  Valid values are between "1" and "32768".
-CREATE INDEX ON t USING ivfflat (val) WITH (lists = 32769);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 32769);
 ERROR:  value 32769 out of bounds for option "lists"
 DETAIL:  Valid values are between "1" and "32768".
 SHOW ivfflat.probes;

test/expected/ivfflat_unlogged.out

@@ -1,7 +1,7 @@
 SET enable_seqscan = off;
 CREATE UNLOGGED TABLE t (val vector(3));
 INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE INDEX ON t USING ivfflat (val) WITH (lists = 1);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 1);
 SELECT * FROM t ORDER BY val <-> '[3,3,3]';
    val   
 ---------

test/expected/ivfflat_vector_cosine.out

@@ -11,9 +11,16 @@ SELECT * FROM t ORDER BY val <=> '[3,3,3]';
  [1,2,4]
 (3 rows)
 
-SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector);
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
- val 
+ count 
------
+-------
-(0 rows)
+     3
+(1 row)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2;
+ count 
+-------
+     3
+(1 row)
 
 DROP TABLE t;

test/expected/ivfflat_vector_ip.out

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

test/expected/ivfflat_vector_l2.out

@@ -0,0 +1,36 @@
+SET enable_seqscan = off;
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING 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]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector)) t2;
+ count 
+-------
+     4
+(1 row)
+
+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/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

@@ -63,38 +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:  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;
@@ -104,15 +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

@@ -3,12 +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 '[1,2,3]'::vector::real[];
+SELECT '{{1}}'::real[]::vector;
+
+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));
+CREATE TABLE t (val vector(3), val2 halfvec(3), val3 sparsevec(3));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+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

@@ -1,29 +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 vector_dims('[1,2,3]');
-
-SELECT round(vector_norm('[1,1]')::numeric, 5);
-SELECT vector_norm('[3,4]');
-SELECT vector_norm('[0,1]');
-
-SELECT l2_distance('[0,0]', '[3,4]');
-SELECT l2_distance('[0,0]', '[0,1]');
-SELECT l2_distance('[1,2]', '[3]');
-
-SELECT inner_product('[1,2]', '[3,4]');
-SELECT inner_product('[1,2]', '[3]');
-
-SELECT cosine_distance('[1,2]', '[2,4]');
-SELECT cosine_distance('[1,2]', '[0,0]');
-SELECT cosine_distance('[1,1]', '[1,1]');
-SELECT cosine_distance('[1,1]', '[-1,-1]');
-SELECT cosine_distance('[1,2]', '[3]');
-
-SELECT 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 vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;

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_options.sql

@@ -0,0 +1,13 @@
+CREATE TABLE t (val vector(3));
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 1);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 101);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 3);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (ef_construction = 1001);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops) WITH (m = 16, ef_construction = 31);
+
+SHOW hnsw.ef_search;
+
+SET hnsw.ef_search = 0;
+SET hnsw.ef_search = 1001;
+
+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_unlogged.sql

@@ -0,0 +1,9 @@
+SET enable_seqscan = off;
+
+CREATE UNLOGGED TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops);
+
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+DROP TABLE t;

test/sql/hnsw_vector_cosine.sql

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

test/sql/hnsw_vector_ip.sql

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

test/sql/hnsw_vector_l2.sql

@@ -2,12 +2,15 @@ SET enable_seqscan = off;
 
 CREATE TABLE t (val vector(3));
 INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE INDEX ON t USING ivfflat (val) WITH (lists = 1);
+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;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
 DROP TABLE t;

test/sql/ivfflat_halfvec_cosine.sql

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

test/sql/ivfflat_halfvec_ip.sql

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

test/sql/ivfflat_halfvec_l2.sql

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

test/sql/ivfflat_options.sql

@@ -1,8 +1,6 @@
-SET enable_seqscan = off;
-
 CREATE TABLE t (val vector(3));
-CREATE INDEX ON t USING ivfflat (val) WITH (lists = 0);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 0);
-CREATE INDEX ON t USING ivfflat (val) WITH (lists = 32769);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 32769);
 
 SHOW ivfflat.probes;
 

test/sql/ivfflat_unlogged.sql

@@ -2,7 +2,7 @@ SET enable_seqscan = off;
 
 CREATE UNLOGGED TABLE t (val vector(3));
 INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE INDEX ON t USING ivfflat (val) WITH (lists = 1);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 1);
 
 SELECT * FROM t ORDER BY val <-> '[3,3,3]';
 

test/sql/ivfflat_vector_cosine.sql

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

test/sql/ivfflat_vector_ip.sql

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

test/sql/ivfflat_vector_l2.sql

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