Added comments [skip ci]

Co-authored-by: Narek Galstyan <narekg@berkeley.edu>
Co-authored-by: Di Qi <di@lantern.dev>

.editorconfig

@@ -1,6 +1,6 @@
 root = true
 
-[*.{c,h,pl,pm}]
+[*.{c,h,pl,pm,sql}]
 indent_style = tab
 indent_size = tab
 tab_width = 4

.github/workflows/build.yml

@@ -1,39 +1,132 @@
 name: build
 on: [push, pull_request]
 jobs:
-  build:
+  ubuntu:
     runs-on: ${{ matrix.os }}
+    if: ${{ !startsWith(github.ref_name, 'mac') && !startsWith(github.ref_name, 'windows') }}
     strategy:
       fail-fast: false
       matrix:
-        os: [ubuntu-latest]
-        postgres: [15, 14, 13, 12, 11, 10]
         include:
-        - os: macos-latest
-          postgres: 14
+          # - postgres: 18
+          #   os: ubuntu-24.04
+          - postgres: 17
+            os: ubuntu-24.04
+          - postgres: 16
+            os: ubuntu-22.04
+          - postgres: 15
+            os: ubuntu-22.04
+          - postgres: 14
+            os: ubuntu-20.04
+          - postgres: 13
+            os: ubuntu-20.04
     steps:
-    - uses: actions/checkout@v3
-    - uses: ankane/setup-postgres@v1
-      with:
-        postgres-version: ${{ matrix.postgres }}
-        dev-files: true
-    - if: ${{ startsWith(matrix.os, 'ubuntu') }}
-      run: sudo apt-get update && sudo apt-get install libipc-run-perl
-    - run: make
-    - if: ${{ startsWith(matrix.os, 'ubuntu') }}
-      run: |
-        export PG_CONFIG=`which pg_config`
-        sudo --preserve-env=PG_CONFIG make install
-    - if: ${{ startsWith(matrix.os, 'macos') }}
-      run: make install
-    - run: make installcheck
-    - if: ${{ failure() }}
-      run: cat regression.diffs
-    - if: ${{ startsWith(matrix.os, 'ubuntu') }}
-      run: make prove_installcheck
-    - if: ${{ startsWith(matrix.os, 'macos') }}
-      run: |
-        brew install cpanm && cpanm IPC::Run
-        wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_14_5.tar.gz
-        tar xf REL_14_5.tar.gz
-        make prove_installcheck PROVE=prove PROVE_FLAGS="-I ./postgres-REL_14_5/src/test/perl" PERL5LIB="/Users/runner/perl5/lib/perl5"
+      - uses: actions/checkout@v4
+      - uses: ankane/setup-postgres@v1
+        with:
+          postgres-version: ${{ matrix.postgres }}
+          dev-files: true
+      - run: make
+        env:
+          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
+      - run: make installcheck
+      - if: ${{ failure() }}
+        run: cat regression.diffs
+      - run: |
+          sudo apt-get update
+          sudo apt-get install libipc-run-perl
+      - run: make prove_installcheck
+  mac:
+    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@v4
+      - uses: ankane/setup-postgres@v1
+        with:
+          postgres-version: ${{ matrix.postgres }}
+      - run: make
+        env:
+          PG_CFLAGS: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter
+      - run: make install
+      - run: make installcheck
+      - if: ${{ failure() }}
+        run: cat regression.diffs
+      # Homebrew Postgres does not enable TAP tests, so need to download
+      - run: |
+          brew install cpanm
+          cpanm --notest IPC::Run
+          wget -q https://github.com/postgres/postgres/archive/refs/tags/$TAG.tar.gz
+          tar xf $TAG.tar.gz
+          mv postgres-$TAG postgres
+        env:
+          TAG: ${{ matrix.postgres == 16 && 'REL_16_2' || 'REL_14_11' }}
+      - run: make prove_installcheck PROVE_FLAGS="-I ./postgres/src/test/perl -I ./test/perl"
+        env:
+          PERL5LIB: /Users/runner/perl5/lib/perl5
+      - run: make clean && $(brew --prefix llvm@15)/bin/scan-build --status-bugs make
+        env:
+          PG_CFLAGS: -DUSE_ASSERT_CHECKING
+  windows:
+    runs-on: windows-latest
+    if: ${{ !startsWith(github.ref_name, 'mac') }}
+    steps:
+      - uses: actions/checkout@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" && ^
+          nmake /NOLOGO /F Makefile.win && ^
+          nmake /NOLOGO /F Makefile.win install && ^
+          nmake /NOLOGO /F Makefile.win installcheck && ^
+          nmake /NOLOGO /F Makefile.win clean && ^
+          nmake /NOLOGO /F Makefile.win uninstall
+        shell: cmd
+      - if: ${{ failure() }}
+        run: cat regression.diffs
+  i386:
+    if: ${{ !startsWith(github.ref_name, 'mac') && !startsWith(github.ref_name, 'windows') }}
+    runs-on: ubuntu-latest
+    container:
+      image: debian:12
+      options: --platform linux/386
+    steps:
+      - run: apt-get update && apt-get install -y build-essential git libipc-run-perl postgresql-15 postgresql-server-dev-15 sudo
+      - run: service postgresql start
+      - run: |
+          git clone https://github.com/${{ github.repository }}.git pgvector
+          cd pgvector
+          git 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: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter -Wno-sign-compare
+      - if: ${{ failure() }}
+        run: cat pgvector/regression.diffs
+  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
+          check-ub: yes
+      - run: make OPTFLAGS=""
+      - run: sudo --preserve-env=PG_CONFIG make install
+      - run: make installcheck

.gitignore

@@ -1,4 +1,5 @@
 /dist/
+/log/
 /results/
 /tmp_check/
 /sql/vector--?.?.?.sql
@@ -6,3 +7,8 @@ regression.*
 *.o
 *.so
 *.bc
+*.dll
+*.dylib
+*.obj
+*.lib
+*.exp

CHANGELOG.md

@@ -1,10 +1,136 @@
+## 0.8.0 (unreleased)
+
+- Added casts for arrays to `sparsevec`
+- Reduced memory usage for HNSW index scans
+- Dropped support for Postgres 12
+
+## 0.7.4 (2024-08-05)
+
+- Fixed locking for parallel HNSW index builds
+- Fixed compilation error with GCC 14 on i386 when SSE2 is not enabled
+
+## 0.7.3 (2024-07-22)
+
+- Fixed `failed to add index item` error with `sparsevec`
+- Fixed compilation error with FreeBSD ARM
+- Fixed compilation warning with MSVC and Postgres 16
+
+## 0.7.2 (2024-06-11)
+
+- Fixed initialization fork for indexes on unlogged tables
+
+## 0.7.1 (2024-06-03)
+
+- Improved performance of on-disk HNSW index builds
+- Fixed `undefined symbol` error with GCC 8
+- Fixed compilation error with universal binaries on Mac
+- Fixed compilation warning with Clang < 14
+
+## 0.7.0 (2024-04-29)
+
+- Added `halfvec` type
+- Added `sparsevec` type
+- Added support for indexing `bit` type
+- Added support for indexing L1 distance with HNSW
+- Added `binary_quantize` function
+- Added `hamming_distance` function
+- Added `jaccard_distance` function
+- Added `l2_normalize` function
+- Added `subvector` function
+- Added concatenate operator for vectors
+- 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
+- Fixed segmentation fault with text input
+- Fixed consecutive delimiters with text input
+
+## 0.4.3 (2023-06-10)
+
+- Improved cost estimation
+- Improved support for spaces with text input
+- Fixed infinite and NaN values with binary input
+- Fixed infinite values with vector addition and subtraction
+- Fixed infinite values with list centers
+- Fixed compilation error when `float8` is pass by reference
+- Fixed compilation error on PowerPC
+- Fixed segmentation fault with index creation on i386
+
+## 0.4.2 (2023-05-13)
+
+- Added notice when index created with little data
+- Fixed dimensions check for some direct function calls
+- Fixed installation error with Postgres 12.0-12.2
+
+## 0.4.1 (2023-03-21)
+
+- Improved performance of cosine distance
+- Fixed index scan count
+
+## 0.4.0 (2023-01-11)
+
+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`
+- Increased max dimensions for vector from 1024 to 16000
+- Increased max dimensions for index from 1024 to 2000
+- Improved accuracy of text parsing for certain inputs
+- Added `avg` aggregate for vector
+- Added experimental support for Windows
+- Dropped support for Postgres 10
+
 ## 0.3.2 (2022-11-22)
 
 - Fixed `invalid memory alloc request size` error
 
 ## 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

@@ -1,9 +1,12 @@
-FROM postgres:15
+ARG PG_MAJOR=16
+FROM postgres:$PG_MAJOR
+ARG PG_MAJOR
 
 COPY . /tmp/pgvector
 
 RUN apt-get update && \
-		apt-get install -y --no-install-recommends build-essential postgresql-server-dev-15 && \
+		apt-mark hold locales && \
+		apt-get install -y --no-install-recommends build-essential postgresql-server-dev-$PG_MAJOR && \
 		cd /tmp/pgvector && \
 		make clean && \
 		make OPTFLAGS="" && \
@@ -11,6 +14,7 @@ RUN apt-get update && \
 		mkdir /usr/share/doc/pgvector && \
 		cp LICENSE README.md /usr/share/doc/pgvector && \
 		rm -r /tmp/pgvector && \
-		apt-get remove -y build-essential postgresql-server-dev-15 && \
+		apt-get remove -y build-essential postgresql-server-dev-$PG_MAJOR && \
 		apt-get autoremove -y && \
+		apt-mark unhold locales && \
 		rm -rf /var/lib/apt/lists/*

LICENSE

@@ -1,4 +1,4 @@
-Portions Copyright (c) 1996-2021, 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": "0.3.2",
+	"version": "0.7.4",
 	"maintainer": [
 		"Andrew Kane <andrew@ankane.org>"
 	],
@@ -12,7 +12,7 @@
 	"prereqs": {
 		"runtime": {
 			"requires": {
-				"PostgreSQL": "10.0.0"
+				"PostgreSQL": "12.0.0"
 			}
 		}
 	},
@@ -20,7 +20,7 @@
 		"vector": {
 			"file": "sql/vector.sql",
 			"docfile": "README.md",
-			"version": "0.3.2",
+			"version": "0.7.4",
 			"abstract": "Open-source vector similarity search for Postgres"
 		}
 	},

Makefile

@@ -1,23 +1,32 @@
 EXTENSION = vector
-EXTVERSION = 0.3.2
+EXTVERSION = 0.7.4
 
 MODULE_big = vector
-DATA = $(wildcard sql/*--*.sql)
-OBJS = src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
+DATA = $(wildcard sql/*--*--*.sql)
+DATA_built = sql/$(EXTENSION)--$(EXTVERSION).sql
+OBJS = src/bitutils.o src/bitvec.o src/halfutils.o src/halfvec.o src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/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
+REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
 
+# To compile for portability, run: make OPTFLAGS=""
 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
 		OPTFLAGS =
 	endif
 endif
 
+# PowerPC doesn't support -march=native
+ifneq ($(filter ppc64%, $(shell uname -m)), )
+	OPTFLAGS =
+endif
+
 # For auto-vectorization:
 # - GCC (needs -ftree-vectorize OR -O3) - https://gcc.gnu.org/projects/tree-ssa/vectorization.html
 # - Clang (could use pragma instead) - https://llvm.org/docs/Vectorizers.html
@@ -34,13 +43,16 @@ all: sql/$(EXTENSION)--$(EXTVERSION).sql
 sql/$(EXTENSION)--$(EXTVERSION).sql: sql/$(EXTENSION).sql
 	cp $< $@
 
-EXTRA_CLEAN = sql/$(EXTENSION)--$(EXTVERSION).sql
-
 PG_CONFIG ?= pg_config
 PGXS := $(shell $(PG_CONFIG) --pgxs)
 include $(PGXS)
 
-# for Postgres 15
+# for Mac
+ifeq ($(PROVE),)
+	PROVE = prove
+endif
+
+# for Postgres < 15
 PROVE_FLAGS += -I ./test/perl
 
 prove_installcheck:
@@ -53,7 +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 -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 --build-arg PG_MAJOR=$(PG_MAJOR) -t pgvector/pgvector:pg$(PG_MAJOR) -t pgvector/pgvector:$(EXTVERSION)-pg$(PG_MAJOR) .

Makefile.win

@@ -0,0 +1,74 @@
+EXTENSION = vector
+EXTVERSION = 0.7.4
+
+DATA_built = sql\$(EXTENSION)--$(EXTVERSION).sql
+OBJS = src\bitutils.obj src\bitvec.obj src\halfutils.obj src\halfvec.obj src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\sparsevec.obj src\vector.obj
+HEADERS = src\halfvec.h src\sparsevec.h src\vector.h
+
+REGRESS = bit btree cast copy halfvec hnsw_bit hnsw_halfvec hnsw_sparsevec hnsw_vector ivfflat_bit ivfflat_halfvec ivfflat_vector sparsevec vector_type
+REGRESS_OPTS = --inputdir=test --load-extension=$(EXTENSION)
+
+# For /arch flags
+# https://learn.microsoft.com/en-us/cpp/build/reference/arch-minimum-cpu-architecture
+OPTFLAGS =
+
+# For auto-vectorization:
+# - MSVC (needs /O2 /fp:fast) - https://learn.microsoft.com/en-us/cpp/parallel/auto-parallelization-and-auto-vectorization?#auto-vectorizer
+PG_CFLAGS = $(PG_CFLAGS) $(OPTFLAGS) /O2 /fp:fast
+
+# Debug MSVC auto-vectorization
+# https://learn.microsoft.com/en-us/cpp/error-messages/tool-errors/vectorizer-and-parallelizer-messages
+# PG_CFLAGS = $(PG_CFLAGS) /Qvec-report:2
+
+# TODO use pg_config
+!ifndef PGROOT
+!error PGROOT is not set
+!endif
+BINDIR = $(PGROOT)\bin
+INCLUDEDIR = $(PGROOT)\include
+INCLUDEDIR_SERVER = $(PGROOT)\include\server
+LIBDIR = $(PGROOT)\lib
+PKGLIBDIR = $(PGROOT)\lib
+SHAREDIR = $(PGROOT)\share
+
+CFLAGS = /nologo /I"$(INCLUDEDIR_SERVER)\port\win32_msvc" /I"$(INCLUDEDIR_SERVER)\port\win32" /I"$(INCLUDEDIR_SERVER)" /I"$(INCLUDEDIR)"
+
+CFLAGS = $(CFLAGS) $(PG_CFLAGS)
+
+SHLIB = $(EXTENSION).dll
+
+LIBS = "$(LIBDIR)\postgres.lib"
+
+all: $(SHLIB) $(DATA_built)
+
+.c.obj:
+	$(CC) $(CFLAGS) /c $< /Fo$@
+
+$(SHLIB): $(OBJS)
+	$(CC) $(CFLAGS) $(OBJS) $(LIBS) /link /DLL /OUT:$(SHLIB)
+
+sql\$(EXTENSION)--$(EXTVERSION).sql: sql\$(EXTENSION).sql
+	copy sql\$(EXTENSION).sql $@
+
+install: all
+	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) $(REGRESS)
+
+uninstall:
+	del /f "$(PKGLIBDIR)\$(SHLIB)"
+	del /f "$(SHAREDIR)\extension\$(EXTENSION).control"
+	del /f "$(SHAREDIR)\extension\$(EXTENSION)--*.sql"
+	del /f "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)\*.h"
+	rmdir "$(INCLUDEDIR_SERVER)\extension\$(EXTENSION)"
+
+clean:
+	del /f $(SHLIB) $(EXTENSION).lib $(EXTENSION).exp
+	del /f $(DATA_built)
+	del /f $(OBJS)
+	del /f /s /q results regression.diffs regression.out tmp_check tmp_check_iso log output_iso

sql/vector--0.2.0--0.2.1.sql

@@ -7,13 +7,13 @@ DROP CAST (double precision[] AS vector);
 DROP CAST (numeric[] AS vector);
 
 CREATE CAST (integer[] AS vector)
-  WITH FUNCTION array_to_vector(integer[], integer, boolean) AS ASSIGNMENT;
+	WITH FUNCTION array_to_vector(integer[], integer, boolean) AS ASSIGNMENT;
 
 CREATE CAST (real[] AS vector)
-  WITH FUNCTION array_to_vector(real[], integer, boolean) AS ASSIGNMENT;
+	WITH FUNCTION array_to_vector(real[], integer, boolean) AS ASSIGNMENT;
 
 CREATE CAST (double precision[] AS vector)
-  WITH FUNCTION array_to_vector(double precision[], integer, boolean) AS ASSIGNMENT;
+	WITH FUNCTION array_to_vector(double precision[], integer, boolean) AS ASSIGNMENT;
 
 CREATE CAST (numeric[] AS vector)
-  WITH FUNCTION array_to_vector(numeric[], integer, boolean) AS ASSIGNMENT;
+	WITH FUNCTION array_to_vector(numeric[], integer, boolean) AS ASSIGNMENT;

sql/vector--0.3.2--0.4.0.sql

@@ -0,0 +1,23 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.4.0'" to load this file. \quit
+
+-- remove this single line for Postgres < 13
+ALTER TYPE vector SET (STORAGE = extended);
+
+CREATE FUNCTION vector_accum(double precision[], vector) RETURNS double precision[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_avg(double precision[]) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_combine(double precision[], double precision[]) RETURNS double precision[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE AGGREGATE avg(vector) (
+	SFUNC = vector_accum,
+	STYPE = double precision[],
+	FINALFUNC = vector_avg,
+	COMBINEFUNC = vector_combine,
+	INITCOND = '{0}',
+	PARALLEL = SAFE
+);

sql/vector--0.4.0--0.4.1.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.4.1'" to load this file. \quit

sql/vector--0.4.1--0.4.2.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.4.2'" to load this file. \quit

sql/vector--0.4.2--0.4.3.sql

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

sql/vector--0.4.3--0.4.4.sql

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

sql/vector--0.4.4--0.5.0.sql

@@ -0,0 +1,43 @@
+-- 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 +1,569 @@
+-- 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 l2_normalize(vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION binary_quantize(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 vector_concat(vector, vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE OPERATOR <+> (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR || (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
+);
+
+CREATE FUNCTION ivfflat_halfvec_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE FUNCTION ivfflat_bit_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE FUNCTION hnsw_halfvec_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE FUNCTION hnsw_bit_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE FUNCTION hnsw_sparsevec_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE OPERATOR CLASS vector_l1_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <+> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(vector, vector);
+
+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 vector_dims(halfvec) RETURNS integer
+	AS 'MODULE_PATHNAME', 'halfvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_normalize(halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME', 'halfvec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION binary_quantize(halfvec) RETURNS bit
+	AS 'MODULE_PATHNAME', 'halfvec_binary_quantize' 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_add(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_sub(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_mul(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_concat(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_lt(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_le(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_eq(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_ne(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_ge(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_gt(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_cmp(halfvec, halfvec) RETURNS int4
+	AS 'MODULE_PATHNAME' 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_accum(double precision[], halfvec) RETURNS double precision[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_avg(double precision[]) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_combine(double precision[], double precision[]) RETURNS double precision[]
+	AS 'MODULE_PATHNAME', 'vector_combine' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE AGGREGATE avg(halfvec) (
+	SFUNC = halfvec_accum,
+	STYPE = double precision[],
+	FINALFUNC = halfvec_avg,
+	COMBINEFUNC = halfvec_combine,
+	INITCOND = '{0}',
+	PARALLEL = SAFE
+);
+
+CREATE AGGREGATE sum(halfvec) (
+	SFUNC = halfvec_add,
+	STYPE = halfvec,
+	COMBINEFUNC = halfvec_add,
+	PARALLEL = SAFE
+);
+
+CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+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 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 vector)
+	WITH FUNCTION halfvec_to_vector(halfvec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (vector AS halfvec)
+	WITH FUNCTION vector_to_halfvec(vector, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (halfvec AS real[])
+	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS ASSIGNMENT;
+
+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 <+> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR + (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_add,
+	COMMUTATOR = +
+);
+
+CREATE OPERATOR - (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_sub
+);
+
+CREATE OPERATOR * (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_mul,
+	COMMUTATOR = *
+);
+
+CREATE OPERATOR || (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_concat
+);
+
+CREATE OPERATOR < (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+CREATE OPERATOR CLASS halfvec_ops
+	DEFAULT FOR TYPE halfvec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 halfvec_cmp(halfvec, halfvec);
+
+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),
+	FUNCTION 5 ivfflat_halfvec_support(internal);
+
+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 l2_norm(halfvec),
+	FUNCTION 5 ivfflat_halfvec_support(internal);
+
+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 l2_norm(halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 l2_norm(halfvec),
+	FUNCTION 5 ivfflat_halfvec_support(internal);
+
+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),
+	FUNCTION 3 hnsw_halfvec_support(internal);
+
+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),
+	FUNCTION 3 hnsw_halfvec_support(internal);
+
+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 l2_norm(halfvec),
+	FUNCTION 3 hnsw_halfvec_support(internal);
+
+CREATE OPERATOR CLASS halfvec_l1_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <+> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(halfvec, halfvec),
+	FUNCTION 3 hnsw_halfvec_support(internal);
+
+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 ivfflat AS
+	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 hamming_distance(bit, bit),
+	FUNCTION 3 hamming_distance(bit, bit),
+	FUNCTION 5 ivfflat_bit_support(internal);
+
+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),
+	FUNCTION 3 hnsw_bit_support(internal);
+
+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),
+	FUNCTION 3 hnsw_bit_support(internal);
+
+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 l1_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_normalize(sparsevec) RETURNS sparsevec
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_lt(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_le(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_eq(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_ne(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_ge(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_gt(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_cmp(sparsevec, sparsevec) RETURNS int4
+	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 FUNCTION halfvec_to_sparsevec(halfvec, integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_to_halfvec(sparsevec, integer, boolean) RETURNS halfvec
+	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 ASSIGNMENT;
+
+CREATE CAST (vector AS sparsevec)
+	WITH FUNCTION vector_to_sparsevec(vector, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (sparsevec AS halfvec)
+	WITH FUNCTION sparsevec_to_halfvec(sparsevec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (halfvec AS sparsevec)
+	WITH FUNCTION halfvec_to_sparsevec(halfvec, 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 <+> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR < (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+CREATE OPERATOR CLASS sparsevec_ops
+	DEFAULT FOR TYPE sparsevec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 sparsevec_cmp(sparsevec, sparsevec);
+
+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),
+	FUNCTION 3 hnsw_sparsevec_support(internal);
+
+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),
+	FUNCTION 3 hnsw_sparsevec_support(internal);
+
+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 l2_norm(sparsevec),
+	FUNCTION 3 hnsw_sparsevec_support(internal);
+
+CREATE OPERATOR CLASS sparsevec_l1_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <+> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(sparsevec, sparsevec),
+	FUNCTION 3 hnsw_sparsevec_support(internal);

sql/vector--0.7.0--0.7.1.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.7.1'" to load this file. \quit

sql/vector--0.7.1--0.7.2.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.7.2'" to load this file. \quit

sql/vector--0.7.2--0.7.3.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.7.3'" to load this file. \quit

sql/vector--0.7.3--0.7.4.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.7.4'" to load this file. \quit

sql/vector--0.7.4--0.8.0.sql

@@ -0,0 +1,26 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.8.0'" to load this file. \quit
+
+CREATE FUNCTION array_to_sparsevec(integer[], integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_sparsevec(real[], integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_sparsevec(double precision[], integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_sparsevec(numeric[], integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (integer[] AS sparsevec)
+	WITH FUNCTION array_to_sparsevec(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (real[] AS sparsevec)
+	WITH FUNCTION array_to_sparsevec(real[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (double precision[] AS sparsevec)
+	WITH FUNCTION array_to_sparsevec(double precision[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (numeric[] AS sparsevec)
+	WITH FUNCTION array_to_sparsevec(numeric[], integer, boolean) AS ASSIGNMENT;

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;
 
@@ -25,10 +25,11 @@ CREATE TYPE vector (
 	OUTPUT    = vector_out,
 	TYPMOD_IN = vector_typmod_in,
 	RECEIVE   = vector_recv,
-	SEND      = vector_send
+	SEND      = vector_send,
+	STORAGE   = external
 );
 
--- functions
+-- vector functions
 
 CREATE FUNCTION l2_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -39,19 +40,37 @@ CREATE FUNCTION inner_product(vector, vector) RETURNS float8
 CREATE FUNCTION cosine_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION l1_distance(vector, vector) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE FUNCTION vector_dims(vector) RETURNS integer
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION vector_norm(vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION l2_normalize(vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION binary_quantize(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_add(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION vector_sub(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- private functions
+CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_concat(vector, vector) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
 CREATE FUNCTION vector_lt(vector, vector) RETURNS bool
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -83,7 +102,34 @@ CREATE FUNCTION vector_negative_inner_product(vector, vector) RETURNS float8
 CREATE FUNCTION vector_spherical_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- cast functions
+CREATE FUNCTION vector_accum(double precision[], vector) RETURNS double precision[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_avg(double precision[]) RETURNS vector
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_combine(double precision[], double precision[]) RETURNS double precision[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- vector aggregates
+
+CREATE AGGREGATE avg(vector) (
+	SFUNC = vector_accum,
+	STYPE = double precision[],
+	FINALFUNC = vector_avg,
+	COMBINEFUNC = vector_combine,
+	INITCOND = '{0}',
+	PARALLEL = SAFE
+);
+
+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;
@@ -103,7 +149,7 @@ 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;
@@ -123,7 +169,7 @@ 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,
@@ -140,14 +186,27 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR <+> (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
 CREATE OPERATOR + (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_add,
 	COMMUTATOR = +
 );
 
 CREATE OPERATOR - (
-	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_sub,
-	COMMUTATOR = -
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_sub
+);
+
+CREATE OPERATOR * (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_mul,
+	COMMUTATOR = *
+);
+
+CREATE OPERATOR || (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
 );
 
 CREATE OPERATOR < (
@@ -156,11 +215,10 @@ 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 = (
@@ -175,11 +233,10 @@ 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 > (
@@ -188,7 +245,7 @@ CREATE OPERATOR > (
 	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
 );
 
--- access method
+-- access methods
 
 CREATE FUNCTION ivfflathandler(internal) RETURNS index_am_handler
 	AS 'MODULE_PATHNAME' LANGUAGE C;
@@ -197,7 +254,31 @@ 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';
+
+-- access method private functions
+
+CREATE FUNCTION ivfflat_halfvec_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE FUNCTION ivfflat_bit_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE FUNCTION hnsw_halfvec_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE FUNCTION hnsw_bit_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE FUNCTION hnsw_sparsevec_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+-- vector opclasses
 
 CREATE OPERATOR CLASS vector_ops
 	DEFAULT FOR TYPE vector USING btree AS
@@ -228,3 +309,610 @@ 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);
+
+CREATE OPERATOR CLASS vector_l1_ops
+	FOR TYPE vector USING hnsw AS
+	OPERATOR 1 <+> (vector, vector) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(vector, vector);
+
+-- 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 vector_dims(halfvec) RETURNS integer
+	AS 'MODULE_PATHNAME', 'halfvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'halfvec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_normalize(halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME', 'halfvec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION binary_quantize(halfvec) RETURNS bit
+	AS 'MODULE_PATHNAME', 'halfvec_binary_quantize' 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_add(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_sub(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_mul(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_concat(halfvec, halfvec) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_lt(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_le(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_eq(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_ne(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_ge(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_gt(halfvec, halfvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_cmp(halfvec, halfvec) RETURNS int4
+	AS 'MODULE_PATHNAME' 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_accum(double precision[], halfvec) RETURNS double precision[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_avg(double precision[]) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION halfvec_combine(double precision[], double precision[]) RETURNS double precision[]
+	AS 'MODULE_PATHNAME', 'vector_combine' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- halfvec aggregates
+
+CREATE AGGREGATE avg(halfvec) (
+	SFUNC = halfvec_accum,
+	STYPE = double precision[],
+	FINALFUNC = halfvec_avg,
+	COMBINEFUNC = halfvec_combine,
+	INITCOND = '{0}',
+	PARALLEL = SAFE
+);
+
+CREATE AGGREGATE sum(halfvec) (
+	SFUNC = halfvec_add,
+	STYPE = halfvec,
+	COMBINEFUNC = halfvec_add,
+	PARALLEL = SAFE
+);
+
+-- halfvec cast functions
+
+CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+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 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 vector)
+	WITH FUNCTION halfvec_to_vector(halfvec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (vector AS halfvec)
+	WITH FUNCTION vector_to_halfvec(vector, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (halfvec AS real[])
+	WITH FUNCTION halfvec_to_float4(halfvec, integer, boolean) AS ASSIGNMENT;
+
+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 = '<=>'
+);
+
+CREATE OPERATOR <+> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR + (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_add,
+	COMMUTATOR = +
+);
+
+CREATE OPERATOR - (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_sub
+);
+
+CREATE OPERATOR * (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_mul,
+	COMMUTATOR = *
+);
+
+CREATE OPERATOR || (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_concat
+);
+
+CREATE OPERATOR < (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = halfvec, RIGHTARG = halfvec, PROCEDURE = halfvec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+-- halfvec opclasses
+
+CREATE OPERATOR CLASS halfvec_ops
+	DEFAULT FOR TYPE halfvec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 halfvec_cmp(halfvec, halfvec);
+
+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),
+	FUNCTION 5 ivfflat_halfvec_support(internal);
+
+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 l2_norm(halfvec),
+	FUNCTION 5 ivfflat_halfvec_support(internal);
+
+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 l2_norm(halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 l2_norm(halfvec),
+	FUNCTION 5 ivfflat_halfvec_support(internal);
+
+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),
+	FUNCTION 3 hnsw_halfvec_support(internal);
+
+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),
+	FUNCTION 3 hnsw_halfvec_support(internal);
+
+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 l2_norm(halfvec),
+	FUNCTION 3 hnsw_halfvec_support(internal);
+
+CREATE OPERATOR CLASS halfvec_l1_ops
+	FOR TYPE halfvec USING hnsw AS
+	OPERATOR 1 <+> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(halfvec, halfvec),
+	FUNCTION 3 hnsw_halfvec_support(internal);
+
+-- 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;
+
+-- bit operators
+
+CREATE OPERATOR <~> (
+	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = hamming_distance,
+	COMMUTATOR = '<~>'
+);
+
+CREATE OPERATOR <%> (
+	LEFTARG = bit, RIGHTARG = bit, PROCEDURE = jaccard_distance,
+	COMMUTATOR = '<%>'
+);
+
+-- bit opclasses
+
+CREATE OPERATOR CLASS bit_hamming_ops
+	FOR TYPE bit USING ivfflat AS
+	OPERATOR 1 <~> (bit, bit) FOR ORDER BY float_ops,
+	FUNCTION 1 hamming_distance(bit, bit),
+	FUNCTION 3 hamming_distance(bit, bit),
+	FUNCTION 5 ivfflat_bit_support(internal);
+
+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),
+	FUNCTION 3 hnsw_bit_support(internal);
+
+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),
+	FUNCTION 3 hnsw_bit_support(internal);
+
+--- 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 l1_distance(sparsevec, sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(sparsevec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_normalize(sparsevec) RETURNS sparsevec
+	AS 'MODULE_PATHNAME', 'sparsevec_l2_normalize' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- sparsevec private functions
+
+CREATE FUNCTION sparsevec_lt(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_le(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_eq(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_ne(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_ge(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_gt(sparsevec, sparsevec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_cmp(sparsevec, sparsevec) RETURNS int4
+	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;
+
+-- 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;
+
+CREATE FUNCTION halfvec_to_sparsevec(halfvec, integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION sparsevec_to_halfvec(sparsevec, integer, boolean) RETURNS halfvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_sparsevec(integer[], integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_sparsevec(real[], integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_sparsevec(double precision[], integer, boolean) RETURNS sparsevec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_sparsevec(numeric[], integer, boolean) RETURNS sparsevec
+	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 ASSIGNMENT;
+
+CREATE CAST (vector AS sparsevec)
+	WITH FUNCTION vector_to_sparsevec(vector, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (sparsevec AS halfvec)
+	WITH FUNCTION sparsevec_to_halfvec(sparsevec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (halfvec AS sparsevec)
+	WITH FUNCTION halfvec_to_sparsevec(halfvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (integer[] AS sparsevec)
+	WITH FUNCTION array_to_sparsevec(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (real[] AS sparsevec)
+	WITH FUNCTION array_to_sparsevec(real[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (double precision[] AS sparsevec)
+	WITH FUNCTION array_to_sparsevec(double precision[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (numeric[] AS sparsevec)
+	WITH FUNCTION array_to_sparsevec(numeric[], integer, boolean) AS ASSIGNMENT;
+
+-- 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 = '<=>'
+);
+
+CREATE OPERATOR <+> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR < (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = sparsevec, RIGHTARG = sparsevec, PROCEDURE = sparsevec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+-- sparsevec opclasses
+
+CREATE OPERATOR CLASS sparsevec_ops
+	DEFAULT FOR TYPE sparsevec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 sparsevec_cmp(sparsevec, sparsevec);
+
+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),
+	FUNCTION 3 hnsw_sparsevec_support(internal);
+
+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),
+	FUNCTION 3 hnsw_sparsevec_support(internal);
+
+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 l2_norm(sparsevec),
+	FUNCTION 3 hnsw_sparsevec_support(internal);
+
+CREATE OPERATOR CLASS sparsevec_l1_ops
+	FOR TYPE sparsevec USING hnsw AS
+	OPERATOR 1 <+> (sparsevec, sparsevec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(sparsevec, sparsevec),
+	FUNCTION 3 hnsw_sparsevec_support(internal);

src/bitutils.c

@@ -0,0 +1,222 @@
+#include "postgres.h"
+
+#include "bitutils.h"
+#include "halfvec.h"			/* for USE_DISPATCH and USE_TARGET_CLONES */
+#include "port/pg_bitutils.h"
+
+#if defined(USE_DISPATCH)
+#define BIT_DISPATCH
+#endif
+
+#ifdef BIT_DISPATCH
+#include <immintrin.h>
+
+#if defined(USE__GET_CPUID)
+#include <cpuid.h>
+#else
+#include <intrin.h>
+#endif
+
+#ifdef _MSC_VER
+#define TARGET_AVX512_POPCOUNT
+#else
+#define TARGET_AVX512_POPCOUNT __attribute__((target("avx512f,avx512vpopcntdq")))
+#endif
+#endif
+
+/* Disable for LLVM due to crash with bitcode generation */
+#if defined(USE_TARGET_CLONES) && !defined(__POPCNT__) && !defined(__llvm__)
+#define BIT_TARGET_CLONES __attribute__((target_clones("default", "popcnt")))
+#else
+#define BIT_TARGET_CLONES
+#endif
+
+/* Use built-ins when possible for inlining */
+#if defined(HAVE__BUILTIN_POPCOUNT) && defined(HAVE_LONG_INT_64)
+#define popcount64(x) __builtin_popcountl(x)
+#elif defined(HAVE__BUILTIN_POPCOUNT) && defined(HAVE_LONG_LONG_INT_64)
+#define popcount64(x) __builtin_popcountll(x)
+#elif !defined(_MSC_VER)
+/* Fails to resolve with MSVC */
+#define popcount64(x) pg_popcount64(x)
+#endif
+
+uint64		(*BitHammingDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance);
+double		(*BitJaccardDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb);
+
+BIT_TARGET_CLONES static uint64
+BitHammingDistanceDefault(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance)
+{
+#ifdef popcount64
+	for (; bytes >= sizeof(uint64); bytes -= sizeof(uint64))
+	{
+		uint64		axs;
+		uint64		bxs;
+
+		/* Ensure aligned */
+		memcpy(&axs, ax, sizeof(uint64));
+		memcpy(&bxs, bx, sizeof(uint64));
+
+		distance += popcount64(axs ^ bxs);
+
+		ax += sizeof(uint64);
+		bx += sizeof(uint64);
+	}
+#endif
+
+	for (uint32 i = 0; i < bytes; i++)
+		distance += pg_number_of_ones[ax[i] ^ bx[i]];
+
+	return distance;
+}
+
+#ifdef BIT_DISPATCH
+TARGET_AVX512_POPCOUNT static uint64
+BitHammingDistanceAvx512Popcount(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance)
+{
+	__m512i		dist = _mm512_setzero_si512();
+
+	for (; bytes >= sizeof(__m512i); bytes -= sizeof(__m512i))
+	{
+		__m512i		axs = _mm512_loadu_si512((const __m512i *) ax);
+		__m512i		bxs = _mm512_loadu_si512((const __m512i *) bx);
+
+		dist = _mm512_add_epi64(dist, _mm512_popcnt_epi64(_mm512_xor_si512(axs, bxs)));
+
+		ax += sizeof(__m512i);
+		bx += sizeof(__m512i);
+	}
+
+	distance += _mm512_reduce_add_epi64(dist);
+
+	return BitHammingDistanceDefault(bytes, ax, bx, distance);
+}
+#endif
+
+BIT_TARGET_CLONES static double
+BitJaccardDistanceDefault(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb)
+{
+#ifdef popcount64
+	for (; bytes >= sizeof(uint64); bytes -= sizeof(uint64))
+	{
+		uint64		axs;
+		uint64		bxs;
+
+		/* Ensure aligned */
+		memcpy(&axs, ax, sizeof(uint64));
+		memcpy(&bxs, bx, sizeof(uint64));
+
+		ab += popcount64(axs & bxs);
+		aa += popcount64(axs);
+		bb += popcount64(bxs);
+
+		ax += sizeof(uint64);
+		bx += sizeof(uint64);
+	}
+#endif
+
+	for (uint32 i = 0; i < bytes; i++)
+	{
+		ab += pg_number_of_ones[ax[i] & bx[i]];
+		aa += pg_number_of_ones[ax[i]];
+		bb += pg_number_of_ones[bx[i]];
+	}
+
+	if (ab == 0)
+		return 1;
+	else
+		return 1 - (ab / ((double) (aa + bb - ab)));
+}
+
+#ifdef BIT_DISPATCH
+TARGET_AVX512_POPCOUNT static double
+BitJaccardDistanceAvx512Popcount(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb)
+{
+	__m512i		abx = _mm512_setzero_si512();
+	__m512i		aax = _mm512_setzero_si512();
+	__m512i		bbx = _mm512_setzero_si512();
+
+	for (; bytes >= sizeof(__m512i); bytes -= sizeof(__m512i))
+	{
+		__m512i		axs = _mm512_loadu_si512((const __m512i *) ax);
+		__m512i		bxs = _mm512_loadu_si512((const __m512i *) bx);
+
+		abx = _mm512_add_epi64(abx, _mm512_popcnt_epi64(_mm512_and_si512(axs, bxs)));
+		aax = _mm512_add_epi64(aax, _mm512_popcnt_epi64(axs));
+		bbx = _mm512_add_epi64(bbx, _mm512_popcnt_epi64(bxs));
+
+		ax += sizeof(__m512i);
+		bx += sizeof(__m512i);
+	}
+
+	ab += _mm512_reduce_add_epi64(abx);
+	aa += _mm512_reduce_add_epi64(aax);
+	bb += _mm512_reduce_add_epi64(bbx);
+
+	return BitJaccardDistanceDefault(bytes, ax, bx, ab, aa, bb);
+}
+#endif
+
+#ifdef BIT_DISPATCH
+#define CPU_FEATURE_OSXSAVE         (1 << 27)	/* F1 ECX */
+#define CPU_FEATURE_AVX512F         (1 << 16)	/* F7,0 EBX */
+#define CPU_FEATURE_AVX512VPOPCNTDQ (1 << 14)	/* F7,0 ECX */
+
+#ifdef _MSC_VER
+#define TARGET_XSAVE
+#else
+#define TARGET_XSAVE __attribute__((target("xsave")))
+#endif
+
+TARGET_XSAVE static bool
+SupportsAvx512Popcount()
+{
+	unsigned int exx[4] = {0, 0, 0, 0};
+
+#if defined(USE__GET_CPUID)
+	__get_cpuid(1, &exx[0], &exx[1], &exx[2], &exx[3]);
+#else
+	__cpuid(exx, 1);
+#endif
+
+	/* Check OS supports XSAVE */
+	if ((exx[2] & CPU_FEATURE_OSXSAVE) != CPU_FEATURE_OSXSAVE)
+		return false;
+
+	/* Check XMM, YMM, and ZMM registers are enabled */
+	if ((_xgetbv(0) & 0xe6) != 0xe6)
+		return false;
+
+#if defined(USE__GET_CPUID)
+	__get_cpuid_count(7, 0, &exx[0], &exx[1], &exx[2], &exx[3]);
+#else
+	__cpuidex(exx, 7, 0);
+#endif
+
+	/* Check AVX512F */
+	if ((exx[1] & CPU_FEATURE_AVX512F) != CPU_FEATURE_AVX512F)
+		return false;
+
+	/* Check AVX512VPOPCNTDQ */
+	return (exx[2] & CPU_FEATURE_AVX512VPOPCNTDQ) == CPU_FEATURE_AVX512VPOPCNTDQ;
+}
+#endif
+
+void
+BitvecInit(void)
+{
+	/*
+	 * Could skip pointer when single function, but no difference in
+	 * performance
+	 */
+	BitHammingDistance = BitHammingDistanceDefault;
+	BitJaccardDistance = BitJaccardDistanceDefault;
+
+#ifdef BIT_DISPATCH
+	if (SupportsAvx512Popcount())
+	{
+		BitHammingDistance = BitHammingDistanceAvx512Popcount;
+		BitJaccardDistance = BitJaccardDistanceAvx512Popcount;
+	}
+#endif
+}

src/bitutils.h

@@ -0,0 +1,16 @@
+#ifndef BITUTILS_H
+#define BITUTILS_H
+
+#include "postgres.h"
+
+/* Check version in first header */
+#if PG_VERSION_NUM < 130000
+#error "Requires PostgreSQL 13+"
+#endif
+
+extern uint64 (*BitHammingDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance);
+extern double (*BitJaccardDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb);
+
+void		BitvecInit(void);
+
+#endif

src/bitvec.c

@@ -0,0 +1,69 @@
+#include "postgres.h"
+
+#include "bitutils.h"
+#include "bitvec.h"
+#include "utils/varbit.h"
+#include "vector.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
+ */
+FUNCTION_PREFIX 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);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) BitHammingDistance(VARBITBYTES(a), VARBITS(a), VARBITS(b), 0));
+}
+
+/*
+ * Get the Jaccard distance between two bit vectors
+ */
+FUNCTION_PREFIX 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);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(BitJaccardDistance(VARBITBYTES(a), VARBITS(a), VARBITS(b), 0, 0, 0));
+}

src/bitvec.h

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

src/halfutils.c

@@ -0,0 +1,298 @@
+#include "postgres.h"
+
+#include "halfutils.h"
+#include "halfvec.h"
+
+#ifdef HALFVEC_DISPATCH
+#include <immintrin.h>
+
+#if defined(USE__GET_CPUID)
+#include <cpuid.h>
+#else
+#include <intrin.h>
+#endif
+
+#ifdef _MSC_VER
+#define TARGET_F16C
+#else
+#define TARGET_F16C __attribute__((target("avx,f16c,fma")))
+#endif
+#endif
+
+float		(*HalfvecL2SquaredDistance) (int dim, half * ax, half * bx);
+float		(*HalfvecInnerProduct) (int dim, half * ax, half * bx);
+double		(*HalfvecCosineSimilarity) (int dim, half * ax, half * bx);
+float		(*HalfvecL1Distance) (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 static float
+HalfvecL2SquaredDistanceF16c(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 static float
+HalfvecInnerProductF16c(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
+
+static double
+HalfvecCosineSimilarityDefault(int dim, half * ax, half * bx)
+{
+	float		similarity = 0.0;
+	float		norma = 0.0;
+	float		normb = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		axi = HalfToFloat4(ax[i]);
+		float		bxi = HalfToFloat4(bx[i]);
+
+		similarity += axi * bxi;
+		norma += axi * axi;
+		normb += bxi * bxi;
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	return (double) similarity / sqrt((double) norma * (double) normb);
+}
+
+#ifdef HALFVEC_DISPATCH
+TARGET_F16C static double
+HalfvecCosineSimilarityF16c(int dim, half * ax, half * bx)
+{
+	float		similarity;
+	float		norma;
+	float		normb;
+	int			i;
+	float		s[8];
+	int			count = (dim / 8) * 8;
+	__m256		sim = _mm256_setzero_ps();
+	__m256		na = _mm256_setzero_ps();
+	__m256		nb = _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);
+
+		sim = _mm256_fmadd_ps(axs, bxs, sim);
+		na = _mm256_fmadd_ps(axs, axs, na);
+		nb = _mm256_fmadd_ps(bxs, bxs, nb);
+	}
+
+	_mm256_storeu_ps(s, sim);
+	similarity = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	_mm256_storeu_ps(s, na);
+	norma = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	_mm256_storeu_ps(s, nb);
+	normb = s[0] + s[1] + s[2] + s[3] + s[4] + s[5] + s[6] + s[7];
+
+	/* Auto-vectorized */
+	for (; i < dim; i++)
+	{
+		float		axi = HalfToFloat4(ax[i]);
+		float		bxi = HalfToFloat4(bx[i]);
+
+		similarity += axi * bxi;
+		norma += axi * axi;
+		normb += bxi * bxi;
+	}
+
+	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
+	return (double) similarity / sqrt((double) norma * (double) normb);
+}
+#endif
+
+static float
+HalfvecL1DistanceDefault(int dim, half * ax, half * bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += fabsf(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+
+	return distance;
+}
+
+#ifdef HALFVEC_DISPATCH
+/* Does not require FMA, but keep logic simple */
+TARGET_F16C static float
+HalfvecL1DistanceF16c(int dim, half * ax, half * bx)
+{
+	float		distance;
+	int			i;
+	float		s[8];
+	int			count = (dim / 8) * 8;
+	__m256		dist = _mm256_setzero_ps();
+	__m256		sign = _mm256_set1_ps(-0.0);
+
+	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_add_ps(dist, _mm256_andnot_ps(sign, _mm256_sub_ps(axs, bxs)));
+	}
+
+	_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 += fabsf(HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]));
+
+	return distance;
+}
+#endif
+
+#ifdef HALFVEC_DISPATCH
+#define CPU_FEATURE_FMA     (1 << 12)
+#define CPU_FEATURE_OSXSAVE (1 << 27)
+#define CPU_FEATURE_AVX     (1 << 28)
+#define CPU_FEATURE_F16C    (1 << 29)
+
+#ifdef _MSC_VER
+#define TARGET_XSAVE
+#else
+#define TARGET_XSAVE __attribute__((target("xsave")))
+#endif
+
+TARGET_XSAVE static bool
+SupportsCpuFeature(unsigned int feature)
+{
+	unsigned int exx[4] = {0, 0, 0, 0};
+
+#if defined(USE__GET_CPUID)
+	__get_cpuid(1, &exx[0], &exx[1], &exx[2], &exx[3]);
+#else
+	__cpuid(exx, 1);
+#endif
+
+	/* Check OS supports XSAVE */
+	if ((exx[2] & CPU_FEATURE_OSXSAVE) != CPU_FEATURE_OSXSAVE)
+		return false;
+
+	/* Check XMM and YMM registers are enabled */
+	if ((_xgetbv(0) & 6) != 6)
+		return false;
+
+	/* Now check features */
+	return (exx[2] & feature) == feature;
+}
+#endif
+
+void
+HalfvecInit(void)
+{
+	/*
+	 * Could skip pointer when single function, but no difference in
+	 * performance
+	 */
+	HalfvecL2SquaredDistance = HalfvecL2SquaredDistanceDefault;
+	HalfvecInnerProduct = HalfvecInnerProductDefault;
+	HalfvecCosineSimilarity = HalfvecCosineSimilarityDefault;
+	HalfvecL1Distance = HalfvecL1DistanceDefault;
+
+#ifdef HALFVEC_DISPATCH
+	if (SupportsCpuFeature(CPU_FEATURE_AVX | CPU_FEATURE_F16C | CPU_FEATURE_FMA))
+	{
+		HalfvecL2SquaredDistance = HalfvecL2SquaredDistanceF16c;
+		HalfvecInnerProduct = HalfvecInnerProductF16c;
+		HalfvecCosineSimilarity = HalfvecCosineSimilarityF16c;
+		/* Does not require FMA, but keep logic simple */
+		HalfvecL1Distance = HalfvecL1DistanceF16c;
+	}
+#endif
+}

src/halfutils.h

@@ -0,0 +1,263 @@
+#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);
+extern double (*HalfvecCosineSimilarity) (int dim, half * ax, half * bx);
+extern float (*HalfvecL1Distance) (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
+}
+
+/*
+ * Check if half is zero
+ */
+static inline bool
+HalfIsZero(half num)
+{
+#ifdef FLT16_SUPPORT
+	return num == 0;
+#else
+	return (num & 0x7FFF) == 0x0000;
+#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
+	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
+	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.h

@@ -0,0 +1,70 @@
+#ifndef HALFVEC_H
+#define HALFVEC_H
+
+#define __STDC_WANT_IEC_60559_TYPES_EXT__
+
+#include <float.h>
+
+/* We use two types of dispatching: intrinsics and target_clones */
+/* TODO Move to better place */
+#ifndef DISABLE_DISPATCH
+/* Only enable for more recent compilers to keep build process simple */
+#if defined(__x86_64__) && defined(__GNUC__) && __GNUC__ >= 9
+#define USE_DISPATCH
+#elif defined(__x86_64__) && defined(__clang_major__) && __clang_major__ >= 7
+#define USE_DISPATCH
+#elif defined(_M_AMD64) && defined(_MSC_VER) && _MSC_VER >= 1920
+#define USE_DISPATCH
+#endif
+#endif
+
+/* target_clones requires glibc */
+#if defined(USE_DISPATCH) && defined(__gnu_linux__) && defined(__has_attribute)
+/* Use separate line for portability */
+#if __has_attribute(target_clones)
+#define USE_TARGET_CLONES
+#endif
+#endif
+
+/* Apple clang check needed for universal binaries on Mac */
+#if defined(USE_DISPATCH) && (defined(HAVE__GET_CPUID) || defined(__apple_build_version__))
+#define USE__GET_CPUID
+#endif
+
+#if defined(USE_DISPATCH)
+#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) && !defined(__FreeBSD__) && (!defined(__i386__) || defined(__SSE2__))
+#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 16000
+
+#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;			/* reserved for future use, always zero */
+	half		x[FLEXIBLE_ARRAY_MEMBER];
+}			HalfVector;
+
+HalfVector *InitHalfVector(int dim);
+
+#endif

src/hnsw.c

@@ -0,0 +1,244 @@
+#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/float.h"
+#include "utils/guc.h"
+#include "utils/selfuncs.h"
+
+#if PG_VERSION_NUM < 150000
+#define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
+#endif
+
+int			hnsw_ef_search;
+bool		hnsw_streaming;
+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, AccessExclusiveLock);
+	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, AccessExclusiveLock);
+
+	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);
+
+	/* TODO Figure out name */
+	DefineCustomBoolVariable("hnsw.streaming", "Use streaming mode",
+							 NULL, &hnsw_streaming,
+							 HNSW_DEFAULT_STREAMING, PGC_USERSET, 0, NULL, NULL, NULL);
+
+	/* TODO Add option for limiting iterative search */
+
+	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 = get_float8_infinity();
+		*indexTotalCost = get_float8_infinity();
+		*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;
+
+	/* TODO Adjust for selectivity for iterative scans */
+
+	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)},
+	};
+
+	return (bytea *) build_reloptions(reloptions, validate,
+									  hnsw_relopt_kind,
+									  sizeof(HnswOptions),
+									  tab, lengthof(tab));
+}
+
+/*
+ * 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
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(hnswhandler);
+Datum
+hnswhandler(PG_FUNCTION_ARGS)
+{
+	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);
+
+	amroutine->amstrategies = 0;
+	amroutine->amsupport = 3;
+	amroutine->amoptsprocnum = 0;
+	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;
+#if PG_VERSION_NUM >= 170000
+	amroutine->amcanbuildparallel = true;
+#endif
+	amroutine->amcaninclude = false;
+	amroutine->amusemaintenanceworkmem = false; /* not used during VACUUM */
+#if PG_VERSION_NUM >= 160000
+	amroutine->amsummarizing = false;
+#endif
+	amroutine->amparallelvacuumoptions = VACUUM_OPTION_PARALLEL_BULKDEL;
+	amroutine->amkeytype = InvalidOid;
+
+	/* Interface functions */
+	amroutine->ambuild = hnswbuild;
+	amroutine->ambuildempty = hnswbuildempty;
+	amroutine->aminsert = hnswinsert;
+#if PG_VERSION_NUM >= 170000
+	amroutine->aminsertcleanup = NULL;
+#endif
+	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 +1,504 @@
+#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"
+
+#ifdef HNSW_BENCH
+#include "portability/instr_time.h"
+#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_TYPE_INFO_PROC 3
+
+#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
+#define HNSW_DEFAULT_STREAMING	false
+
+/* 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
+
+/* 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))
+
+#ifdef HNSW_BENCH
+#define HnswBench(name, code) \
+	do { \
+		instr_time	start; \
+		instr_time	duration; \
+		INSTR_TIME_SET_CURRENT(start); \
+		(code); \
+		INSTR_TIME_SET_CURRENT(duration); \
+		INSTR_TIME_SUBTRACT(duration, start); \
+		elog(INFO, "%s: %.3f ms", name, INSTR_TIME_GET_MILLISEC(duration)); \
+	} while (0)
+#else
+#define HnswBench(name, code) (code)
+#endif
+
+#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
+
+#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 bool hnsw_streaming;
+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;
+	uint8		version;
+	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 HnswSearchCandidate
+{
+	pairingheap_node c_node;
+	pairingheap_node w_node;
+	HnswElementPtr element;
+	float		distance;
+}			HnswSearchCandidate;
+
+#define HnswGetSearchCandidate(membername, ptr) pairingheap_container(HnswSearchCandidate, membername, ptr)
+#define HnswGetSearchCandidateConst(membername, ptr) pairingheap_const_container(HnswSearchCandidate, membername, ptr)
+
+/* 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 HnswTypeInfo
+{
+	int			maxDimensions;
+	Datum		(*normalize) (PG_FUNCTION_ARGS);
+	void		(*checkValue) (Pointer v);
+}			HnswTypeInfo;
+
+typedef struct HnswBuildState
+{
+	/* Info */
+	Relation	heap;
+	Relation	index;
+	IndexInfo  *indexInfo;
+	ForkNumber	forkNum;
+	const		HnswTypeInfo *typeInfo;
+
+	/* 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		version;
+	ItemPointerData heaptids[HNSW_HEAPTIDS];
+	ItemPointerData neighbortid;
+	uint16		unused;
+	Vector		data;
+}			HnswElementTupleData;
+
+typedef HnswElementTupleData * HnswElementTuple;
+
+typedef struct HnswNeighborTupleData
+{
+	uint8		type;
+	uint8		version;
+	uint16		count;
+	ItemPointerData indextids[FLEXIBLE_ARRAY_MEMBER];
+}			HnswNeighborTupleData;
+
+typedef HnswNeighborTupleData * HnswNeighborTuple;
+
+typedef union
+{
+	struct pointerhash_hash *pointers;
+	struct offsethash_hash *offsets;
+	struct tidhash_hash *tids;
+}			visited_hash;
+
+typedef struct HnswScanOpaqueData
+{
+	const		HnswTypeInfo *typeInfo;
+	bool		first;
+	List	   *w;
+	visited_hash v;
+	pairingheap *discarded;
+	Datum		q;
+	int			m;
+	int64		tuples;
+	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);
+Datum		HnswNormValue(const HnswTypeInfo * typeInfo, Oid collation, Datum value);
+bool		HnswCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value);
+Buffer		HnswNewBuffer(Relation index, ForkNumber forkNum);
+void		HnswInitPage(Buffer buf, Page page);
+void		HnswInit(void);
+List	   *HnswSearchLayer(char *base, Datum q, List *ep, int ef, int lc, Relation index, FmgrInfo *procinfo, Oid collation, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited);
+HnswElement HnswGetEntryPoint(Relation index);
+void		HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
+void	   *HnswAlloc(HnswAllocator * allocator, Size size);
+HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
+HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
+void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
+HnswSearchCandidate *HnswEntryCandidate(char *base, HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
+void		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, float *maxDistance);
+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);
+const		HnswTypeInfo *HnswGetTypeInfo(Relation index);
+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 +1,700 @@
+#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 etupSize, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *newInsertPage, uint8 *tupleVersion)
+{
+	OffsetNumber offno;
+	OffsetNumber maxoffno = PageGetMaxOffsetNumber(page);
+
+	for (offno = FirstOffsetNumber; offno <= maxoffno; offno = OffsetNumberNext(offno))
+	{
+		ItemId		eitemid = PageGetItemId(page, offno);
+		HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, eitemid);
+
+		/* 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		nitemid;
+			Size		pageFree;
+			Size		npageFree;
+
+			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);
+			}
+
+			nitemid = PageGetItemId(*npage, neighborOffno);
+
+			/* Ensure aligned for space check */
+			Assert(etupSize == MAXALIGN(etupSize));
+			Assert(ntupSize == MAXALIGN(ntupSize));
+
+			/*
+			 * Calculate free space individually since tuples are overwritten
+			 * individually (in separate calls to PageIndexTupleOverwrite)
+			 */
+			pageFree = ItemIdGetLength(eitemid) + PageGetExactFreeSpace(page);
+			npageFree = ItemIdGetLength(nitemid);
+			if (neighborPage != elementPage)
+				npageFree += PageGetExactFreeSpace(*npage);
+			else if (pageFree >= etupSize)
+				npageFree += pageFree - etupSize;
+
+			/* Check for space */
+			if (pageFree >= etupSize && npageFree >= ntupSize)
+			{
+				*freeOffno = offno;
+				*freeNeighborOffno = neighborOffno;
+				*tupleVersion = etup->version;
+				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;
+	uint8		tupleVersion;
+	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, etupSize, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage, &tupleVersion))
+		{
+			if (nbuf != buf)
+			{
+				if (building)
+					npage = BufferGetPage(nbuf);
+				else
+					npage = GenericXLogRegisterBuffer(state, nbuf, 0);
+			}
+
+			/* Set tuple version */
+			etup->version = tupleVersion;
+			ntup->version = tupleVersion;
+
+			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. Could use
+			 * optimistic locking to retry if another update occurs before
+			 * getting exclusive lock.
+			 */
+			HnswLoadNeighbors(neighborElement, index, m);
+
+			/*
+			 * Could improve performance for vacuuming by checking neighbors
+			 * against list of elements being deleted to find index. It's
+			 * important to exclude already deleted elements for this since
+			 * they can be replaced at any time.
+			 */
+
+			/* Select neighbors */
+			HnswUpdateConnection(NULL, e, hc, lm, lc, &idx, index, procinfo, collation);
+
+			/* 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;
+	const		HnswTypeInfo *typeInfo = HnswGetTypeInfo(index);
+	FmgrInfo   *normprocinfo;
+	Oid			collation = index->rd_indcollation[0];
+
+	/* Detoast once for all calls */
+	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+
+	/* Check value */
+	if (typeInfo->checkValue != NULL)
+		typeInfo->checkValue(DatumGetPointer(value));
+
+	/* Normalize if needed */
+	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
+	if (normprocinfo != NULL)
+	{
+		if (!HnswCheckNorm(normprocinfo, collation, value))
+			return;
+
+		value = HnswNormValue(typeInfo, collation, value);
+	}
+
+	HnswInsertTupleOnDisk(index, value, values, isnull, heap_tid, false);
+}
+
+/*
+ * 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 +1,309 @@
+#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);
+
+	so->q = q;
+	so->m = m;
+
+	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, NULL, NULL, true);
+		ep = w;
+	}
+
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL, &so->v, &so->discarded, true);
+}
+
+/*
+ * Resume scan at ground level with discarded candidates
+ */
+static List *
+ResumeScanItems(IndexScanDesc scan)
+{
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	Relation	index = scan->indexRelation;
+	FmgrInfo   *procinfo = so->procinfo;
+	Oid			collation = so->collation;
+	List	   *ep = NIL;
+	char	   *base = NULL;
+	int			batch_size = hnsw_ef_search;
+
+	if (pairingheap_is_empty(so->discarded))
+		return NIL;
+
+	/* Get next batch of candidates */
+	for (int i = 0; i < batch_size; i++)
+	{
+		HnswSearchCandidate *hc;
+
+		if (pairingheap_is_empty(so->discarded))
+			break;
+
+		hc = HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded));
+
+		ep = lappend(ep, hc);
+	}
+
+	return HnswSearchLayer(base, so->q, ep, batch_size, 0, index, procinfo, collation, so->m, false, NULL, &so->v, &so->discarded, false);
+}
+
+/*
+ * 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)));
+
+		/* Normalize if needed */
+		if (so->normprocinfo != NULL)
+			value = HnswNormValue(so->typeInfo, so->collation, value);
+	}
+
+	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->typeInfo = HnswGetTypeInfo(index);
+	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;
+
+	if (!so->first)
+	{
+		pairingheap_reset(so->discarded);
+		tidhash_reset(so->v.tids);
+	}
+	so->first = true;
+	so->tuples = 0;
+	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);
+
+		HnswBench("scan iteration", so->w = GetScanItems(scan, value));
+
+		/* Release shared lock */
+		UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+		so->first = false;
+
+#if defined(HNSW_MEMORY)
+		elog(INFO, "memory: %zu KB", MemoryContextMemAllocated(so->tmpCtx, false) / 1024);
+#endif
+	}
+
+	for (;;)
+	{
+		char	   *base = NULL;
+		HnswSearchCandidate *hc;
+		HnswElement element;
+		ItemPointer heaptid;
+
+		if (list_length(so->w) == 0)
+		{
+			if (!hnsw_streaming)
+				break;
+
+			/* Prevent scans from consuming too much memory */
+			if (MemoryContextMemAllocated(so->tmpCtx, false) > (Size) work_mem * 1024L)
+			{
+				if (pairingheap_is_empty(so->discarded))
+				{
+					ereport(NOTICE,
+							(errmsg("hnsw iterative search exceeded work_mem after " INT64_FORMAT " tuples", so->tuples),
+							 errhint("Increase work_mem to scan more tuples.")));
+
+					break;
+				}
+
+				/* Return remaining tuples */
+				so->w = lappend(so->w, HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded)));
+			}
+			else
+			{
+				/*
+				 * Locking ensures when neighbors are read, the elements they
+				 * reference will not be deleted (and replaced) during the
+				 * iteration.
+				 *
+				 * Elements loaded into memory on previous iterations may have
+				 * been deleted (and replaced), so when reading neighbors, the
+				 * element version must be checked.
+				 */
+				LockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+				HnswBench("scan iteration", so->w = ResumeScanItems(scan));
+
+				UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+#if defined(HNSW_MEMORY)
+				elog(INFO, "memory: %zu KB", MemoryContextMemAllocated(so->tmpCtx, false) / 1024);
+#endif
+			}
+
+			if (list_length(so->w) == 0)
+				break;
+		}
+
+		hc = llast(so->w);
+		element = HnswPtrAccess(base, hc->element);
+
+		/* Move to next element if no valid heap TIDs */
+		if (element->heaptidsLength == 0)
+		{
+			so->w = list_delete_last(so->w);
+
+			/* Mark memory as free for next iteration */
+			if (hnsw_streaming)
+			{
+				pfree(element);
+				pfree(hc);
+			}
+
+			continue;
+		}
+
+		so->tuples++;
+
+		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 +1,654 @@
+#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, NULL);
+
+		/* 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, NULL);
+
+			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]);
+
+			/* Increment version */
+			/* This is used to avoid incorrect reads for iterative scans */
+			/* Reserve some bits for future use */
+			etup->version++;
+			if (etup->version > 15)
+				etup->version = 1;
+			ntup->version = etup->version;
+
+			/*
+			 * We modified the tuples in place, no need to call
+			 * PageIndexTupleOverwrite
+			 */
+
+			/* 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

@@ -2,61 +2,51 @@
 
 #include <float.h>
 
+#include "access/table.h"
+#include "access/tableam.h"
+#include "access/parallel.h"
+#include "access/xact.h"
+#include "bitvec.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
+#if PG_VERSION_NUM >= 140000
+#include "utils/backend_status.h"
+#include "utils/wait_event.h"
 #endif
 
-#if PG_VERSION_NUM >= 110000
-#include "catalog/pg_operator_d.h"
-#include "catalog/pg_type_d.h"
-#else
-#include "catalog/pg_operator.h"
-#include "catalog/pg_type.h"
-#endif
-
-#if PG_VERSION_NUM >= 130000
-#define CALLBACK_ITEM_POINTER ItemPointer tid
-#else
-#define CALLBACK_ITEM_POINTER HeapTuple hup
-#endif
-
-#if PG_VERSION_NUM >= 120000
-#define UpdateProgress(index, val) pgstat_progress_update_param(index, val)
-#else
-#define UpdateProgress(index, val) ((void)val)
-#endif
+#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)
 
 /*
- * Callback for sampling
+ * Add sample
  */
 static void
-SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
-			   bool *isnull, bool tupleIsAlive, void *state)
+AddSample(Datum *values, IvfflatBuildState * buildstate)
 {
-	IvfflatBuildState *buildstate = (IvfflatBuildState *) state;
 	VectorArray samples = buildstate->samples;
 	int			targsamples = samples->maxlen;
-	Datum		value = values[0];
 
-	/* Skip nulls */
-	if (isnull[0])
-		return;
+	/* Detoast once for all calls */
+	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
 
 	/*
 	 * Normalize with KMEANS_NORM_PROC since spherical distance function
@@ -64,13 +54,15 @@ SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	 */
 	if (buildstate->kmeansnormprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->normvec))
+		if (!IvfflatCheckNorm(buildstate->kmeansnormprocinfo, buildstate->collation, value))
 			return;
+
+		value = IvfflatNormValue(buildstate->typeInfo, buildstate->collation, value);
 	}
 
 	if (samples->length < targsamples)
 	{
-		VectorArraySet(samples, samples->length, DatumGetVector(value));
+		VectorArraySet(samples, samples->length, DatumGetPointer(value));
 		samples->length++;
 	}
 	else
@@ -87,13 +79,38 @@ SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 #endif
 
 			Assert(k >= 0 && k < targsamples);
-			VectorArraySet(samples, k, DatumGetVector(value));
+			VectorArraySet(samples, k, DatumGetPointer(value));
 		}
 
 		buildstate->rowstoskip -= 1;
 	}
 }
 
+/*
+ * Callback for sampling
+ */
+static void
+SampleCallback(Relation index, ItemPointer tid, Datum *values,
+			   bool *isnull, bool tupleIsAlive, void *state)
+{
+	IvfflatBuildState *buildstate = (IvfflatBuildState *) state;
+	MemoryContext oldCtx;
+
+	/* Skip nulls */
+	if (isnull[0])
+		return;
+
+	/* Use memory context since detoast can allocate */
+	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
+
+	/* Add sample */
+	AddSample(values, buildstate);
+
+	/* Reset memory context */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextReset(buildstate->tmpCtx);
+}
+
 /*
  * Sample rows with same logic as ANALYZE
  */
@@ -103,62 +120,46 @@ SampleRows(IvfflatBuildState * buildstate)
 	int			targsamples = buildstate->samples->maxlen;
 	BlockNumber totalblocks = RelationGetNumberOfBlocks(buildstate->heap);
 
-	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_SAMPLE);
-
 	buildstate->rowstoskip = -1;
 
-	BlockSampler_Init(&buildstate->bs, totalblocks, targsamples, random());
+	BlockSampler_Init(&buildstate->bs, totalblocks, targsamples, RandomInt());
 
 	reservoir_init_selection_state(&buildstate->rstate, targsamples);
 	while (BlockSampler_HasMore(&buildstate->bs))
 	{
 		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);
-#elif PG_VERSION_NUM >= 110000
-		IndexBuildHeapRangeScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-								false, true, targblock, 1, SampleCallback, (void *) buildstate, NULL);
-#else
-		IndexBuildHeapRangeScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-								false, true, targblock, 1, SampleCallback, (void *) buildstate);
-#endif
 	}
 }
 
 /*
- * Callback for table_index_build_scan
+ * Add tuple to sort
  */
 static void
-BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
-			  bool *isnull, bool tupleIsAlive, void *state)
+AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState * buildstate)
 {
-	IvfflatBuildState *buildstate = (IvfflatBuildState *) state;
 	double		distance;
 	double		minDistance = DBL_MAX;
-	int			closestCenter = -1;
+	int			closestCenter = 0;
 	VectorArray centers = buildstate->centers;
 	TupleTableSlot *slot = buildstate->slot;
-	Datum		value = values[0];
-	int			i;
 
-#if PG_VERSION_NUM < 130000
-	ItemPointer tid = &hup->t_self;
-#endif
-
-	if (isnull[0])
-		return;
+	/* Detoast once for all calls */
+	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
 
 	/* Normalize if needed */
 	if (buildstate->normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->normvec))
+		if (!IvfflatCheckNorm(buildstate->normprocinfo, buildstate->collation, value))
 			return;
+
+		value = IvfflatNormValue(buildstate->typeInfo, buildstate->collation, value);
 	}
 
 	/* 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))));
 
@@ -196,6 +197,31 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	buildstate->indtuples++;
 }
 
+/*
+ * Callback for table_index_build_scan
+ */
+static void
+BuildCallback(Relation index, ItemPointer tid, Datum *values,
+			  bool *isnull, bool tupleIsAlive, void *state)
+{
+	IvfflatBuildState *buildstate = (IvfflatBuildState *) state;
+	MemoryContext oldCtx;
+
+	/* Skip nulls */
+	if (isnull[0])
+		return;
+
+	/* Use memory context since detoast can allocate */
+	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
+
+	/* Add tuple to sort */
+	AddTupleToSort(index, tid, values, buildstate);
+
+	/* Reset memory context */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextReset(buildstate->tmpCtx);
+}
+
 /*
  * Get index tuple from sort state
  */
@@ -205,11 +231,7 @@ GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot,
 	Datum		value;
 	bool		isnull;
 
-#if PG_VERSION_NUM >= 100000
 	if (tuplesort_gettupleslot(sortstate, true, false, slot, NULL))
-#else
-	if (tuplesort_gettupleslot(sortstate, true, slot, NULL))
-#endif
 	{
 		*list = DatumGetInt32(slot_getattr(slot, 1, &isnull));
 		value = slot_getattr(slot, 3, &isnull);
@@ -228,32 +250,27 @@ 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();
@@ -267,7 +284,8 @@ 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);
 
@@ -277,7 +295,7 @@ 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);
 		}
@@ -287,7 +305,7 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 		IvfflatCommitBuffer(buf, state);
 
 		/* Set the start and insert pages */
-		IvfflatUpdateList(index, state, buildstate->listInfo[i], insertPage, InvalidBlockNumber, startPage, forkNum);
+		IvfflatUpdateList(index, buildstate->listInfo[i], insertPage, InvalidBlockNumber, startPage, forkNum);
 	}
 }
 
@@ -300,13 +318,27 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->heap = heap;
 	buildstate->index = index;
 	buildstate->indexInfo = indexInfo;
+	buildstate->typeInfo = IvfflatGetTypeInfo(index);
 
 	buildstate->lists = IvfflatGetLists(index);
 	buildstate->dimensions = TupleDescAttr(index->rd_att, 0)->atttypmod;
 
+	/* Disallow varbit since require fixed dimensions */
+	if (TupleDescAttr(index->rd_att, 0)->atttypid == VARBITOID)
+		ereport(ERROR,
+				(errcode(ERRCODE_FEATURE_NOT_SUPPORTED),
+				 errmsg("type not supported for ivfflat index")));
+
 	/* Require column to have dimensions to be indexed */
 	if (buildstate->dimensions < 0)
-		elog(ERROR, "column does not have dimensions");
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("column does not have dimensions")));
+
+	if (buildstate->dimensions > buildstate->typeInfo->maxDimensions)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("column cannot have more than %d dimensions for ivfflat index", buildstate->typeInfo->maxDimensions)));
 
 	buildstate->reltuples = 0;
 	buildstate->indtuples = 0;
@@ -318,42 +350,33 @@ 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 */
-	/* 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");
+	if (buildstate->kmeansnormprocinfo != NULL && buildstate->dimensions == 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("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);
-#if PG_VERSION_NUM >= 110000
 	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 3, "vector", RelationGetDescr(index)->attrs[0].atttypid, -1, 0);
-#else
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 3, "vector", RelationGetDescr(index)->attrs[0]->atttypid, -1, 0);
-#endif
 
-#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, buildstate->typeInfo->itemSize(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);
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	buildstate->inertia = 0;
 	buildstate->listSums = palloc0(sizeof(double) * buildstate->lists);
 	buildstate->listCounts = palloc0(sizeof(int) * buildstate->lists);
 #endif
+
+	buildstate->ivfleader = NULL;
 }
 
 /*
@@ -362,14 +385,15 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 static void
 FreeBuildState(IvfflatBuildState * buildstate)
 {
-	pfree(buildstate->centers);
+	VectorArrayFree(buildstate->centers);
 	pfree(buildstate->listInfo);
-	pfree(buildstate->normvec);
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	pfree(buildstate->listSums);
 	pfree(buildstate->listCounts);
 #endif
+
+	MemoryContextDelete(buildstate->tmpCtx);
 }
 
 /*
@@ -380,6 +404,8 @@ ComputeCenters(IvfflatBuildState * buildstate)
 {
 	int			numSamples;
 
+	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 */
 	numSamples = buildstate->lists * 50;
@@ -392,16 +418,25 @@ 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);
 
+		if (buildstate->samples->length < buildstate->lists)
+		{
+			ereport(NOTICE,
+					(errmsg("ivfflat index created with little data"),
+					 errdetail("This will cause low recall."),
+					 errhint("Drop the index until the table has more data.")));
+		}
+	}
+
 	/* Calculate centers */
-	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_KMEANS);
-	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers));
+	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers, buildstate->typeInfo));
 
 	/* Free samples before we allocate more memory */
-	pfree(buildstate->samples);
+	VectorArrayFree(buildstate->samples);
 }
 
 /*
@@ -437,33 +472,36 @@ 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		itemsz;
+	Size		listSize;
 	IvfflatList list;
 
-	itemsz = MAXALIGN(IVFFLAT_LIST_SIZE(dimensions));
-	list = palloc(itemsz);
+	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(centers->itemsize));
+	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;
+
+		/* Zero memory for each list */
+		MemSet(list, 0, listSize);
+
 		/* Load list */
 		list->startPage = InvalidBlockNumber;
 		list->insertPage = InvalidBlockNumber;
-		memcpy(&list->center, VectorArrayGet(centers, i), VECTOR_SIZE(dimensions));
+		memcpy(&list->center, VectorArrayGet(centers, i), VARSIZE_ANY(VectorArrayGet(centers, i)));
 
 		/* 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));
 
@@ -477,17 +515,17 @@ 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;
 
@@ -522,50 +560,434 @@ PrintKmeansMetrics(IvfflatBuildState * buildstate)
 }
 #endif
 
+/*
+ * Initialize build sort state
+ */
+static Tuplesortstate *
+InitBuildSortState(TupleDesc tupdesc, int memory, SortCoordinate coordinate)
+{
+	AttrNumber	attNums[] = {1};
+	Oid			sortOperators[] = {Int4LessOperator};
+	Oid			sortCollations[] = {InvalidOid};
+	bool		nullsFirstFlags[] = {false};
+
+	return tuplesort_begin_heap(tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, memory, coordinate, false);
+}
+
+/*
+ * 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;
+
+	/* 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 = InitBuildSortState(buildstate.tupdesc, sortmem, coordinate);
+	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
+AssignTuples(IvfflatBuildState * buildstate)
+{
+	int			parallel_workers = 0;
+	SortCoordinate coordinate = NULL;
+
+	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 = InitBuildSortState(buildstate->tupdesc, maintenance_work_mem, coordinate);
+
+	/* 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
+	}
+}
+
 /*
  * Create entry pages
  */
 static void
 CreateEntryPages(IvfflatBuildState * buildstate, ForkNumber forkNum)
 {
-	AttrNumber	attNums[] = {1};
-	Oid			sortOperators[] = {Float8LessOperator};
-	Oid			sortCollations[] = {InvalidOid};
-	bool		nullsFirstFlags[] = {false};
-
-	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_SORT);
-
-#if PG_VERSION_NUM >= 110000
-	buildstate->sortstate = tuplesort_begin_heap(buildstate->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, maintenance_work_mem, NULL, false);
-#else
-	buildstate->sortstate = tuplesort_begin_heap(buildstate->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, maintenance_work_mem, false);
-#endif
-
-	/* Add tuples to sort */
-	if (buildstate->heap != NULL)
-	{
-#if PG_VERSION_NUM >= 120000
-		buildstate->reltuples = table_index_build_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-													   true, true, BuildCallback, (void *) buildstate, NULL);
-#elif PG_VERSION_NUM >= 110000
-		buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-												   true, BuildCallback, (void *) buildstate, NULL);
-#else
-		buildstate->reltuples = IndexBuildHeapScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-												   true, BuildCallback, (void *) buildstate);
-#endif
-	}
+	/* Assign */
+	IvfflatBench("assign tuples", AssignTuples(buildstate));
 
 	/* Sort */
-	tuplesort_performsort(buildstate->sortstate);
+	IvfflatBench("sort tuples", tuplesort_performsort(buildstate->sortstate));
 
-#ifdef IVFFLAT_KMEANS_DEBUG
-	PrintKmeansMetrics(buildstate);
-#endif
+	/* Load */
+	IvfflatBench("load tuples", InsertTuples(buildstate->index, buildstate, forkNum));
 
-	/* Insert */
-	InsertTuples(buildstate->index, buildstate, forkNum);
+	/* End sort */
 	tuplesort_end(buildstate->sortstate);
+
+	/* End parallel build */
+	if (buildstate->ivfleader)
+		IvfflatEndParallel(buildstate->ivfleader);
 }
 
 /*
@@ -582,7 +1004,11 @@ BuildIndex(Relation heap, Relation index, IndexInfo *indexInfo,
 	/* Create pages */
 	CreateMetaPage(index, buildstate->dimensions, buildstate->lists, forkNum);
 	CreateListPages(index, buildstate->centers, buildstate->dimensions, buildstate->lists, forkNum, &buildstate->listInfo);
-	IvfflatBench("CreateEntryPages", CreateEntryPages(buildstate, forkNum));
+	CreateEntryPages(buildstate, forkNum);
+
+	/* Write WAL for initialization fork since GenericXLog functions do not */
+	if (forkNum == INIT_FORKNUM)
+		log_newpage_range(index, forkNum, 0, RelationGetNumberOfBlocksInFork(index, forkNum), true);
 
 	FreeBuildState(buildstate);
 }

src/ivfflat.c

@@ -3,13 +3,17 @@
 #include <float.h>
 
 #include "access/amapi.h"
+#include "access/reloptions.h"
+#include "commands/progress.h"
 #include "commands/vacuum.h"
 #include "ivfflat.h"
+#include "utils/float.h"
 #include "utils/guc.h"
 #include "utils/selfuncs.h"
+#include "utils/spccache.h"
 
-#if PG_VERSION_NUM >= 120000
-#include "commands/progress.h"
+#if PG_VERSION_NUM < 150000
+#define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
 #endif
 
 int			ivfflat_probes;
@@ -19,25 +23,22 @@ 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
-#if PG_VERSION_NUM >= 130000
-					  ,AccessExclusiveLock
-#endif
-		);
+					  IVFFLAT_DEFAULT_LISTS, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS, AccessExclusiveLock);
 
 	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)
 {
@@ -45,19 +46,16 @@ ivfflatbuildphasename(int64 phasenum)
 	{
 		case PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE:
 			return "initializing";
-		case PROGRESS_IVFFLAT_PHASE_SAMPLE:
-			return "sampling table";
 		case PROGRESS_IVFFLAT_PHASE_KMEANS:
 			return "performing k-means";
-		case PROGRESS_IVFFLAT_PHASE_SORT:
-			return "sorting tuples";
+		case PROGRESS_IVFFLAT_PHASE_ASSIGN:
+			return "assigning tuples";
 		case PROGRESS_IVFFLAT_PHASE_LOAD:
 			return "loading tuples";
 		default:
 			return NULL;
 	}
 }
-#endif
 
 /*
  * Estimate the cost of an index scan
@@ -65,60 +63,76 @@ ivfflatbuildphasename(int64 phasenum)
 static void
 ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 					Cost *indexStartupCost, Cost *indexTotalCost,
-					Selectivity *indexSelectivity, double *indexCorrelation
-#if PG_VERSION_NUM >= 100000
-					,double *indexPages
-#endif
-)
+					Selectivity *indexSelectivity, double *indexCorrelation,
+					double *indexPages)
 {
 	GenericCosts costs;
 	int			lists;
 	double		ratio;
-	Relation	indexRel;
-#if PG_VERSION_NUM < 120000
-	List	   *qinfos;
-#endif
+	double		spc_seq_page_cost;
+	Relation	index;
 
 	/* Never use index without order */
 	if (path->indexorderbys == NULL)
 	{
-		*indexStartupCost = DBL_MAX;
-		*indexTotalCost = DBL_MAX;
+		*indexStartupCost = get_float8_infinity();
+		*indexTotalCost = get_float8_infinity();
 		*indexSelectivity = 0;
 		*indexCorrelation = 0;
-#if PG_VERSION_NUM >= 100000
 		*indexPages = 0;
-#endif
 		return;
 	}
 
 	MemSet(&costs, 0, sizeof(costs));
 
-#if PG_VERSION_NUM >= 120000
-	genericcostestimate(root, path, loop_count, &costs);
-#else
-	qinfos = deconstruct_indexquals(path);
-	genericcostestimate(root, path, loop_count, qinfos, &costs);
-#endif
-
-	indexRel = index_open(path->indexinfo->indexoid, NoLock);
-	lists = IvfflatGetLists(indexRel);
-	index_close(indexRel, NoLock);
+	index = index_open(path->indexinfo->indexoid, NoLock);
+	IvfflatGetMetaPageInfo(index, &lists, NULL);
+	index_close(index, NoLock);
 
+	/* Get the ratio of lists that we need to visit */
 	ratio = ((double) ivfflat_probes) / lists;
-	if (ratio > 1)
-		ratio = 1;
+	if (ratio > 1.0)
+		ratio = 1.0;
 
-	costs.indexTotalCost *= ratio;
+	/*
+	 * This gives us the subset of tuples to visit. This value is passed into
+	 * the generic cost estimator to determine the number of pages to visit
+	 * during the index scan.
+	 */
+	costs.numIndexTuples = path->indexinfo->tuples * ratio;
 
-	/* Startup cost and total cost are same */
+	genericcostestimate(root, path, loop_count, &costs);
+
+	get_tablespace_page_costs(path->indexinfo->reltablespace, NULL, &spc_seq_page_cost);
+
+	/* Adjust cost if needed since TOAST not included in seq scan cost */
+	if (costs.numIndexPages > path->indexinfo->rel->pages && ratio < 0.5)
+	{
+		/* Change all page cost from random to sequential */
+		costs.indexTotalCost -= costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+
+		/* Remove cost of extra pages */
+		costs.indexTotalCost -= (costs.numIndexPages - path->indexinfo->rel->pages) * spc_seq_page_cost;
+	}
+	else
+	{
+		/* Change some page cost from random to sequential */
+		costs.indexTotalCost -= 0.5 * costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+	}
+
+	/*
+	 * If the list selectivity is lower than what is returned from the generic
+	 * cost estimator, use that.
+	 */
+	if (ratio < costs.indexSelectivity)
+		costs.indexSelectivity = ratio;
+
+	/* Use total cost since most work happens before first tuple is returned */
 	*indexStartupCost = costs.indexTotalCost;
 	*indexTotalCost = costs.indexTotalCost;
 	*indexSelectivity = costs.indexSelectivity;
 	*indexCorrelation = costs.indexCorrelation;
-#if PG_VERSION_NUM >= 100000
 	*indexPages = costs.numIndexPages;
-#endif
 }
 
 /*
@@ -131,23 +145,10 @@ ivfflatoptions(Datum reloptions, bool validate)
 		{"lists", RELOPT_TYPE_INT, offsetof(IvfflatOptions, lists)},
 	};
 
-#if PG_VERSION_NUM >= 130000
 	return (bytea *) build_reloptions(reloptions, validate,
 									  ivfflat_relopt_kind,
 									  sizeof(IvfflatOptions),
 									  tab, lengthof(tab));
-#else
-	relopt_value *options;
-	int			numoptions;
-	IvfflatOptions *rdopts;
-
-	options = parseRelOptions(reloptions, validate, ivfflat_relopt_kind, &numoptions);
-	rdopts = allocateReloptStruct(sizeof(IvfflatOptions), options, numoptions);
-	fillRelOptions((void *) rdopts, sizeof(IvfflatOptions), options, numoptions,
-				   validate, tab, lengthof(tab));
-
-	return (bytea *) rdopts;
-#endif
 }
 
 /*
@@ -164,17 +165,15 @@ ivfflatvalidate(Oid opclassoid)
  *
  * See https://www.postgresql.org/docs/current/index-api.html
  */
-PG_FUNCTION_INFO_V1(ivfflathandler);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(ivfflathandler);
 Datum
 ivfflathandler(PG_FUNCTION_ARGS)
 {
 	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);
 
 	amroutine->amstrategies = 0;
-	amroutine->amsupport = 4;
-#if PG_VERSION_NUM >= 130000
+	amroutine->amsupport = 5;
 	amroutine->amoptsprocnum = 0;
-#endif
 	amroutine->amcanorder = false;
 	amroutine->amcanorderbyop = true;
 	amroutine->amcanbackward = false;	/* can change direction mid-scan */
@@ -186,31 +185,32 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	amroutine->amstorage = false;
 	amroutine->amclusterable = false;
 	amroutine->ampredlocks = false;
-#if PG_VERSION_NUM >= 100000
 	amroutine->amcanparallel = false;
+#if PG_VERSION_NUM >= 170000
+	amroutine->amcanbuildparallel = true;
 #endif
-#if PG_VERSION_NUM >= 110000
 	amroutine->amcaninclude = false;
-#endif
-#if PG_VERSION_NUM >= 130000
 	amroutine->amusemaintenanceworkmem = false; /* not used during VACUUM */
-	amroutine->amparallelvacuumoptions = VACUUM_OPTION_PARALLEL_BULKDEL;
+#if PG_VERSION_NUM >= 160000
+	amroutine->amsummarizing = false;
 #endif
+	amroutine->amparallelvacuumoptions = VACUUM_OPTION_PARALLEL_BULKDEL;
 	amroutine->amkeytype = InvalidOid;
 
 	/* Interface functions */
 	amroutine->ambuild = ivfflatbuild;
 	amroutine->ambuildempty = ivfflatbuildempty;
 	amroutine->aminsert = ivfflatinsert;
+#if PG_VERSION_NUM >= 170000
+	amroutine->aminsertcleanup = NULL;
+#endif
 	amroutine->ambulkdelete = ivfflatbulkdelete;
 	amroutine->amvacuumcleanup = ivfflatvacuumcleanup;
 	amroutine->amcanreturn = NULL;	/* tuple not included in heapsort */
 	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;
@@ -224,11 +224,9 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	amroutine->amrestrpos = NULL;
 
 	/* Interface functions to support parallel index scans */
-#if PG_VERSION_NUM >= 100000
 	amroutine->amestimateparallelscan = NULL;
 	amroutine->aminitparallelscan = NULL;
 	amroutine->amparallelrescan = NULL;
-#endif
 
 	PG_RETURN_POINTER(amroutine);
 }

src/ivfflat.h

@@ -3,26 +3,32 @@
 
 #include "postgres.h"
 
+#include "access/genam.h"
 #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 random() */
 #include "utils/sampling.h"
 #include "utils/tuplesort.h"
 #include "vector.h"
 
+#if PG_VERSION_NUM >= 150000
+#include "common/pg_prng.h"
+#endif
+
 #ifdef IVFFLAT_BENCH
 #include "portability/instr_time.h"
 #endif
 
-#if PG_VERSION_NUM < 100000
-#error "Requires PostgreSQL 10+"
-#endif
+#define IVFFLAT_MAX_DIM 2000
 
 /* Support functions */
 #define IVFFLAT_DISTANCE_PROC 1
 #define IVFFLAT_NORM_PROC 2
 #define IVFFLAT_KMEANS_DISTANCE_PROC 3
 #define IVFFLAT_KMEANS_NORM_PROC 4
+#define IVFFLAT_TYPE_INFO_PROC 5
 
 #define IVFFLAT_VERSION	1
 #define IVFFLAT_MAGIC_NUMBER 0x14FF1A7
@@ -32,17 +38,19 @@
 #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
 
 /* Build phases */
 /* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
-#define PROGRESS_IVFFLAT_PHASE_SAMPLE	2
-#define PROGRESS_IVFFLAT_PHASE_KMEANS	3
-#define PROGRESS_IVFFLAT_PHASE_SORT		4
-#define PROGRESS_IVFFLAT_PHASE_LOAD		5
+#define PROGRESS_IVFFLAT_PHASE_KMEANS	2
+#define PROGRESS_IVFFLAT_PHASE_ASSIGN	3
+#define PROGRESS_IVFFLAT_PHASE_LOAD		4
 
-#define IVFFLAT_LIST_SIZE(_dim)	(offsetof(IvfflatListData, center) + VECTOR_SIZE(_dim))
+#define IVFFLAT_LIST_SIZE(size)	(offsetof(IvfflatListData, center) + size)
 
 #define IvfflatPageGetOpaque(page)	((IvfflatPageOpaque) PageGetSpecialPointer(page))
 #define IvfflatPageGetMeta(page)	((IvfflatMetaPageData *) PageGetContents(page))
@@ -62,6 +70,14 @@
 #define IvfflatBench(name, code) (code)
 #endif
 
+#if PG_VERSION_NUM >= 150000
+#define RandomDouble() pg_prng_double(&pg_global_prng_state)
+#define RandomInt() pg_prng_uint32(&pg_global_prng_state)
+#else
+#define RandomDouble() (((double) random()) / MAX_RANDOM_VALUE)
+#define RandomInt() random()
+#endif
+
 /* Variables */
 extern int	ivfflat_probes;
 
@@ -70,7 +86,8 @@ typedef struct VectorArrayData
 	int			length;
 	int			maxlen;
 	int			dim;
-	Vector		items[FLEXIBLE_ARRAY_MEMBER];
+	Size		itemsize;
+	char	   *items;
 }			VectorArrayData;
 
 typedef VectorArrayData * VectorArray;
@@ -88,12 +105,66 @@ 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 IvfflatTypeInfo
+{
+	int			maxDimensions;
+	Datum		(*normalize) (PG_FUNCTION_ARGS);
+	Size		(*itemSize) (int dimensions);
+	void		(*updateCenter) (Pointer v, int dimensions, float *x);
+	void		(*sumCenter) (Pointer v, float *x);
+}			IvfflatTypeInfo;
+
 typedef struct IvfflatBuildState
 {
 	/* Info */
 	Relation	heap;
 	Relation	index;
 	IndexInfo  *indexInfo;
+	const		IvfflatTypeInfo *typeInfo;
 
 	/* Settings */
 	int			dimensions;
@@ -113,7 +184,6 @@ typedef struct IvfflatBuildState
 	VectorArray samples;
 	VectorArray centers;
 	ListInfo   *listInfo;
-	Vector	   *normvec;
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	double		inertia;
@@ -130,6 +200,12 @@ typedef struct IvfflatBuildState
 	Tuplesortstate *sortstate;
 	TupleDesc	tupdesc;
 	TupleTableSlot *slot;
+
+	/* Memory */
+	MemoryContext tmpCtx;
+
+	/* Parallel builds */
+	IvfflatLeader *ivfleader;
 }			IvfflatBuildState;
 
 typedef struct IvfflatMetaPageData
@@ -169,9 +245,10 @@ typedef struct IvfflatScanList
 
 typedef struct IvfflatScanOpaqueData
 {
+	const		IvfflatTypeInfo *typeInfo;
 	int			probes;
+	int			dimensions;
 	bool		first;
-	Buffer		buf;
 
 	/* Sorting */
 	Tuplesortstate *sortstate;
@@ -183,6 +260,7 @@ typedef struct IvfflatScanOpaqueData
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
 	Oid			collation;
+	Datum		(*distfunc) (FmgrInfo *flinfo, Oid collation, Datum arg1, Datum arg2);
 
 	/* Lists */
 	pairingheap *listQueue;
@@ -191,25 +269,40 @@ typedef struct IvfflatScanOpaqueData
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;
 
-#define VECTOR_ARRAY_SIZE(_length, _dim) (offsetof(VectorArrayData, items) + _length * VECTOR_SIZE(_dim))
-#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) _arr + offsetof(VectorArrayData, items) + (_offset) * VECTOR_SIZE(_arr->dim))
-#define VectorArrayGet(_arr, _offset) ((Vector *) VECTOR_ARRAY_OFFSET(_arr, _offset))
-#define VectorArraySet(_arr, _offset, _val) (memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, VECTOR_SIZE(_arr->dim)))
+#define VECTOR_ARRAY_SIZE(_length, _size) (sizeof(VectorArrayData) + (_length) * MAXALIGN(_size))
+
+/* Use functions instead of macros to avoid double evaluation */
+
+static inline Pointer
+VectorArrayGet(VectorArray arr, int offset)
+{
+	return ((char *) arr->items) + (offset * arr->itemsize);
+}
+
+static inline void
+VectorArraySet(VectorArray arr, int offset, Pointer val)
+{
+	memcpy(VectorArrayGet(arr, offset), val, VARSIZE_ANY(val));
+}
 
 /* Methods */
-void		_PG_init(void);
-VectorArray VectorArrayInit(int maxlen, int dimensions);
-void		PrintVectorArray(char *msg, VectorArray arr);
-void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
-FmgrInfo   *IvfflatOptionalProcInfo(Relation rel, uint16 procnum);
-bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+VectorArray VectorArrayInit(int maxlen, int dimensions, Size itemsize);
+void		VectorArrayFree(VectorArray arr);
+void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers, const IvfflatTypeInfo * typeInfo);
+FmgrInfo   *IvfflatOptionalProcInfo(Relation index, uint16 procnum);
+Datum		IvfflatNormValue(const IvfflatTypeInfo * typeInfo, Oid collation, Datum value);
+bool		IvfflatCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value);
 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);
+const		IvfflatTypeInfo *IvfflatGetTypeInfo(Relation index);
+PGDLLEXPORT void IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc);
 
 /* Index access methods */
 IndexBuildResult *ivfflatbuild(Relation heap, Relation index, IndexInfo *indexInfo);
@@ -218,9 +311,7 @@ bool		ivfflatinsert(Relation index, Datum *values, bool *isnull, ItemPointer hea
 #if PG_VERSION_NUM >= 140000
 						  ,bool indexUnchanged
 #endif
-#if PG_VERSION_NUM >= 100000
 						  ,IndexInfo *indexInfo
-#endif
 );
 IndexBulkDeleteResult *ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats, IndexBulkDeleteCallback callback, void *callback_state);
 IndexBulkDeleteResult *ivfflatvacuumcleanup(IndexVacuumInfo *info, IndexBulkDeleteResult *stats);

src/ivfinsert.c

@@ -2,43 +2,51 @@
 
 #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;
 
-	procinfo = index_getprocinfo(rel, 1, IVFFLAT_DISTANCE_PROC);
-	collation = rel->rd_indcollation[0];
+	/* Avoid compiler warning */
+	listInfo->blkno = nextblkno;
+	listInfo->offno = FirstOffsetNumber;
+
+	procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
+	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)));
 
-			if (distance < minDistance)
+			if (distance < minDistance || !BlockNumberIsValid(*insertPage))
 			{
 				*insertPage = list->insertPage;
 				listInfo->blkno = nextblkno;
@@ -57,8 +65,12 @@ FindInsertPage(Relation rel, Datum *values, BlockNumber *insertPage, ListInfo *
  * Insert a tuple into the index
  */
 static void
-InsertTuple(Relation rel, IndexTuple itup, Relation heapRel, Datum *values)
+InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel)
 {
+	const		IvfflatTypeInfo *typeInfo = IvfflatGetTypeInfo(index);
+	IndexTuple	itup;
+	Datum		value;
+	FmgrInfo   *normprocinfo;
 	Buffer		buf;
 	Page		page;
 	GenericXLogState *state;
@@ -67,21 +79,44 @@ InsertTuple(Relation rel, IndexTuple itup, Relation heapRel, Datum *values)
 	ListInfo	listInfo;
 	BlockNumber originalInsertPage;
 
+	/* Detoast once for all calls */
+	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+
+	/* Normalize if needed */
+	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
+	if (normprocinfo != NULL)
+	{
+		Oid			collation = index->rd_indcollation[0];
+
+		if (!IvfflatCheckNorm(normprocinfo, collation, value))
+			return;
+
+		value = IvfflatNormValue(typeInfo, collation, value);
+	}
+
+	/* Ensure index is valid */
+	IvfflatGetMetaPageInfo(index, NULL, NULL);
+
 	/* 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(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)
@@ -97,23 +132,16 @@ InsertTuple(Relation rel, IndexTuple itup, Relation heapRel, Datum *values)
 		}
 		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);
-			newpage = GenericXLogRegisterBuffer(state, newbuf, GENERIC_XLOG_FULL_IMAGE);
+			LockRelationForExtension(index, ExclusiveLock);
+			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 */
@@ -123,28 +151,28 @@ InsertTuple(Relation rel, IndexTuple itup, Relation heapRel, Datum *values)
 			IvfflatPageGetOpaque(page)->nextblkno = insertPage;
 
 			/* Commit */
-			MarkBufferDirty(newbuf);
-			MarkBufferDirty(buf);
 			GenericXLogFinish(state);
 
-			/* Unlock extend relation lock as early as possible */
-			UnlockReleaseBuffer(metabuf);
-
-			/* Unlock rest */
-			UnlockReleaseBuffer(newbuf);
+			/* Unlock previous buffer */
 			UnlockReleaseBuffer(buf);
+
+			/* Prepare new buffer */
+			state = GenericXLogStart(index);
+			buf = newbuf;
+			page = GenericXLogRegisterBuffer(state, buf, 0);
+			break;
 		}
 	}
 
 	/* 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);
 }
 
 /*
@@ -156,36 +184,31 @@ ivfflatinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid,
 #if PG_VERSION_NUM >= 140000
 			  ,bool indexUnchanged
 #endif
-#if PG_VERSION_NUM >= 100000
 			  ,IndexInfo *indexInfo
-#endif
 )
 {
-	IndexTuple	itup;
-	Datum		value;
-	FmgrInfo   *normprocinfo;
+	MemoryContext oldCtx;
+	MemoryContext insertCtx;
 
+	/* Skip nulls */
 	if (isnull[0])
 		return false;
 
-	value = values[0];
+	/*
+	 * Use memory context since detoast, IvfflatNormValue, and
+	 * index_form_tuple can allocate
+	 */
+	insertCtx = AllocSetContextCreate(CurrentMemoryContext,
+									  "Ivfflat insert temporary context",
+									  ALLOCSET_DEFAULT_SIZES);
+	oldCtx = MemoryContextSwitchTo(insertCtx);
 
-	/* Normalize if needed */
-	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
-	if (normprocinfo != NULL)
-	{
-		if (!IvfflatNormValue(normprocinfo, index->rd_indcollation[0], &value, NULL))
-			return false;
-	}
+	/* Insert tuple */
+	InsertTuple(index, values, isnull, heap_tid, heap);
 
-	itup = index_form_tuple(RelationGetDescr(index), &value, isnull);
-	itup->t_tid = *heap_tid;
-	InsertTuple(index, itup, heap, &value);
-	pfree(itup);
-
-	/* Clean up if we allocated a new value */
-	if (value != values[0])
-		pfree(DatumGetPointer(value));
+	/* Delete memory context */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(insertCtx);
 
 	return false;
 }

src/ivfkmeans.c

@@ -1,19 +1,17 @@
 #include "postgres.h"
 
 #include <float.h>
+#include <math.h>
 
+#include "bitvec.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
-
-#if PG_VERSION_NUM >= 150000
-#include "common/pg_prng.h"
-#endif
-
-#if PG_VERSION_NUM >= 150000
-#define RandomDouble() pg_prng_double(&pg_global_prng_state)
-#else
-#define RandomDouble() (((double) random()) / MAX_RANDOM_VALUE)
-#endif
+#include "utils/builtins.h"
+#include "utils/datum.h"
+#include "utils/memutils.h"
+#include "vector.h"
 
 /*
  * Initialize with kmeans++
@@ -25,12 +23,7 @@ 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;
@@ -39,25 +32,29 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 	collation = index->rd_indcollation[0];
 
 	/* Choose an initial center uniformly at random */
-	VectorArraySet(centers, 0, VectorArrayGet(samples, random() % samples->length));
+	VectorArraySet(centers, 0, VectorArrayGet(samples, RandomInt() % samples->length));
 	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;
@@ -92,77 +89,162 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 }
 
 /*
- * Apply norm to vector
- */
-static inline void
-ApplyNorm(FmgrInfo *normprocinfo, Oid collation, Vector * vec)
-{
-	int			i;
-	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(vec)));
-
-	/* TODO Handle zero norm */
-	if (norm > 0)
-	{
-		for (i = 0; i < vec->dim; i++)
-			vec->x[i] /= norm;
-	}
-}
-
-/*
- * Compare vectors
- */
-static int
-CompareVectors(const void *a, const void *b)
-{
-	return vector_cmp_internal((Vector *) a, (Vector *) b);
-}
-
-/*
- * Quick approach if we have little data
+ * Norm centers
  */
 static void
-QuickCenters(Relation index, VectorArray samples, VectorArray centers)
+NormCenters(const IvfflatTypeInfo * typeInfo, Oid collation, VectorArray centers)
 {
-	int			i;
-	int			j;
-	Vector	   *vec;
-	int			dimensions = centers->dim;
-	Oid			collation = index->rd_indcollation[0];
-	FmgrInfo   *normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
+	MemoryContext normCtx = AllocSetContextCreate(CurrentMemoryContext,
+												  "Ivfflat norm temporary context",
+												  ALLOCSET_DEFAULT_SIZES);
+	MemoryContext oldCtx = MemoryContextSwitchTo(normCtx);
 
-	/* Copy existing vectors while avoiding duplicates */
-	if (samples->length > 0)
+	for (int j = 0; j < centers->length; j++)
 	{
-		qsort(samples->items, samples->length, VECTOR_SIZE(samples->dim), CompareVectors);
-		for (i = 0; i < samples->length; i++)
-		{
-			vec = VectorArrayGet(samples, i);
+		Datum		center = PointerGetDatum(VectorArrayGet(centers, j));
+		Datum		newCenter = IvfflatNormValue(typeInfo, collation, center);
+		Size		size = VARSIZE_ANY(DatumGetPointer(newCenter));
 
-			if (i == 0 || CompareVectors(vec, VectorArrayGet(samples, i - 1)) != 0)
-			{
-				VectorArraySet(centers, centers->length, vec);
-				centers->length++;
-			}
-		}
+		if (size > centers->itemsize)
+			elog(ERROR, "safety check failed");
+
+		memcpy(DatumGetPointer(center), DatumGetPointer(newCenter), size);
+		MemoryContextReset(normCtx);
 	}
 
-	/* Fill remaining with random data */
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(normCtx);
+}
+
+/*
+ * Quick approach if we have no data
+ */
+static void
+RandomCenters(Relation index, VectorArray centers, const IvfflatTypeInfo * typeInfo)
+{
+	int			dimensions = centers->dim;
+	FmgrInfo   *normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
+	Oid			collation = index->rd_indcollation[0];
+	float	   *x = (float *) palloc(sizeof(float) * dimensions);
+
+	/* Fill with random data */
 	while (centers->length < centers->maxlen)
 	{
-		vec = VectorArrayGet(centers, centers->length);
+		Pointer		center = VectorArrayGet(centers, centers->length);
 
-		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
-		vec->dim = dimensions;
+		for (int i = 0; i < dimensions; i++)
+			x[i] = (float) RandomDouble();
 
-		for (j = 0; j < dimensions; j++)
-			vec->x[j] = RandomDouble();
-
-		/* Normalize if needed (only needed for random centers) */
-		if (normprocinfo != NULL)
-			ApplyNorm(normprocinfo, collation, vec);
+		typeInfo->updateCenter(center, dimensions, x);
 
 		centers->length++;
 	}
+
+	if (normprocinfo != NULL)
+		NormCenters(typeInfo, collation, centers);
+}
+
+#ifdef IVFFLAT_MEMORY
+/*
+ * Show memory usage
+ */
+static void
+ShowMemoryUsage(MemoryContext context, Size estimatedSize)
+{
+	elog(INFO, "total memory: %zu MB",
+		 MemoryContextMemAllocated(context, true) / (1024 * 1024));
+	elog(INFO, "estimated memory: %zu MB", estimatedSize / (1024 * 1024));
+}
+#endif
+
+/*
+ * Sum centers
+ */
+static void
+SumCenters(VectorArray samples, float *agg, int *closestCenters, const IvfflatTypeInfo * typeInfo)
+{
+	for (int j = 0; j < samples->length; j++)
+	{
+		float	   *x = agg + ((int64) closestCenters[j] * samples->dim);
+
+		typeInfo->sumCenter(VectorArrayGet(samples, j), x);
+	}
+}
+
+/*
+ * Update centers
+ */
+static void
+UpdateCenters(float *agg, VectorArray centers, const IvfflatTypeInfo * typeInfo)
+{
+	for (int j = 0; j < centers->length; j++)
+	{
+		float	   *x = agg + ((int64) j * centers->dim);
+
+		typeInfo->updateCenter(VectorArrayGet(centers, j), centers->dim, x);
+	}
+}
+
+/*
+ * Compute new centers
+ */
+static void
+ComputeNewCenters(VectorArray samples, float *agg, VectorArray newCenters, int *centerCounts, int *closestCenters, FmgrInfo *normprocinfo, Oid collation, const IvfflatTypeInfo * typeInfo)
+{
+	int			dimensions = newCenters->dim;
+	int			numCenters = newCenters->length;
+	int			numSamples = samples->length;
+
+	/* Reset sum and count */
+	for (int j = 0; j < numCenters; j++)
+	{
+		float	   *x = agg + ((int64) j * dimensions);
+
+		for (int k = 0; k < dimensions; k++)
+			x[k] = 0.0;
+
+		centerCounts[j] = 0;
+	}
+
+	/* Increment sum of closest center */
+	SumCenters(samples, agg, closestCenters, typeInfo);
+
+	/* 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++)
+	{
+		float	   *x = agg + ((int64) j * dimensions);
+
+		if (centerCounts[j] > 0)
+		{
+			/* Double avoids overflow, but requires more memory */
+			/* TODO Update bounds */
+			for (int k = 0; k < dimensions; k++)
+			{
+				if (isinf(x[k]))
+					x[k] = x[k] > 0 ? FLT_MAX : -FLT_MAX;
+			}
+
+			for (int k = 0; k < dimensions; k++)
+				x[k] /= centerCounts[j];
+		}
+		else
+		{
+			/* TODO Handle empty centers properly */
+			for (int k = 0; k < dimensions; k++)
+				x[k] = RandomDouble();
+		}
+	}
+
+	/* Set new centers */
+	UpdateCenters(agg, newCenters, typeInfo);
+
+	/* Normalize if needed */
+	if (normprocinfo != NULL)
+		NormCenters(typeInfo, collation, newCenters);
 }
 
 /*
@@ -174,20 +256,16 @@ 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, const IvfflatTypeInfo * typeInfo)
 {
 	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;
+	float	   *agg;
 	int		   *centerCounts;
 	int		   *closestCenters;
 	float	   *lowerBound;
@@ -195,19 +273,12 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	float	   *s;
 	float	   *halfcdist;
 	float	   *newcdist;
-	int			changes;
-	double		minDistance;
-	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		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->dim);
-	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, dimensions);
+	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->itemsize);
+	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->itemsize);
+	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, centers->itemsize);
+	Size		aggSize = sizeof(float) * (int64) numCenters * dimensions;
 	Size		centerCountsSize = sizeof(int) * numCenters;
 	Size		closestCentersSize = sizeof(int) * numSamples;
 	Size		lowerBoundSize = sizeof(float) * numSamples * numCenters;
@@ -217,11 +288,11 @@ 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 + aggSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
 
 	/* Check memory requirements */
 	/* Add one to error message to ceil */
-	if (totalSize / 1024 > maintenance_work_mem)
+	if (totalSize > (Size) maintenance_work_mem * 1024L)
 		ereport(ERROR,
 				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
 				 errmsg("memory required is %zu MB, maintenance_work_mem is %d MB",
@@ -238,6 +309,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 	/* Allocate space */
 	/* Use float instead of double to save memory */
+	agg = palloc(aggSize);
 	centerCounts = palloc(centerCountsSize);
 	closestCenters = palloc(closestCentersSize);
 	lowerBound = palloc_extended(lowerBoundSize, MCXT_ALLOC_HUGE);
@@ -246,28 +318,28 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	halfcdist = palloc_extended(halfcdistSize, MCXT_ALLOC_HUGE);
 	newcdist = palloc(newcdistSize);
 
-	newCenters = VectorArrayInit(numCenters, dimensions);
-	for (j = 0; j < numCenters; j++)
-	{
-		vec = VectorArrayGet(newCenters, j);
-		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
-		vec->dim = dimensions;
-	}
+	/* Initialize new centers */
+	newCenters = VectorArrayInit(numCenters, dimensions, centers->itemsize);
+	newCenters->length = numCenters;
+
+#ifdef IVFFLAT_MEMORY
+	ShowMemoryUsage(MemoryContextGetParent(CurrentMemoryContext), 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;
-		closestCenter = -1;
+		float		minDistance = FLT_MAX;
+		int			closestCenter = 0;
 
 		/* Find closest center */
-		for (k = 0; k < numCenters; k++)
+		for (int64 k = 0; k < numCenters; k++)
 		{
 			/* TODO Use Lemma 1 in k-means++ initialization */
-			distance = lowerBound[j * numCenters + k];
+			float		distance = lowerBound[j * numCenters + k];
 
 			if (distance < minDistance)
 			{
@@ -281,33 +353,37 @@ 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;
 
@@ -321,16 +397,21 @@ 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;
@@ -341,12 +422,12 @@ 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;
@@ -360,7 +441,7 @@ 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;
@@ -374,64 +455,22 @@ 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++)
-		{
-			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)
-			{
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] /= centerCounts[j];
-			}
-			else
-			{
-				/* TODO Handle empty centers properly */
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] = RandomDouble();
-			}
-
-			/* Normalize if needed */
-			if (normprocinfo != NULL)
-				ApplyNorm(normprocinfo, collation, vec);
-		}
+		ComputeNewCenters(samples, agg, newCenters, centerCounts, closestCenters, normprocinfo, collation, typeInfo);
 
 		/* 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;
@@ -442,64 +481,78 @@ 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++)
-			memcpy(VectorArrayGet(centers, j), VectorArrayGet(newCenters, j), VECTOR_SIZE(dimensions));
+		for (int j = 0; j < numCenters; j++)
+			VectorArraySet(centers, j, VectorArrayGet(newCenters, j));
 
 		if (changes == 0 && iteration != 0)
 			break;
 	}
+}
 
-	pfree(newCenters);
-	pfree(centerCounts);
-	pfree(closestCenters);
-	pfree(lowerBound);
-	pfree(upperBound);
-	pfree(s);
-	pfree(halfcdist);
-	pfree(newcdist);
+/*
+ * Ensure no NaN or infinite values
+ */
+static void
+CheckElements(VectorArray centers, const IvfflatTypeInfo * typeInfo)
+{
+	float	   *scratch = palloc(sizeof(float) * centers->dim);
+
+	for (int i = 0; i < centers->length; i++)
+	{
+		for (int j = 0; j < centers->dim; j++)
+			scratch[j] = 0;
+
+		/* /fp:fast may not propagate NaN with MSVC, but that's alright */
+		typeInfo->sumCenter(VectorArrayGet(centers, i), scratch);
+
+		for (int j = 0; j < centers->dim; j++)
+		{
+			if (isnan(scratch[j]))
+				elog(ERROR, "NaN detected. Please report a bug.");
+
+			if (isinf(scratch[j]))
+				elog(ERROR, "Infinite value detected. Please report a bug.");
+		}
+	}
+}
+
+/*
+ * Ensure no zero vectors for cosine distance
+ */
+static void
+CheckNorms(VectorArray centers, Relation index)
+{
+	/* Check NORM_PROC instead of KMEANS_NORM_PROC */
+	FmgrInfo   *normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
+	Oid			collation = index->rd_indcollation[0];
+
+	if (normprocinfo == NULL)
+		return;
+
+	for (int i = 0; i < centers->length; i++)
+	{
+		double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(VectorArrayGet(centers, i))));
+
+		if (norm == 0)
+			elog(ERROR, "Zero norm detected. Please report a bug.");
+	}
 }
 
 /*
  * Detect issues with centers
  */
 static void
-CheckCenters(Relation index, VectorArray centers)
+CheckCenters(Relation index, VectorArray centers, const IvfflatTypeInfo * typeInfo)
 {
-	FmgrInfo   *normprocinfo;
-	Oid			collation;
-	int			i;
-	double		norm;
-
 	if (centers->length != centers->maxlen)
 		elog(ERROR, "Not enough centers. Please report a bug.");
 
-	/* Ensure no duplicate centers */
-	/* Fine to sort in-place */
-	qsort(centers->items, centers->length, VECTOR_SIZE(centers->dim), CompareVectors);
-	for (i = 1; i < centers->length; i++)
-	{
-		if (CompareVectors(VectorArrayGet(centers, i), VectorArrayGet(centers, i - 1)) == 0)
-			elog(ERROR, "Duplicate centers detected. Please report a bug.");
-	}
-
-	/* Ensure no zero vectors for cosine distance */
-	/* Check NORM_PROC instead of KMEANS_NORM_PROC */
-	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
-	if (normprocinfo != NULL)
-	{
-		collation = index->rd_indcollation[0];
-
-		for (i = 0; i < centers->length; i++)
-		{
-			norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(VectorArrayGet(centers, i))));
-			if (norm == 0)
-				elog(ERROR, "Zero norm detected. Please report a bug.");
-		}
-	}
+	CheckElements(centers, typeInfo);
+	CheckNorms(centers, index);
 }
 
 /*
@@ -507,12 +560,20 @@ 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, const IvfflatTypeInfo * typeInfo)
 {
-	if (samples->length <= centers->maxlen)
-		QuickCenters(index, samples, centers);
-	else
-		ElkanKmeans(index, samples, centers);
+	MemoryContext kmeansCtx = AllocSetContextCreate(CurrentMemoryContext,
+													"Ivfflat kmeans temporary context",
+													ALLOCSET_DEFAULT_SIZES);
+	MemoryContext oldCtx = MemoryContextSwitchTo(kmeansCtx);
 
-	CheckCenters(index, centers);
+	if (samples->length == 0)
+		RandomCenters(index, centers, typeInfo);
+	else
+		ElkanKmeans(index, samples, centers, typeInfo);
+
+	CheckCenters(index, centers, typeInfo);
+
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(kmeansCtx);
 }

src/ivfscan.c

@@ -3,16 +3,16 @@
 #include <float.h>
 
 #include "access/relscan.h"
-#include "ivfflat.h"
-#include "miscadmin.h"
-#include "storage/bufmgr.h"
-
-#if PG_VERSION_NUM >= 110000
 #include "catalog/pg_operator_d.h"
 #include "catalog/pg_type_d.h"
-#else
-#include "catalog/pg_operator.h"
-#include "catalog/pg_type.h"
+#include "lib/pairingheap.h"
+#include "ivfflat.h"
+#include "miscadmin.h"
+#include "pgstat.h"
+#include "storage/bufmgr.h"
+
+#ifdef IVFFLAT_MEMORY
+#include "utils/memutils.h"
 #endif
 
 /*
@@ -36,36 +36,36 @@ CompareLists(const pairingheap_node *a, const pairingheap_node *b, void *arg)
 static void
 GetScanLists(IndexScanDesc scan, Datum value)
 {
-	Buffer		cbuf;
-	Page		cpage;
-	IvfflatList list;
-	OffsetNumber offno;
-	OffsetNumber maxoffno;
+	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 	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));
+			distance = DatumGetFloat8(so->distfunc(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;
@@ -80,6 +80,8 @@ GetScanLists(IndexScanDesc scan, Datum value)
 			}
 			else if (distance < maxDistance)
 			{
+				IvfflatScanList *scanlist;
+
 				/* Remove */
 				scanlist = (IvfflatScanList *) pairingheap_remove_first(so->listQueue);
 
@@ -106,21 +108,9 @@ 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);
-
-#if PG_VERSION_NUM >= 120000
+	double		tuples = 0;
 	TupleTableSlot *slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsVirtual);
-#else
-	TupleTableSlot *slot = MakeSingleTupleTableSlot(so->tupdesc);
-#endif
 
 	/*
 	 * Reuse same set of shared buffers for scan
@@ -132,19 +122,28 @@ 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);
 
 				/*
@@ -154,15 +153,15 @@ GetScanItems(IndexScanDesc scan, Datum value)
 				 * performance
 				 */
 				ExecClearTuple(slot);
-				slot->tts_values[0] = FunctionCall2Coll(so->procinfo, so->collation, datum, value);
+				slot->tts_values[0] = so->distfunc(so->procinfo, so->collation, 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);
+
+				tuples++;
 			}
 
 			searchPage = IvfflatPageGetOpaque(page)->nextblkno;
@@ -171,9 +170,71 @@ GetScanItems(IndexScanDesc scan, Datum value)
 		}
 	}
 
+	FreeAccessStrategy(bas);
+
+	if (tuples < 100)
+		ereport(DEBUG1,
+				(errmsg("index scan found few tuples"),
+				 errdetail("Index may have been created with little data."),
+				 errhint("Recreate the index and possibly decrease lists.")));
+
 	tuplesort_performsort(so->sortstate);
 }
 
+/*
+ * Zero distance
+ */
+static Datum
+ZeroDistance(FmgrInfo *flinfo, Oid collation, Datum arg1, Datum arg2)
+{
+	return Float8GetDatum(0.0);
+}
+
+/*
+ * Get scan value
+ */
+static Datum
+GetScanValue(IndexScanDesc scan)
+{
+	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
+	Datum		value;
+
+	if (scan->orderByData->sk_flags & SK_ISNULL)
+	{
+		value = PointerGetDatum(NULL);
+		so->distfunc = ZeroDistance;
+	}
+	else
+	{
+		value = scan->orderByData->sk_argument;
+		so->distfunc = FunctionCall2Coll;
+
+		/* Value should not be compressed or toasted */
+		Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
+		Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
+
+		/* Normalize if needed */
+		if (so->normprocinfo != NULL)
+			value = IvfflatNormValue(so->typeInfo, so->collation, value);
+	}
+
+	return value;
+}
+
+/*
+ * Initialize scan sort state
+ */
+static Tuplesortstate *
+InitScanSortState(TupleDesc tupdesc)
+{
+	AttrNumber	attNums[] = {1};
+	Oid			sortOperators[] = {Float8LessOperator};
+	Oid			sortCollations[] = {InvalidOid};
+	bool		nullsFirstFlags[] = {false};
+
+	return tuplesort_begin_heap(tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, work_mem, NULL, false);
+}
+
 /*
  * Prepare for an index scan
  */
@@ -183,22 +244,22 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	IndexScanDesc scan;
 	IvfflatScanOpaque so;
 	int			lists;
-	AttrNumber	attNums[] = {1};
-	Oid			sortOperators[] = {Float8LessOperator};
-	Oid			sortCollations[] = {InvalidOid};
-	bool		nullsFirstFlags[] = {false};
+	int			dimensions;
 	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->typeInfo = IvfflatGetTypeInfo(index);
 	so->first = true;
 	so->probes = probes;
+	so->dimensions = dimensions;
 
 	/* Set support functions */
 	so->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
@@ -206,27 +267,14 @@ 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(3);
-#else
-	so->tupdesc = CreateTemplateTupleDesc(3, false);
-#endif
+	so->tupdesc = CreateTemplateTupleDesc(2);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
-	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
-	TupleDescInitEntry(so->tupdesc, (AttrNumber) 3, "indexblkno", INT4OID, -1, 0);
+	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "heaptid", TIDOID, -1, 0);
 
 	/* Prep sort */
-#if PG_VERSION_NUM >= 110000
-	so->sortstate = tuplesort_begin_heap(so->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, work_mem, NULL, false);
-#else
-	so->sortstate = tuplesort_begin_heap(so->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, work_mem, false);
-#endif
+	so->sortstate = InitScanSortState(so->tupdesc);
 
-#if PG_VERSION_NUM >= 120000
 	so->slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsMinimalTuple);
-#else
-	so->slot = MakeSingleTupleTableSlot(so->tupdesc);
-#endif
 
 	so->listQueue = pairingheap_allocate(CompareLists, scan);
 
@@ -243,10 +291,8 @@ ivfflatrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 
-#if PG_VERSION_NUM >= 130000
 	if (!so->first)
 		tuplesort_reset(so->sortstate);
-#endif
 
 	so->first = true;
 	pairingheap_reset(so->listQueue);
@@ -276,58 +322,38 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 	{
 		Datum		value;
 
+		/* Count index scan for stats */
+		pgstat_count_index_scan(scan->indexRelation);
+
 		/* Safety check */
 		if (scan->orderByData == NULL)
 			elog(ERROR, "cannot scan ivfflat index without order");
 
-		/* No items will match if null */
-		if (scan->orderByData->sk_flags & SK_ISNULL)
-			return false;
-
-		value = scan->orderByData->sk_argument;
-
-		if (so->normprocinfo != NULL)
-		{
-			/* No items will match if normalization fails */
-			if (!IvfflatNormValue(so->normprocinfo, so->collation, &value, NULL))
-				return false;
-		}
+		/* Requires MVCC-compliant snapshot as not able to pin during sorting */
+		/* https://www.postgresql.org/docs/current/index-locking.html */
+		if (!IsMVCCSnapshot(scan->xs_snapshot))
+			elog(ERROR, "non-MVCC snapshots are not supported with ivfflat");
 
+		value = GetScanValue(scan);
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
 		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;
 
+#if defined(IVFFLAT_MEMORY)
+		elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
+#endif
+
 		/* Clean up if we allocated a new value */
 		if (value != scan->orderByData->sk_argument)
 			pfree(DatumGetPointer(value));
 	}
 
-#if PG_VERSION_NUM >= 100000
 	if (tuplesort_gettupleslot(so->sortstate, true, false, so->slot, NULL))
-#else
-	if (tuplesort_gettupleslot(so->sortstate, true, so->slot, NULL))
-#endif
 	{
-		ItemPointer tid = (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);
+		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->slot, 2, &so->isnull));
 
+		scan->xs_heaptid = *heaptid;
+		scan->xs_recheck = false;
 		scan->xs_recheckorderby = false;
 		return true;
 	}
@@ -343,10 +369,6 @@ 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

@@ -1,33 +1,41 @@
 #include "postgres.h"
 
+#include "access/generic_xlog.h"
+#include "bitvec.h"
+#include "catalog/pg_type.h"
+#include "fmgr.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "storage/bufmgr.h"
-#include "vector.h"
 
 /*
  * Allocate a vector array
  */
 VectorArray
-VectorArrayInit(int maxlen, int dimensions)
+VectorArrayInit(int maxlen, int dimensions, Size itemsize)
 {
-	VectorArray res = palloc_extended(VECTOR_ARRAY_SIZE(maxlen, dimensions), MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
+	VectorArray res = palloc(sizeof(VectorArrayData));
+
+	/* Ensure items are aligned to prevent UB */
+	itemsize = MAXALIGN(itemsize);
 
 	res->length = 0;
 	res->maxlen = maxlen;
 	res->dim = dimensions;
+	res->itemsize = itemsize;
+	res->items = palloc_extended(maxlen * itemsize, MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
 	return res;
 }
 
 /*
- * Print vector array - useful for debugging
+ * Free a vector array
  */
 void
-PrintVectorArray(char *msg, VectorArray arr)
+VectorArrayFree(VectorArray arr)
 {
-	int			i;
-
-	for (i = 0; i < arr->length; i++)
-		PrintVector(msg, VectorArrayGet(arr, i));
+	pfree(arr->items);
+	pfree(arr);
 }
 
 /*
@@ -48,47 +56,30 @@ 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);
 }
 
 /*
- * Divide by the norm
- *
- * Returns false if value should not be indexed
- *
- * The caller needs to free the pointer stored in value
- * if it's different than the original value
+ * Normalize value
+ */
+Datum
+IvfflatNormValue(const IvfflatTypeInfo * typeInfo, Oid collation, Datum value)
+{
+	return DirectFunctionCall1Coll(typeInfo->normalize, collation, value);
+}
+
+/*
+ * Check if non-zero norm
  */
 bool
-IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result)
+IvfflatCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value)
 {
-	Vector	   *v;
-	int			i;
-	double		norm;
-
-	norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
-
-	if (norm > 0)
-	{
-		v = (Vector *) DatumGetPointer(*value);
-
-		if (result == NULL)
-			result = InitVector(v->dim);
-
-		for (i = 0; i < v->dim; i++)
-			result->x[i] = v->x[i] / norm;
-
-		*value = PointerGetDatum(result);
-
-		return true;
-	}
-
-	return false;
+	return DatumGetFloat8(FunctionCall1Coll(procinfo, collation, value)) > 0;
 }
 
 /*
@@ -131,7 +122,6 @@ IvfflatInitRegisterPage(Relation index, Buffer *buf, Page *page, GenericXLogStat
 void
 IvfflatCommitBuffer(Buffer buf, GenericXLogState *state)
 {
-	MarkBufferDirty(buf);
 	GenericXLogFinish(state);
 	UnlockReleaseBuffer(buf);
 }
@@ -155,8 +145,6 @@ IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **st
 	IvfflatInitPage(newbuf, newpage);
 
 	/* Commit */
-	MarkBufferDirty(*buf);
-	MarkBufferDirty(newbuf);
 	GenericXLogFinish(*state);
 
 	/* Unlock */
@@ -167,16 +155,44 @@ 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);
+
+	if (unlikely(metap->magicNumber != IVFFLAT_MAGIC_NUMBER))
+		elog(ERROR, "ivfflat index is not valid");
+
+	if (lists != NULL)
+		*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;
 
@@ -212,3 +228,146 @@ IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo,
 		UnlockReleaseBuffer(buf);
 	}
 }
+
+PGDLLEXPORT Datum l2_normalize(PG_FUNCTION_ARGS);
+PGDLLEXPORT Datum halfvec_l2_normalize(PG_FUNCTION_ARGS);
+PGDLLEXPORT Datum sparsevec_l2_normalize(PG_FUNCTION_ARGS);
+
+static Size
+VectorItemSize(int dimensions)
+{
+	return VECTOR_SIZE(dimensions);
+}
+
+static Size
+HalfvecItemSize(int dimensions)
+{
+	return HALFVEC_SIZE(dimensions);
+}
+
+static Size
+BitItemSize(int dimensions)
+{
+	return VARBITTOTALLEN(dimensions);
+}
+
+static void
+VectorUpdateCenter(Pointer v, int dimensions, float *x)
+{
+	Vector	   *vec = (Vector *) v;
+
+	SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
+	vec->dim = dimensions;
+
+	for (int k = 0; k < dimensions; k++)
+		vec->x[k] = x[k];
+}
+
+static void
+HalfvecUpdateCenter(Pointer v, int dimensions, float *x)
+{
+	HalfVector *vec = (HalfVector *) v;
+
+	SET_VARSIZE(vec, HALFVEC_SIZE(dimensions));
+	vec->dim = dimensions;
+
+	for (int k = 0; k < dimensions; k++)
+		vec->x[k] = Float4ToHalfUnchecked(x[k]);
+}
+
+static void
+BitUpdateCenter(Pointer v, int dimensions, float *x)
+{
+	VarBit	   *vec = (VarBit *) v;
+	unsigned char *nx = VARBITS(vec);
+
+	SET_VARSIZE(vec, VARBITTOTALLEN(dimensions));
+	VARBITLEN(vec) = dimensions;
+
+	for (uint32 k = 0; k < VARBITBYTES(vec); k++)
+		nx[k] = 0;
+
+	for (int k = 0; k < dimensions; k++)
+		nx[k / 8] |= (x[k] > 0.5 ? 1 : 0) << (7 - (k % 8));
+}
+
+static void
+VectorSumCenter(Pointer v, float *x)
+{
+	Vector	   *vec = (Vector *) v;
+
+	for (int k = 0; k < vec->dim; k++)
+		x[k] += vec->x[k];
+}
+
+static void
+HalfvecSumCenter(Pointer v, float *x)
+{
+	HalfVector *vec = (HalfVector *) v;
+
+	for (int k = 0; k < vec->dim; k++)
+		x[k] += HalfToFloat4(vec->x[k]);
+}
+
+static void
+BitSumCenter(Pointer v, float *x)
+{
+	VarBit	   *vec = (VarBit *) v;
+
+	for (int k = 0; k < VARBITLEN(vec); k++)
+		x[k] += (float) (((VARBITS(vec)[k / 8]) >> (7 - (k % 8))) & 0x01);
+}
+
+/*
+ * Get type info
+ */
+const		IvfflatTypeInfo *
+IvfflatGetTypeInfo(Relation index)
+{
+	FmgrInfo   *procinfo = IvfflatOptionalProcInfo(index, IVFFLAT_TYPE_INFO_PROC);
+
+	if (procinfo == NULL)
+	{
+		static const IvfflatTypeInfo typeInfo = {
+			.maxDimensions = IVFFLAT_MAX_DIM,
+			.normalize = l2_normalize,
+			.itemSize = VectorItemSize,
+			.updateCenter = VectorUpdateCenter,
+			.sumCenter = VectorSumCenter
+		};
+
+		return (&typeInfo);
+	}
+	else
+		return (const IvfflatTypeInfo *) DatumGetPointer(FunctionCall0Coll(procinfo, InvalidOid));
+}
+
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(ivfflat_halfvec_support);
+Datum
+ivfflat_halfvec_support(PG_FUNCTION_ARGS)
+{
+	static const IvfflatTypeInfo typeInfo = {
+		.maxDimensions = IVFFLAT_MAX_DIM * 2,
+		.normalize = halfvec_l2_normalize,
+		.itemSize = HalfvecItemSize,
+		.updateCenter = HalfvecUpdateCenter,
+		.sumCenter = HalfvecSumCenter
+	};
+
+	PG_RETURN_POINTER(&typeInfo);
+};
+
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(ivfflat_bit_support);
+Datum
+ivfflat_bit_support(PG_FUNCTION_ARGS)
+{
+	static const IvfflatTypeInfo typeInfo = {
+		.maxDimensions = IVFFLAT_MAX_DIM * 32,
+		.normalize = NULL,
+		.itemSize = BitItemSize,
+		.updateCenter = BitUpdateCenter,
+		.sumCenter = BitSumCenter
+	};
+
+	PG_RETURN_POINTER(&typeInfo);
+};

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;
-	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;
+	BlockNumber blkno = IVFFLAT_HEAD_BLKNO;
 	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;
-		nextblkno = IvfflatPageGetOpaque(cpage)->nextblkno;
+		listInfo.blkno = blkno;
+		blkno = IvfflatPageGetOpaque(cpage)->nextblkno;
 
 		UnlockReleaseBuffer(cbuf);
 
 		for (coffno = FirstOffsetNumber; coffno <= cmaxoffno; coffno = OffsetNumberNext(coffno))
 		{
-			searchPage = startPages[coffno - FirstOffsetNumber];
-			insertPage = InvalidBlockNumber;
+			BlockNumber searchPage = startPages[coffno - FirstOffsetNumber];
+			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));
-					htup = &(itup->t_tid);
+					IndexTuple	itup = (IndexTuple) PageGetItem(page, PageGetItemId(page, offno));
+					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
@@ -127,11 +125,13 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 			if (BlockNumberIsValid(insertPage))
 			{
 				listInfo.offno = coffno;
-				IvfflatUpdateList(index, state, listInfo, insertPage, InvalidBlockNumber, InvalidBlockNumber, MAIN_FORKNUM);
+				IvfflatUpdateList(index, listInfo, insertPage, InvalidBlockNumber, InvalidBlockNumber, MAIN_FORKNUM);
 			}
 		}
 	}
 
+	FreeAccessStrategy(bas);
+
 	return stats;
 }
 
@@ -143,6 +143,11 @@ ivfflatvacuumcleanup(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;
 

src/sparsevec.h

@@ -0,0 +1,40 @@
+#ifndef SPARSEVEC_H
+#define SPARSEVEC_H
+
+#define SPARSEVEC_MAX_DIM 1000000000
+#define SPARSEVEC_MAX_NNZ 16000
+
+#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)
+
+/*
+ * Indices use 0-based numbering for the on-disk (and binary) format (consistent with C)
+ * and are always sorted. Values come after indices.
+ */
+typedef struct SparseVector
+{
+	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int32		dim;			/* number of dimensions */
+	int32		nnz;			/* number of non-zero elements */
+	int32		unused;			/* reserved for future use, always zero */
+	int32		indices[FLEXIBLE_ARRAY_MEMBER];
+}			SparseVector;
+
+/* Use functions instead of macros to avoid double evaluation */
+
+static inline Size
+SPARSEVEC_SIZE(int nnz)
+{
+	return offsetof(SparseVector, indices) + (nnz * sizeof(int32)) + (nnz * sizeof(float));
+}
+
+static inline float *
+SPARSEVEC_VALUES(SparseVector * x)
+{
+	return (float *) (((char *) x) + offsetof(SparseVector, indices) + (x->nnz * sizeof(int32)));
+}
+
+SparseVector *InitSparseVector(int dim, int nnz);
+
+#endif

src/vector.h

@@ -1,9 +1,7 @@
 #ifndef VECTOR_H
 #define VECTOR_H
 
-#include "postgres.h"
-
-#define VECTOR_MAX_DIM 1024
+#define VECTOR_MAX_DIM 16000
 
 #define VECTOR_SIZE(_dim)		(offsetof(Vector, x) + sizeof(float)*(_dim))
 #define DatumGetVector(x)		((Vector *) PG_DETOAST_DATUM(x))
@@ -14,28 +12,19 @@ typedef struct Vector
 {
 	int32		vl_len_;		/* varlena header (do not touch directly!) */
 	int16		dim;			/* number of dimensions */
-	int16		unused;
+	int16		unused;			/* reserved for future use, always zero */
 	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;
-}
+/* TODO Move to better place */
+#if PG_VERSION_NUM >= 160000
+#define FUNCTION_PREFIX
+#else
+#define FUNCTION_PREFIX PGDLLEXPORT
+#endif
 
 #endif

test/expected/bit.out

@@ -0,0 +1,140 @@
+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('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
+ hamming_distance 
+------------------
+                0
+(1 row)
+
+SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
+ hamming_distance 
+------------------
+              513
+(1 row)
+
+SELECT hamming_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
+ hamming_distance 
+------------------
+                2
+(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('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
+ jaccard_distance 
+------------------
+                0
+(1 row)
+
+SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
+ jaccard_distance 
+------------------
+              0.5
+(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/btree.out

@@ -1,6 +1,5 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
 SET enable_seqscan = off;
+-- vector
 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 (val);
@@ -10,10 +9,53 @@ SELECT * FROM t WHERE val = '[1,2,3]';
  [1,2,3]
 (1 row)
 
-SELECT * FROM t ORDER BY val LIMIT 1;
+SELECT * FROM t ORDER BY val;
    val   
 ---------
  [0,0,0]
-(1 row)
+ [1,1,1]
+ [1,2,3]
+ 
+(4 rows)
+
+DROP TABLE t;
+-- halfvec
+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 (val);
+SELECT * FROM t WHERE val = '[1,2,3]';
+   val   
+---------
+ [1,2,3]
+(1 row)
+
+SELECT * FROM t ORDER BY val;
+   val   
+---------
+ [0,0,0]
+ [1,1,1]
+ [1,2,3]
+ 
+(4 rows)
+
+DROP TABLE t;
+-- sparsevec
+CREATE TABLE t (val sparsevec(3));
+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 (val);
+SELECT * FROM t WHERE val = '{1:1,2:2,3:3}/3';
+       val       
+-----------------
+ {1:1,2:2,3:3}/3
+(1 row)
+
+SELECT * FROM t ORDER BY val;
+       val       
+-----------------
+ {}/3
+ {1:1,2:1,3:1}/3
+ {1:1,2:2,3:3}/3
+ 
+(4 rows)
 
 DROP TABLE t;

test/expected/cast.out

@@ -1,5 +1,3 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
 SELECT ARRAY[1,2,3]::vector;
   array  
 ---------
@@ -24,8 +22,34 @@ SELECT ARRAY[1,2,3]::float8[]::vector;
  [1,2,3]
 (1 row)
 
+SELECT ARRAY[1,2,3]::numeric[]::vector;
+  array  
+---------
+ [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;
@@ -34,14 +58,216 @@ 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[];
- float4  
+SELECT '{{1}}'::real[]::vector;
+ERROR:  array must be 1-D
+SELECT '{1,2,3}'::double precision[]::vector;
+ vector  
 ---------
- {1,2,3}
+ [1,2,3]
 (1 row)
 
-SELECT array_agg(n)::vector FROM generate_series(1, 1025) n;
-ERROR:  vector cannot have more than 1024 dimensions
+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 '[0,1.5,0,3.5,0]'::halfvec::sparsevec;
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec(5);
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec;
+     halfvec     
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec(5);
+     halfvec     
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{}/16001'::sparsevec::halfvec;
+ERROR:  halfvec cannot have more than 16000 dimensions
+SELECT '{1:65520}/1'::sparsevec::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '{1:1e-8}/1'::sparsevec::halfvec;
+ halfvec 
+---------
+ [0]
+(1 row)
+
+SELECT ARRAY[1,0,2,0,3,0]::sparsevec;
+      array      
+-----------------
+ {1:1,3:2,5:3}/6
+(1 row)
+
+SELECT ARRAY[1.0,0.0,2.0,0.0,3.0,0.0]::sparsevec;
+      array      
+-----------------
+ {1:1,3:2,5:3}/6
+(1 row)
+
+SELECT ARRAY[1,0,2,0,3,0]::float4[]::sparsevec;
+      array      
+-----------------
+ {1:1,3:2,5:3}/6
+(1 row)
+
+SELECT ARRAY[1,0,2,0,3,0]::float8[]::sparsevec;
+      array      
+-----------------
+ {1:1,3:2,5:3}/6
+(1 row)
+
+SELECT ARRAY[1,0,2,0,3,0]::numeric[]::sparsevec;
+      array      
+-----------------
+ {1:1,3:2,5:3}/6
+(1 row)
+
+SELECT '{1,0,2,0,3,0}'::real[]::sparsevec;
+    sparsevec    
+-----------------
+ {1:1,3:2,5:3}/6
+(1 row)
+
+SELECT '{1,0,2,0,3,0}'::real[]::sparsevec(6);
+    sparsevec    
+-----------------
+ {1:1,3:2,5:3}/6
+(1 row)
+
+SELECT '{1,0,2,0,3,0}'::real[]::sparsevec(5);
+ERROR:  expected 5 dimensions, not 6
+SELECT '{NULL}'::real[]::sparsevec;
+ERROR:  array must not contain nulls
+SELECT '{NaN}'::real[]::sparsevec;
+ERROR:  NaN not allowed in sparsevec
+SELECT '{Infinity}'::real[]::sparsevec;
+ERROR:  infinite value not allowed in sparsevec
+SELECT '{-Infinity}'::real[]::sparsevec;
+ERROR:  infinite value not allowed in sparsevec
+SELECT '{}'::real[]::sparsevec;
+ERROR:  sparsevec must have at least 1 dimension
+SELECT '{{1}}'::real[]::sparsevec;
+ERROR:  array must be 1-D
+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;
+ERROR:  vector cannot have more than 16000 dimensions
 -- ensure no error
 SELECT ARRAY[1,2,3] = ARRAY[1,2,3];
  ?column? 

test/expected/copy.out

@@ -1,10 +1,9 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
+-- vector
 CREATE TABLE t (val vector(3));
 INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
 CREATE TABLE t2 (val vector(3));
-\copy t TO '/tmp/data.bin' WITH (FORMAT binary)
-\copy t2 FROM '/tmp/data.bin' WITH (FORMAT binary)
+\copy t TO 'results/vector.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/vector.bin' WITH (FORMAT binary)
 SELECT * FROM t2 ORDER BY val;
    val   
 ---------
@@ -16,3 +15,37 @@ SELECT * FROM t2 ORDER BY val;
 
 DROP TABLE t;
 DROP TABLE t2;
+-- halfvec
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE TABLE t2 (val halfvec(3));
+\copy t TO 'results/halfvec.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/halfvec.bin' WITH (FORMAT binary)
+SELECT * FROM t2 ORDER BY val;
+   val   
+---------
+ [0,0,0]
+ [1,1,1]
+ [1,2,3]
+ 
+(4 rows)
+
+DROP TABLE t;
+DROP TABLE t2;
+-- sparsevec
+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 TABLE t2 (val sparsevec(3));
+\copy t TO 'results/sparsevec.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/sparsevec.bin' WITH (FORMAT binary)
+SELECT * FROM t2 ORDER BY val;
+       val       
+-----------------
+ {}/3
+ {1:1,2:1,3:1}/3
+ {1:1,2:2,3:3}/3
+ 
+(4 rows)
+
+DROP TABLE t;
+DROP TABLE t2;

test/expected/functions.out

@@ -1,56 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-SELECT '[1,2,3]'::vector + '[4,5,6]';
- ?column? 
-----------
- [5,7,9]
-(1 row)
-
-SELECT '[1,2,3]'::vector - '[4,5,6]';
-  ?column?  
-------------
- [-3,-3,-3]
-(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 round(l2_distance('[1,2]', '[0,0]')::numeric, 5);
-  round  
----------
- 2.23607
-(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 round(cosine_distance('[1,2]', '[2,4]')::numeric, 5);
-  round  
----------
- 0.00000
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[0,0]');
- cosine_distance 
------------------
-             NaN
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1

test/expected/halfvec.out

@@ -0,0 +1,636 @@
+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
+SELECT '[1,2,3]'::halfvec + '[4,5,6]';
+ ?column? 
+----------
+ [5,7,9]
+(1 row)
+
+SELECT '[65519]'::halfvec + '[65519]';
+ERROR:  value out of range: overflow
+SELECT '[1,2]'::halfvec + '[3]';
+ERROR:  different halfvec dimensions 2 and 1
+SELECT '[1,2,3]'::halfvec - '[4,5,6]';
+  ?column?  
+------------
+ [-3,-3,-3]
+(1 row)
+
+SELECT '[-65519]'::halfvec - '[65519]';
+ERROR:  value out of range: overflow
+SELECT '[1,2]'::halfvec - '[3]';
+ERROR:  different halfvec dimensions 2 and 1
+SELECT '[1,2,3]'::halfvec * '[4,5,6]';
+ ?column?  
+-----------
+ [4,10,18]
+(1 row)
+
+SELECT '[65519]'::halfvec * '[65519]';
+ERROR:  value out of range: overflow
+SELECT '[1e-7]'::halfvec * '[1e-7]';
+ERROR:  value out of range: underflow
+SELECT '[1,2]'::halfvec * '[3]';
+ERROR:  different halfvec dimensions 2 and 1
+SELECT '[1,2,3]'::halfvec || '[4,5]';
+  ?column?   
+-------------
+ [1,2,3,4,5]
+(1 row)
+
+SELECT array_fill(0, ARRAY[16000])::halfvec || '[1]';
+ERROR:  halfvec cannot have more than 16000 dimensions
+SELECT '[1,2,3]'::halfvec < '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec < '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec <= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec <= '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec = '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec = '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec != '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec != '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec >= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec >= '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::halfvec > '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::halfvec > '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT halfvec_cmp('[1,2,3]', '[1,2,3]');
+ halfvec_cmp 
+-------------
+           0
+(1 row)
+
+SELECT halfvec_cmp('[1,2,3]', '[0,0,0]');
+ halfvec_cmp 
+-------------
+           1
+(1 row)
+
+SELECT halfvec_cmp('[0,0,0]', '[1,2,3]');
+ halfvec_cmp 
+-------------
+          -1
+(1 row)
+
+SELECT halfvec_cmp('[1,2]', '[1,2,3]');
+ halfvec_cmp 
+-------------
+          -1
+(1 row)
+
+SELECT halfvec_cmp('[1,2,3]', '[1,2]');
+ halfvec_cmp 
+-------------
+           1
+(1 row)
+
+SELECT halfvec_cmp('[1,2]', '[2,3,4]');
+ halfvec_cmp 
+-------------
+          -1
+(1 row)
+
+SELECT halfvec_cmp('[2,3]', '[1,2,3]');
+ halfvec_cmp 
+-------------
+           1
+(1 row)
+
+SELECT vector_dims('[1,2,3]'::halfvec);
+ vector_dims 
+-------------
+           3
+(1 row)
+
+SELECT round(l2_norm('[1,1]'::halfvec)::numeric, 5);
+  round  
+---------
+ 1.41421
+(1 row)
+
+SELECT l2_norm('[3,4]'::halfvec);
+ l2_norm 
+---------
+       5
+(1 row)
+
+SELECT l2_norm('[0,1]'::halfvec);
+ l2_norm 
+---------
+       1
+(1 row)
+
+SELECT l2_norm('[0,0]'::halfvec);
+ l2_norm 
+---------
+       0
+(1 row)
+
+SELECT l2_norm('[2]'::halfvec);
+ l2_norm 
+---------
+       2
+(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 cosine_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
+ 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 l1_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+ l1_distance 
+-------------
+           0
+(1 row)
+
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[0,3,2,5,4,7,6,9,8]');
+ l1_distance 
+-------------
+           9
+(1 row)
+
+SELECT '[0,0]'::halfvec <+> '[3,4]';
+ ?column? 
+----------
+        7
+(1 row)
+
+SELECT l2_normalize('[3,4]'::halfvec);
+      l2_normalize      
+------------------------
+ [0.60009766,0.7998047]
+(1 row)
+
+SELECT l2_normalize('[3,0]'::halfvec);
+ l2_normalize 
+--------------
+ [1,0]
+(1 row)
+
+SELECT l2_normalize('[0,0.1]'::halfvec);
+ l2_normalize 
+--------------
+ [0,1]
+(1 row)
+
+SELECT l2_normalize('[0,0]'::halfvec);
+ l2_normalize 
+--------------
+ [0,0]
+(1 row)
+
+SELECT l2_normalize('[65504]'::halfvec);
+ l2_normalize 
+--------------
+ [1]
+(1 row)
+
+SELECT binary_quantize('[1,0,-1]'::halfvec);
+ binary_quantize 
+-----------------
+ 100
+(1 row)
+
+SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::halfvec);
+ binary_quantize 
+-----------------
+ 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
+SELECT subvector('[1,2,3,4,5]'::halfvec, 2147483647, 10);
+ERROR:  halfvec must have at least 1 dimension
+SELECT subvector('[1,2,3,4,5]'::halfvec, 3, 2147483647);
+ subvector 
+-----------
+ [3,4,5]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::halfvec, -2147483644, 2147483647);
+ subvector 
+-----------
+ [1,2]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]']) v;
+    avg    
+-----------
+ [2,3.5,5]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]', NULL]) v;
+    avg    
+-----------
+ [2,3.5,5]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY[]::halfvec[]) v;
+ avg 
+-----
+ 
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2]'::halfvec, '[3]']) v;
+ERROR:  expected 2 dimensions, not 1
+SELECT avg(v) FROM unnest(ARRAY['[65504]'::halfvec, '[65504]']) v;
+   avg   
+---------
+ [65504]
+(1 row)
+
+SELECT halfvec_avg(array_agg(n)) FROM generate_series(1, 16002) n;
+ERROR:  halfvec cannot have more than 16000 dimensions
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]']) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]', NULL]) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY[]::halfvec[]) v;
+ sum 
+-----
+ 
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::halfvec, '[3]']) v;
+ERROR:  different halfvec dimensions 2 and 1
+SELECT sum(v) FROM unnest(ARRAY['[65504]'::halfvec, '[65504]']) v;
+ERROR:  value out of range: overflow

test/expected/hnsw_bit.out

@@ -0,0 +1,51 @@
+SET enable_seqscan = off;
+-- hamming
+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;
+-- jaccard
+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;
+-- varbit
+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_halfvec.out

@@ -0,0 +1,102 @@
+SET enable_seqscan = off;
+-- L2
+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;
+-- inner product
+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;
+-- cosine
+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;
+-- L1
+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_l1_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <+> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::halfvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_sparsevec.out

@@ -0,0 +1,112 @@
+SET enable_seqscan = off;
+-- L2
+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;
+-- inner product
+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;
+-- cosine
+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;
+-- L1
+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_l1_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)
+
+DROP TABLE t;
+-- non-zero elements
+CREATE TABLE t (val sparsevec(1001));
+INSERT INTO t (val) VALUES (array_fill(1, ARRAY[1001])::vector::sparsevec);
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+ERROR:  sparsevec cannot have more than 1000 non-zero elements for hnsw index
+TRUNCATE t;
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+INSERT INTO t (val) VALUES (array_fill(1, ARRAY[1001])::vector::sparsevec);
+ERROR:  sparsevec cannot have more than 1000 non-zero elements for hnsw index
+DROP TABLE t;

test/expected/hnsw_vector.out

@@ -0,0 +1,142 @@
+SET enable_seqscan = off;
+-- L2
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT 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;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+ val 
+-----
+(0 rows)
+
+DROP TABLE t;
+-- inner product
+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;
+-- cosine
+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;
+-- L1
+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_l1_ops);
+INSERT INTO t (val) VALUES ('[1,2,4]');
+SELECT * FROM t ORDER BY val <+> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,2,4]
+ [1,1,1]
+ [0,0,0]
+(4 rows)
+
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::vector)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;
+-- unlogged
+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;
+-- options
+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/input.out

@@ -1,64 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-SELECT '[1,2,3]'::vector;
- vector  
----------
- [1,2,3]
-(1 row)
-
-SELECT '[-1,2,3]'::vector;
-  vector  
-----------
- [-1,2,3]
-(1 row)
-
-SELECT '[hello,1]'::vector;
-ERROR:  invalid input syntax for type vector: "hello"
-LINE 1: SELECT '[hello,1]'::vector;
-               ^
-SELECT '[NaN,1]'::vector;
-ERROR:  NaN not allowed in vector
-LINE 1: SELECT '[NaN,1]'::vector;
-               ^
-SELECT '[Infinity,1]'::vector;
-ERROR:  infinite value not allowed in vector
-LINE 1: SELECT '[Infinity,1]'::vector;
-               ^
-SELECT '[-Infinity,1]'::vector;
-ERROR:  infinite value not allowed in vector
-LINE 1: SELECT '[-Infinity,1]'::vector;
-               ^
-SELECT '[1,2,3'::vector;
-ERROR:  malformed vector literal
-LINE 1: SELECT '[1,2,3'::vector;
-               ^
-DETAIL:  Unexpected end of input.
-SELECT '[1,2,3]9'::vector;
-ERROR:  malformed vector literal
-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"
-LINE 1: SELECT '1,2,3'::vector;
-               ^
-DETAIL:  Vector contents must start with "[".
-SELECT '[]'::vector;
-ERROR:  vector must have at least 1 dimension
-LINE 1: SELECT '[]'::vector;
-               ^
-SELECT '[1,]'::vector;
-ERROR:  invalid input syntax for type vector: "]"
-LINE 1: SELECT '[1,]'::vector;
-               ^
-SELECT '[1,2,3]'::vector(2);
-ERROR:  expected 2 dimensions, not 3
-SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
- unnest  
----------
- [1,2,3]
- [4,5,6]
-(2 rows)
-
-SELECT '{"[1,2,3]"}'::vector(2)[];
-ERROR:  expected 2 dimensions, not 3

test/expected/ivfflat_bit.out

@@ -0,0 +1,37 @@
+SET enable_seqscan = off;
+-- hamming
+CREATE TABLE t (val bit(3));
+INSERT INTO t (val) VALUES (B'000'), (B'100'), (B'111'), (NULL);
+CREATE INDEX ON t USING ivfflat (val bit_hamming_ops) WITH (lists = 1);
+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;
+-- varbit
+CREATE TABLE t (val varbit(3));
+CREATE INDEX ON t USING ivfflat (val bit_hamming_ops) WITH (lists = 1);
+ERROR:  type not supported for ivfflat index
+CREATE INDEX ON t USING ivfflat ((val::bit(3)) bit_hamming_ops) WITH (lists = 1);
+NOTICE:  ivfflat index created with little data
+DETAIL:  This will cause low recall.
+HINT:  Drop the index until the table has more data.
+CREATE INDEX ON t USING ivfflat ((val::bit(64001)) bit_hamming_ops) WITH (lists = 1);
+ERROR:  column cannot have more than 64000 dimensions for ivfflat index
+CREATE INDEX ON t USING ivfflat ((val::bit(2)) bit_hamming_ops) WITH (lists = 5);
+NOTICE:  ivfflat index created with little data
+DETAIL:  This will cause low recall.
+HINT:  Drop the index until the table has more data.
+DROP TABLE t;

test/expected/ivfflat_cosine.out

@@ -1,21 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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_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 * FROM t ORDER BY val <=> (SELECT NULL::vector);
- val 
------
-(0 rows)
-
-DROP TABLE t;

test/expected/ivfflat_halfvec.out

@@ -0,0 +1,84 @@
+SET enable_seqscan = off;
+-- L2
+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;
+-- inner product
+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;
+-- cosine
+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_ip.out

@@ -1,22 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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_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 * FROM t ORDER BY val <#> (SELECT NULL::vector);
- val 
------
-(0 rows)
-
-DROP TABLE t;

test/expected/ivfflat_l2.out

@@ -1,28 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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);
-INSERT INTO t (val) VALUES ('[1,2,4]');
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-   val   
----------
- [1,2,3]
- [1,2,4]
- [1,1,1]
- [0,0,0]
-(4 rows)
-
-SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
- val 
------
-(0 rows)
-
-SELECT COUNT(*) FROM t;
- count 
--------
-     5
-(1 row)
-
-DROP TABLE t;

test/expected/ivfflat_options.out

@@ -1,17 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-SET enable_seqscan = off;
-CREATE TABLE t (val vector(3));
-CREATE INDEX ON t USING ivfflat (val) 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);
-ERROR:  value 32769 out of bounds for option "lists"
-DETAIL:  Valid values are between "1" and "32768".
-SHOW ivfflat.probes;
- ivfflat.probes 
-----------------
- 1
-(1 row)
-
-DROP TABLE t;

test/expected/ivfflat_unlogged.out

@@ -1,15 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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);
-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/ivfflat_vector.out

@@ -0,0 +1,112 @@
+SET enable_seqscan = off;
+-- L2
+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;
+-- inner product
+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_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::vector)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;
+-- cosine
+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_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::vector)) t2;
+ count 
+-------
+     3
+(1 row)
+
+DROP TABLE t;
+-- unlogged
+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 vector_l2_ops) WITH (lists = 1);
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+DROP TABLE t;
+-- options
+CREATE TABLE t (val vector(3));
+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 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;
+ ivfflat.probes 
+----------------
+ 1
+(1 row)
+
+DROP TABLE t;

test/expected/sparsevec.out

@@ -0,0 +1,653 @@
+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;
+  sparsevec  
+-------------
+ {1:1,2:1}/2
+(1 row)
+
+SELECT '{1:1,1:1}/2'::sparsevec;
+ERROR:  sparsevec indices must not contain duplicates
+LINE 1: SELECT '{1:1,1:1}/2'::sparsevec;
+               ^
+SELECT '{1:1,2:1,1:1}/2'::sparsevec;
+ERROR:  sparsevec indices must not contain duplicates
+LINE 1: SELECT '{1:1,2:1,1:1}/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 '{}/1000000001'::sparsevec;
+ERROR:  sparsevec cannot have more than 1000000000 dimensions
+LINE 1: SELECT '{}/1000000001'::sparsevec;
+               ^
+SELECT '{}/2147483648'::sparsevec;
+ERROR:  sparsevec cannot have more than 1000000000 dimensions
+LINE 1: SELECT '{}/2147483648'::sparsevec;
+               ^
+SELECT '{}/-2147483649'::sparsevec;
+ERROR:  sparsevec must have at least 1 dimension
+LINE 1: SELECT '{}/-2147483649'::sparsevec;
+               ^
+SELECT '{}/9223372036854775808'::sparsevec;
+ERROR:  sparsevec cannot have more than 1000000000 dimensions
+LINE 1: SELECT '{}/9223372036854775808'::sparsevec;
+               ^
+SELECT '{}/-9223372036854775809'::sparsevec;
+ERROR:  sparsevec must have at least 1 dimension
+LINE 1: SELECT '{}/-9223372036854775809'::sparsevec;
+               ^
+SELECT '{2147483647:1}/1'::sparsevec;
+ERROR:  sparsevec index out of bounds
+LINE 1: SELECT '{2147483647:1}/1'::sparsevec;
+               ^
+SELECT '{2147483648:1}/1'::sparsevec;
+ERROR:  sparsevec index out of bounds
+LINE 1: SELECT '{2147483648:1}/1'::sparsevec;
+               ^
+SELECT '{-2147483648:1}/1'::sparsevec;
+ERROR:  sparsevec index out of bounds
+LINE 1: SELECT '{-2147483648:1}/1'::sparsevec;
+               ^
+SELECT '{-2147483649:1}/1'::sparsevec;
+ERROR:  sparsevec index out of bounds
+LINE 1: SELECT '{-2147483649:1}/1'::sparsevec;
+               ^
+SELECT '{0:1}/1'::sparsevec;
+ERROR:  sparsevec index out of bounds
+LINE 1: SELECT '{0:1}/1'::sparsevec;
+               ^
+SELECT '{2:1}/1'::sparsevec;
+ERROR:  sparsevec index out of bounds
+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(1000000001);
+ERROR:  dimensions for type sparsevec cannot exceed 1000000000
+LINE 1: SELECT '{}/3'::sparsevec(1000000001);
+                       ^
+SELECT '{1:1,2:2,3:3}/3'::sparsevec < '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec < '{1:1,2:2}/2';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec <= '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec <= '{1:1,2:2}/2';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec = '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec = '{1:1,2:2}/2';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec != '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec != '{1:1,2:2}/2';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec >= '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec >= '{1:1,2:2}/2';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec > '{1:1,2:2,3:3}/3';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec > '{1:1,2:2}/2';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{1:1,2:2,3:3}/3');
+ sparsevec_cmp 
+---------------
+             0
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{}/3');
+ sparsevec_cmp 
+---------------
+             1
+(1 row)
+
+SELECT sparsevec_cmp('{}/3', '{1:1,2:2,3:3}/3');
+ sparsevec_cmp 
+---------------
+            -1
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2}/2', '{1:1,2:2,3:3}/3');
+ sparsevec_cmp 
+---------------
+            -1
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{1:1,2:2}/2');
+ sparsevec_cmp 
+---------------
+             1
+(1 row)
+
+SELECT sparsevec_cmp('{1:1,2:2}/2', '{1:2,2:3,3:4}/3');
+ sparsevec_cmp 
+---------------
+            -1
+(1 row)
+
+SELECT sparsevec_cmp('{1:2,2:3}/2', '{1:1,2:2,3:3}/3');
+ sparsevec_cmp 
+---------------
+             1
+(1 row)
+
+SELECT round(l2_norm('{1:1,2:1}/2'::sparsevec)::numeric, 5);
+  round  
+---------
+ 1.41421
+(1 row)
+
+SELECT l2_norm('{1:3,2:4}/2'::sparsevec);
+ l2_norm 
+---------
+       5
+(1 row)
+
+SELECT l2_norm('{2:1}/2'::sparsevec);
+ l2_norm 
+---------
+       1
+(1 row)
+
+SELECT l2_norm('{1:3e37,2:4e37}/2'::sparsevec)::real;
+ l2_norm 
+---------
+   5e+37
+(1 row)
+
+SELECT l2_norm('{}/2'::sparsevec);
+ l2_norm 
+---------
+       0
+(1 row)
+
+SELECT l2_norm('{1:2}/1'::sparsevec);
+ l2_norm 
+---------
+       2
+(1 row)
+
+SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('{1:3}/2'::sparsevec, '{2:4}/2');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('{2:4}/2'::sparsevec, '{1:3}/2');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('{1:3,2:4}/2'::sparsevec, '{}/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 inner_product('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+ERROR:  different sparsevec dimensions 2 and 1
+SELECT inner_product('{1:1,3:3}/4'::sparsevec, '{2:2,4:4}/4');
+ inner_product 
+---------------
+             0
+(1 row)
+
+SELECT inner_product('{2:2,4:4}/4'::sparsevec, '{1:1,3:3}/4');
+ inner_product 
+---------------
+             0
+(1 row)
+
+SELECT inner_product('{1:1,3:3,5:5}/5'::sparsevec, '{2:4,3:6,4:8}/5');
+ inner_product 
+---------------
+            18
+(1 row)
+
+SELECT inner_product('{1:1}/2'::sparsevec, '{}/2');
+ inner_product 
+---------------
+             0
+(1 row)
+
+SELECT inner_product('{}/2'::sparsevec, '{1:1}/2');
+ inner_product 
+---------------
+             0
+(1 row)
+
+SELECT inner_product('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
+ inner_product 
+---------------
+      Infinity
+(1 row)
+
+SELECT inner_product('{1:1,3:3,5:5}/5'::sparsevec, '{2:4,3:6,4:8}/5');
+ inner_product 
+---------------
+            18
+(1 row)
+
+SELECT '{1:1,2:2}/2'::sparsevec <#> '{1:3,2:4}/2';
+ ?column? 
+----------
+      -11
+(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 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('{1:1}/2'::sparsevec, '{2:2}/2');
+ cosine_distance 
+-----------------
+               1
+(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('{2:2}/2'::sparsevec, '{1:2}/2');
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+ERROR:  different sparsevec dimensions 2 and 1
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:1.1,2:1.1}/2');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1.1,2:-1.1}/2');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('{}/1'::sparsevec, '{}/1');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT '{1:1,2:2}/2'::sparsevec <=> '{1:2,2:4}/2';
+ ?column? 
+----------
+        0
+(1 row)
+
+SELECT l1_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('{}/2'::sparsevec, '{2:1}/2');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+ERROR:  different sparsevec dimensions 2 and 1
+SELECT l1_distance('{1:3e38}/1'::sparsevec, '{1:-3e38}/1');
+ l1_distance 
+-------------
+    Infinity
+(1 row)
+
+SELECT l1_distance('{1:1,3:3,5:5,7:7}/8'::sparsevec, '{2:2,4:4,6:6,8:8}/8');
+ l1_distance 
+-------------
+          36
+(1 row)
+
+SELECT l1_distance('{1:1,3:3,5:5,7:7,9:9}/9'::sparsevec, '{2:2,4:4,6:6,8:8}/9');
+ l1_distance 
+-------------
+          45
+(1 row)
+
+SELECT '{}/2'::sparsevec <+> '{1:3,2:4}/2';
+ ?column? 
+----------
+        7
+(1 row)
+
+SELECT l2_normalize('{1:3,2:4}/2'::sparsevec);
+  l2_normalize   
+-----------------
+ {1:0.6,2:0.8}/2
+(1 row)
+
+SELECT l2_normalize('{1:3}/2'::sparsevec);
+ l2_normalize 
+--------------
+ {1:1}/2
+(1 row)
+
+SELECT l2_normalize('{2:0.1}/2'::sparsevec);
+ l2_normalize 
+--------------
+ {2:1}/2
+(1 row)
+
+SELECT l2_normalize('{}/2'::sparsevec);
+ l2_normalize 
+--------------
+ {}/2
+(1 row)
+
+SELECT l2_normalize('{1:3e38}/1'::sparsevec);
+ l2_normalize 
+--------------
+ {1:1}/1
+(1 row)
+
+SELECT l2_normalize('{1:3e38,2:1e-37}/2'::sparsevec);
+ l2_normalize 
+--------------
+ {1:1}/2
+(1 row)
+
+SELECT l2_normalize('{2:3e37,4:3e-37,6:4e37,8:4e-37}/9'::sparsevec);
+  l2_normalize   
+-----------------
+ {2:0.6,6:0.8}/9
+(1 row)
+

test/expected/vector_type.out

@@ -0,0 +1,672 @@
+SELECT '[1,2,3]'::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[-1,-2,-3]'::vector;
+   vector   
+------------
+ [-1,-2,-3]
+(1 row)
+
+SELECT '[1.,2.,3.]'::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT ' [ 1,  2 ,    3  ] '::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1.23456]'::vector;
+  vector   
+-----------
+ [1.23456]
+(1 row)
+
+SELECT '[hello,1]'::vector;
+ERROR:  invalid input syntax for type vector: "[hello,1]"
+LINE 1: SELECT '[hello,1]'::vector;
+               ^
+SELECT '[NaN,1]'::vector;
+ERROR:  NaN not allowed in vector
+LINE 1: SELECT '[NaN,1]'::vector;
+               ^
+SELECT '[Infinity,1]'::vector;
+ERROR:  infinite value not allowed in vector
+LINE 1: SELECT '[Infinity,1]'::vector;
+               ^
+SELECT '[-Infinity,1]'::vector;
+ERROR:  infinite value not allowed in vector
+LINE 1: SELECT '[-Infinity,1]'::vector;
+               ^
+SELECT '[1.5e38,-1.5e38]'::vector;
+       vector       
+--------------------
+ [1.5e+38,-1.5e+38]
+(1 row)
+
+SELECT '[1.5e+38,-1.5e+38]'::vector;
+       vector       
+--------------------
+ [1.5e+38,-1.5e+38]
+(1 row)
+
+SELECT '[1.5e-38,-1.5e-38]'::vector;
+       vector       
+--------------------
+ [1.5e-38,-1.5e-38]
+(1 row)
+
+SELECT '[4e38,1]'::vector;
+ERROR:  "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:  invalid input syntax for type vector: "[1,2,3"
+LINE 1: SELECT '[1,2,3'::vector;
+               ^
+SELECT '[1,2,3]9'::vector;
+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:  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:  invalid input syntax for type vector: "["
+LINE 1: SELECT '['::vector;
+               ^
+SELECT '[ '::vector;
+ERROR:  invalid input syntax for type vector: "[ "
+LINE 1: SELECT '[ '::vector;
+               ^
+SELECT '[,'::vector;
+ERROR:  invalid input syntax for type vector: "[,"
+LINE 1: SELECT '[,'::vector;
+               ^
+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;
+               ^
+SELECT '[1a]'::vector;
+ERROR:  invalid input syntax for type vector: "[1a]"
+LINE 1: SELECT '[1a]'::vector;
+               ^
+SELECT '[1,,3]'::vector;
+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  
+---------
+ [1,2,3]
+ [4,5,6]
+(2 rows)
+
+SELECT '{"[1,2,3]"}'::vector(2)[];
+ERROR:  expected 2 dimensions, not 3
+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]'::vector + '[3]';
+ERROR:  different vector dimensions 2 and 1
+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]'::vector - '[3]';
+ERROR:  different vector dimensions 2 and 1
+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]'::vector * '[3]';
+ERROR:  different vector dimensions 2 and 1
+SELECT '[1,2,3]'::vector || '[4,5]';
+  ?column?   
+-------------
+ [1,2,3,4,5]
+(1 row)
+
+SELECT array_fill(0, ARRAY[16000])::vector || '[1]';
+ERROR:  vector cannot have more than 16000 dimensions
+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);
+ 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 vector_norm('[0,0]');
+ vector_norm 
+-------------
+           0
+(1 row)
+
+SELECT vector_norm('[2]');
+ vector_norm 
+-------------
+           2
+(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 l2_distance('[1,1,1,1,1,1,1,1,1]'::vector, '[1,1,1,1,1,1,1,4,5]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT '[0,0]'::vector <-> '[3,4]';
+ ?column? 
+----------
+        5
+(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 inner_product('[1,1,1,1,1,1,1,1,1]'::vector, '[1,2,3,4,5,6,7,8,9]');
+ inner_product 
+---------------
+            45
+(1 row)
+
+SELECT '[1,2]'::vector <#> '[3,4]';
+ ?column? 
+----------
+      -11
+(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 cosine_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[1,2,3,4,5,6,7,8,9]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT '[1,2]'::vector <=> '[2,4]';
+ ?column? 
+----------
+        0
+(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 l1_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[1,2,3,4,5,6,7,8,9]');
+ l1_distance 
+-------------
+           0
+(1 row)
+
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::vector, '[0,3,2,5,4,7,6,9,8]');
+ l1_distance 
+-------------
+           9
+(1 row)
+
+SELECT '[0,0]'::vector <+> '[3,4]';
+ ?column? 
+----------
+        7
+(1 row)
+
+SELECT l2_normalize('[3,4]'::vector);
+ l2_normalize 
+--------------
+ [0.6,0.8]
+(1 row)
+
+SELECT l2_normalize('[3,0]'::vector);
+ l2_normalize 
+--------------
+ [1,0]
+(1 row)
+
+SELECT l2_normalize('[0,0.1]'::vector);
+ l2_normalize 
+--------------
+ [0,1]
+(1 row)
+
+SELECT l2_normalize('[0,0]'::vector);
+ l2_normalize 
+--------------
+ [0,0]
+(1 row)
+
+SELECT l2_normalize('[3e38]'::vector);
+ l2_normalize 
+--------------
+ [1]
+(1 row)
+
+SELECT binary_quantize('[1,0,-1]'::vector);
+ binary_quantize 
+-----------------
+ 100
+(1 row)
+
+SELECT binary_quantize('[0,0.1,-0.2,-0.3,0.4,0.5,0.6,-0.7,0.8,-0.9,1]'::vector);
+ binary_quantize 
+-----------------
+ 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 subvector('[1,2,3,4,5]'::vector, 2147483647, 10);
+ERROR:  vector must have at least 1 dimension
+SELECT subvector('[1,2,3,4,5]'::vector, 3, 2147483647);
+ subvector 
+-----------
+ [3,4,5]
+(1 row)
+
+SELECT subvector('[1,2,3,4,5]'::vector, -2147483644, 2147483647);
+ subvector 
+-----------
+ [1,2]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
+    avg    
+-----------
+ [2,3.5,5]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
+    avg    
+-----------
+ [2,3.5,5]
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
+ avg 
+-----
+ 
+(1 row)
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+ERROR:  expected 2 dimensions, not 1
+SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
+   avg   
+---------
+ [3e+38]
+(1 row)
+
+SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
+ERROR:  vector cannot have more than 16000 dimensions
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
+   sum    
+----------
+ [4,7,10]
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
+ sum 
+-----
+ 
+(1 row)
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
+ERROR:  different vector dimensions 2 and 1
+SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
+ERROR:  value out of range: overflow

test/perl/PostgreSQL/Test/Cluster.pm

@@ -0,0 +1,11 @@
+package PostgreSQL::Test::Cluster;
+
+use PostgresNode;
+
+sub new
+{
+	my ($class, $name) = @_;
+	return get_new_node($name);
+}
+
+1;

test/perl/PostgreSQL/Test/Utils.pm

@@ -0,0 +1,5 @@
+package PostgreSQL::Test::Utils;
+
+use TestLib;
+
+1;

test/perl/PostgresNode.pm

@@ -1,8 +0,0 @@
-use PostgreSQL::Test::Cluster;
-
-sub get_new_node
-{
-	return PostgreSQL::Test::Cluster->new(@_);
-}
-
-1;

test/perl/TestLib.pm

@@ -1,3 +0,0 @@
-use PostgreSQL::Test::Utils;
-
-1;

test/sql/bit.sql

@@ -0,0 +1,27 @@
+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('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
+SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
+SELECT hamming_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
+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('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
+SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
+SELECT jaccard_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
+SELECT jaccard_distance('', '');
+SELECT jaccard_distance('1111', '000');
+SELECT jaccard_distance('1111', '0000'::varbit(5));
+SELECT jaccard_distance('1111', '00000'::varbit(5));

test/sql/btree.sql

@@ -1,12 +1,34 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
 SET enable_seqscan = off;
 
+-- vector
+
 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 (val);
 
 SELECT * FROM t WHERE val = '[1,2,3]';
-SELECT * FROM t ORDER BY val LIMIT 1;
+SELECT * FROM t ORDER BY val;
+
+DROP TABLE t;
+
+-- halfvec
+
+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 (val);
+
+SELECT * FROM t WHERE val = '[1,2,3]';
+SELECT * FROM t ORDER BY val;
+
+DROP TABLE t;
+
+-- sparsevec
+
+CREATE TABLE t (val sparsevec(3));
+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 (val);
+
+SELECT * FROM t WHERE val = '{1:1,2:2,3:3}/3';
+SELECT * FROM t ORDER BY val;
 
 DROP TABLE t;

test/sql/cast.sql

@@ -1,17 +1,81 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-
 SELECT ARRAY[1,2,3]::vector;
 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 array_agg(n)::vector FROM generate_series(1, 1025) n;
+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 '[0,1.5,0,3.5,0]'::halfvec::sparsevec;
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec(5);
+SELECT '[0,1.5,0,3.5,0]'::halfvec::sparsevec(4);
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec;
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec(5);
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::halfvec(4);
+SELECT '{}/16001'::sparsevec::halfvec;
+SELECT '{1:65520}/1'::sparsevec::halfvec;
+SELECT '{1:1e-8}/1'::sparsevec::halfvec;
+
+SELECT ARRAY[1,0,2,0,3,0]::sparsevec;
+SELECT ARRAY[1.0,0.0,2.0,0.0,3.0,0.0]::sparsevec;
+SELECT ARRAY[1,0,2,0,3,0]::float4[]::sparsevec;
+SELECT ARRAY[1,0,2,0,3,0]::float8[]::sparsevec;
+SELECT ARRAY[1,0,2,0,3,0]::numeric[]::sparsevec;
+
+SELECT '{1,0,2,0,3,0}'::real[]::sparsevec;
+SELECT '{1,0,2,0,3,0}'::real[]::sparsevec(6);
+SELECT '{1,0,2,0,3,0}'::real[]::sparsevec(5);
+SELECT '{NULL}'::real[]::sparsevec;
+SELECT '{NaN}'::real[]::sparsevec;
+SELECT '{Infinity}'::real[]::sparsevec;
+SELECT '{-Infinity}'::real[]::sparsevec;
+SELECT '{}'::real[]::sparsevec;
+SELECT '{{1}}'::real[]::sparsevec;
+
+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;
 
 -- ensure no error
 SELECT ARRAY[1,2,3] = ARRAY[1,2,3];

test/sql/copy.sql

@@ -1,13 +1,42 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
+-- vector
 
 CREATE TABLE t (val vector(3));
 INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
 
 CREATE TABLE t2 (val vector(3));
 
-\copy t TO '/tmp/data.bin' WITH (FORMAT binary)
-\copy t2 FROM '/tmp/data.bin' WITH (FORMAT binary)
+\copy t TO 'results/vector.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/vector.bin' WITH (FORMAT binary)
+
+SELECT * FROM t2 ORDER BY val;
+
+DROP TABLE t;
+DROP TABLE t2;
+
+-- halfvec
+
+CREATE TABLE t (val halfvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+
+CREATE TABLE t2 (val halfvec(3));
+
+\copy t TO 'results/halfvec.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/halfvec.bin' WITH (FORMAT binary)
+
+SELECT * FROM t2 ORDER BY val;
+
+DROP TABLE t;
+DROP TABLE t2;
+
+-- sparsevec
+
+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 TABLE t2 (val sparsevec(3));
+
+\copy t TO 'results/sparsevec.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/sparsevec.bin' WITH (FORMAT binary)
 
 SELECT * FROM t2 ORDER BY val;
 

test/sql/functions.sql

@@ -1,18 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-
-SELECT '[1,2,3]'::vector + '[4,5,6]';
-SELECT '[1,2,3]'::vector - '[4,5,6]';
-
-SELECT vector_dims('[1,2,3]');
-SELECT round(vector_norm('[1,1]')::numeric, 5);
-
-SELECT round(l2_distance('[1,2]', '[0,0]')::numeric, 5);
-SELECT l2_distance('[1,2]', '[3]');
-
-SELECT inner_product('[1,2]', '[3,4]');
-SELECT inner_product('[1,2]', '[3]');
-
-SELECT round(cosine_distance('[1,2]', '[2,4]')::numeric, 5);
-SELECT cosine_distance('[1,2]', '[0,0]');
-SELECT cosine_distance('[1,2]', '[3]');

test/sql/halfvec.sql

@@ -0,0 +1,147 @@
+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)[];
+
+SELECT '[1,2,3]'::halfvec + '[4,5,6]';
+SELECT '[65519]'::halfvec + '[65519]';
+SELECT '[1,2]'::halfvec + '[3]';
+
+SELECT '[1,2,3]'::halfvec - '[4,5,6]';
+SELECT '[-65519]'::halfvec - '[65519]';
+SELECT '[1,2]'::halfvec - '[3]';
+
+SELECT '[1,2,3]'::halfvec * '[4,5,6]';
+SELECT '[65519]'::halfvec * '[65519]';
+SELECT '[1e-7]'::halfvec * '[1e-7]';
+SELECT '[1,2]'::halfvec * '[3]';
+
+SELECT '[1,2,3]'::halfvec || '[4,5]';
+SELECT array_fill(0, ARRAY[16000])::halfvec || '[1]';
+
+SELECT '[1,2,3]'::halfvec < '[1,2,3]';
+SELECT '[1,2,3]'::halfvec < '[1,2]';
+SELECT '[1,2,3]'::halfvec <= '[1,2,3]';
+SELECT '[1,2,3]'::halfvec <= '[1,2]';
+SELECT '[1,2,3]'::halfvec = '[1,2,3]';
+SELECT '[1,2,3]'::halfvec = '[1,2]';
+SELECT '[1,2,3]'::halfvec != '[1,2,3]';
+SELECT '[1,2,3]'::halfvec != '[1,2]';
+SELECT '[1,2,3]'::halfvec >= '[1,2,3]';
+SELECT '[1,2,3]'::halfvec >= '[1,2]';
+SELECT '[1,2,3]'::halfvec > '[1,2,3]';
+SELECT '[1,2,3]'::halfvec > '[1,2]';
+
+SELECT halfvec_cmp('[1,2,3]', '[1,2,3]');
+SELECT halfvec_cmp('[1,2,3]', '[0,0,0]');
+SELECT halfvec_cmp('[0,0,0]', '[1,2,3]');
+SELECT halfvec_cmp('[1,2]', '[1,2,3]');
+SELECT halfvec_cmp('[1,2,3]', '[1,2]');
+SELECT halfvec_cmp('[1,2]', '[2,3,4]');
+SELECT halfvec_cmp('[2,3]', '[1,2,3]');
+
+SELECT vector_dims('[1,2,3]'::halfvec);
+
+SELECT round(l2_norm('[1,1]'::halfvec)::numeric, 5);
+SELECT l2_norm('[3,4]'::halfvec);
+SELECT l2_norm('[0,1]'::halfvec);
+SELECT l2_norm('[0,0]'::halfvec);
+SELECT l2_norm('[2]'::halfvec);
+
+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 cosine_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+SELECT cosine_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[-1,-2,-3,-4,-5,-6,-7,-8,-9]');
+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 l1_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
+SELECT l1_distance('[1,2,3,4,5,6,7,8,9]'::halfvec, '[0,3,2,5,4,7,6,9,8]');
+SELECT '[0,0]'::halfvec <+> '[3,4]';
+
+SELECT l2_normalize('[3,4]'::halfvec);
+SELECT l2_normalize('[3,0]'::halfvec);
+SELECT l2_normalize('[0,0.1]'::halfvec);
+SELECT l2_normalize('[0,0]'::halfvec);
+SELECT l2_normalize('[65504]'::halfvec);
+
+SELECT binary_quantize('[1,0,-1]'::halfvec);
+SELECT binary_quantize('[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);
+SELECT subvector('[1,2,3,4,5]'::halfvec, 2147483647, 10);
+SELECT subvector('[1,2,3,4,5]'::halfvec, 3, 2147483647);
+SELECT subvector('[1,2,3,4,5]'::halfvec, -2147483644, 2147483647);
+
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]']) v;
+SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]', NULL]) v;
+SELECT avg(v) FROM unnest(ARRAY[]::halfvec[]) v;
+SELECT avg(v) FROM unnest(ARRAY['[1,2]'::halfvec, '[3]']) v;
+SELECT avg(v) FROM unnest(ARRAY['[65504]'::halfvec, '[65504]']) v;
+SELECT halfvec_avg(array_agg(n)) FROM generate_series(1, 16002) n;
+
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]']) v;
+SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::halfvec, '[3,5,7]', NULL]) v;
+SELECT sum(v) FROM unnest(ARRAY[]::halfvec[]) v;
+SELECT sum(v) FROM unnest(ARRAY['[1,2]'::halfvec, '[3]']) v;
+SELECT sum(v) FROM unnest(ARRAY['[65504]'::halfvec, '[65504]']) v;

test/sql/hnsw_bit.sql

@@ -0,0 +1,35 @@
+SET enable_seqscan = off;
+
+-- hamming
+
+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;
+
+-- jaccard
+
+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;
+
+-- varbit
+
+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_halfvec.sql

@@ -0,0 +1,58 @@
+SET enable_seqscan = off;
+
+-- L2
+
+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;
+
+-- inner product
+
+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;
+
+-- cosine
+
+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;
+
+-- L1
+
+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_l1_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <+> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::halfvec)) t2;
+
+DROP TABLE t;

test/sql/hnsw_sparsevec.sql

@@ -0,0 +1,68 @@
+SET enable_seqscan = off;
+
+-- L2
+
+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;
+
+-- inner product
+
+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;
+
+-- cosine
+
+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;
+
+-- L1
+
+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_l1_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;
+
+-- non-zero elements
+
+CREATE TABLE t (val sparsevec(1001));
+INSERT INTO t (val) VALUES (array_fill(1, ARRAY[1001])::vector::sparsevec);
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+TRUNCATE t;
+CREATE INDEX ON t USING hnsw (val sparsevec_l2_ops);
+INSERT INTO t (val) VALUES (array_fill(1, ARRAY[1001])::vector::sparsevec);
+DROP TABLE t;

test/sql/hnsw_vector.sql

@@ -0,0 +1,84 @@
+SET enable_seqscan = off;
+
+-- L2
+
+CREATE TABLE t (val vector(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val vector_l2_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+SELECT 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;
+
+-- inner product
+
+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;
+
+-- cosine
+
+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;
+
+-- L1
+
+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_l1_ops);
+
+INSERT INTO t (val) VALUES ('[1,2,4]');
+
+SELECT * FROM t ORDER BY val <+> '[3,3,3]';
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <+> (SELECT NULL::vector)) t2;
+
+DROP TABLE t;
+
+-- unlogged
+
+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;
+
+-- options
+
+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/input.sql

@@ -1,18 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-
-SELECT '[1,2,3]'::vector;
-SELECT '[-1,2,3]'::vector;
-SELECT '[hello,1]'::vector;
-SELECT '[NaN,1]'::vector;
-SELECT '[Infinity,1]'::vector;
-SELECT '[-Infinity,1]'::vector;
-SELECT '[1,2,3'::vector;
-SELECT '[1,2,3]9'::vector;
-SELECT '1,2,3'::vector;
-SELECT '[]'::vector;
-SELECT '[1,]'::vector;
-SELECT '[1,2,3]'::vector(2);
-
-SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
-SELECT '{"[1,2,3]"}'::vector(2)[];

test/sql/ivfflat_bit.sql

@@ -0,0 +1,23 @@
+SET enable_seqscan = off;
+
+-- hamming
+
+CREATE TABLE t (val bit(3));
+INSERT INTO t (val) VALUES (B'000'), (B'100'), (B'111'), (NULL);
+CREATE INDEX ON t USING ivfflat (val bit_hamming_ops) WITH (lists = 1);
+
+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;
+
+-- varbit
+
+CREATE TABLE t (val varbit(3));
+CREATE INDEX ON t USING ivfflat (val bit_hamming_ops) WITH (lists = 1);
+CREATE INDEX ON t USING ivfflat ((val::bit(3)) bit_hamming_ops) WITH (lists = 1);
+CREATE INDEX ON t USING ivfflat ((val::bit(64001)) bit_hamming_ops) WITH (lists = 1);
+CREATE INDEX ON t USING ivfflat ((val::bit(2)) bit_hamming_ops) WITH (lists = 5);
+DROP TABLE t;

test/sql/ivfflat_cosine.sql

@@ -1,14 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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_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);
-
-DROP TABLE t;

test/sql/ivfflat_halfvec.sql

@@ -0,0 +1,45 @@
+SET enable_seqscan = off;
+
+-- L2
+
+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;
+
+-- inner product
+
+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;
+
+-- cosine
+
+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_ip.sql

@@ -1,14 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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_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);
-
-DROP TABLE t;

test/sql/ivfflat_l2.sql

@@ -1,15 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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);
-
-INSERT INTO t (val) VALUES ('[1,2,4]');
-
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
-SELECT COUNT(*) FROM t;
-
-DROP TABLE t;

test/sql/ivfflat_options.sql

@@ -1,11 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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) WITH (lists = 32769);
-
-SHOW ivfflat.probes;
-
-DROP TABLE t;

test/sql/ivfflat_unlogged.sql

@@ -1,11 +0,0 @@
-SET client_min_messages = warning;
-CREATE EXTENSION IF NOT EXISTS vector;
-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);
-
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-
-DROP TABLE t;

test/sql/ivfflat_vector.sql

@@ -0,0 +1,65 @@
+SET enable_seqscan = off;
+
+-- L2
+
+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;
+
+-- inner product
+
+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_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::vector)) t2;
+
+DROP TABLE t;
+
+-- cosine
+
+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_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::vector)) t2;
+
+DROP TABLE t;
+
+-- unlogged
+
+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 vector_l2_ops) WITH (lists = 1);
+
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+DROP TABLE t;
+
+-- options
+
+CREATE TABLE t (val vector(3));
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 0);
+CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 32769);
+
+SHOW ivfflat.probes;
+
+DROP TABLE t;

test/sql/sparsevec.sql

@@ -0,0 +1,134 @@
+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 '{1:1,1:1}/2'::sparsevec;
+SELECT '{1:1,2:1,1:1}/2'::sparsevec;
+SELECT '{}/5'::sparsevec;
+SELECT '{}/-1'::sparsevec;
+SELECT '{}/1000000001'::sparsevec;
+SELECT '{}/2147483648'::sparsevec;
+SELECT '{}/-2147483649'::sparsevec;
+SELECT '{}/9223372036854775808'::sparsevec;
+SELECT '{}/-9223372036854775809'::sparsevec;
+SELECT '{2147483647:1}/1'::sparsevec;
+SELECT '{2147483648:1}/1'::sparsevec;
+SELECT '{-2147483648:1}/1'::sparsevec;
+SELECT '{-2147483649:1}/1'::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(1000000001);
+
+SELECT '{1:1,2:2,3:3}/3'::sparsevec < '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec < '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec <= '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec <= '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec = '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec = '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec != '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec != '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec >= '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec >= '{1:1,2:2}/2';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec > '{1:1,2:2,3:3}/3';
+SELECT '{1:1,2:2,3:3}/3'::sparsevec > '{1:1,2:2}/2';
+
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{1:1,2:2,3:3}/3');
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{}/3');
+SELECT sparsevec_cmp('{}/3', '{1:1,2:2,3:3}/3');
+SELECT sparsevec_cmp('{1:1,2:2}/2', '{1:1,2:2,3:3}/3');
+SELECT sparsevec_cmp('{1:1,2:2,3:3}/3', '{1:1,2:2}/2');
+SELECT sparsevec_cmp('{1:1,2:2}/2', '{1:2,2:3,3:4}/3');
+SELECT sparsevec_cmp('{1:2,2:3}/2', '{1:1,2:2,3:3}/3');
+
+SELECT round(l2_norm('{1:1,2:1}/2'::sparsevec)::numeric, 5);
+SELECT l2_norm('{1:3,2:4}/2'::sparsevec);
+SELECT l2_norm('{2:1}/2'::sparsevec);
+SELECT l2_norm('{1:3e37,2:4e37}/2'::sparsevec)::real;
+SELECT l2_norm('{}/2'::sparsevec);
+SELECT l2_norm('{1:2}/1'::sparsevec);
+
+SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+SELECT l2_distance('{1:3}/2'::sparsevec, '{2:4}/2');
+SELECT l2_distance('{2:4}/2'::sparsevec, '{1:3}/2');
+SELECT l2_distance('{1:3,2:4}/2'::sparsevec, '{}/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 inner_product('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+SELECT inner_product('{1:1,3:3}/4'::sparsevec, '{2:2,4:4}/4');
+SELECT inner_product('{2:2,4:4}/4'::sparsevec, '{1:1,3:3}/4');
+SELECT inner_product('{1:1,3:3,5:5}/5'::sparsevec, '{2:4,3:6,4:8}/5');
+SELECT inner_product('{1:1}/2'::sparsevec, '{}/2');
+SELECT inner_product('{}/2'::sparsevec, '{1:1}/2');
+SELECT inner_product('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
+SELECT inner_product('{1:1,3:3,5:5}/5'::sparsevec, '{2:4,3:6,4:8}/5');
+SELECT '{1:1,2:2}/2'::sparsevec <#> '{1:3,2:4}/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('{1:1}/2'::sparsevec, '{2:2}/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('{2:2}/2'::sparsevec, '{1:2}/2');
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:1.1,2:1.1}/2');
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1.1,2:-1.1}/2');
+SELECT cosine_distance('{1:3e38}/1'::sparsevec, '{1:3e38}/1');
+SELECT cosine_distance('{}/1'::sparsevec, '{}/1');
+SELECT '{1:1,2:2}/2'::sparsevec <=> '{1:2,2:4}/2';
+
+SELECT l1_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+SELECT l1_distance('{}/2'::sparsevec, '{2:1}/2');
+SELECT l1_distance('{1:1,2:2}/2'::sparsevec, '{1:3}/1');
+SELECT l1_distance('{1:3e38}/1'::sparsevec, '{1:-3e38}/1');
+SELECT l1_distance('{1:1,3:3,5:5,7:7}/8'::sparsevec, '{2:2,4:4,6:6,8:8}/8');
+SELECT l1_distance('{1:1,3:3,5:5,7:7,9:9}/9'::sparsevec, '{2:2,4:4,6:6,8:8}/9');
+SELECT '{}/2'::sparsevec <+> '{1:3,2:4}/2';
+
+SELECT l2_normalize('{1:3,2:4}/2'::sparsevec);
+SELECT l2_normalize('{1:3}/2'::sparsevec);
+SELECT l2_normalize('{2:0.1}/2'::sparsevec);
+SELECT l2_normalize('{}/2'::sparsevec);
+SELECT l2_normalize('{1:3e38}/1'::sparsevec);
+SELECT l2_normalize('{1:3e38,2:1e-37}/2'::sparsevec);
+SELECT l2_normalize('{2:3e37,4:3e-37,6:4e37,8:4e-37}/9'::sparsevec);