Use integer[] for consistency [skip ci]

This reverts commit 772ab69de6.

.github/workflows/build.yml

@@ -8,17 +8,17 @@ jobs:
       fail-fast: false
       matrix:
         include:
+          # - postgres: 18
+          #   os: ubuntu-24.04
           - postgres: 17
-            os: ubuntu-22.04
+            os: ubuntu-24.04
           - postgres: 16
             os: ubuntu-22.04
           - postgres: 15
             os: ubuntu-22.04
           - postgres: 14
-            os: ubuntu-22.04
-          - postgres: 13
             os: ubuntu-20.04
-          - postgres: 12
+          - postgres: 13
             os: ubuntu-20.04
     steps:
       - uses: actions/checkout@v4
@@ -40,13 +40,21 @@ jobs:
           sudo apt-get install libipc-run-perl
       - run: make prove_installcheck
   mac:
-    runs-on: macos-latest
+    runs-on: ${{ matrix.os }}
     if: ${{ !startsWith(github.ref_name, 'windows') }}
+    strategy:
+      fail-fast: false
+      matrix:
+        include:
+          - postgres: 16
+            os: macos-14
+          - postgres: 14
+            os: macos-13
     steps:
       - uses: actions/checkout@v4
       - uses: ankane/setup-postgres@v1
         with:
-          postgres-version: 14
+          postgres-version: ${{ matrix.postgres }}
       - run: make
         env:
           PG_CFLAGS: -DUSE_ASSERT_CHECKING -Wall -Wextra -Werror -Wno-unused-parameter
@@ -54,13 +62,19 @@ jobs:
       - run: make installcheck
       - if: ${{ failure() }}
         run: cat regression.diffs
+      # Homebrew Postgres does not enable TAP tests, so need to download
       - run: |
           brew install cpanm
           cpanm --notest IPC::Run
-          wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_14_10.tar.gz
-          tar xf REL_14_10.tar.gz
-      - run: make prove_installcheck PROVE_FLAGS="-I ./postgres-REL_14_10/src/test/perl" PERL5LIB="/Users/runner/perl5/lib/perl5"
-      - run: make clean && /usr/local/opt/llvm@15/bin/scan-build --status-bugs make
+          wget -q https://github.com/postgres/postgres/archive/refs/tags/$TAG.tar.gz
+          tar xf $TAG.tar.gz
+          mv postgres-$TAG postgres
+        env:
+          TAG: ${{ matrix.postgres == 16 && 'REL_16_2' || 'REL_14_11' }}
+      - run: make prove_installcheck PROVE_FLAGS="-I ./postgres/src/test/perl -I ./test/perl"
+        env:
+          PERL5LIB: /Users/runner/perl5/lib/perl5
+      - run: make clean && $(brew --prefix llvm@15)/bin/scan-build --status-bugs make
         env:
           PG_CFLAGS: -DUSE_ASSERT_CHECKING
   windows:
@@ -73,13 +87,14 @@ jobs:
           postgres-version: 14
       - run: |
           call "C:\Program Files\Microsoft Visual Studio\2022\Enterprise\VC\Auxiliary\Build\vcvars64.bat" && ^
-          cd %TEMP% && ^
           nmake /NOLOGO /F Makefile.win && ^
           nmake /NOLOGO /F Makefile.win install && ^
           nmake /NOLOGO /F Makefile.win installcheck && ^
           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
@@ -101,6 +116,8 @@ jobs:
           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
@@ -109,6 +126,7 @@ jobs:
       - uses: ankane/setup-postgres-valgrind@v1
         with:
           postgres-version: 16
-      - run: make
+          check-ub: yes
+      - run: make OPTFLAGS=""
       - run: sudo --preserve-env=PG_CONFIG make install
       - run: make installcheck

CHANGELOG.md

@@ -1,3 +1,50 @@
+## 0.8.0 (unreleased)
+
+- Added support for iterative index scans
+- Added `intvec` type
+- Added casts for arrays to `sparsevec`
+- Improved cost estimation
+- Improved performance of HNSW inserts and on-disk index builds
+- 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

Dockerfile

@@ -1,4 +1,4 @@
-ARG PG_MAJOR=16
+ARG PG_MAJOR=17
 FROM postgres:$PG_MAJOR
 ARG PG_MAJOR
 

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": "0.6.2",
+	"version": "0.7.4",
 	"maintainer": [
 		"Andrew Kane <andrew@ankane.org>"
 	],
@@ -20,7 +20,7 @@
 		"vector": {
 			"file": "sql/vector.sql",
 			"docfile": "README.md",
-			"version": "0.6.2",
+			"version": "0.7.4",
 			"abstract": "Open-source vector similarity search for Postgres"
 		}
 	},

Makefile

@@ -1,18 +1,20 @@
 EXTENSION = vector
-EXTVERSION = 0.6.2
+EXTVERSION = 0.7.4
 
 MODULE_big = vector
-DATA = $(wildcard sql/*--*.sql)
-OBJS = src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/vector.o
-HEADERS = src/vector.h
+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/intvec.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/intvec.h src/sparsevec.h src/vector.h
 
 TESTS = $(wildcard test/sql/*.sql)
 REGRESS = $(patsubst test/sql/%.sql,%,$(TESTS))
 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
@@ -41,8 +43,6 @@ 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 $(PGXS)
@@ -52,7 +52,7 @@ ifeq ($(PROVE),)
 	PROVE = prove
 endif
 
-# for Postgres 15
+# for Postgres < 15
 PROVE_FLAGS += -I ./test/perl
 
 prove_installcheck:
@@ -66,7 +66,7 @@ dist:
 	git archive --format zip --prefix=$(EXTENSION)-$(EXTVERSION)/ --output dist/$(EXTENSION)-$(EXTVERSION).zip master
 
 # for Docker
-PG_MAJOR ?= 16
+PG_MAJOR ?= 17
 
 .PHONY: docker
 

Makefile.win

@@ -1,10 +1,11 @@
 EXTENSION = vector
-EXTVERSION = 0.6.2
+EXTVERSION = 0.7.4
 
-OBJS = src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\vector.obj
-HEADERS = src\vector.h
+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\intvec.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\intvec.h src\sparsevec.h src\vector.h
 
-REGRESS = btree cast copy functions input ivfflat_cosine ivfflat_ip ivfflat_l2 ivfflat_options ivfflat_unlogged
+REGRESS = bit 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
@@ -19,11 +20,6 @@ PG_CFLAGS = $(PG_CFLAGS) $(OPTFLAGS) /O2 /fp:fast
 # https://learn.microsoft.com/en-us/cpp/error-messages/tool-errors/vectorizer-and-parallelizer-messages
 # PG_CFLAGS = $(PG_CFLAGS) /Qvec-report:2
 
-all: sql\$(EXTENSION)--$(EXTVERSION).sql
-
-sql\$(EXTENSION)--$(EXTVERSION).sql: sql\$(EXTENSION).sql
-	copy sql\$(EXTENSION).sql $@
-
 # TODO use pg_config
 !ifndef PGROOT
 !error PGROOT is not set
@@ -43,15 +39,18 @@ 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)
 
-all: $(SHLIB)
+sql\$(EXTENSION)--$(EXTVERSION).sql: sql\$(EXTENSION).sql
+	copy sql\$(EXTENSION).sql $@
 
-install:
+install: all
 	copy $(SHLIB) "$(PKGLIBDIR)"
 	copy $(EXTENSION).control "$(SHAREDIR)\extension"
 	copy sql\$(EXTENSION)--*.sql "$(SHAREDIR)\extension"
@@ -70,6 +69,6 @@ uninstall:
 
 clean:
 	del /f $(SHLIB) $(EXTENSION).lib $(EXTENSION).exp
+	del /f $(DATA_built)
 	del /f $(OBJS)
-	del /f sql\$(EXTENSION)--$(EXTVERSION).sql
 	del /f /s /q results regression.diffs regression.out tmp_check tmp_check_iso log output_iso

README.md

@@ -5,7 +5,8 @@ Open-source vector similarity search for Postgres
 Store your vectors with the rest of your data. Supports:
 
 - exact and approximate nearest neighbor search
-- L2 distance, inner product, and cosine distance
+- single-precision, half-precision, binary, and sparse vectors
+- L2 distance, inner product, cosine distance, L1 distance, Hamming distance, and Jaccard distance
 - any [language](#languages) with a Postgres client
 
 Plus [ACID](https://en.wikipedia.org/wiki/ACID) compliance, point-in-time recovery, JOINs, and all of the other [great features](https://www.postgresql.org/about/) of Postgres
@@ -20,7 +21,7 @@ Compile and install the extension (supports Postgres 12+)
 
 ```sh
 cd /tmp
-git clone --branch v0.6.2 https://github.com/pgvector/pgvector.git
+git clone --branch v0.7.4 https://github.com/pgvector/pgvector.git
 cd pgvector
 make
 make install # may need sudo
@@ -45,12 +46,14 @@ Then use `nmake` to build:
 ```cmd
 set "PGROOT=C:\Program Files\PostgreSQL\16"
 cd %TEMP%
-git clone --branch v0.6.2 https://github.com/pgvector/pgvector.git
+git clone --branch v0.7.4 https://github.com/pgvector/pgvector.git
 cd pgvector
 nmake /F Makefile.win
 nmake /F Makefile.win install
 ```
 
+Note: Postgres 17 is not supported yet due to an upstream issue
+
 See the [installation notes](#installation-notes---windows) if you run into issues
 
 You can also install it with [Docker](#docker) or [conda-forge](#conda-forge).
@@ -81,7 +84,7 @@ Get the nearest neighbors by L2 distance
 SELECT * FROM items ORDER BY embedding <-> '[3,1,2]' LIMIT 5;
 ```
 
-Also supports inner product (`<#>`) and cosine distance (`<=>`)
+Also supports inner product (`<#>`), cosine distance (`<=>`), and L1 distance (`<+>`, added in 0.7.0)
 
 Note: `<#>` returns the negative inner product since Postgres only supports `ASC` order index scans on operators
 
@@ -99,13 +102,15 @@ Or add a vector column to an existing table
 ALTER TABLE items ADD COLUMN embedding vector(3);
 ```
 
+Also supports [half-precision](#half-precision-vectors), [binary](#binary-vectors), and [sparse](#sparse-vectors) vectors
+
 Insert vectors
 
 ```sql
 INSERT INTO items (embedding) VALUES ('[1,2,3]'), ('[4,5,6]');
 ```
 
-Or load vectors in bulk using `COPY` ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/bulk_loading.py))
+Or load vectors in bulk using `COPY` ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/loading/example.py))
 
 ```sql
 COPY items (embedding) FROM STDIN WITH (FORMAT BINARY);
@@ -138,6 +143,15 @@ Get the nearest neighbors to a vector
 SELECT * FROM items ORDER BY embedding <-> '[3,1,2]' LIMIT 5;
 ```
 
+Supported distance functions are:
+
+- `<->` - L2 distance
+- `<#>` - (negative) inner product
+- `<=>` - cosine distance
+- `<+>` - L1 distance (added in 0.7.0)
+- `<~>` - Hamming distance (binary vectors, added in 0.7.0)
+- `<%>` - Jaccard distance (binary vectors, added in 0.7.0)
+
 Get the nearest neighbors to a row
 
 ```sql
@@ -194,7 +208,7 @@ You can add an index to use approximate nearest neighbor search, which trades so
 
 Supported index types are:
 
-- [HNSW](#hnsw) - added in 0.5.0
+- [HNSW](#hnsw)
 - [IVFFlat](#ivfflat)
 
 ## HNSW
@@ -209,6 +223,8 @@ L2 distance
 CREATE INDEX ON items USING hnsw (embedding vector_l2_ops);
 ```
 
+Note: Use `halfvec_l2_ops` for `halfvec`, `intvec_l2_ops` for `intvec`, and `sparsevec_l2_ops` for `sparsevec` (and similar with the other distance functions)
+
 Inner product
 
 ```sql
@@ -221,7 +237,31 @@ Cosine distance
 CREATE INDEX ON items USING hnsw (embedding vector_cosine_ops);
 ```
 
-Vectors with up to 2,000 dimensions can be indexed.
+L1 distance - added in 0.7.0
+
+```sql
+CREATE INDEX ON items USING hnsw (embedding vector_l1_ops);
+```
+
+Hamming distance - added in 0.7.0
+
+```sql
+CREATE INDEX ON items USING hnsw (embedding bit_hamming_ops);
+```
+
+Jaccard distance - added in 0.7.0
+
+```sql
+CREATE INDEX ON items USING hnsw (embedding bit_jaccard_ops);
+```
+
+Supported types are:
+
+- `vector` - up to 2,000 dimensions
+- `halfvec` - up to 4,000 dimensions (added in 0.7.0)
+- `intvec` - up to 8,000 dimensions (added in 0.8.0)
+- `bit` - up to 64,000 dimensions (added in 0.7.0)
+- `sparsevec` - up to 1,000 non-zero elements (added in 0.7.0)
 
 ### Index Options
 
@@ -314,6 +354,8 @@ L2 distance
 CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 100);
 ```
 
+Note: Use `halfvec_l2_ops` for `halfvec` (and similar with the other distance functions)
+
 Inner product
 
 ```sql
@@ -326,7 +368,17 @@ Cosine distance
 CREATE INDEX ON items USING ivfflat (embedding vector_cosine_ops) WITH (lists = 100);
 ```
 
-Vectors with up to 2,000 dimensions can be indexed.
+Hamming distance - added in 0.7.0
+
+```sql
+CREATE INDEX ON items USING ivfflat (embedding bit_hamming_ops) WITH (lists = 100);
+```
+
+Supported types are:
+
+- `vector` - up to 2,000 dimensions
+- `halfvec` - up to 4,000 dimensions (added in 0.7.0)
+- `bit` - up to 64,000 dimensions (added in 0.7.0)
 
 ### Query Options
 
@@ -400,6 +452,113 @@ Use [partitioning](https://www.postgresql.org/docs/current/ddl-partitioning.html
 CREATE TABLE items (embedding vector(3), category_id int) PARTITION BY LIST(category_id);
 ```
 
+## Half-Precision Vectors
+
+*Added in 0.7.0*
+
+Use the `halfvec` type to store half-precision vectors
+
+```sql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding halfvec(3));
+```
+
+## Half-Precision Indexing
+
+*Added in 0.7.0*
+
+Index vectors at half precision for smaller indexes
+
+```sql
+CREATE INDEX ON items USING hnsw ((embedding::halfvec(3)) halfvec_l2_ops);
+```
+
+Get the nearest neighbors
+
+```sql
+SELECT * FROM items ORDER BY embedding::halfvec(3) <-> '[1,2,3]' LIMIT 5;
+```
+
+## Integer Vectors
+
+*Added in 0.8.0*
+
+Use the `intvec` type to store 8-bit integer vectors
+
+```sql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding intvec(3));
+```
+
+## Binary Vectors
+
+Use the `bit` type to store binary vectors ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/imagehash/example.py))
+
+```sql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding bit(3));
+INSERT INTO items (embedding) VALUES ('000'), ('111');
+```
+
+Get the nearest neighbors by Hamming distance (added in 0.7.0)
+
+```sql
+SELECT * FROM items ORDER BY embedding <~> '101' LIMIT 5;
+```
+
+Or (before 0.7.0)
+
+```sql
+SELECT * FROM items ORDER BY bit_count(embedding # '101') LIMIT 5;
+```
+
+Also supports Jaccard distance (`<%>`)
+
+## Binary Quantization
+
+*Added in 0.7.0*
+
+Use expression indexing for binary quantization
+
+```sql
+CREATE INDEX ON items USING hnsw ((binary_quantize(embedding)::bit(3)) bit_hamming_ops);
+```
+
+Get the nearest neighbors by Hamming distance
+
+```sql
+SELECT * FROM items ORDER BY binary_quantize(embedding)::bit(3) <~> binary_quantize('[1,-2,3]') LIMIT 5;
+```
+
+Re-rank by the original vectors for better recall
+
+```sql
+SELECT * FROM (
+    SELECT * FROM items ORDER BY binary_quantize(embedding)::bit(3) <~> binary_quantize('[1,-2,3]') LIMIT 20
+) ORDER BY embedding <=> '[1,-2,3]' LIMIT 5;
+```
+
+## Sparse Vectors
+
+*Added in 0.7.0*
+
+Use the `sparsevec` type to store sparse vectors
+
+```sql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding sparsevec(5));
+```
+
+Insert vectors
+
+```sql
+INSERT INTO items (embedding) VALUES ('{1:1,3:2,5:3}/5'), ('{1:4,3:5,5:6}/5');
+```
+
+The format is `{index1:value1,index2:value2}/dimensions` and indices start at 1 like SQL arrays
+
+Get the nearest neighbors by L2 distance
+
+```sql
+SELECT * FROM items ORDER BY embedding <-> '{1:3,3:1,5:2}/5' LIMIT 5;
+```
+
 ## Hybrid Search
 
 Use together with Postgres [full-text search](https://www.postgresql.org/docs/current/textsearch-intro.html) for hybrid search.
@@ -409,17 +568,53 @@ SELECT id, content FROM items, plainto_tsquery('hello search') query
     WHERE textsearch @@ query ORDER BY ts_rank_cd(textsearch, query) DESC LIMIT 5;
 ```
 
-You can use [Reciprocal Rank Fusion](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search_rrf.py) or a [cross-encoder](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search.py) to combine results.
+You can use [Reciprocal Rank Fusion](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search/rrf.py) or a [cross-encoder](https://github.com/pgvector/pgvector-python/blob/master/examples/hybrid_search/cross_encoder.py) to combine results.
+
+## Indexing Subvectors
+
+*Added in 0.7.0*
+
+Use expression indexing to index subvectors
+
+```sql
+CREATE INDEX ON items USING hnsw ((subvector(embedding, 1, 3)::vector(3)) vector_cosine_ops);
+```
+
+Get the nearest neighbors by cosine distance
+
+```sql
+SELECT * FROM items ORDER BY subvector(embedding, 1, 3)::vector(3) <=> subvector('[1,2,3,4,5]'::vector, 1, 3) LIMIT 5;
+```
+
+Re-rank by the full vectors for better recall
+
+```sql
+SELECT * FROM (
+    SELECT * FROM items ORDER BY subvector(embedding, 1, 3)::vector(3) <=> subvector('[1,2,3,4,5]'::vector, 1, 3) LIMIT 20
+) ORDER BY embedding <=> '[1,2,3,4,5]' LIMIT 5;
+```
 
 ## Performance
 
 ### Tuning
 
-Use a tool like [PgTune](https://pgtune.leopard.in.ua/) to set initial values for Postgres server parameters.
+Use a tool like [PgTune](https://pgtune.leopard.in.ua/) to set initial values for Postgres server parameters. For instance, `shared_buffers` should typically be 25% of the server’s memory. You can find the config file with:
+
+```sql
+SHOW config_file;
+```
+
+And check individual settings with:
+
+```sql
+SHOW shared_buffers;
+```
+
+Be sure to restart Postgres for changes to take effect.
 
 ### Loading
 
-Use `COPY` for bulk loading data ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/bulk_loading.py)).
+Use `COPY` for bulk loading data ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/loading/example.py)).
 
 ```sql
 COPY items (embedding) FROM STDIN WITH (FORMAT BINARY);
@@ -509,7 +704,7 @@ Scale pgvector the same way you scale Postgres.
 
 Scale vertically by increasing memory, CPU, and storage on a single instance. Use existing tools to [tune parameters](#tuning) and [monitor performance](#monitoring).
 
-Scale horizontally with [replicas](https://www.postgresql.org/docs/current/hot-standby.html), or use [Citus](https://github.com/citusdata/citus) or another approach for sharding ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/citus.py)).
+Scale horizontally with [replicas](https://www.postgresql.org/docs/current/hot-standby.html), or use [Citus](https://github.com/citusdata/citus) or another approach for sharding ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/citus/example.py)).
 
 ## Languages
 
@@ -553,7 +748,7 @@ Yes, pgvector uses the write-ahead log (WAL), which allows for replication and p
 
 #### What if I want to index vectors with more than 2,000 dimensions?
 
-You’ll need to use [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction) at the moment.
+You can use [half-precision indexing](#half-precision-indexing) to index up to 4,000 dimensions or [binary quantization](#binary-quantization) to index up to 64,000 dimensions. Another option is [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction).
 
 #### Can I store vectors with different dimensions in the same column?
 
@@ -616,7 +811,7 @@ SELECT pg_size_pretty(pg_relation_size('index_name'));
 
 #### Why isn’t a query using an index?
 
-The query needs to have an `ORDER BY` and `LIMIT`, and the `ORDER BY` must be the result of a distance operator, not an expression.
+The query needs to have an `ORDER BY` and `LIMIT`, and the `ORDER BY` must be the result of a distance operator (not an expression) in ascending order.
 
 ```sql
 -- index
@@ -659,6 +854,8 @@ ALTER TABLE items ALTER COLUMN embedding SET STORAGE PLAIN;
 
 Results are limited by the size of the dynamic candidate list (`hnsw.ef_search`). There may be even less results due to dead tuples or filtering conditions in the query. We recommend setting `hnsw.ef_search` to at least twice the `LIMIT` of the query. If you need more than 500 results, use an IVFFlat index instead.
 
+Also, note that `NULL` vectors are not indexed (as well as zero vectors for cosine distance).
+
 #### Why are there less results for a query after adding an IVFFlat index?
 
 The index was likely created with too little data for the number of lists. Drop the index until the table has more data.
@@ -669,11 +866,18 @@ DROP INDEX index_name;
 
 Results can also be limited by the number of probes (`ivfflat.probes`).
 
+Also, note that `NULL` vectors are not indexed (as well as zero vectors for cosine distance).
+
 ## Reference
 
+- [Vector](#vector-type)
+- [Halfvec](#halfvec-type)
+- [Bit](#bit-type)
+- [Sparsevec](#sparsevec-type)
+
 ### Vector Type
 
-Each vector takes `4 * dimensions + 8` bytes of storage. Each element is a single precision floating-point number (like the `real` type in Postgres), and all elements must be finite (no `NaN`, `Infinity` or `-Infinity`). Vectors can have up to 16,000 dimensions.
+Each vector takes `4 * dimensions + 8` bytes of storage. Each element is a single-precision floating-point number (like the `real` type in Postgres), and all elements must be finite (no `NaN`, `Infinity` or `-Infinity`). Vectors can have up to 16,000 dimensions.
 
 ### Vector Operators
 
@@ -682,28 +886,137 @@ Operator | Description | Added
 \+ | element-wise addition |
 \- | element-wise subtraction |
 \* | element-wise multiplication | 0.5.0
+\|\| | concatenate | 0.7.0
 <-> | Euclidean distance |
 <#> | negative inner product |
 <=> | cosine distance |
+<+> | taxicab distance | 0.7.0
 
 ### Vector Functions
 
 Function | Description | Added
 --- | --- | ---
+binary_quantize(vector) → bit | binary quantize | 0.7.0
 cosine_distance(vector, vector) → double precision | cosine distance |
 inner_product(vector, vector) → double precision | inner product |
-l2_distance(vector, vector) → double precision | Euclidean distance |
 l1_distance(vector, vector) → double precision | taxicab distance | 0.5.0
+l2_distance(vector, vector) → double precision | Euclidean distance |
+l2_normalize(vector) → vector | Normalize with Euclidean norm | 0.7.0
+subvector(vector, integer, integer) → vector | subvector | 0.7.0
 vector_dims(vector) → integer | number of dimensions |
 vector_norm(vector) → double precision | Euclidean norm |
 
-### Aggregate Functions
+### Vector Aggregate Functions
 
 Function | Description | Added
 --- | --- | ---
 avg(vector) → vector | average |
 sum(vector) → vector | sum | 0.5.0
 
+### Halfvec Type
+
+Each half vector takes `2 * dimensions + 8` bytes of storage. Each element is a half-precision floating-point number, and all elements must be finite (no `NaN`, `Infinity` or `-Infinity`). Half vectors can have up to 16,000 dimensions.
+
+### Halfvec Operators
+
+Operator | Description | Added
+--- | --- | ---
+\+ | element-wise addition | 0.7.0
+\- | element-wise subtraction | 0.7.0
+\* | element-wise multiplication | 0.7.0
+\|\| | concatenate | 0.7.0
+<-> | Euclidean distance | 0.7.0
+<#> | negative inner product | 0.7.0
+<=> | cosine distance | 0.7.0
+<+> | taxicab distance | 0.7.0
+
+### Halfvec Functions
+
+Function | Description | Added
+--- | --- | ---
+binary_quantize(halfvec) → bit | binary quantize | 0.7.0
+cosine_distance(halfvec, halfvec) → double precision | cosine distance | 0.7.0
+inner_product(halfvec, halfvec) → double precision | inner product | 0.7.0
+l1_distance(halfvec, halfvec) → double precision | taxicab distance | 0.7.0
+l2_distance(halfvec, halfvec) → double precision | Euclidean distance | 0.7.0
+l2_norm(halfvec) → double precision | Euclidean norm | 0.7.0
+l2_normalize(halfvec) → halfvec | Normalize with Euclidean norm | 0.7.0
+subvector(halfvec, integer, integer) → halfvec | subvector | 0.7.0
+vector_dims(halfvec) → integer | number of dimensions | 0.7.0
+
+### Halfvec Aggregate Functions
+
+Function | Description | Added
+--- | --- | ---
+avg(halfvec) → halfvec | average | 0.7.0
+sum(halfvec) → halfvec | sum | 0.7.0
+
+### Intvec Type
+
+Each int vector takes `dimensions + 8` bytes of storage. Each element is a single byte signed integer. Int vectors can have up to 16,000 dimensions.
+
+### Intvec Operators
+
+Operator | Description | Added
+--- | --- | ---
+<-> | Euclidean distance | 0.8.0
+<#> | negative inner product | 0.8.0
+<=> | cosine distance | 0.8.0
+<+> | taxicab distance | 0.8.0
+
+### Intvec Functions
+
+Function | Description | Added
+--- | --- | ---
+cosine_distance(intvec, intvec) → double precision | cosine distance | 0.8.0
+inner_product(intvec, intvec) → double precision | inner product | 0.8.0
+l1_distance(intvec, intvec) → double precision | taxicab distance | 0.8.0
+l2_distance(intvec, intvec) → double precision | Euclidean distance | 0.8.0
+l2_norm(intvec) → double precision | Euclidean norm | 0.8.0
+vector_dims(intvec) → integer | number of dimensions | 0.8.0
+
+### Bit Type
+
+Each bit vector takes `dimensions / 8 + 8` bytes of storage. See the [Postgres docs](https://www.postgresql.org/docs/current/datatype-bit.html) for more info.
+
+### Bit Operators
+
+Operator | Description | Added
+--- | --- | ---
+<~> | Hamming distance | 0.7.0
+<%> | Jaccard distance | 0.7.0
+
+### Bit Functions
+
+Function | Description | Added
+--- | --- | ---
+hamming_distance(bit, bit) → double precision | Hamming distance | 0.7.0
+jaccard_distance(bit, bit) → double precision | Jaccard distance | 0.7.0
+
+### Sparsevec Type
+
+Each sparse vector takes `8 * non-zero elements + 16` bytes of storage. Each element is a single-precision floating-point number, and all elements must be finite (no `NaN`, `Infinity` or `-Infinity`). Sparse vectors can have up to 16,000 non-zero elements.
+
+### Sparsevec Operators
+
+Operator | Description | Added
+--- | --- | ---
+<-> | Euclidean distance | 0.7.0
+<#> | negative inner product | 0.7.0
+<=> | cosine distance | 0.7.0
+<+> | taxicab distance | 0.7.0
+
+### Sparsevec Functions
+
+Function | Description | Added
+--- | --- | ---
+cosine_distance(sparsevec, sparsevec) → double precision | cosine distance | 0.7.0
+inner_product(sparsevec, sparsevec) → double precision | inner product | 0.7.0
+l1_distance(sparsevec, sparsevec) → double precision | taxicab distance | 0.7.0
+l2_distance(sparsevec, sparsevec) → double precision | Euclidean distance | 0.7.0
+l2_norm(sparsevec) → double precision | Euclidean norm | 0.7.0
+l2_normalize(sparsevec) → sparsevec | Normalize with Euclidean norm | 0.7.0
+
 ## Installation Notes - Linux and Mac
 
 ### Postgres Location
@@ -711,7 +1024,7 @@ sum(vector) → vector | sum | 0.5.0
 If your machine has multiple Postgres installations, specify the path to [pg_config](https://www.postgresql.org/docs/current/app-pgconfig.html) with:
 
 ```sh
-export PG_CONFIG=/Library/PostgreSQL/16/bin/pg_config
+export PG_CONFIG=/Library/PostgreSQL/17/bin/pg_config
 ```
 
 Then re-run the installation instructions (run `make clean` before `make` if needed). If `sudo` is needed for `make install`, use:
@@ -722,11 +1035,11 @@ sudo --preserve-env=PG_CONFIG make install
 
 A few common paths on Mac are:
 
-- EDB installer - `/Library/PostgreSQL/16/bin/pg_config`
-- Homebrew (arm64) - `/opt/homebrew/opt/postgresql@16/bin/pg_config`
-- Homebrew (x86-64) - `/usr/local/opt/postgresql@16/bin/pg_config`
+- EDB installer - `/Library/PostgreSQL/17/bin/pg_config`
+- Homebrew (arm64) - `/opt/homebrew/opt/postgresql@17/bin/pg_config`
+- Homebrew (x86-64) - `/usr/local/opt/postgresql@17/bin/pg_config`
 
-Note: Replace `16` with your Postgres server version
+Note: Replace `17` with your Postgres server version
 
 ### Missing Header
 
@@ -735,10 +1048,10 @@ If compilation fails with `fatal error: postgres.h: No such file or directory`,
 For Ubuntu and Debian, use:
 
 ```sh
-sudo apt install postgresql-server-dev-16
+sudo apt install postgresql-server-dev-17
 ```
 
-Note: Replace `16` with your Postgres server version
+Note: Replace `17` with your Postgres server version
 
 ### Missing SDK
 
@@ -771,17 +1084,17 @@ If installation fails with `Access is denied`, re-run the installation instructi
 Get the [Docker image](https://hub.docker.com/r/pgvector/pgvector) with:
 
 ```sh
-docker pull pgvector/pgvector:pg16
+docker pull pgvector/pgvector:pg17
 ```
 
-This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (replace `16` with your Postgres server version, and run it the same way).
+This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres) (replace `17` with your Postgres server version, and run it the same way).
 
 You can also build the image manually:
 
 ```sh
-git clone --branch v0.6.2 https://github.com/pgvector/pgvector.git
+git clone --branch v0.7.4 https://github.com/pgvector/pgvector.git
 cd pgvector
-docker build --build-arg PG_MAJOR=16 -t myuser/pgvector .
+docker build --pull --build-arg PG_MAJOR=17 -t myuser/pgvector .
 ```
 
 ### Homebrew
@@ -792,7 +1105,7 @@ With Homebrew Postgres, you can use:
 brew install pgvector
 ```
 
-Note: This only adds it to the `postgresql@14` formula
+Note: This only adds it to the `postgresql@17` and `postgresql@14` formulas
 
 ### PGXN
 
@@ -807,29 +1120,29 @@ pgxn install vector
 Debian and Ubuntu packages are available from the [PostgreSQL APT Repository](https://wiki.postgresql.org/wiki/Apt). Follow the [setup instructions](https://wiki.postgresql.org/wiki/Apt#Quickstart) and run:
 
 ```sh
-sudo apt install postgresql-16-pgvector
+sudo apt install postgresql-17-pgvector
 ```
 
-Note: Replace `16` with your Postgres server version
+Note: Replace `17` with your Postgres server version
 
 ### Yum
 
 RPM packages are available from the [PostgreSQL Yum Repository](https://yum.postgresql.org/). Follow the [setup instructions](https://www.postgresql.org/download/linux/redhat/) for your distribution and run:
 
 ```sh
-sudo yum install pgvector_16
+sudo yum install pgvector_17
 # or
-sudo dnf install pgvector_16
+sudo dnf install pgvector_17
 ```
 
-Note: Replace `16` with your Postgres server version
+Note: Replace `17` with your Postgres server version
 
 ### pkg
 
 Install the FreeBSD package with:
 
 ```sh
-pkg install postgresql15-pg_vector
+pkg install postgresql15-pgvector
 ```
 
 or the port with:

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 +1,208 @@
+-- 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 hnsw_intvec_support(internal) RETURNS internal
+	AS 'MODULE_PATHNAME' LANGUAGE C;
+
+CREATE TYPE intvec;
+
+CREATE FUNCTION intvec_in(cstring, oid, integer) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_out(intvec) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_recv(internal, oid, integer) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_send(intvec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE intvec (
+	INPUT     = intvec_in,
+	OUTPUT    = intvec_out,
+	TYPMOD_IN = intvec_typmod_in,
+	RECEIVE   = intvec_recv,
+	SEND      = intvec_send,
+	STORAGE   = external
+);
+
+CREATE FUNCTION l2_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_dims(intvec) RETURNS integer
+	AS 'MODULE_PATHNAME', 'intvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_lt(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_le(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_eq(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_ne(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_ge(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_gt(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_cmp(intvec, intvec) RETURNS int4
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_l2_squared_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_negative_inner_product(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec(intvec, integer, boolean) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_intvec(integer[], integer, boolean) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_to_integer(intvec, integer, boolean) RETURNS integer[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE CAST (intvec AS intvec)
+	WITH FUNCTION intvec(intvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (intvec AS integer[])
+	WITH FUNCTION intvec_to_integer(intvec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (integer[] AS intvec)
+	WITH FUNCTION array_to_intvec(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE OPERATOR <-> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+CREATE OPERATOR <+> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR < (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+CREATE OPERATOR CLASS intvec_ops
+	DEFAULT FOR TYPE intvec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 intvec_cmp(intvec, intvec);
+
+CREATE OPERATOR CLASS intvec_l2_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <-> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 intvec_l2_squared_distance(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_ip_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <#> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 intvec_negative_inner_product(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_cosine_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <=> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 cosine_distance(intvec, intvec),
+	FUNCTION 2 l2_norm(intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_l1_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <+> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+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;
 
@@ -29,7 +29,7 @@ CREATE TYPE vector (
 	STORAGE   = external
 );
 
--- functions
+-- vector functions
 
 CREATE FUNCTION l2_distance(vector, vector) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -49,6 +49,17 @@ CREATE FUNCTION vector_dims(vector) RETURNS integer
 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;
 
@@ -58,7 +69,8 @@ CREATE FUNCTION vector_sub(vector, vector) RETURNS vector
 CREATE FUNCTION vector_mul(vector, vector) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- private functions
+CREATE FUNCTION 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;
@@ -99,7 +111,7 @@ CREATE FUNCTION vector_avg(double precision[]) RETURNS vector
 CREATE FUNCTION vector_combine(double precision[], double precision[]) RETURNS double precision[]
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
--- aggregates
+-- vector aggregates
 
 CREATE AGGREGATE avg(vector) (
 	SFUNC = vector_accum,
@@ -117,7 +129,7 @@ CREATE AGGREGATE sum(vector) (
 	PARALLEL = SAFE
 );
 
--- cast functions
+-- vector cast functions
 
 CREATE FUNCTION vector(vector, integer, boolean) RETURNS vector
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
@@ -137,7 +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;
@@ -157,7 +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,
@@ -174,6 +186,11 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR <+> (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
 CREATE OPERATOR + (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_add,
 	COMMUTATOR = +
@@ -188,6 +205,10 @@ CREATE OPERATOR * (
 	COMMUTATOR = *
 );
 
+CREATE OPERATOR || (
+	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_concat
+);
+
 CREATE OPERATOR < (
 	LEFTARG = vector, RIGHTARG = vector, PROCEDURE = vector_lt,
 	COMMUTATOR = > , NEGATOR = >= ,
@@ -240,7 +261,27 @@ CREATE ACCESS METHOD hnsw TYPE INDEX HANDLER hnswhandler;
 
 COMMENT ON ACCESS METHOD hnsw IS 'hnsw index access method';
 
--- opclasses
+-- 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_intvec_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
@@ -287,3 +328,787 @@ CREATE OPERATOR CLASS vector_cosine_ops
 	OPERATOR 1 <=> (vector, vector) FOR ORDER BY float_ops,
 	FUNCTION 1 vector_negative_inner_product(vector, vector),
 	FUNCTION 2 vector_norm(vector);
+
+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);
+
+-- intvec type
+
+CREATE TYPE intvec;
+
+CREATE FUNCTION intvec_in(cstring, oid, integer) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_out(intvec) RETURNS cstring
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_typmod_in(cstring[]) RETURNS integer
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_recv(internal, oid, integer) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_send(intvec) RETURNS bytea
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE TYPE intvec (
+	INPUT     = intvec_in,
+	OUTPUT    = intvec_out,
+	TYPMOD_IN = intvec_typmod_in,
+	RECEIVE   = intvec_recv,
+	SEND      = intvec_send,
+	STORAGE   = external
+);
+
+-- intvec functions
+
+CREATE FUNCTION l2_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l2_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION inner_product(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_inner_product' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION cosine_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_cosine_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l1_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l1_distance' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION vector_dims(intvec) RETURNS integer
+	AS 'MODULE_PATHNAME', 'intvec_vector_dims' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION l2_norm(intvec) RETURNS float8
+	AS 'MODULE_PATHNAME', 'intvec_l2_norm' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- intvec private functions
+
+CREATE FUNCTION intvec_lt(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_le(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_eq(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_ne(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_ge(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_gt(intvec, intvec) RETURNS bool
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_cmp(intvec, intvec) RETURNS int4
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_l2_squared_distance(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_negative_inner_product(intvec, intvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- intvec cast functions
+
+CREATE FUNCTION intvec(intvec, integer, boolean) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION array_to_intvec(integer[], integer, boolean) RETURNS intvec
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+CREATE FUNCTION intvec_to_integer(intvec, integer, boolean) RETURNS integer[]
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
+-- intvec casts
+
+CREATE CAST (intvec AS intvec)
+	WITH FUNCTION intvec(intvec, integer, boolean) AS IMPLICIT;
+
+CREATE CAST (intvec AS integer[])
+	WITH FUNCTION intvec_to_integer(intvec, integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (integer[] AS intvec)
+	WITH FUNCTION array_to_intvec(integer[], integer, boolean) AS ASSIGNMENT;
+
+-- intvec operators
+
+CREATE OPERATOR <-> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = l2_distance,
+	COMMUTATOR = '<->'
+);
+
+CREATE OPERATOR <#> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_negative_inner_product,
+	COMMUTATOR = '<#>'
+);
+
+CREATE OPERATOR <=> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = cosine_distance,
+	COMMUTATOR = '<=>'
+);
+
+CREATE OPERATOR <+> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = l1_distance,
+	COMMUTATOR = '<+>'
+);
+
+CREATE OPERATOR < (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_lt,
+	COMMUTATOR = > , NEGATOR = >= ,
+	RESTRICT = scalarltsel, JOIN = scalarltjoinsel
+);
+
+CREATE OPERATOR <= (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_le,
+	COMMUTATOR = >= , NEGATOR = > ,
+	RESTRICT = scalarlesel, JOIN = scalarlejoinsel
+);
+
+CREATE OPERATOR = (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_eq,
+	COMMUTATOR = = , NEGATOR = <> ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR <> (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_ne,
+	COMMUTATOR = <> , NEGATOR = = ,
+	RESTRICT = eqsel, JOIN = eqjoinsel
+);
+
+CREATE OPERATOR >= (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_ge,
+	COMMUTATOR = <= , NEGATOR = < ,
+	RESTRICT = scalargesel, JOIN = scalargejoinsel
+);
+
+CREATE OPERATOR > (
+	LEFTARG = intvec, RIGHTARG = intvec, PROCEDURE = intvec_gt,
+	COMMUTATOR = < , NEGATOR = <= ,
+	RESTRICT = scalargtsel, JOIN = scalargtjoinsel
+);
+
+-- intvec opclasses
+
+CREATE OPERATOR CLASS intvec_ops
+	DEFAULT FOR TYPE intvec USING btree AS
+	OPERATOR 1 < ,
+	OPERATOR 2 <= ,
+	OPERATOR 3 = ,
+	OPERATOR 4 >= ,
+	OPERATOR 5 > ,
+	FUNCTION 1 intvec_cmp(intvec, intvec);
+
+CREATE OPERATOR CLASS intvec_l2_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <-> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 intvec_l2_squared_distance(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_ip_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <#> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 intvec_negative_inner_product(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_cosine_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <=> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 cosine_distance(intvec, intvec),
+	FUNCTION 2 l2_norm(intvec),
+	FUNCTION 3 hnsw_intvec_support(internal);
+
+CREATE OPERATOR CLASS intvec_l1_ops
+	FOR TYPE intvec USING hnsw AS
+	OPERATOR 1 <+> (intvec, intvec) FOR ORDER BY float_ops,
+	FUNCTION 1 l1_distance(intvec, intvec),
+	FUNCTION 3 hnsw_intvec_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

@@ -9,14 +9,25 @@
 #include "commands/vacuum.h"
 #include "hnsw.h"
 #include "miscadmin.h"
+#include "utils/float.h"
 #include "utils/guc.h"
 #include "utils/selfuncs.h"
+#include "utils/spccache.h"
 
 #if PG_VERSION_NUM < 150000
 #define MarkGUCPrefixReserved(x) EmitWarningsOnPlaceholders(x)
 #endif
 
+static const struct config_enum_entry hnsw_iterative_search_options[] = {
+	{"off", HNSW_ITERATIVE_SEARCH_OFF, false},
+	{"relaxed_order", HNSW_ITERATIVE_SEARCH_RELAXED, false},
+	{"strict_order", HNSW_ITERATIVE_SEARCH_STRICT, false},
+	{NULL, 0, false}
+};
+
 int			hnsw_ef_search;
+int			hnsw_max_search_tuples;
+int			hnsw_iterative_search;
 int			hnsw_lock_tranche_id;
 static relopt_kind hnsw_relopt_kind;
 
@@ -59,22 +70,23 @@ HnswInit(void)
 
 	hnsw_relopt_kind = add_reloption_kind();
 	add_int_reloption(hnsw_relopt_kind, "m", "Max number of connections",
-					  HNSW_DEFAULT_M, HNSW_MIN_M, HNSW_MAX_M
-#if PG_VERSION_NUM >= 130000
-					  ,AccessExclusiveLock
-#endif
-		);
+					  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
-#if PG_VERSION_NUM >= 130000
-					  ,AccessExclusiveLock
-#endif
-		);
+					  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);
 
+	DefineCustomEnumVariable("hnsw.iterative_search", "Sets the iterative search mode",
+							 NULL, &hnsw_iterative_search,
+							 HNSW_ITERATIVE_SEARCH_OFF, hnsw_iterative_search_options, PGC_USERSET, 0, NULL, NULL, NULL);
+
+	/* This is approximate and does not apply to the initial scan */
+	DefineCustomIntVariable("hnsw.max_search_tuples", "Sets the max number of candidates to visit for iterative search",
+							"-1 means no limit", &hnsw_max_search_tuples,
+							-1, -1, INT_MAX, PGC_USERSET, 0, NULL, NULL, NULL);
+
 	MarkGUCPrefixReserved("hnsw");
 }
 
@@ -106,14 +118,16 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 {
 	GenericCosts costs;
 	int			m;
-	int			entryLevel;
+	double		ratio;
+	double		startupPages;
+	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;
 		*indexPages = 0;
@@ -122,21 +136,71 @@ hnswcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 
 	MemSet(&costs, 0, sizeof(costs));
 
+	genericcostestimate(root, path, loop_count, &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);
+	/*
+	 * HNSW cost estimation follows a formula that accounts for the total
+	 * number of tuples indexed combined with the parameters that most
+	 * influence the duration of the index scan, namely: m - the number of
+	 * tuples that are scanned in each step of the HNSW graph traversal
+	 * ef_search - which influences the total number of steps taken at layer 0
+	 *
+	 * The source of the vector data can impact how many steps it takes to
+	 * converge on the set of vectors to return to the executor. Currently, we
+	 * use a hardcoded scaling factor (HNSWScanScalingFactor) to help
+	 * influence that, but this could later become a configurable parameter
+	 * based on the cost estimations.
+	 *
+	 * The tuple estimator formula is below:
+	 *
+	 * numIndexTuples = entryLevel * m + layer0TuplesMax * layer0Selectivity
+	 *
+	 * "entryLevel * m" represents the floor of tuples we need to scan to get
+	 * to layer 0 (L0).
+	 *
+	 * "layer0TuplesMax" is the estimated total number of tuples we'd scan at
+	 * L0 if we weren't discarding already visited tuples as part of the scan.
+	 *
+	 * "layer0Selectivity" estimates the percentage of tuples that are scanned
+	 * at L0, accounting for previously visited tuples, multiplied by the
+	 * "scalingFactor" (currently hardcoded).
+	 */
+	if (path->indexinfo->tuples > 0)
+	{
+		double		scalingFactor = 0.55;
+		int			entryLevel = (int) (log(path->indexinfo->tuples) * HnswGetMl(m));
+		int			layer0TuplesMax = HnswGetLayerM(m, 0) * hnsw_ef_search;
+		double		layer0Selectivity = scalingFactor * log(path->indexinfo->tuples) / (log(m) * (1 + log(hnsw_ef_search)));
 
-	/* 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;
+		ratio = (entryLevel * m + layer0TuplesMax * layer0Selectivity) / path->indexinfo->tuples;
 
-	genericcostestimate(root, path, loop_count, &costs);
+		if (ratio > 1)
+			ratio = 1;
+	}
+	else
+		ratio = 1;
 
-	/* Use total cost since most work happens before first tuple is returned */
-	*indexStartupCost = costs.indexTotalCost;
+	get_tablespace_page_costs(path->indexinfo->reltablespace, NULL, &spc_seq_page_cost);
+
+	/* Startup cost is cost before returning the first row */
+	costs.indexStartupCost = costs.indexTotalCost * ratio;
+
+	/* Adjust cost if needed since TOAST not included in seq scan cost */
+	startupPages = costs.numIndexPages * ratio;
+	if (startupPages > path->indexinfo->rel->pages && ratio < 0.5)
+	{
+		/* Change all page cost from random to sequential */
+		costs.indexStartupCost -= startupPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+
+		/* Remove cost of extra pages */
+		costs.indexStartupCost -= (startupPages - path->indexinfo->rel->pages) * spc_seq_page_cost;
+	}
+
+	*indexStartupCost = costs.indexStartupCost;
 	*indexTotalCost = costs.indexTotalCost;
 	*indexSelectivity = costs.indexSelectivity;
 	*indexCorrelation = costs.indexCorrelation;
@@ -154,23 +218,10 @@ hnswoptions(Datum reloptions, bool validate)
 		{"ef_construction", RELOPT_TYPE_INT, offsetof(HnswOptions, efConstruction)},
 	};
 
-#if PG_VERSION_NUM >= 130000
 	return (bytea *) build_reloptions(reloptions, validate,
 									  hnsw_relopt_kind,
 									  sizeof(HnswOptions),
 									  tab, lengthof(tab));
-#else
-	relopt_value *options;
-	int			numoptions;
-	HnswOptions *rdopts;
-
-	options = parseRelOptions(reloptions, validate, hnsw_relopt_kind, &numoptions);
-	rdopts = allocateReloptStruct(sizeof(HnswOptions), options, numoptions);
-	fillRelOptions((void *) rdopts, sizeof(HnswOptions), options, numoptions,
-				   validate, tab, lengthof(tab));
-
-	return (bytea *) rdopts;
-#endif
 }
 
 /*
@@ -187,17 +238,15 @@ hnswvalidate(Oid opclassoid)
  *
  * See https://www.postgresql.org/docs/current/index-api.html
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(hnswhandler);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(hnswhandler);
 Datum
 hnswhandler(PG_FUNCTION_ARGS)
 {
 	IndexAmRoutine *amroutine = makeNode(IndexAmRoutine);
 
 	amroutine->amstrategies = 0;
-	amroutine->amsupport = 2;
-#if PG_VERSION_NUM >= 130000
+	amroutine->amsupport = 3;
 	amroutine->amoptsprocnum = 0;
-#endif
 	amroutine->amcanorder = false;
 	amroutine->amcanorderbyop = true;
 	amroutine->amcanbackward = false;	/* can change direction mid-scan */
@@ -210,17 +259,24 @@ hnswhandler(PG_FUNCTION_ARGS)
 	amroutine->amclusterable = false;
 	amroutine->ampredlocks = false;
 	amroutine->amcanparallel = false;
-	amroutine->amcaninclude = false;
-#if PG_VERSION_NUM >= 130000
-	amroutine->amusemaintenanceworkmem = false; /* not used during VACUUM */
-	amroutine->amparallelvacuumoptions = VACUUM_OPTION_PARALLEL_BULKDEL;
+#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;

src/hnsw.h

@@ -12,15 +12,13 @@
 #include "utils/sampling.h"
 #include "vector.h"
 
-#if PG_VERSION_NUM < 120000
-#error "Requires PostgreSQL 12+"
-#endif
-
 #define HNSW_MAX_DIM 2000
+#define HNSW_MAX_NNZ 1000
 
 /* Support functions */
 #define HNSW_DISTANCE_PROC 1
 #define HNSW_NORM_PROC 2
+#define HNSW_TYPE_INFO_PROC 3
 
 #define HNSW_VERSION	1
 #define HNSW_MAGIC_NUMBER 0xA953A953
@@ -78,11 +76,6 @@
 #define SeedRandom(seed) srandom(seed)
 #endif
 
-#if PG_VERSION_NUM < 130000
-#define list_delete_last(list) list_truncate(list, list_length(list) - 1)
-#define list_sort(list, cmp) ((list) = list_qsort(list, cmp))
-#endif
-
 #define HnswIsElementTuple(tup) ((tup)->type == HNSW_ELEMENT_TUPLE_TYPE)
 #define HnswIsNeighborTuple(tup) ((tup)->type == HNSW_NEIGHBOR_TUPLE_TYPE)
 
@@ -95,6 +88,9 @@
 /* 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 HnswGetSearchCandidate(membername, ptr) pairingheap_container(HnswSearchCandidate, membername, ptr)
+#define HnswGetSearchCandidateConst(membername, ptr) pairingheap_const_container(HnswSearchCandidate, membername, ptr)
+
 #define HnswGetValue(base, element) PointerGetDatum(HnswPtrAccess(base, (element)->value))
 
 #if PG_VERSION_NUM < 140005
@@ -113,8 +109,17 @@
 
 /* Variables */
 extern int	hnsw_ef_search;
+extern int	hnsw_iterative_search;
+extern int	hnsw_max_search_tuples;
 extern int	hnsw_lock_tranche_id;
 
+typedef enum HnswIterativeSearchMode
+{
+	HNSW_ITERATIVE_SEARCH_OFF,
+	HNSW_ITERATIVE_SEARCH_RELAXED,
+	HNSW_ITERATIVE_SEARCH_STRICT
+}			HnswIterativeSearchMode;
+
 typedef struct HnswElementData HnswElementData;
 typedef struct HnswNeighborArray HnswNeighborArray;
 
@@ -136,6 +141,7 @@ struct HnswElementData
 	uint8		heaptidsLength;
 	uint8		level;
 	uint8		deleted;
+	uint8		version;
 	uint32		hash;
 	HnswNeighborsPtr neighbors;
 	BlockNumber blkno;
@@ -162,11 +168,13 @@ struct HnswNeighborArray
 	HnswCandidate items[FLEXIBLE_ARRAY_MEMBER];
 };
 
-typedef struct HnswPairingHeapNode
+typedef struct HnswSearchCandidate
 {
-	pairingheap_node ph_node;
-	HnswCandidate *inner;
-}			HnswPairingHeapNode;
+	pairingheap_node c_node;
+	pairingheap_node w_node;
+	HnswElementPtr element;
+	double		distance;
+}			HnswSearchCandidate;
 
 /* HNSW index options */
 typedef struct HnswOptions
@@ -190,8 +198,8 @@ typedef struct HnswGraph
 
 	/* Allocations state */
 	LWLock		allocatorLock;
-	long		memoryUsed;
-	long		memoryTotal;
+	Size		memoryUsed;
+	Size		memoryTotal;
 
 	/* Flushed state */
 	LWLock		flushLock;
@@ -235,6 +243,25 @@ typedef struct HnswAllocator
 	void	   *state;
 }			HnswAllocator;
 
+typedef struct HnswTypeInfo
+{
+	int			maxDimensions;
+	Datum		(*normalize) (PG_FUNCTION_ARGS);
+	void		(*checkValue) (Pointer v);
+}			HnswTypeInfo;
+
+typedef struct HnswSupport
+{
+	FmgrInfo   *procinfo;
+	FmgrInfo   *normprocinfo;
+	Oid			collation;
+}			HnswSupport;
+
+typedef struct HnswQuery
+{
+	Datum		value;
+}			HnswQuery;
+
 typedef struct HnswBuildState
 {
 	/* Info */
@@ -242,6 +269,7 @@ typedef struct HnswBuildState
 	Relation	index;
 	IndexInfo  *indexInfo;
 	ForkNumber	forkNum;
+	const		HnswTypeInfo *typeInfo;
 
 	/* Settings */
 	int			dimensions;
@@ -253,16 +281,13 @@ typedef struct HnswBuildState
 	double		reltuples;
 
 	/* Support functions */
-	FmgrInfo   *procinfo;
-	FmgrInfo   *normprocinfo;
-	Oid			collation;
+	HnswSupport support;
 
 	/* Variables */
 	HnswGraph	graphData;
 	HnswGraph  *graph;
 	double		ml;
 	int			maxLevel;
-	Vector	   *normvec;
 
 	/* Memory */
 	MemoryContext graphCtx;
@@ -304,10 +329,10 @@ typedef struct HnswElementTupleData
 	uint8		type;
 	uint8		level;
 	uint8		deleted;
-	uint8		unused;
+	uint8		version;
 	ItemPointerData heaptids[HNSW_HEAPTIDS];
 	ItemPointerData neighbortid;
-	uint16		unused2;
+	uint16		unused;
 	Vector		data;
 }			HnswElementTupleData;
 
@@ -316,23 +341,41 @@ typedef HnswElementTupleData * HnswElementTuple;
 typedef struct HnswNeighborTupleData
 {
 	uint8		type;
-	uint8		unused;
+	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 union
+{
+	HnswElement element;
+	ItemPointerData indextid;
+}			HnswUnvisited;
+
 typedef struct HnswScanOpaqueData
 {
+	const		HnswTypeInfo *typeInfo;
 	bool		first;
 	List	   *w;
+	visited_hash v;
+	pairingheap *discarded;
+	HnswQuery	q;
+	int			m;
+	int64		tuples;
+	double		previousDistance;
 	MemoryContext tmpCtx;
 
 	/* Support functions */
-	FmgrInfo   *procinfo;
-	FmgrInfo   *normprocinfo;
-	Oid			collation;
+	HnswSupport support;
 }			HnswScanOpaqueData;
 
 typedef HnswScanOpaqueData * HnswScanOpaque;
@@ -350,8 +393,7 @@ typedef struct HnswVacuumState
 	int			efConstruction;
 
 	/* Support functions */
-	FmgrInfo   *procinfo;
-	Oid			collation;
+	HnswSupport support;
 
 	/* Variables */
 	struct tidhash_hash *deleted;
@@ -367,30 +409,35 @@ typedef struct HnswVacuumState
 int			HnswGetM(Relation index);
 int			HnswGetEfConstruction(Relation index);
 FmgrInfo   *HnswOptionalProcInfo(Relation index, uint16 procnum);
-bool		HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+void		HnswInitSupport(HnswSupport * support, Relation index);
+Datum		HnswNormValue(const HnswTypeInfo * typeInfo, Oid collation, Datum value);
+bool		HnswCheckNorm(HnswSupport * support, 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);
+List	   *HnswSearchLayer(char *base, HnswQuery * q, List *ep, int ef, int lc, Relation index, HnswSupport * support, int m, bool inserting, HnswElement skipElement, visited_hash * v, pairingheap **discarded, bool initVisited, int64 *tuples);
 HnswElement HnswGetEntryPoint(Relation index);
 void		HnswGetMetaPageInfo(Relation index, int *m, HnswElement * entryPoint);
 void	   *HnswAlloc(HnswAllocator * allocator, Size size);
 HnswElement HnswInitElement(char *base, ItemPointer tid, int m, double ml, int maxLevel, HnswAllocator * alloc);
 HnswElement HnswInitElementFromBlock(BlockNumber blkno, OffsetNumber offno);
-void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, FmgrInfo *procinfo, Oid collation, int m, int efConstruction, bool existing);
-HnswCandidate *HnswEntryCandidate(char *base, HnswElement em, Datum q, Relation rel, FmgrInfo *procinfo, Oid collation, bool loadVec);
+void		HnswFindElementNeighbors(char *base, HnswElement element, HnswElement entryPoint, Relation index, HnswSupport * support, int m, int efConstruction, bool existing);
+HnswSearchCandidate *HnswEntryCandidate(char *base, HnswElement em, HnswQuery * q, Relation rel, HnswSupport * support, 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);
+HnswNeighborArray *HnswInitNeighborArray(int lm, HnswAllocator * allocator);
 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);
+bool		HnswInsertTupleOnDisk(Relation index, HnswSupport * support, Datum value, ItemPointer heaptid, bool building);
+void		HnswUpdateNeighborsOnDisk(Relation index, HnswSupport * support, HnswElement e, int m, bool checkExisting, bool building);
 void		HnswLoadElementFromTuple(HnswElement element, HnswElementTuple etup, bool loadHeaptids, bool loadVec);
-void		HnswLoadElement(HnswElement element, float *distance, Datum *q, Relation index, FmgrInfo *procinfo, Oid collation, bool loadVec);
+void		HnswLoadElement(HnswElement element, double *distance, HnswQuery * q, Relation index, HnswSupport * support, bool loadVec, double *maxDistance);
+bool		HnswFormIndexValue(Datum *out, Datum *values, bool *isnull, const HnswTypeInfo * typeInfo, HnswSupport * support);
 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		HnswUpdateConnection(char *base, HnswNeighborArray * neighbors, HnswElement newElement, float distance, int lm, int *updateIdx, Relation index, HnswSupport * support);
+bool		HnswLoadNeighborTids(HnswElement element, ItemPointerData *indextids, Relation index, int m, int lm, int lc);
 void		HnswInitLockTranche(void);
+const		HnswTypeInfo *HnswGetTypeInfo(Relation index);
 PGDLLEXPORT void HnswParallelBuildMain(dsm_segment *seg, shm_toc *toc);
 
 /* Index access methods */

src/hnswbuild.c

@@ -44,6 +44,7 @@
 #include "access/xact.h"
 #include "access/xloginsert.h"
 #include "catalog/index.h"
+#include "catalog/pg_type_d.h"
 #include "commands/progress.h"
 #include "hnsw.h"
 #include "miscadmin.h"
@@ -59,12 +60,6 @@
 #include "pgstat.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 >= 140000
 #include "utils/backend_status.h"
 #include "utils/wait_event.h"
@@ -74,10 +69,6 @@
 #define PARALLEL_KEY_HNSW_AREA			UINT64CONST(0xA000000000000002)
 #define PARALLEL_KEY_QUERY_TEXT			UINT64CONST(0xA000000000000003)
 
-#if PG_VERSION_NUM < 130000
-#define GENERATIONCHUNK_RAWSIZE (SIZEOF_SIZE_T + SIZEOF_VOID_P * 2)
-#endif
-
 /*
  * Create the metapage
  */
@@ -191,7 +182,9 @@ CreateGraphPages(HnswBuildState * buildstate)
 
 		/* Initial size check */
 		if (etupSize > HNSW_TUPLE_ALLOC_SIZE)
-			elog(ERROR, "index tuple too large");
+			ereport(ERROR,
+					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+					 errmsg("index tuple too large")));
 
 		HnswSetElementTuple(base, etup, element);
 
@@ -373,12 +366,18 @@ AddElementInMemory(char *base, HnswGraph * graph, HnswElement element)
  * Update neighbors
  */
 static void
-UpdateNeighborsInMemory(char *base, FmgrInfo *procinfo, Oid collation, HnswElement e, int m)
+UpdateNeighborsInMemory(char *base, HnswSupport * support, HnswElement e, int m)
 {
 	for (int lc = e->level; lc >= 0; lc--)
 	{
 		int			lm = HnswGetLayerM(m, lc);
-		HnswNeighborArray *neighbors = HnswGetNeighbors(base, e, lc);
+		Size		neighborsSize = HNSW_NEIGHBOR_ARRAY_SIZE(lm);
+		HnswNeighborArray *neighbors = palloc(neighborsSize);
+
+		/* Copy neighbors to local memory */
+		LWLockAcquire(&e->lock, LW_SHARED);
+		memcpy(neighbors, HnswGetNeighbors(base, e, lc), neighborsSize);
+		LWLockRelease(&e->lock);
 
 		for (int i = 0; i < neighbors->length; i++)
 		{
@@ -388,9 +387,8 @@ UpdateNeighborsInMemory(char *base, FmgrInfo *procinfo, Oid collation, HnswEleme
 			/* Keep scan-build happy on Mac x86-64 */
 			Assert(neighborElement);
 
-			/* Use element for lock instead of hc since hc can be replaced */
 			LWLockAcquire(&neighborElement->lock, LW_EXCLUSIVE);
-			HnswUpdateConnection(base, e, hc, lm, lc, NULL, NULL, procinfo, collation);
+			HnswUpdateConnection(base, HnswGetNeighbors(base, neighborElement, lc), e, hc->distance, lm, NULL, NULL, support);
 			LWLockRelease(&neighborElement->lock);
 		}
 	}
@@ -400,7 +398,7 @@ UpdateNeighborsInMemory(char *base, FmgrInfo *procinfo, Oid collation, HnswEleme
  * Update graph in memory
  */
 static void
-UpdateGraphInMemory(FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement entryPoint, HnswBuildState * buildstate)
+UpdateGraphInMemory(HnswSupport * support, HnswElement element, int m, int efConstruction, HnswElement entryPoint, HnswBuildState * buildstate)
 {
 	HnswGraph  *graph = buildstate->graph;
 	char	   *base = buildstate->hnswarea;
@@ -413,7 +411,7 @@ UpdateGraphInMemory(FmgrInfo *procinfo, Oid collation, HnswElement element, int
 	AddElementInMemory(base, graph, element);
 
 	/* Update neighbors */
-	UpdateNeighborsInMemory(base, procinfo, collation, element, m);
+	UpdateNeighborsInMemory(base, support, element, m);
 
 	/* Update entry point if needed (already have lock) */
 	if (entryPoint == NULL || element->level > entryPoint->level)
@@ -426,9 +424,8 @@ UpdateGraphInMemory(FmgrInfo *procinfo, Oid collation, HnswElement element, int
 static void
 InsertTupleInMemory(HnswBuildState * buildstate, HnswElement element)
 {
-	FmgrInfo   *procinfo = buildstate->procinfo;
-	Oid			collation = buildstate->collation;
 	HnswGraph  *graph = buildstate->graph;
+	HnswSupport *support = &buildstate->support;
 	HnswElement entryPoint;
 	LWLock	   *entryLock = &graph->entryLock;
 	LWLock	   *entryWaitLock = &graph->entryWaitLock;
@@ -460,10 +457,10 @@ InsertTupleInMemory(HnswBuildState * buildstate, HnswElement element)
 	}
 
 	/* Find neighbors for element */
-	HnswFindElementNeighbors(base, element, entryPoint, NULL, procinfo, collation, m, efConstruction, false);
+	HnswFindElementNeighbors(base, element, entryPoint, NULL, support, m, efConstruction, false);
 
 	/* Update graph in memory */
-	UpdateGraphInMemory(procinfo, collation, element, m, efConstruction, entryPoint, buildstate);
+	UpdateGraphInMemory(support, element, m, efConstruction, entryPoint, buildstate);
 
 	/* Release entry lock */
 	LWLockRelease(entryLock);
@@ -478,20 +475,16 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, Hn
 	HnswGraph  *graph = buildstate->graph;
 	HnswElement element;
 	HnswAllocator *allocator = &buildstate->allocator;
+	HnswSupport *support = &buildstate->support;
 	Size		valueSize;
 	Pointer		valuePtr;
 	LWLock	   *flushLock = &graph->flushLock;
 	char	   *base = buildstate->hnswarea;
+	Datum		value;
 
-	/* Detoast once for all calls */
-	Datum		value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
-
-	/* Normalize if needed */
-	if (buildstate->normprocinfo != NULL)
-	{
-		if (!HnswNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->normvec))
-			return false;
-	}
+	/* Form index value */
+	if (!HnswFormIndexValue(&value, values, isnull, buildstate->typeInfo, support))
+		return false;
 
 	/* Get datum size */
 	valueSize = VARSIZE_ANY(DatumGetPointer(value));
@@ -504,7 +497,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, Hn
 	{
 		LWLockRelease(flushLock);
 
-		return HnswInsertTupleOnDisk(index, value, values, isnull, heaptid, true);
+		return HnswInsertTupleOnDisk(index, support, value, heaptid, true);
 	}
 
 	/*
@@ -536,7 +529,7 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, Hn
 
 		LWLockRelease(flushLock);
 
-		return HnswInsertTupleOnDisk(index, value, values, isnull, heaptid, true);
+		return HnswInsertTupleOnDisk(index, support, value, heaptid, true);
 	}
 
 	/* Ok, we can proceed to allocate the element */
@@ -570,17 +563,13 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid, Hn
  * Callback for table_index_build_scan
  */
 static void
-BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
+BuildCallback(Relation index, ItemPointer tid, Datum *values,
 			  bool *isnull, bool tupleIsAlive, void *state)
 {
 	HnswBuildState *buildstate = (HnswBuildState *) state;
 	HnswGraph  *graph = buildstate->graph;
 	MemoryContext oldCtx;
 
-#if PG_VERSION_NUM < 130000
-	ItemPointer tid = &hup->t_self;
-#endif
-
 	/* Skip nulls */
 	if (isnull[0])
 		return;
@@ -606,7 +595,7 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
  * Initialize the graph
  */
 static void
-InitGraph(HnswGraph * graph, char *base, long memoryTotal)
+InitGraph(HnswGraph * graph, char *base, Size memoryTotal)
 {
 	/* Initialize the lock tranche if needed */
 	HnswInitLockTranche();
@@ -643,11 +632,7 @@ HnswMemoryContextAlloc(Size size, void *state)
 	HnswBuildState *buildstate = (HnswBuildState *) state;
 	void	   *chunk = MemoryContextAlloc(buildstate->graphCtx, size);
 
-#if PG_VERSION_NUM >= 130000
 	buildstate->graphData.memoryUsed = MemoryContextMemAllocated(buildstate->graphCtx, false);
-#else
-	buildstate->graphData.memoryUsed += MAXALIGN(size);
-#endif
 
 	return chunk;
 }
@@ -675,37 +660,45 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	buildstate->index = index;
 	buildstate->indexInfo = indexInfo;
 	buildstate->forkNum = forkNum;
+	buildstate->typeInfo = HnswGetTypeInfo(index);
 
 	buildstate->m = HnswGetM(index);
 	buildstate->efConstruction = HnswGetEfConstruction(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 hnsw 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 > HNSW_MAX_DIM)
-		elog(ERROR, "column cannot have more than %d dimensions for hnsw index", HNSW_MAX_DIM);
+	if (buildstate->dimensions > buildstate->typeInfo->maxDimensions)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("column cannot have more than %d dimensions for hnsw index", buildstate->typeInfo->maxDimensions)));
 
 	if (buildstate->efConstruction < 2 * buildstate->m)
-		elog(ERROR, "ef_construction must be greater than or equal to 2 * m");
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("ef_construction must be greater than or equal to 2 * m")));
 
 	buildstate->reltuples = 0;
 	buildstate->indtuples = 0;
 
 	/* Get support functions */
-	buildstate->procinfo = index_getprocinfo(index, 1, HNSW_DISTANCE_PROC);
-	buildstate->normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
-	buildstate->collation = index->rd_indcollation[0];
+	HnswInitSupport(&buildstate->support, index);
 
-	InitGraph(&buildstate->graphData, NULL, maintenance_work_mem * 1024L);
+	InitGraph(&buildstate->graphData, NULL, (Size) maintenance_work_mem * 1024L);
 	buildstate->graph = &buildstate->graphData;
 	buildstate->ml = HnswGetMl(buildstate->m);
 	buildstate->maxLevel = HnswGetMaxLevel(buildstate->m);
 
-	/* Reuse for each tuple */
-	buildstate->normvec = InitVector(buildstate->dimensions);
-
 	buildstate->graphCtx = GenerationContextCreate(CurrentMemoryContext,
 												   "Hnsw build graph context",
 #if PG_VERSION_NUM >= 150000
@@ -729,7 +722,6 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 static void
 FreeBuildState(HnswBuildState * buildstate)
 {
-	pfree(buildstate->normvec);
 	MemoryContextDelete(buildstate->graphCtx);
 	MemoryContextDelete(buildstate->tmpCtx);
 }
@@ -1112,8 +1104,8 @@ BuildIndex(Relation heap, Relation index, IndexInfo *indexInfo,
 
 	BuildGraph(buildstate, forkNum);
 
-	if (RelationNeedsWAL(index))
-		log_newpage_range(index, forkNum, 0, RelationGetNumberOfBlocks(index), true);
+	if (RelationNeedsWAL(index) || forkNum == INIT_FORKNUM)
+		log_newpage_range(index, forkNum, 0, RelationGetNumberOfBlocksInFork(index, forkNum), true);
 
 	FreeBuildState(buildstate);
 }

src/hnswinsert.c

@@ -36,14 +36,15 @@ GetInsertPage(Relation index)
  * Check for a free offset
  */
 static bool
-HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size ntupSize, Buffer *nbuf, Page *npage, OffsetNumber *freeOffno, OffsetNumber *freeNeighborOffno, BlockNumber *newInsertPage)
+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))
 	{
-		HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, PageGetItemId(page, offno));
+		ItemId		eitemid = PageGetItemId(page, offno);
+		HnswElementTuple etup = (HnswElementTuple) PageGetItem(page, eitemid);
 
 		/* Skip neighbor tuples */
 		if (!HnswIsElementTuple(etup))
@@ -54,7 +55,9 @@ HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size
 			BlockNumber elementPage = BufferGetBlockNumber(buf);
 			BlockNumber neighborPage = ItemPointerGetBlockNumber(&etup->neighbortid);
 			OffsetNumber neighborOffno = ItemPointerGetOffsetNumber(&etup->neighbortid);
-			ItemId		itemid;
+			ItemId		nitemid;
+			Size		pageFree;
+			Size		npageFree;
 
 			if (!BlockNumberIsValid(*newInsertPage))
 				*newInsertPage = elementPage;
@@ -73,13 +76,29 @@ HnswFreeOffset(Relation index, Buffer buf, Page page, HnswElement element, Size
 				*npage = BufferGetPage(*nbuf);
 			}
 
-			itemid = PageGetItemId(*npage, neighborOffno);
+			nitemid = PageGetItemId(*npage, neighborOffno);
 
-			/* Check for space on neighbor tuple page */
-			if (PageGetFreeSpace(*npage) + ItemIdGetLength(itemid) - sizeof(ItemIdData) >= ntupSize)
+			/* 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)
@@ -135,6 +154,7 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 	OffsetNumber freeOffno = InvalidOffsetNumber;
 	OffsetNumber freeNeighborOffno = InvalidOffsetNumber;
 	BlockNumber newInsertPage = InvalidBlockNumber;
+	uint8		tupleVersion;
 	char	   *base = NULL;
 
 	/* Calculate sizes */
@@ -184,7 +204,7 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 		}
 
 		/* Next, try space from a deleted element */
-		if (HnswFreeOffset(index, buf, page, e, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage))
+		if (HnswFreeOffset(index, buf, page, e, etupSize, ntupSize, &nbuf, &npage, &freeOffno, &freeNeighborOffno, &newInsertPage, &tupleVersion))
 		{
 			if (nbuf != buf)
 			{
@@ -194,6 +214,10 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 					npage = GenericXLogRegisterBuffer(state, nbuf, 0);
 			}
 
+			/* Set tuple version */
+			etup->version = tupleVersion;
+			ntup->version = tupleVersion;
+
 			break;
 		}
 
@@ -316,6 +340,107 @@ AddElementOnDisk(Relation index, HnswElement e, int m, BlockNumber insertPage, B
 		*updatedInsertPage = newInsertPage;
 }
 
+/*
+ * Load neighbors
+ */
+static HnswNeighborArray *
+HnswLoadNeighbors(HnswElement element, Relation index, int m, int lm, int lc)
+{
+	char	   *base = NULL;
+	HnswNeighborArray *neighbors = HnswInitNeighborArray(lm, NULL);
+	ItemPointerData indextids[HNSW_MAX_M * 2];
+
+	if (!HnswLoadNeighborTids(element, indextids, index, m, lm, lc))
+		return neighbors;
+
+	for (int i = 0; i < lm; i++)
+	{
+		ItemPointer indextid = &indextids[i];
+		HnswElement e;
+		HnswCandidate *hc;
+
+		if (!ItemPointerIsValid(indextid))
+			break;
+
+		e = HnswInitElementFromBlock(ItemPointerGetBlockNumber(indextid), ItemPointerGetOffsetNumber(indextid));
+		hc = &neighbors->items[neighbors->length++];
+		HnswPtrStore(base, hc->element, e);
+	}
+
+	return neighbors;
+}
+
+/*
+ * Load elements for insert
+ */
+static void
+LoadElementsForInsert(HnswNeighborArray * neighbors, HnswQuery * q, int *idx, Relation index, HnswSupport * support)
+{
+	char	   *base = NULL;
+
+	for (int i = 0; i < neighbors->length; i++)
+	{
+		HnswCandidate *hc = &neighbors->items[i];
+		HnswElement element = HnswPtrAccess(base, hc->element);
+		double		distance;
+
+		HnswLoadElement(element, &distance, q, index, support, true, NULL);
+		hc->distance = distance;
+
+		/* Prune element if being deleted */
+		if (element->heaptidsLength == 0)
+		{
+			*idx = i;
+			break;
+		}
+	}
+}
+
+/*
+ * Get update index
+ */
+static int
+GetUpdateIndex(HnswElement element, HnswElement newElement, float distance, int m, int lm, int lc, Relation index, HnswSupport * support, MemoryContext updateCtx)
+{
+	char	   *base = NULL;
+	int			idx = -1;
+	HnswNeighborArray *neighbors;
+	MemoryContext oldCtx = MemoryContextSwitchTo(updateCtx);
+
+	/*
+	 * 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.
+	 */
+	neighbors = HnswLoadNeighbors(element, index, m, lm, lc);
+
+	/*
+	 * 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.
+	 */
+
+	if (neighbors->length < lm)
+		idx = -2;
+	else
+	{
+		HnswQuery	q;
+
+		q.value = HnswGetValue(base, element);
+
+		LoadElementsForInsert(neighbors, &q, &idx, index, support);
+
+		if (idx == -1)
+			HnswUpdateConnection(base, neighbors, newElement, distance, lm, &idx, index, support);
+	}
+
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextReset(updateCtx);
+
+	return idx;
+}
+
 /*
  * Check if connection already exists
  */
@@ -336,14 +461,94 @@ ConnectionExists(HnswElement e, HnswNeighborTuple ntup, int startIdx, int lm)
 	return false;
 }
 
+/*
+ * Update neighbor
+ */
+static void
+UpdateNeighborOnDisk(HnswElement element, HnswElement newElement, int idx, int m, int lm, int lc, Relation index, bool checkExisting, bool building)
+{
+	Buffer		buf;
+	Page		page;
+	GenericXLogState *state;
+	HnswNeighborTuple ntup;
+	int			startIdx;
+	OffsetNumber offno = element->neighborOffno;
+
+	/* Register page */
+	buf = ReadBuffer(index, element->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 = (element->level - lc) * m;
+
+	/* Check for existing connection */
+	if (checkExisting && ConnectionExists(newElement, 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, newElement->blkno, newElement->offno);
+
+		/* Commit */
+		if (building)
+			MarkBufferDirty(buf);
+		else
+			GenericXLogFinish(state);
+	}
+	else if (!building)
+		GenericXLogAbort(state);
+
+	UnlockReleaseBuffer(buf);
+}
+
 /*
  * Update neighbors
  */
 void
-HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement e, int m, bool checkExisting, bool building)
+HnswUpdateNeighborsOnDisk(Relation index, HnswSupport * support, HnswElement e, int m, bool checkExisting, bool building)
 {
 	char	   *base = NULL;
 
+	/* Use separate memory context to improve performance for larger vectors */
+	MemoryContext updateCtx = GenerationContextCreate(CurrentMemoryContext,
+													  "Hnsw insert update context",
+#if PG_VERSION_NUM >= 150000
+													  128 * 1024, 128 * 1024,
+#endif
+													  128 * 1024);
+
 	for (int lc = e->level; lc >= 0; lc--)
 	{
 		int			lm = HnswGetLayerM(m, lc);
@@ -352,92 +557,20 @@ HnswUpdateNeighborsOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, Hns
 		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;
+			int			idx;
 
-			/* Get latest neighbors since they may have changed */
-			/* Do not lock yet since selecting neighbors can take time */
-			HnswLoadNeighbors(neighborElement, index, m);
-
-			/*
-			 * Could improve performance for vacuuming by checking neighbors
-			 * against list of elements being deleted to find index. It's
-			 * important to exclude already deleted elements for this since
-			 * they can be replaced at any time.
-			 */
-
-			/* Select neighbors */
-			HnswUpdateConnection(NULL, e, hc, lm, lc, &idx, index, procinfo, collation);
+			idx = GetUpdateIndex(neighborElement, e, hc->distance, m, lm, lc, index, support, updateCtx);
 
 			/* 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);
+			UpdateNeighborOnDisk(neighborElement, e, idx, m, lm, lc, index, checkExisting, building);
 		}
 	}
+
+	MemoryContextDelete(updateCtx);
 }
 
 /*
@@ -527,7 +660,7 @@ FindDuplicateOnDisk(Relation index, HnswElement element, bool building)
  * Update graph on disk
  */
 static void
-UpdateGraphOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement element, int m, int efConstruction, HnswElement entryPoint, bool building)
+UpdateGraphOnDisk(Relation index, HnswSupport * support, HnswElement element, int m, int efConstruction, HnswElement entryPoint, bool building)
 {
 	BlockNumber newInsertPage = InvalidBlockNumber;
 
@@ -543,7 +676,7 @@ UpdateGraphOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement
 		HnswUpdateMetaPage(index, 0, NULL, newInsertPage, MAIN_FORKNUM, building);
 
 	/* Update neighbors */
-	HnswUpdateNeighborsOnDisk(index, procinfo, collation, element, m, false, building);
+	HnswUpdateNeighborsOnDisk(index, support, element, m, false, building);
 
 	/* Update entry point if needed */
 	if (entryPoint == NULL || element->level > entryPoint->level)
@@ -554,14 +687,12 @@ UpdateGraphOnDisk(Relation index, FmgrInfo *procinfo, Oid collation, HnswElement
  * Insert a tuple into the index
  */
 bool
-HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull, ItemPointer heap_tid, bool building)
+HnswInsertTupleOnDisk(Relation index, HnswSupport * support, Datum value, ItemPointer heaptid, 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;
 
@@ -576,7 +707,7 @@ HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull,
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
 
 	/* Create an element */
-	element = HnswInitElement(base, heap_tid, m, HnswGetMl(m), HnswGetMaxLevel(m), NULL);
+	element = HnswInitElement(base, heaptid, m, HnswGetMl(m), HnswGetMaxLevel(m), NULL);
 	HnswPtrStore(base, element->value, DatumGetPointer(value));
 
 	/* Prevent concurrent inserts when likely updating entry point */
@@ -594,10 +725,10 @@ HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull,
 	}
 
 	/* Find neighbors for element */
-	HnswFindElementNeighbors(base, element, entryPoint, index, procinfo, collation, m, efConstruction, false);
+	HnswFindElementNeighbors(base, element, entryPoint, index, support, m, efConstruction, false);
 
 	/* Update graph on disk */
-	UpdateGraphOnDisk(index, procinfo, collation, element, m, efConstruction, entryPoint, building);
+	UpdateGraphOnDisk(index, support, element, m, efConstruction, entryPoint, building);
 
 	/* Release lock */
 	UnlockPage(index, HNSW_UPDATE_LOCK, lockmode);
@@ -609,24 +740,19 @@ HnswInsertTupleOnDisk(Relation index, Datum value, Datum *values, bool *isnull,
  * Insert a tuple into the index
  */
 static void
-HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid)
+HnswInsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heaptid)
 {
 	Datum		value;
-	FmgrInfo   *normprocinfo;
-	Oid			collation = index->rd_indcollation[0];
+	const		HnswTypeInfo *typeInfo = HnswGetTypeInfo(index);
+	HnswSupport support;
 
-	/* Detoast once for all calls */
-	value = PointerGetDatum(PG_DETOAST_DATUM(values[0]));
+	HnswInitSupport(&support, index);
 
-	/* Normalize if needed */
-	normprocinfo = HnswOptionalProcInfo(index, HNSW_NORM_PROC);
-	if (normprocinfo != NULL)
-	{
-		if (!HnswNormValue(normprocinfo, collation, &value, NULL))
-			return;
-	}
+	/* Form index value */
+	if (!HnswFormIndexValue(&value, values, isnull, typeInfo, &support))
+		return;
 
-	HnswInsertTupleOnDisk(index, value, values, isnull, heap_tid, false);
+	HnswInsertTupleOnDisk(index, &support, value, heaptid, false);
 }
 
 /*

src/hnswscan.c

@@ -5,62 +5,74 @@
 #include "pgstat.h"
 #include "storage/bufmgr.h"
 #include "storage/lmgr.h"
+#include "utils/float.h"
 #include "utils/memutils.h"
 
 /*
  * Algorithm 5 from paper
  */
 static List *
-GetScanItems(IndexScanDesc scan, Datum q)
+GetScanItems(IndexScanDesc scan, Datum value)
 {
 	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
 	Relation	index = scan->indexRelation;
-	FmgrInfo   *procinfo = so->procinfo;
-	Oid			collation = so->collation;
+	HnswSupport *support = &so->support;
 	List	   *ep;
 	List	   *w;
 	int			m;
 	HnswElement entryPoint;
 	char	   *base = NULL;
+	HnswQuery  *q = &so->q;
 
 	/* Get m and entry point */
 	HnswGetMetaPageInfo(index, &m, &entryPoint);
 
+	q->value = value;
+	so->m = m;
+
 	if (entryPoint == NULL)
 		return NIL;
 
-	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, procinfo, collation, false));
+	ep = list_make1(HnswEntryCandidate(base, entryPoint, q, index, support, false));
 
 	for (int lc = entryPoint->level; lc >= 1; lc--)
 	{
-		w = HnswSearchLayer(base, q, ep, 1, lc, index, procinfo, collation, m, false, NULL);
+		w = HnswSearchLayer(base, q, ep, 1, lc, index, support, m, false, NULL, NULL, NULL, true, NULL);
 		ep = w;
 	}
 
-	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, procinfo, collation, m, false, NULL);
+	return HnswSearchLayer(base, q, ep, hnsw_ef_search, 0, index, support, m, false, NULL, &so->v, hnsw_iterative_search != HNSW_ITERATIVE_SEARCH_OFF ? &so->discarded : NULL, true, &so->tuples);
 }
 
 /*
- * Get dimensions from metapage
+ * Resume scan at ground level with discarded candidates
  */
-static int
-GetDimensions(Relation index)
+static List *
+ResumeScanItems(IndexScanDesc scan)
 {
-	Buffer		buf;
-	Page		page;
-	HnswMetaPage metap;
-	int			dimensions;
+	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
+	Relation	index = scan->indexRelation;
+	List	   *ep = NIL;
+	char	   *base = NULL;
+	int			batch_size = hnsw_ef_search;
 
-	buf = ReadBuffer(index, HNSW_METAPAGE_BLKNO);
-	LockBuffer(buf, BUFFER_LOCK_SHARE);
-	page = BufferGetPage(buf);
-	metap = HnswPageGetMeta(page);
+	if (pairingheap_is_empty(so->discarded))
+		return NIL;
 
-	dimensions = metap->dimensions;
+	/* Get next batch of candidates */
+	for (int i = 0; i < batch_size; i++)
+	{
+		HnswSearchCandidate *sc;
 
-	UnlockReleaseBuffer(buf);
+		if (pairingheap_is_empty(so->discarded))
+			break;
 
-	return dimensions;
+		sc = HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded));
+
+		ep = lappend(ep, sc);
+	}
+
+	return HnswSearchLayer(base, &so->q, ep, batch_size, 0, index, &so->support, so->m, false, NULL, &so->v, &so->discarded, false, &so->tuples);
 }
 
 /*
@@ -73,7 +85,7 @@ GetScanValue(IndexScanDesc scan)
 	Datum		value;
 
 	if (scan->orderByData->sk_flags & SK_ISNULL)
-		value = PointerGetDatum(InitVector(GetDimensions(scan->indexRelation)));
+		value = PointerGetDatum(NULL);
 	else
 	{
 		value = scan->orderByData->sk_argument;
@@ -82,14 +94,25 @@ GetScanValue(IndexScanDesc scan)
 		Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
 		Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
 
-		/* Fine if normalization fails */
-		if (so->normprocinfo != NULL)
-			HnswNormValue(so->normprocinfo, so->collation, &value, NULL);
+		/* Normalize if needed */
+		if (so->support.normprocinfo != NULL)
+			value = HnswNormValue(so->typeInfo, so->support.collation, value);
 	}
 
 	return value;
 }
 
+#if defined(HNSW_MEMORY)
+/*
+ * Show memory usage
+ */
+static void
+ShowMemoryUsage(HnswScanOpaque so)
+{
+	elog(INFO, "memory: %zu KB, tuples: " INT64_FORMAT, MemoryContextMemAllocated(so->tmpCtx, false) / 1024, so->tuples);
+}
+#endif
+
 /*
  * Prepare for an index scan
  */
@@ -102,15 +125,21 @@ hnswbeginscan(Relation index, int nkeys, int norderbys)
 	scan = RelationGetIndexScan(index, nkeys, norderbys);
 
 	so = (HnswScanOpaque) palloc(sizeof(HnswScanOpaqueData));
+	so->typeInfo = HnswGetTypeInfo(index);
 	so->first = true;
+	so->v.tids = NULL;
+	so->discarded = NULL;
+
+	/*
+	 * Use a lower max allocation size than default to allow scanning more
+	 * tuples for iterative search before exceeding work_mem
+	 */
 	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
 									   "Hnsw scan temporary context",
-									   ALLOCSET_DEFAULT_SIZES);
+									   0, 8 * 1024, 512 * 1024);
 
 	/* 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];
+	HnswInitSupport(&so->support, index);
 
 	scan->opaque = so;
 
@@ -125,7 +154,15 @@ hnswrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int no
 {
 	HnswScanOpaque so = (HnswScanOpaque) scan->opaque;
 
+	if (so->v.tids != NULL)
+		tidhash_reset(so->v.tids);
+
+	if (so->discarded != NULL)
+		pairingheap_reset(so->discarded);
+
 	so->first = true;
+	so->tuples = 0;
+	so->previousDistance = -get_float8_infinity();
 	MemoryContextReset(so->tmpCtx);
 
 	if (keys && scan->numberOfKeys > 0)
@@ -181,24 +218,106 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
 
 		so->first = false;
+
+#if defined(HNSW_MEMORY)
+		ShowMemoryUsage(so);
+#endif
 	}
 
-	while (list_length(so->w) > 0)
+	for (;;)
 	{
 		char	   *base = NULL;
-		HnswCandidate *hc = llast(so->w);
-		HnswElement element = HnswPtrAccess(base, hc->element);
+		HnswSearchCandidate *sc;
+		HnswElement element;
 		ItemPointer heaptid;
 
+		if (list_length(so->w) == 0)
+		{
+			if (hnsw_iterative_search == HNSW_ITERATIVE_SEARCH_OFF)
+				break;
+
+			/* Empty index */
+			if (so->discarded == NULL)
+				break;
+
+			/* Reached max number of tuples */
+			if (hnsw_max_search_tuples != -1 && so->tuples >= hnsw_max_search_tuples)
+			{
+				if (pairingheap_is_empty(so->discarded))
+					break;
+
+				/* Return remaining tuples */
+				so->w = lappend(so->w, HnswGetSearchCandidate(w_node, pairingheap_remove_first(so->discarded)));
+			}
+			/* Prevent scans from consuming too much memory */
+			else if (MemoryContextMemAllocated(so->tmpCtx, false) > (Size) work_mem * 1024L)
+			{
+				if (pairingheap_is_empty(so->discarded))
+				{
+					ereport(DEBUG1,
+							(errmsg("hnsw index scan 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);
+
+				so->w = ResumeScanItems(scan);
+
+				UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
+
+#if defined(HNSW_MEMORY)
+				ShowMemoryUsage(so);
+#endif
+			}
+
+			if (list_length(so->w) == 0)
+				break;
+		}
+
+		sc = llast(so->w);
+		element = HnswPtrAccess(base, sc->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_iterative_search != HNSW_ITERATIVE_SEARCH_OFF)
+			{
+				pfree(element);
+				pfree(sc);
+			}
+
 			continue;
 		}
 
 		heaptid = &element->heaptids[--element->heaptidsLength];
 
+		if (hnsw_iterative_search == HNSW_ITERATIVE_SEARCH_STRICT)
+		{
+			if (sc->distance < so->previousDistance)
+				continue;
+
+			so->previousDistance = sc->distance;
+		}
+
 		MemoryContextSwitchTo(oldCtx);
 
 		scan->xs_heaptid = *heaptid;

src/hnswvacuum.c

@@ -184,13 +184,12 @@ static void
 RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswElement entryPoint)
 {
 	Relation	index = vacuumstate->index;
+	HnswSupport *support = &vacuumstate->support;
 	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);
@@ -205,7 +204,7 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	element->heaptidsLength = 0;
 
 	/* Find neighbors for element, skipping itself */
-	HnswFindElementNeighbors(base, element, entryPoint, index, procinfo, collation, m, efConstruction, true);
+	HnswFindElementNeighbors(base, element, entryPoint, index, support, m, efConstruction, true);
 
 	/* Zero memory for each element */
 	MemSet(ntup, 0, HNSW_TUPLE_ALLOC_SIZE);
@@ -229,7 +228,7 @@ RepairGraphElement(HnswVacuumState * vacuumstate, HnswElement element, HnswEleme
 	UnlockReleaseBuffer(buf);
 
 	/* Update neighbors */
-	HnswUpdateNeighborsOnDisk(index, procinfo, collation, element, m, true, false);
+	HnswUpdateNeighborsOnDisk(index, support, element, m, true, false);
 }
 
 /*
@@ -239,6 +238,7 @@ static void
 RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 {
 	Relation	index = vacuumstate->index;
+	HnswSupport *support = &vacuumstate->support;
 	HnswElement highestPoint = &vacuumstate->highestPoint;
 	HnswElement entryPoint;
 	MemoryContext oldCtx = MemoryContextSwitchTo(vacuumstate->tmpCtx);
@@ -256,7 +256,7 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 		LockPage(index, HNSW_UPDATE_LOCK, ShareLock);
 
 		/* Load element */
-		HnswLoadElement(highestPoint, NULL, NULL, index, vacuumstate->procinfo, vacuumstate->collation, true);
+		HnswLoadElement(highestPoint, NULL, NULL, index, support, true, NULL);
 
 		/* Repair if needed */
 		if (NeedsUpdated(vacuumstate, highestPoint))
@@ -294,7 +294,7 @@ RepairGraphEntryPoint(HnswVacuumState * vacuumstate)
 			 * 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);
+			HnswLoadElement(entryPoint, NULL, NULL, index, support, true, NULL);
 
 			if (NeedsUpdated(vacuumstate, entryPoint))
 			{
@@ -527,6 +527,14 @@ MarkDeleted(HnswVacuumState * vacuumstate)
 			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
@@ -573,13 +581,13 @@ InitVacuumState(HnswVacuumState * vacuumstate, IndexVacuumInfo *info, IndexBulkD
 	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);
 
+	HnswInitSupport(&vacuumstate->support, index);
+
 	/* Get m from metapage */
 	HnswGetMetaPageInfo(index, &vacuumstate->m, NULL);
 

src/intvec.c

@@ -0,0 +1,754 @@
+#include "postgres.h"
+
+#include <limits.h>
+#include <math.h>
+
+#include "catalog/pg_type.h"
+#include "fmgr.h"
+#include "intvec.h"
+#include "lib/stringinfo.h"
+#include "libpq/pqformat.h"
+#include "utils/array.h"
+#include "utils/builtins.h"
+#include "utils/lsyscache.h"
+
+/*
+ * Ensure same dimensions
+ */
+static inline void
+CheckDims(IntVector * a, IntVector * b)
+{
+	if (a->dim != b->dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different intvec dimensions %d and %d", a->dim, b->dim)));
+}
+
+/*
+ * Ensure expected dimensions
+ */
+static inline void
+CheckExpectedDim(int32 typmod, int dim)
+{
+	if (typmod != -1 && typmod != dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected %d dimensions, not %d", typmod, dim)));
+}
+
+/*
+ * Ensure valid dimensions
+ */
+static inline void
+CheckDim(int dim)
+{
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("intvec must have at least 1 dimension")));
+
+	if (dim > INTVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("intvec cannot have more than %d dimensions", INTVEC_MAX_DIM)));
+}
+
+/*
+ * Ensure element in range
+ */
+static inline void
+CheckElement(long value)
+{
+	if (value < SCHAR_MIN || value > SCHAR_MAX)
+		ereport(ERROR,
+				(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+				 errmsg("value \"%ld\" is out of range for type intvec", value)));
+}
+
+/*
+ * Allocate and initialize a new int vector
+ */
+IntVector *
+InitIntVector(int dim)
+{
+	IntVector  *result;
+	int			size;
+
+	size = INTVEC_SIZE(dim);
+	result = (IntVector *) palloc0(size);
+	SET_VARSIZE(result, size);
+	result->dim = dim;
+
+	return result;
+}
+
+/*
+ * Check for whitespace, since array_isspace() is static
+ */
+static inline bool
+intvec_isspace(char ch)
+{
+	if (ch == ' ' ||
+		ch == '\t' ||
+		ch == '\n' ||
+		ch == '\r' ||
+		ch == '\v' ||
+		ch == '\f')
+		return true;
+	return false;
+}
+
+/*
+ * Convert textual representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_in);
+Datum
+intvec_in(PG_FUNCTION_ARGS)
+{
+	char	   *lit = PG_GETARG_CSTRING(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	int8		x[INTVEC_MAX_DIM];
+	int			dim = 0;
+	char	   *pt = lit;
+	IntVector  *result;
+
+	while (intvec_isspace(*pt))
+		pt++;
+
+	if (*pt != '[')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type intvec: \"%s\"", lit),
+				 errdetail("Vector contents must start with \"[\".")));
+
+	pt++;
+
+	while (intvec_isspace(*pt))
+		pt++;
+
+	if (*pt == ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("intvec must have at least 1 dimension")));
+
+	for (;;)
+	{
+		long		val;
+		char	   *stringEnd;
+
+		if (dim == INTVEC_MAX_DIM)
+			ereport(ERROR,
+					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+					 errmsg("intvec cannot have more than %d dimensions", VECTOR_MAX_DIM)));
+
+		while (intvec_isspace(*pt))
+			pt++;
+
+		/* Check for empty string like float4in */
+		if (*pt == '\0')
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type intvec: \"%s\"", lit)));
+
+		errno = 0;
+
+		/* Use similar logic as int2vectorin */
+		val = strtol(pt, &stringEnd, 10);
+
+		if (stringEnd == pt)
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type intvec: \"%s\"", lit)));
+
+		/* Check for range error like float4in */
+		if (errno == ERANGE || val < SCHAR_MIN || val > SCHAR_MAX)
+			ereport(ERROR,
+					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+					 errmsg("\"%s\" is out of range for type intvec", pnstrdup(pt, stringEnd - pt))));
+
+		CheckElement(val);
+		x[dim++] = val;
+
+		pt = stringEnd;
+
+		while (intvec_isspace(*pt))
+			pt++;
+
+		if (*pt == ',')
+			pt++;
+		else if (*pt == ']')
+		{
+			pt++;
+			break;
+		}
+		else
+			ereport(ERROR,
+					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+					 errmsg("invalid input syntax for type intvec: \"%s\"", lit)));
+	}
+
+	/* Only whitespace is allowed after the closing brace */
+	while (intvec_isspace(*pt))
+		pt++;
+
+	if (*pt != '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type intvec: \"%s\"", lit),
+				 errdetail("Junk after closing right brace.")));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	result = InitIntVector(dim);
+	for (int i = 0; i < dim; i++)
+		result->x[i] = x[i];
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert internal representation to textual representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_out);
+Datum
+intvec_out(PG_FUNCTION_ARGS)
+{
+	IntVector  *vector = PG_GETARG_INTVEC_P(0);
+	int			dim = vector->dim;
+	char	   *buf;
+	char	   *ptr;
+
+	/*
+	 * Need:
+	 *
+	 * dim * 4 bytes for elements (-128 to 127)
+	 *
+	 * dim - 1 bytes for separator
+	 *
+	 * 3 bytes for [, ], and \0
+	 */
+	buf = (char *) palloc(5 * dim + 2);
+	ptr = buf;
+
+	*ptr = '[';
+	ptr++;
+	for (int i = 0; i < dim; i++)
+	{
+		if (i > 0)
+		{
+			*ptr = ',';
+			ptr++;
+		}
+
+#if PG_VERSION_NUM >= 140000
+		ptr += pg_ltoa(vector->x[i], ptr);
+#else
+		pg_ltoa(vector->x[i], ptr);
+		while (*ptr != '\0')
+			ptr++;
+#endif
+	}
+	*ptr = ']';
+	ptr++;
+	*ptr = '\0';
+
+	PG_FREE_IF_COPY(vector, 0);
+	PG_RETURN_CSTRING(buf);
+}
+
+/*
+ * Convert type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_typmod_in);
+Datum
+intvec_typmod_in(PG_FUNCTION_ARGS)
+{
+	ArrayType  *ta = PG_GETARG_ARRAYTYPE_P(0);
+	int32	   *tl;
+	int			n;
+
+	tl = ArrayGetIntegerTypmods(ta, &n);
+
+	if (n != 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("invalid type modifier")));
+
+	if (*tl < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type intvec must be at least 1")));
+
+	if (*tl > INTVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type intvec cannot exceed %d", INTVEC_MAX_DIM)));
+
+	PG_RETURN_INT32(*tl);
+}
+
+/*
+ * Convert external binary representation to internal representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_recv);
+Datum
+intvec_recv(PG_FUNCTION_ARGS)
+{
+	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
+	int32		typmod = PG_GETARG_INT32(2);
+	IntVector  *result;
+	int16		dim;
+	int16		unused;
+
+	dim = pq_getmsgint(buf, sizeof(int16));
+	unused = pq_getmsgint(buf, sizeof(int16));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	if (unused != 0)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected unused to be 0, not %d", unused)));
+
+	result = InitIntVector(dim);
+	for (int i = 0; i < dim; i++)
+		result->x[i] = pq_getmsgint(buf, sizeof(int8));
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert internal representation to the external binary representation
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_send);
+Datum
+intvec_send(PG_FUNCTION_ARGS)
+{
+	IntVector  *vec = PG_GETARG_INTVEC_P(0);
+	StringInfoData buf;
+
+	pq_begintypsend(&buf);
+	pq_sendint(&buf, vec->dim, sizeof(int16));
+	pq_sendint(&buf, vec->unused, sizeof(int16));
+	for (int i = 0; i < vec->dim; i++)
+		pq_sendint8(&buf, vec->x[i]);
+
+	PG_RETURN_BYTEA_P(pq_endtypsend(&buf));
+}
+
+/*
+ * Convert int vector to int vector
+ * This is needed to check the type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec);
+Datum
+intvec(PG_FUNCTION_ARGS)
+{
+	IntVector  *vec = PG_GETARG_INTVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+
+	CheckExpectedDim(typmod, vec->dim);
+
+	PG_RETURN_POINTER(vec);
+}
+
+/*
+ * Convert array to intvec vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(array_to_intvec);
+Datum
+array_to_intvec(PG_FUNCTION_ARGS)
+{
+	ArrayType  *array = PG_GETARG_ARRAYTYPE_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	IntVector  *result;
+	int16		typlen;
+	bool		typbyval;
+	char		typalign;
+	Datum	   *elemsp;
+	int			nelemsp;
+
+	if (ARR_NDIM(array) > 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("array must be 1-D")));
+
+	if (ARR_HASNULL(array) && array_contains_nulls(array))
+		ereport(ERROR,
+				(errcode(ERRCODE_NULL_VALUE_NOT_ALLOWED),
+				 errmsg("array must not contain nulls")));
+
+	get_typlenbyvalalign(ARR_ELEMTYPE(array), &typlen, &typbyval, &typalign);
+	deconstruct_array(array, ARR_ELEMTYPE(array), typlen, typbyval, typalign, &elemsp, NULL, &nelemsp);
+
+	CheckDim(nelemsp);
+	CheckExpectedDim(typmod, nelemsp);
+
+	result = InitIntVector(nelemsp);
+
+	if (ARR_ELEMTYPE(array) == INT4OID)
+	{
+		for (int i = 0; i < nelemsp; i++)
+		{
+			long		l = DatumGetInt32(elemsp[i]);
+
+			CheckElement(l);
+
+			result->x[i] = l;
+		}
+	}
+	else
+	{
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("unsupported array type")));
+	}
+
+	/*
+	 * Free allocation from deconstruct_array. Do not free individual elements
+	 * when pass-by-reference since they point to original array.
+	 */
+	pfree(elemsp);
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Convert int vector to integer[]
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_to_integer);
+Datum
+intvec_to_integer(PG_FUNCTION_ARGS)
+{
+	IntVector  *vec = PG_GETARG_INTVEC_P(0);
+	Datum	   *datums;
+	ArrayType  *result;
+
+	datums = (Datum *) palloc(sizeof(Datum) * vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		datums[i] = Int32GetDatum((int) vec->x[i]);
+
+	result = construct_array(datums, vec->dim, INT4OID, sizeof(int32), true, TYPALIGN_INT);
+
+	pfree(datums);
+
+	PG_RETURN_POINTER(result);
+}
+
+static int
+IntvecL2SquaredDistance(int dim, int8 *ax, int8 *bx)
+{
+	int			distance = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		int			diff = (int) ax[i] - (int) bx[i];
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+
+/*
+ * Get the L2 distance between int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_l2_distance);
+Datum
+intvec_l2_distance(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(sqrt((double) IntvecL2SquaredDistance(a->dim, a->x, b->x)));
+}
+
+/*
+ * Get the L2 squared distance between int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_l2_squared_distance);
+Datum
+intvec_l2_squared_distance(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) IntvecL2SquaredDistance(a->dim, a->x, b->x));
+}
+
+static int
+IntvecInnerProduct(int dim, int8 *ax, int8 *bx)
+{
+	int			distance = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += (int) ax[i] * (int) bx[i];
+
+	return distance;
+}
+
+/*
+ * Get the inner product of two int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_inner_product);
+Datum
+intvec_inner_product(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) IntvecInnerProduct(a->dim, a->x, b->x));
+}
+
+/*
+ * Get the negative inner product of two int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_negative_inner_product);
+Datum
+intvec_negative_inner_product(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) -IntvecInnerProduct(a->dim, a->x, b->x));
+}
+
+static double
+IntvecCosineSimilarity(int dim, int8 *ax, int8 *bx)
+{
+	int			similarity = 0;
+	int			norma = 0;
+	int			normb = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		int			axi = ax[i];
+		int			bxi = 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);
+}
+
+/*
+ * Get the cosine distance between two int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_cosine_distance);
+Datum
+intvec_cosine_distance(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+	double		similarity;
+
+	CheckDims(a, b);
+
+	similarity = IntvecCosineSimilarity(a->dim, a->x, b->x);
+
+#ifdef _MSC_VER
+	/* /fp:fast may not propagate NaN */
+	if (isnan(similarity))
+		PG_RETURN_FLOAT8(NAN);
+#endif
+
+	/* Keep in range */
+	if (similarity > 1)
+		similarity = 1;
+	else if (similarity < -1)
+		similarity = -1;
+
+	PG_RETURN_FLOAT8(1 - similarity);
+}
+
+static int
+IntvecL1Distance(int dim, int8 *ax, int8 *bx)
+{
+	int			distance = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += abs((int) ax[i] - (int) bx[i]);
+
+	return distance;
+}
+
+/*
+ * Get the L1 distance between two int vectors
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_l1_distance);
+Datum
+intvec_l1_distance(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8((double) IntvecL1Distance(a->dim, a->x, b->x));
+}
+
+/*
+ * Get the dimensions of an int vector
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_vector_dims);
+Datum
+intvec_vector_dims(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+
+	PG_RETURN_INT32(a->dim);
+}
+
+/*
+ * Get the L2 norm of an int vector
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(intvec_l2_norm);
+Datum
+intvec_l2_norm(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	int8	   *ax = a->x;
+	int			norm = 0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		norm += (int) ax[i] * (int) ax[i];
+
+	PG_RETURN_FLOAT8(sqrt((double) norm));
+}
+
+/*
+ * Internal helper to compare int vectors
+ */
+static int
+intvec_cmp_internal(IntVector * a, IntVector * b)
+{
+	int			dim = Min(a->dim, b->dim);
+
+	/* Check values before dimensions to be consistent with Postgres arrays */
+	for (int i = 0; i < dim; i++)
+	{
+		if (a->x[i] < b->x[i])
+			return -1;
+
+		if (a->x[i] > b->x[i])
+			return 1;
+	}
+
+	if (a->dim < b->dim)
+		return -1;
+
+	if (a->dim > b->dim)
+		return 1;
+
+	return 0;
+}
+
+/*
+ * Less than
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_lt);
+Datum
+intvec_lt(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) < 0);
+}
+
+/*
+ * Less than or equal
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_le);
+Datum
+intvec_le(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) <= 0);
+}
+
+/*
+ * Equal
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_eq);
+Datum
+intvec_eq(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) == 0);
+}
+
+/*
+ * Not equal
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_ne);
+Datum
+intvec_ne(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) != 0);
+}
+
+/*
+ * Greater than or equal
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_ge);
+Datum
+intvec_ge(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) >= 0);
+}
+
+/*
+ * Greater than
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_gt);
+Datum
+intvec_gt(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_BOOL(intvec_cmp_internal(a, b) > 0);
+}
+
+/*
+ * Compare int vectors
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(intvec_cmp);
+Datum
+intvec_cmp(PG_FUNCTION_ARGS)
+{
+	IntVector  *a = PG_GETARG_INTVEC_P(0);
+	IntVector  *b = PG_GETARG_INTVEC_P(1);
+
+	PG_RETURN_INT32(intvec_cmp_internal(a, b));
+}

src/intvec.h

@@ -0,0 +1,23 @@
+#ifndef INTVEC_H
+#define INTVEC_H
+
+#include "vector.h"
+
+#define INTVEC_MAX_DIM VECTOR_MAX_DIM
+
+#define INTVEC_SIZE(_dim)		(offsetof(IntVector, x) + sizeof(int8)*(_dim))
+#define DatumGetIntVector(x)	((IntVector *) PG_DETOAST_DATUM(x))
+#define PG_GETARG_INTVEC_P(x)	DatumGetIntVector(PG_GETARG_DATUM(x))
+#define PG_RETURN_INTVEC_P(x)	PG_RETURN_POINTER(x)
+
+typedef struct IntVector
+{
+	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int16		dim;			/* number of dimensions */
+	int16		unused;
+	int8		x[FLEXIBLE_ARRAY_MEMBER];
+}			IntVector;
+
+IntVector  *InitIntVector(int dim);
+
+#endif

src/ivfbuild.c

@@ -6,16 +6,19 @@
 #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"
@@ -23,12 +26,6 @@
 #include "pgstat.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 >= 140000
 #include "utils/backend_status.h"
 #include "utils/wait_event.h"
@@ -57,13 +54,15 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 	 */
 	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
@@ -80,7 +79,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 #endif
 
 			Assert(k >= 0 && k < targsamples);
-			VectorArraySet(samples, k, DatumGetVector(value));
+			VectorArraySet(samples, k, DatumGetPointer(value));
 		}
 
 		buildstate->rowstoskip -= 1;
@@ -91,7 +90,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
  * Callback for sampling
  */
 static void
-SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
+SampleCallback(Relation index, ItemPointer tid, Datum *values,
 			   bool *isnull, bool tupleIsAlive, void *state)
 {
 	IvfflatBuildState *buildstate = (IvfflatBuildState *) state;
@@ -105,7 +104,7 @@ SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	oldCtx = MemoryContextSwitchTo(buildstate->tmpCtx);
 
 	/* Add sample */
-	AddSample(values, state);
+	AddSample(values, buildstate);
 
 	/* Reset memory context */
 	MemoryContextSwitchTo(oldCtx);
@@ -153,8 +152,10 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState
 	/* Normalize if needed */
 	if (buildstate->normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(buildstate->normprocinfo, buildstate->collation, &value, buildstate->normvec))
+		if (!IvfflatCheckNorm(buildstate->normprocinfo, buildstate->collation, value))
 			return;
+
+		value = IvfflatNormValue(buildstate->typeInfo, buildstate->collation, value);
 	}
 
 	/* Find the list that minimizes the distance */
@@ -200,16 +201,12 @@ AddTupleToSort(Relation index, ItemPointer tid, Datum *values, IvfflatBuildState
  * Callback for table_index_build_scan
  */
 static void
-BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
+BuildCallback(Relation index, ItemPointer tid, Datum *values,
 			  bool *isnull, bool tupleIsAlive, void *state)
 {
 	IvfflatBuildState *buildstate = (IvfflatBuildState *) state;
 	MemoryContext oldCtx;
 
-#if PG_VERSION_NUM < 130000
-	ItemPointer tid = &hup->t_self;
-#endif
-
 	/* Skip nulls */
 	if (isnull[0])
 		return;
@@ -231,11 +228,11 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 static inline void
 GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot, IndexTuple *itup, int *list)
 {
-	Datum		value;
-	bool		isnull;
-
 	if (tuplesort_gettupleslot(sortstate, true, false, slot, NULL))
 	{
+		Datum		value;
+		bool		isnull;
+
 		*list = DatumGetInt32(slot_getattr(slot, 1, &isnull));
 		value = slot_getattr(slot, 3, &isnull);
 
@@ -257,8 +254,8 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 	IndexTuple	itup = NULL;	/* silence compiler warning */
 	int64		inserted = 0;
 
-	TupleTableSlot *slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsMinimalTuple);
-	TupleDesc	tupdesc = RelationGetDescr(index);
+	TupleTableSlot *slot = MakeSingleTupleTableSlot(buildstate->sortdesc, &TTSOpsMinimalTuple);
+	TupleDesc	tupdesc = buildstate->tupdesc;
 
 	pgstat_progress_update_param(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_LOAD);
 
@@ -321,16 +318,28 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->heap = heap;
 	buildstate->index = index;
 	buildstate->indexInfo = indexInfo;
+	buildstate->typeInfo = IvfflatGetTypeInfo(index);
+	buildstate->tupdesc = RelationGetDescr(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 > IVFFLAT_MAX_DIM)
-		elog(ERROR, "column cannot have more than %d dimensions for ivfflat index", IVFFLAT_MAX_DIM);
+	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;
@@ -343,22 +352,21 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 
 	/* Require more than one dimension for spherical k-means */
 	if (buildstate->kmeansnormprocinfo != NULL && buildstate->dimensions == 1)
-		elog(ERROR, "dimensions must be greater than one for this opclass");
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions must be greater than one for this opclass")));
 
 	/* Create tuple description for sorting */
-	buildstate->tupdesc = CreateTemplateTupleDesc(3);
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 1, "list", INT4OID, -1, 0);
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 3, "vector", RelationGetDescr(index)->attrs[0].atttypid, -1, 0);
+	buildstate->sortdesc = CreateTemplateTupleDesc(3);
+	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 1, "list", INT4OID, -1, 0);
+	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
+	TupleDescInitEntry(buildstate->sortdesc, (AttrNumber) 3, "vector", buildstate->tupdesc->attrs[0].atttypid, -1, 0);
 
-	buildstate->slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsVirtual);
+	buildstate->slot = MakeSingleTupleTableSlot(buildstate->sortdesc, &TTSOpsVirtual);
 
-	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);
@@ -380,7 +388,6 @@ FreeBuildState(IvfflatBuildState * buildstate)
 {
 	VectorArrayFree(buildstate->centers);
 	pfree(buildstate->listInfo);
-	pfree(buildstate->normvec);
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	pfree(buildstate->listSums);
@@ -412,7 +419,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 
 	/* Sample rows */
 	/* TODO Ensure within maintenance_work_mem */
-	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions);
+	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions, buildstate->centers->itemsize);
 	if (buildstate->heap != NULL)
 	{
 		SampleRows(buildstate);
@@ -427,7 +434,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 	}
 
 	/* Calculate centers */
-	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers));
+	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers, buildstate->typeInfo));
 
 	/* Free samples before we allocate more memory */
 	VectorArrayFree(buildstate->samples);
@@ -472,7 +479,7 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	Size		listSize;
 	IvfflatList list;
 
-	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(dimensions));
+	listSize = MAXALIGN(IVFFLAT_LIST_SIZE(centers->itemsize));
 	list = palloc0(listSize);
 
 	buf = IvfflatNewBuffer(index, forkNum);
@@ -482,10 +489,13 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	{
 		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) < listSize)
@@ -551,6 +561,20 @@ 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
  */
@@ -590,7 +614,7 @@ ParallelHeapScan(IvfflatBuildState * buildstate)
  * Perform a worker's portion of a parallel sort
  */
 static void
-IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, Sharedsort *sharedsort, Vector * ivfcenters, int sortmem, bool progress)
+IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, Sharedsort *sharedsort, char *ivfcenters, int sortmem, bool progress)
 {
 	SortCoordinate coordinate;
 	IvfflatBuildState buildstate;
@@ -598,12 +622,6 @@ IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, S
 	double		reltuples;
 	IndexInfo  *indexInfo;
 
-	/* Sort options, which must match AssignTuples */
-	AttrNumber	attNums[] = {1};
-	Oid			sortOperators[] = {Int4LessOperator};
-	Oid			sortCollations[] = {InvalidOid};
-	bool		nullsFirstFlags[] = {false};
-
 	/* Initialize local tuplesort coordination state */
 	coordinate = palloc0(sizeof(SortCoordinateData));
 	coordinate->isWorker = true;
@@ -614,9 +632,9 @@ IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, S
 	indexInfo = BuildIndexInfo(ivfspool->index);
 	indexInfo->ii_Concurrent = ivfshared->isconcurrent;
 	InitBuildState(&buildstate, ivfspool->heap, ivfspool->index, indexInfo);
-	memcpy(buildstate.centers->items, ivfcenters, VECTOR_SIZE(buildstate.centers->dim) * buildstate.centers->maxlen);
+	memcpy(buildstate.centers->items, ivfcenters, buildstate.centers->itemsize * buildstate.centers->maxlen);
 	buildstate.centers->length = buildstate.centers->maxlen;
-	ivfspool->sortstate = tuplesort_begin_heap(buildstate.tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, sortmem, coordinate, false);
+	ivfspool->sortstate = InitBuildSortState(buildstate.sortdesc, sortmem, coordinate);
 	buildstate.sortstate = ivfspool->sortstate;
 	scan = table_beginscan_parallel(ivfspool->heap,
 									ParallelTableScanFromIvfflatShared(ivfshared));
@@ -662,7 +680,7 @@ IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc)
 	IvfflatSpool *ivfspool;
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 	Relation	heapRel;
 	Relation	indexRel;
 	LOCKMODE	heapLockmode;
@@ -776,7 +794,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	Size		estcenters;
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 	IvfflatLeader *ivfleader = (IvfflatLeader *) palloc0(sizeof(IvfflatLeader));
 	bool		leaderparticipates = true;
 	int			querylen;
@@ -803,7 +821,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	shm_toc_estimate_chunk(&pcxt->estimator, estivfshared);
 	estsort = tuplesort_estimate_shared(scantuplesortstates);
 	shm_toc_estimate_chunk(&pcxt->estimator, estsort);
-	estcenters = VECTOR_SIZE(buildstate->dimensions) * buildstate->lists;
+	estcenters = buildstate->centers->itemsize * buildstate->centers->maxlen;
 	shm_toc_estimate_chunk(&pcxt->estimator, estcenters);
 	shm_toc_estimate_keys(&pcxt->estimator, 3);
 
@@ -855,7 +873,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	tuplesort_initialize_shared(sharedsort, scantuplesortstates,
 								pcxt->seg);
 
-	ivfcenters = (Vector *) shm_toc_allocate(pcxt->toc, estcenters);
+	ivfcenters = shm_toc_allocate(pcxt->toc, estcenters);
 	memcpy(ivfcenters, buildstate->centers->items, estcenters);
 
 	shm_toc_insert(pcxt->toc, PARALLEL_KEY_IVFFLAT_SHARED, ivfshared);
@@ -913,12 +931,6 @@ AssignTuples(IvfflatBuildState * buildstate)
 	int			parallel_workers = 0;
 	SortCoordinate coordinate = NULL;
 
-	/* Sort options, which must match IvfflatParallelScanAndSort */
-	AttrNumber	attNums[] = {1};
-	Oid			sortOperators[] = {Int4LessOperator};
-	Oid			sortCollations[] = {InvalidOid};
-	bool		nullsFirstFlags[] = {false};
-
 	pgstat_progress_update_param(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_ASSIGN);
 
 	/* Calculate parallel workers */
@@ -939,7 +951,7 @@ AssignTuples(IvfflatBuildState * buildstate)
 	}
 
 	/* Begin serial/leader tuplesort */
-	buildstate->sortstate = tuplesort_begin_heap(buildstate->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, maintenance_work_mem, coordinate, false);
+	buildstate->sortstate = InitBuildSortState(buildstate->sortdesc, maintenance_work_mem, coordinate);
 
 	/* Add tuples to sort */
 	if (buildstate->heap != NULL)
@@ -995,6 +1007,10 @@ BuildIndex(Relation heap, Relation index, IndexInfo *indexInfo,
 	CreateListPages(index, buildstate->centers, buildstate->dimensions, buildstate->lists, forkNum, &buildstate->listInfo);
 	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

@@ -7,6 +7,7 @@
 #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"
@@ -16,8 +17,16 @@
 #endif
 
 int			ivfflat_probes;
+int			ivfflat_iterative_search;
+int			ivfflat_max_probes;
 static relopt_kind ivfflat_relopt_kind;
 
+static const struct config_enum_entry ivfflat_iterative_search_options[] = {
+	{"off", IVFFLAT_ITERATIVE_SEARCH_OFF, false},
+	{"relaxed_order", IVFFLAT_ITERATIVE_SEARCH_RELAXED, false},
+	{NULL, 0, false}
+};
+
 /*
  * Initialize index options and variables
  */
@@ -26,16 +35,21 @@ IvfflatInit(void)
 {
 	ivfflat_relopt_kind = add_reloption_kind();
 	add_int_reloption(ivfflat_relopt_kind, "lists", "Number of inverted lists",
-					  IVFFLAT_DEFAULT_LISTS, IVFFLAT_MIN_LISTS, 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,
 							IVFFLAT_DEFAULT_PROBES, IVFFLAT_MIN_LISTS, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
 
+	DefineCustomEnumVariable("ivfflat.iterative_search", "Sets the iterative search mode",
+							 NULL, &ivfflat_iterative_search,
+							 IVFFLAT_ITERATIVE_SEARCH_OFF, ivfflat_iterative_search_options, PGC_USERSET, 0, NULL, NULL, NULL);
+
+	/* If this is less than probes, probes is used */
+	DefineCustomIntVariable("ivfflat.max_probes", "Sets the max number of probes for iterative search",
+							"-1 means no limit", &ivfflat_max_probes,
+							-1, -1, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
+
 	MarkGUCPrefixReserved("ivfflat");
 }
 
@@ -72,14 +86,16 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	GenericCosts costs;
 	int			lists;
 	double		ratio;
+	double		sequentialRatio = 0.5;
+	double		startupPages;
 	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;
 		*indexPages = 0;
@@ -88,6 +104,8 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 
 	MemSet(&costs, 0, sizeof(costs));
 
+	genericcostestimate(root, path, loop_count, &costs);
+
 	index = index_open(path->indexinfo->indexoid, NoLock);
 	IvfflatGetMetaPageInfo(index, &lists, NULL);
 	index_close(index, NoLock);
@@ -97,41 +115,26 @@ ivfflatcostestimate(PlannerInfo *root, IndexPath *path, double loop_count,
 	if (ratio > 1.0)
 		ratio = 1.0;
 
-	/*
-	 * This gives us the subset of tuples to visit. This value is passed into
-	 * the generic cost estimator to determine the number of pages to visit
-	 * during the index scan.
-	 */
-	costs.numIndexTuples = path->indexinfo->tuples * ratio;
-
-	genericcostestimate(root, path, loop_count, &costs);
-
 	get_tablespace_page_costs(path->indexinfo->reltablespace, NULL, &spc_seq_page_cost);
 
+	/* Change some page cost from random to sequential */
+	costs.indexTotalCost -= sequentialRatio * costs.numIndexPages * (costs.spc_random_page_cost - spc_seq_page_cost);
+
+	/* Startup cost is cost before returning the first row */
+	costs.indexStartupCost = costs.indexTotalCost * ratio;
+
 	/* Adjust cost if needed since TOAST not included in seq scan cost */
-	if (costs.numIndexPages > path->indexinfo->rel->pages && ratio < 0.5)
+	startupPages = costs.numIndexPages * ratio;
+	if (startupPages > 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);
+		/* Change rest of page cost from random to sequential */
+		costs.indexStartupCost -= (1 - sequentialRatio) * startupPages * (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);
+		costs.indexStartupCost -= (startupPages - path->indexinfo->rel->pages) * 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;
+	*indexStartupCost = costs.indexStartupCost;
 	*indexTotalCost = costs.indexTotalCost;
 	*indexSelectivity = costs.indexSelectivity;
 	*indexCorrelation = costs.indexCorrelation;
@@ -148,23 +151,10 @@ 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
 }
 
 /*
@@ -181,17 +171,15 @@ ivfflatvalidate(Oid opclassoid)
  *
  * See https://www.postgresql.org/docs/current/index-api.html
  */
-PGDLLEXPORT 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 */
@@ -204,17 +192,24 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	amroutine->amclusterable = false;
 	amroutine->ampredlocks = false;
 	amroutine->amcanparallel = false;
-	amroutine->amcaninclude = false;
-#if PG_VERSION_NUM >= 130000
-	amroutine->amusemaintenanceworkmem = false; /* not used during VACUUM */
-	amroutine->amparallelvacuumoptions = VACUUM_OPTION_PARALLEL_BULKDEL;
+#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 = 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 */

src/ivfflat.h

@@ -28,6 +28,7 @@
 #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
@@ -49,7 +50,7 @@
 #define PROGRESS_IVFFLAT_PHASE_ASSIGN	3
 #define PROGRESS_IVFFLAT_PHASE_LOAD		4
 
-#define IVFFLAT_LIST_SIZE(_dim)	(offsetof(IvfflatListData, center) + VECTOR_SIZE(_dim))
+#define IVFFLAT_LIST_SIZE(size)	(offsetof(IvfflatListData, center) + size)
 
 #define IvfflatPageGetOpaque(page)	((IvfflatPageOpaque) PageGetSpecialPointer(page))
 #define IvfflatPageGetMeta(page)	((IvfflatMetaPageData *) PageGetContents(page))
@@ -79,13 +80,22 @@
 
 /* Variables */
 extern int	ivfflat_probes;
+extern int	ivfflat_iterative_search;
+extern int	ivfflat_max_probes;
+
+typedef enum IvfflatIterativeSearchMode
+{
+	IVFFLAT_ITERATIVE_SEARCH_OFF,
+	IVFFLAT_ITERATIVE_SEARCH_RELAXED
+}			IvfflatIterativeSearchMode;
 
 typedef struct VectorArrayData
 {
 	int			length;
 	int			maxlen;
 	int			dim;
-	Vector	   *items;
+	Size		itemsize;
+	char	   *items;
 }			VectorArrayData;
 
 typedef VectorArrayData * VectorArray;
@@ -144,15 +154,26 @@ typedef struct IvfflatLeader
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
 	Snapshot	snapshot;
-	Vector	   *ivfcenters;
+	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;
+	TupleDesc	tupdesc;
 
 	/* Settings */
 	int			dimensions;
@@ -172,7 +193,6 @@ typedef struct IvfflatBuildState
 	VectorArray samples;
 	VectorArray centers;
 	ListInfo   *listInfo;
-	Vector	   *normvec;
 
 #ifdef IVFFLAT_KMEANS_DEBUG
 	double		inertia;
@@ -187,7 +207,7 @@ typedef struct IvfflatBuildState
 
 	/* Sorting */
 	Tuplesortstate *sortstate;
-	TupleDesc	tupdesc;
+	TupleDesc	sortdesc;
 	TupleTableSlot *slot;
 
 	/* Memory */
@@ -234,40 +254,59 @@ typedef struct IvfflatScanList
 
 typedef struct IvfflatScanOpaqueData
 {
+	const		IvfflatTypeInfo *typeInfo;
 	int			probes;
+	int			maxProbes;
 	int			dimensions;
 	bool		first;
+	Datum		value;
+	MemoryContext tmpCtx;
 
 	/* Sorting */
 	Tuplesortstate *sortstate;
 	TupleDesc	tupdesc;
-	TupleTableSlot *slot;
-	bool		isnull;
+	TupleTableSlot *vslot;
+	TupleTableSlot *mslot;
+	BufferAccessStrategy bas;
 
 	/* Support functions */
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
 	Oid			collation;
+	Datum		(*distfunc) (FmgrInfo *flinfo, Oid collation, Datum arg1, Datum arg2);
 
 	/* Lists */
 	pairingheap *listQueue;
-	IvfflatScanList lists[FLEXIBLE_ARRAY_MEMBER];	/* must come last */
+	BlockNumber *listPages;
+	int			listIndex;
+	IvfflatScanList *lists;
 }			IvfflatScanOpaqueData;
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;
 
-#define VECTOR_ARRAY_SIZE(_length, _dim) (sizeof(VectorArrayData) + (_length) * VECTOR_SIZE(_dim))
-#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * VECTOR_SIZE((_arr)->dim))
-#define VectorArrayGet(_arr, _offset) ((Vector *) VECTOR_ARRAY_OFFSET(_arr, _offset))
-#define VectorArraySet(_arr, _offset, _val) memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, VECTOR_SIZE((_arr)->dim))
+#define VECTOR_ARRAY_SIZE(_length, _size) (sizeof(VectorArrayData) + (_length) * 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 */
-VectorArray VectorArrayInit(int maxlen, int dimensions);
+VectorArray VectorArrayInit(int maxlen, int dimensions, Size itemsize);
 void		VectorArrayFree(VectorArray arr);
-void		PrintVectorArray(char *msg, VectorArray arr);
-void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
+void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers, const IvfflatTypeInfo * typeInfo);
 FmgrInfo   *IvfflatOptionalProcInfo(Relation index, uint16 procnum);
-bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
+Datum		IvfflatNormValue(const IvfflatTypeInfo * typeInfo, Oid collation, Datum value);
+bool		IvfflatCheckNorm(FmgrInfo *procinfo, Oid collation, Datum value);
 int			IvfflatGetLists(Relation index);
 void		IvfflatGetMetaPageInfo(Relation index, int *lists, int *dimensions);
 void		IvfflatUpdateList(Relation index, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);
@@ -277,6 +316,7 @@ 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 */

src/ivfinsert.c

@@ -67,6 +67,7 @@ FindInsertPage(Relation index, Datum *values, BlockNumber *insertPage, ListInfo
 static void
 InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heapRel)
 {
+	const		IvfflatTypeInfo *typeInfo = IvfflatGetTypeInfo(index);
 	IndexTuple	itup;
 	Datum		value;
 	FmgrInfo   *normprocinfo;
@@ -85,12 +86,19 @@ InsertTuple(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, R
 	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	if (normprocinfo != NULL)
 	{
-		if (!IvfflatNormValue(normprocinfo, index->rd_indcollation[0], &value, NULL))
+		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(index, values, &insertPage, &listInfo);
+	FindInsertPage(index, &value, &insertPage, &listInfo);
 	Assert(BlockNumberIsValid(insertPage));
 	originalInsertPage = insertPage;
 

src/ivfkmeans.c

@@ -3,12 +3,15 @@
 #include <float.h>
 #include <math.h>
 
+#include "bitvec.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
-
-#ifdef IVFFLAT_MEMORY
+#include "utils/builtins.h"
+#include "utils/datum.h"
 #include "utils/memutils.h"
-#endif
+#include "vector.h"
 
 /*
  * Initialize with kmeans++
@@ -46,12 +49,12 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 
 		for (j = 0; j < numSamples; j++)
 		{
-			Vector	   *vec = VectorArrayGet(samples, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, j));
 			double		distance;
 
 			/* Only need to compute distance for new center */
 			/* TODO Use triangle inequality to reduce distance calculations */
-			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, i))));
+			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, i))));
 
 			/* Set lower bound */
 			lowerBound[j * numCenters + i] = distance;
@@ -86,73 +89,59 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 }
 
 /*
- * Apply norm to vector
- */
-static inline void
-ApplyNorm(FmgrInfo *normprocinfo, Oid collation, Vector * vec)
-{
-	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(vec)));
-
-	/* TODO Handle zero norm */
-	if (norm > 0)
-	{
-		for (int 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			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 (int i = 0; i < samples->length; i++)
-		{
-			Vector	   *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)
 	{
-		Vector	   *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 (int 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
@@ -160,18 +149,104 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
  * Show memory usage
  */
 static void
-ShowMemoryUsage(Size estimatedSize)
+ShowMemoryUsage(MemoryContext context, Size estimatedSize)
 {
-#if PG_VERSION_NUM >= 130000
 	elog(INFO, "total memory: %zu MB",
-		 MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
-#else
-	MemoryContextStats(CurrentMemoryContext);
-#endif
+		 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);
+}
+
 /*
  * Use Elkan for performance. This requires distance function to satisfy triangle inequality.
  *
@@ -181,19 +256,16 @@ ShowMemoryUsage(Size estimatedSize)
  * 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;
-	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;
@@ -203,9 +275,10 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	float	   *newcdist;
 
 	/* 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;
@@ -215,7 +288,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	Size		newcdistSize = sizeof(float) * numCenters;
 
 	/* Calculate total size */
-	Size		totalSize = samplesSize + centersSize + newCentersSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
+	Size		totalSize = samplesSize + centersSize + newCentersSize + aggSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
 
 	/* Check memory requirements */
 	/* Add one to error message to ceil */
@@ -236,6 +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);
@@ -244,29 +318,25 @@ 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(totalSize);
+	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++)
 	{
 		float		minDistance = FLT_MAX;
 		int			closestCenter = 0;
 
 		/* Find closest center */
-		for (k = 0; k < numCenters; k++)
+		for (int64 k = 0; k < numCenters; k++)
 		{
 			/* TODO Use Lemma 1 in k-means++ initialization */
 			float		distance = lowerBound[j * numCenters + k];
@@ -292,13 +362,13 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		CHECK_FOR_INTERRUPTS();
 
 		/* Step 1: For all centers, compute distance */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
-			vec = VectorArrayGet(centers, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(centers, j));
 
-			for (k = j + 1; k < numCenters; k++)
+			for (int64 k = j + 1; k < numCenters; k++)
 			{
-				float		distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
+				float		distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, k))));
 
 				halfcdist[j * numCenters + k] = distance;
 				halfcdist[k * numCenters + j] = distance;
@@ -306,11 +376,11 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		}
 
 		/* For all centers c, compute s(c) */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
 			float		minDistance = FLT_MAX;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
 				float		distance;
 
@@ -327,7 +397,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 		rjreset = iteration != 0;
 
-		for (j = 0; j < numSamples; j++)
+		for (int64 j = 0; j < numSamples; j++)
 		{
 			bool		rj;
 
@@ -337,8 +407,9 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 			rj = rjreset;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
+				Datum		vec;
 				float		dxcx;
 
 				/* Step 3: For all remaining points x and centers c */
@@ -351,12 +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;
@@ -370,7 +441,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 				/* Step 3b */
 				if (dxcx > lowerBound[j * numCenters + k] || dxcx > halfcdist[closestCenters[j] * numCenters + k])
 				{
-					float		dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
+					float		dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, k))));
 
 					/* d(x,c) calculated */
 					lowerBound[j * numCenters + k] = dxc;
@@ -389,66 +460,15 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		}
 
 		/* Step 4: For each center c, let m(c) be mean of all points assigned */
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-			for (k = 0; k < dimensions; k++)
-				vec->x[k] = 0.0;
-
-			centerCounts[j] = 0;
-		}
-
-		for (j = 0; j < numSamples; j++)
-		{
-			int			closestCenter;
-
-			vec = VectorArrayGet(samples, j);
-			closestCenter = closestCenters[j];
-
-			/* Increment sum and count of closest center */
-			newCenter = VectorArrayGet(newCenters, closestCenter);
-			for (k = 0; k < dimensions; k++)
-				newCenter->x[k] += vec->x[k];
-
-			centerCounts[closestCenter] += 1;
-		}
-
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-
-			if (centerCounts[j] > 0)
-			{
-				/* Double avoids overflow, but requires more memory */
-				/* TODO Update bounds */
-				for (k = 0; k < dimensions; k++)
-				{
-					if (isinf(vec->x[k]))
-						vec->x[k] = vec->x[k] > 0 ? FLT_MAX : -FLT_MAX;
-				}
-
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] /= centerCounts[j];
-			}
-			else
-			{
-				/* TODO Handle empty centers properly */
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] = RandomDouble();
-			}
-
-			/* Normalize if needed */
-			if (normprocinfo != NULL)
-				ApplyNorm(normprocinfo, collation, vec);
-		}
+		ComputeNewCenters(samples, 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++)
 			{
 				float		distance = lowerBound[j * numCenters + k] - newcdist[k];
 
@@ -461,77 +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++)
+		for (int j = 0; j < numCenters; j++)
 			VectorArraySet(centers, j, VectorArrayGet(newCenters, j));
 
 		if (changes == 0 && iteration != 0)
 			break;
 	}
+}
 
-	VectorArrayFree(newCenters);
-	pfree(centerCounts);
-	pfree(closestCenters);
-	pfree(lowerBound);
-	pfree(upperBound);
-	pfree(s);
-	pfree(halfcdist);
-	pfree(newcdist);
+/*
+ * 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;
-
 	if (centers->length != centers->maxlen)
 		elog(ERROR, "Not enough centers. Please report a bug.");
 
-	/* Ensure no NaN or infinite values */
-	for (int i = 0; i < centers->length; i++)
-	{
-		Vector	   *vec = VectorArrayGet(centers, i);
-
-		for (int j = 0; j < vec->dim; j++)
-		{
-			if (isnan(vec->x[j]))
-				elog(ERROR, "NaN detected. Please report a bug.");
-
-			if (isinf(vec->x[j]))
-				elog(ERROR, "Infinite value detected. Please report a bug.");
-		}
-	}
-
-	/* Ensure no duplicate centers */
-	/* Fine to sort in-place */
-	qsort(centers->items, centers->length, VECTOR_SIZE(centers->dim), CompareVectors);
-	for (int i = 1; i < centers->length; i++)
-	{
-		if (CompareVectors(VectorArrayGet(centers, i), VectorArrayGet(centers, i - 1)) == 0)
-			elog(ERROR, "Duplicate centers detected. Please report a bug.");
-	}
-
-	/* Ensure no zero vectors for cosine distance */
-	/* Check NORM_PROC instead of KMEANS_NORM_PROC */
-	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
-	if (normprocinfo != NULL)
-	{
-		Oid			collation = index->rd_indcollation[0];
-
-		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.");
-		}
-	}
+	CheckElements(centers, typeInfo);
+	CheckNorms(centers, index);
 }
 
 /*
@@ -539,12 +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

@@ -10,6 +10,10 @@
 #include "miscadmin.h"
 #include "pgstat.h"
 #include "storage/bufmgr.h"
+#include "utils/memutils.h"
+
+#define GetScanList(ptr) pairingheap_container(IvfflatScanList, ph_node, ptr)
+#define GetScanListConst(ptr) pairingheap_const_container(IvfflatScanList, ph_node, ptr)
 
 /*
  * Compare list distances
@@ -17,10 +21,10 @@
 static int
 CompareLists(const pairingheap_node *a, const pairingheap_node *b, void *arg)
 {
-	if (((const IvfflatScanList *) a)->distance > ((const IvfflatScanList *) b)->distance)
+	if (GetScanListConst(a)->distance > GetScanListConst(b)->distance)
 		return 1;
 
-	if (((const IvfflatScanList *) a)->distance < ((const IvfflatScanList *) b)->distance)
+	if (GetScanListConst(a)->distance < GetScanListConst(b)->distance)
 		return -1;
 
 	return 0;
@@ -56,9 +60,9 @@ GetScanLists(IndexScanDesc scan, Datum value)
 			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)
+			if (listCount < so->maxProbes)
 			{
 				IvfflatScanList *scanlist;
 
@@ -71,15 +75,15 @@ GetScanLists(IndexScanDesc scan, Datum value)
 				pairingheap_add(so->listQueue, &scanlist->ph_node);
 
 				/* Calculate max distance */
-				if (listCount == so->probes)
-					maxDistance = ((IvfflatScanList *) pairingheap_first(so->listQueue))->distance;
+				if (listCount == so->maxProbes)
+					maxDistance = GetScanList(pairingheap_first(so->listQueue))->distance;
 			}
 			else if (distance < maxDistance)
 			{
 				IvfflatScanList *scanlist;
 
 				/* Remove */
-				scanlist = (IvfflatScanList *) pairingheap_remove_first(so->listQueue);
+				scanlist = GetScanList(pairingheap_remove_first(so->listQueue));
 
 				/* Reuse */
 				scanlist->startPage = list->startPage;
@@ -87,7 +91,7 @@ GetScanLists(IndexScanDesc scan, Datum value)
 				pairingheap_add(so->listQueue, &scanlist->ph_node);
 
 				/* Update max distance */
-				maxDistance = ((IvfflatScanList *) pairingheap_first(so->listQueue))->distance;
+				maxDistance = GetScanList(pairingheap_first(so->listQueue))->distance;
 			}
 		}
 
@@ -95,6 +99,11 @@ GetScanLists(IndexScanDesc scan, Datum value)
 
 		UnlockReleaseBuffer(cbuf);
 	}
+
+	for (int i = listCount - 1; i >= 0; i--)
+		so->listPages[i] = GetScanList(pairingheap_remove_first(so->listQueue))->startPage;
+
+	Assert(pairingheap_is_empty(so->listQueue));
 }
 
 /*
@@ -106,19 +115,15 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 	TupleDesc	tupdesc = RelationGetDescr(scan->indexRelation);
 	double		tuples = 0;
-	TupleTableSlot *slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsVirtual);
+	TupleTableSlot *slot = so->vslot;
+	int			batchProbes = 0;
 
-	/*
-	 * Reuse same set of shared buffers for scan
-	 *
-	 * See postgres/src/backend/storage/buffer/README for description
-	 */
-	BufferAccessStrategy bas = GetAccessStrategy(BAS_BULKREAD);
+	tuplesort_reset(so->sortstate);
 
 	/* Search closest probes lists */
-	while (!pairingheap_is_empty(so->listQueue))
+	while (so->listIndex < so->maxProbes && (++batchProbes) <= so->probes)
 	{
-		BlockNumber searchPage = ((IvfflatScanList *) pairingheap_remove_first(so->listQueue))->startPage;
+		BlockNumber searchPage = so->listPages[so->listIndex++];
 
 		/* Search all entry pages for list */
 		while (BlockNumberIsValid(searchPage))
@@ -127,7 +132,7 @@ GetScanItems(IndexScanDesc scan, Datum value)
 			Page		page;
 			OffsetNumber maxoffno;
 
-			buf = ReadBufferExtended(scan->indexRelation, MAIN_FORKNUM, searchPage, RBM_NORMAL, bas);
+			buf = ReadBufferExtended(scan->indexRelation, MAIN_FORKNUM, searchPage, RBM_NORMAL, so->bas);
 			LockBuffer(buf, BUFFER_LOCK_SHARE);
 			page = BufferGetPage(buf);
 			maxoffno = PageGetMaxOffsetNumber(page);
@@ -149,7 +154,7 @@ 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;
@@ -166,15 +171,77 @@ GetScanItems(IndexScanDesc scan, Datum value)
 		}
 	}
 
-	FreeAccessStrategy(bas);
-
-	if (tuples < 100)
+	if (tuples < 100 && ivfflat_iterative_search == IVFFLAT_ITERATIVE_SEARCH_OFF)
 		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);
+
+#if defined(IVFFLAT_MEMORY)
+	elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(CurrentMemoryContext, true) / (1024 * 1024));
+#endif
+}
+
+/*
+ * 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)
+		{
+			MemoryContext oldCtx = MemoryContextSwitchTo(so->tmpCtx);
+
+			value = IvfflatNormValue(so->typeInfo, so->collation, value);
+
+			MemoryContextSwitchTo(oldCtx);
+		}
+	}
+
+	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);
 }
 
 /*
@@ -187,23 +254,41 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	IvfflatScanOpaque so;
 	int			lists;
 	int			dimensions;
-	AttrNumber	attNums[] = {1};
-	Oid			sortOperators[] = {Float8LessOperator};
-	Oid			sortCollations[] = {InvalidOid};
-	bool		nullsFirstFlags[] = {false};
 	int			probes = ivfflat_probes;
+	int			maxProbes;
+	MemoryContext oldCtx;
 
 	scan = RelationGetIndexScan(index, nkeys, norderbys);
 
 	/* Get lists and dimensions from metapage */
 	IvfflatGetMetaPageInfo(index, &lists, &dimensions);
 
+	if (ivfflat_iterative_search != IVFFLAT_ITERATIVE_SEARCH_OFF)
+	{
+		maxProbes = ivfflat_max_probes;
+
+		if (maxProbes < 0)
+			maxProbes = lists;
+		else if (maxProbes < probes)
+		{
+			/* TODO Show notice */
+			maxProbes = probes;
+		}
+	}
+	else
+		maxProbes = probes;
+
 	if (probes > lists)
 		probes = lists;
 
-	so = (IvfflatScanOpaque) palloc(offsetof(IvfflatScanOpaqueData, lists) + probes * sizeof(IvfflatScanList));
+	if (maxProbes > lists)
+		maxProbes = lists;
+
+	so = (IvfflatScanOpaque) palloc(sizeof(IvfflatScanOpaqueData));
+	so->typeInfo = IvfflatGetTypeInfo(index);
 	so->first = true;
 	so->probes = probes;
+	so->maxProbes = maxProbes;
 	so->dimensions = dimensions;
 
 	/* Set support functions */
@@ -211,17 +296,37 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	so->normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_NORM_PROC);
 	so->collation = index->rd_indcollation[0];
 
+	so->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
+									   "Ivfflat scan temporary context",
+									   ALLOCSET_DEFAULT_SIZES);
+
+	oldCtx = MemoryContextSwitchTo(so->tmpCtx);
+
 	/* Create tuple description for sorting */
 	so->tupdesc = CreateTemplateTupleDesc(2);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "heaptid", TIDOID, -1, 0);
 
 	/* Prep sort */
-	so->sortstate = tuplesort_begin_heap(so->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, work_mem, NULL, false);
+	so->sortstate = InitScanSortState(so->tupdesc);
 
-	so->slot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsMinimalTuple);
+	/* Need separate slots for puttuple and gettuple */
+	so->vslot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsVirtual);
+	so->mslot = MakeSingleTupleTableSlot(so->tupdesc, &TTSOpsMinimalTuple);
+
+	/*
+	 * Reuse same set of shared buffers for scan
+	 *
+	 * See postgres/src/backend/storage/buffer/README for description
+	 */
+	so->bas = GetAccessStrategy(BAS_BULKREAD);
 
 	so->listQueue = pairingheap_allocate(CompareLists, scan);
+	so->listPages = palloc(maxProbes * sizeof(BlockNumber));
+	so->listIndex = 0;
+	so->lists = palloc(maxProbes * sizeof(IvfflatScanList));
+
+	MemoryContextSwitchTo(oldCtx);
 
 	scan->opaque = so;
 
@@ -236,13 +341,9 @@ 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);
+	so->listIndex = 0;
 
 	if (keys && scan->numberOfKeys > 0)
 		memmove(scan->keyData, keys, scan->numberOfKeys * sizeof(ScanKeyData));
@@ -258,6 +359,8 @@ bool
 ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
+	ItemPointer heaptid;
+	bool		isnull;
 
 	/*
 	 * Index can be used to scan backward, but Postgres doesn't support
@@ -281,41 +384,27 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (!IsMVCCSnapshot(scan->xs_snapshot))
 			elog(ERROR, "non-MVCC snapshots are not supported with ivfflat");
 
-		if (scan->orderByData->sk_flags & SK_ISNULL)
-			value = PointerGetDatum(InitVector(so->dimensions));
-		else
-		{
-			value = scan->orderByData->sk_argument;
-
-			/* Value should not be compressed or toasted */
-			Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
-			Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
-
-			/* Fine if normalization fails */
-			if (so->normprocinfo != NULL)
-				IvfflatNormValue(so->normprocinfo, so->collation, &value, NULL);
-		}
-
+		value = GetScanValue(scan);
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
 		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;
-
-		/* Clean up if we allocated a new value */
-		if (value != scan->orderByData->sk_argument)
-			pfree(DatumGetPointer(value));
+		so->value = value;
 	}
 
-	if (tuplesort_gettupleslot(so->sortstate, true, false, so->slot, NULL))
+	while (!tuplesort_gettupleslot(so->sortstate, true, false, so->mslot, NULL))
 	{
-		ItemPointer heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->slot, 2, &so->isnull));
+		if (so->listIndex == so->maxProbes)
+			return false;
 
-		scan->xs_heaptid = *heaptid;
-		scan->xs_recheck = false;
-		scan->xs_recheckorderby = false;
-		return true;
+		IvfflatBench("GetScanItems", GetScanItems(scan, so->value));
 	}
 
-	return false;
+	heaptid = (ItemPointer) DatumGetPointer(slot_getattr(so->mslot, 2, &isnull));
+
+	scan->xs_heaptid = *heaptid;
+	scan->xs_recheck = false;
+	scan->xs_recheckorderby = false;
+	return true;
 }
 
 /*
@@ -326,9 +415,11 @@ ivfflatendscan(IndexScanDesc scan)
 {
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 
-	pairingheap_free(so->listQueue);
+	/* Free any temporary files */
 	tuplesort_end(so->sortstate);
 
+	MemoryContextDelete(so->tmpCtx);
+
 	pfree(so);
 	scan->opaque = NULL;
 }

src/ivfutils.c

@@ -1,22 +1,30 @@
 #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(sizeof(VectorArrayData));
 
+	/* Ensure items are aligned to prevent UB */
+	itemsize = MAXALIGN(itemsize);
+
 	res->length = 0;
 	res->maxlen = maxlen;
 	res->dim = dimensions;
-	res->items = palloc_extended(maxlen * VECTOR_SIZE(dimensions), MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
+	res->itemsize = itemsize;
+	res->items = palloc_extended(maxlen * itemsize, MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
 	return res;
 }
 
@@ -30,16 +38,6 @@ VectorArrayFree(VectorArray arr)
 	pfree(arr);
 }
 
-/*
- * Print vector array - useful for debugging
- */
-void
-PrintVectorArray(char *msg, VectorArray arr)
-{
-	for (int i = 0; i < arr->length; i++)
-		PrintVector(msg, VectorArrayGet(arr, i));
-}
-
 /*
  * Get the number of lists in the index
  */
@@ -67,34 +65,21 @@ IvfflatOptionalProcInfo(Relation index, uint16 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)
 {
-	double		norm = DatumGetFloat8(FunctionCall1Coll(procinfo, collation, *value));
-
-	if (norm > 0)
-	{
-		Vector	   *v = DatumGetVector(*value);
-
-		if (result == NULL)
-			result = InitVector(v->dim);
-
-		for (int i = 0; i < v->dim; i++)
-			result->x[i] = v->x[i] / norm;
-
-		*value = PointerGetDatum(result);
-
-		return true;
-	}
-
-	return false;
+	return DatumGetFloat8(FunctionCall1Coll(procinfo, collation, value)) > 0;
 }
 
 /*
@@ -185,7 +170,11 @@ IvfflatGetMetaPageInfo(Relation index, int *lists, int *dimensions)
 	page = BufferGetPage(buf);
 	metap = IvfflatPageGetMeta(page);
 
-	*lists = metap->lists;
+	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;
@@ -239,3 +228,146 @@ IvfflatUpdateList(Relation index, 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

@@ -26,7 +26,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 		Page		cpage;
 		OffsetNumber coffno;
 		OffsetNumber cmaxoffno;
-		BlockNumber startPages[MaxOffsetNumber];
+		BlockNumber listPages[MaxOffsetNumber];
 		ListInfo	listInfo;
 
 		cbuf = ReadBuffer(index, blkno);
@@ -40,7 +40,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 		{
 			IvfflatList list = (IvfflatList) PageGetItem(cpage, PageGetItemId(cpage, coffno));
 
-			startPages[coffno - FirstOffsetNumber] = list->startPage;
+			listPages[coffno - FirstOffsetNumber] = list->startPage;
 		}
 
 		listInfo.blkno = blkno;
@@ -50,7 +50,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 
 		for (coffno = FirstOffsetNumber; coffno <= cmaxoffno; coffno = OffsetNumberNext(coffno))
 		{
-			BlockNumber searchPage = startPages[coffno - FirstOffsetNumber];
+			BlockNumber searchPage = listPages[coffno - FirstOffsetNumber];
 			BlockNumber insertPage = InvalidBlockNumber;
 
 			/* Iterate over entry pages */

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.c

@@ -2,14 +2,19 @@
 
 #include <math.h>
 
+#include "bitutils.h"
+#include "bitvec.h"
 #include "catalog/pg_type.h"
 #include "common/shortest_dec.h"
 #include "fmgr.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "hnsw.h"
 #include "ivfflat.h"
 #include "lib/stringinfo.h"
 #include "libpq/pqformat.h"
 #include "port.h"				/* for strtof() */
+#include "sparsevec.h"
 #include "utils/array.h"
 #include "utils/builtins.h"
 #include "utils/float.h"
@@ -21,14 +26,15 @@
 #include "varatt.h"
 #endif
 
-#if PG_VERSION_NUM < 130000
-#define TYPALIGN_DOUBLE 'd'
-#define TYPALIGN_INT 'i'
-#endif
-
 #define STATE_DIMS(x) (ARR_DIMS(x)[0] - 1)
 #define CreateStateDatums(dim) palloc(sizeof(Datum) * (dim + 1))
 
+#if defined(USE_TARGET_CLONES) && !defined(__FMA__)
+#define VECTOR_TARGET_CLONES __attribute__((target_clones("default", "fma")))
+#else
+#define VECTOR_TARGET_CLONES
+#endif
+
 PG_MODULE_MAGIC;
 
 /*
@@ -38,6 +44,8 @@ PGDLLEXPORT void _PG_init(void);
 void
 _PG_init(void)
 {
+	BitvecInit();
+	HalfvecInit();
 	HnswInit();
 	IvfflatInit();
 }
@@ -147,28 +155,10 @@ CheckStateArray(ArrayType *statearray, const char *caller)
 	return (float8 *) ARR_DATA_PTR(statearray);
 }
 
-#if PG_VERSION_NUM < 120003
-static pg_noinline void
-float_overflow_error(void)
-{
-	ereport(ERROR,
-			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-			 errmsg("value out of range: overflow")));
-}
-
-static pg_noinline void
-float_underflow_error(void)
-{
-	ereport(ERROR,
-			(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-			 errmsg("value out of range: underflow")));
-}
-#endif
-
 /*
  * Convert textual representation to internal representation
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_in);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_in);
 Datum
 vector_in(PG_FUNCTION_ARGS)
 {
@@ -176,27 +166,33 @@ vector_in(PG_FUNCTION_ARGS)
 	int32		typmod = PG_GETARG_INT32(2);
 	float		x[VECTOR_MAX_DIM];
 	int			dim = 0;
-	char	   *pt;
-	char	   *stringEnd;
+	char	   *pt = lit;
 	Vector	   *result;
-	char	   *litcopy = pstrdup(lit);
-	char	   *str = litcopy;
 
-	while (vector_isspace(*str))
-		str++;
+	while (vector_isspace(*pt))
+		pt++;
 
-	if (*str != '[')
+	if (*pt != '[')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type vector: \"%s\"", lit),
 				 errdetail("Vector contents must start with \"[\".")));
 
-	str++;
-	pt = strtok(str, ",");
-	stringEnd = pt;
+	pt++;
 
-	while (pt != NULL && *stringEnd != ']')
+	while (vector_isspace(*pt))
+		pt++;
+
+	if (*pt == ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("vector must have at least 1 dimension")));
+
+	for (;;)
 	{
+		float		val;
+		char	   *stringEnd;
+
 		if (dim == VECTOR_MAX_DIM)
 			ereport(ERROR,
 					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
@@ -211,61 +207,55 @@ vector_in(PG_FUNCTION_ARGS)
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
 
+		errno = 0;
+
 		/* Use strtof like float4in to avoid a double-rounding problem */
-		x[dim] = strtof(pt, &stringEnd);
-		CheckElement(x[dim]);
-		dim++;
+		/* Postgres sets LC_NUMERIC to C on startup */
+		val = strtof(pt, &stringEnd);
 
 		if (stringEnd == pt)
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
 
-		while (vector_isspace(*stringEnd))
-			stringEnd++;
+		/* Check for range error like float4in */
+		if (errno == ERANGE && isinf(val))
+			ereport(ERROR,
+					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+					 errmsg("\"%s\" is out of range for type vector", pnstrdup(pt, stringEnd - pt))));
 
-		if (*stringEnd != '\0' && *stringEnd != ']')
+		CheckElement(val);
+		x[dim++] = val;
+
+		pt = stringEnd;
+
+		while (vector_isspace(*pt))
+			pt++;
+
+		if (*pt == ',')
+			pt++;
+		else if (*pt == ']')
+		{
+			pt++;
+			break;
+		}
+		else
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
-
-		pt = strtok(NULL, ",");
 	}
 
-	if (stringEnd == NULL || *stringEnd != ']')
-		ereport(ERROR,
-				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
-				 errdetail("Unexpected end of input.")));
-
-	stringEnd++;
-
 	/* Only whitespace is allowed after the closing brace */
-	while (vector_isspace(*stringEnd))
-		stringEnd++;
+	while (vector_isspace(*pt))
+		pt++;
 
-	if (*stringEnd != '\0')
+	if (*pt != '\0')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed vector literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type vector: \"%s\"", lit),
 				 errdetail("Junk after closing right brace.")));
 
-	/* Ensure no consecutive delimiters since strtok skips */
-	for (pt = lit + 1; *pt != '\0'; pt++)
-	{
-		if (pt[-1] == ',' && *pt == ',')
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("malformed vector literal: \"%s\"", lit)));
-	}
-
-	if (dim < 1)
-		ereport(ERROR,
-				(errcode(ERRCODE_DATA_EXCEPTION),
-				 errmsg("vector must have at least 1 dimension")));
-
-	pfree(litcopy);
-
+	CheckDim(dim);
 	CheckExpectedDim(typmod, dim);
 
 	result = InitVector(dim);
@@ -275,10 +265,13 @@ vector_in(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+#define AppendChar(ptr, c) (*(ptr)++ = (c))
+#define AppendFloat(ptr, f) ((ptr) += float_to_shortest_decimal_bufn((f), (ptr)))
+
 /*
  * Convert internal representation to textual representation
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_out);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_out);
 Datum
 vector_out(PG_FUNCTION_ARGS)
 {
@@ -286,7 +279,6 @@ vector_out(PG_FUNCTION_ARGS)
 	int			dim = vector->dim;
 	char	   *buf;
 	char	   *ptr;
-	int			n;
 
 	/*
 	 * Need:
@@ -301,21 +293,17 @@ vector_out(PG_FUNCTION_ARGS)
 	buf = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN * dim + 2);
 	ptr = buf;
 
-	*ptr = '[';
-	ptr++;
+	AppendChar(ptr, '[');
+
 	for (int i = 0; i < dim; i++)
 	{
 		if (i > 0)
-		{
-			*ptr = ',';
-			ptr++;
-		}
+			AppendChar(ptr, ',');
 
-		n = float_to_shortest_decimal_bufn(vector->x[i], ptr);
-		ptr += n;
+		AppendFloat(ptr, vector->x[i]);
 	}
-	*ptr = ']';
-	ptr++;
+
+	AppendChar(ptr, ']');
 	*ptr = '\0';
 
 	PG_FREE_IF_COPY(vector, 0);
@@ -337,7 +325,7 @@ PrintVector(char *msg, Vector * vector)
 /*
  * Convert type modifier
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_typmod_in);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_typmod_in);
 Datum
 vector_typmod_in(PG_FUNCTION_ARGS)
 {
@@ -368,7 +356,7 @@ vector_typmod_in(PG_FUNCTION_ARGS)
 /*
  * Convert external binary representation to internal representation
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_recv);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_recv);
 Datum
 vector_recv(PG_FUNCTION_ARGS)
 {
@@ -402,7 +390,7 @@ vector_recv(PG_FUNCTION_ARGS)
 /*
  * Convert internal representation to the external binary representation
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_send);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_send);
 Datum
 vector_send(PG_FUNCTION_ARGS)
 {
@@ -422,7 +410,7 @@ vector_send(PG_FUNCTION_ARGS)
  * Convert vector to vector
  * This is needed to check the type modifier
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector);
 Datum
 vector(PG_FUNCTION_ARGS)
 {
@@ -437,7 +425,7 @@ vector(PG_FUNCTION_ARGS)
 /*
  * Convert array to vector
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(array_to_vector);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(array_to_vector);
 Datum
 array_to_vector(PG_FUNCTION_ARGS)
 {
@@ -511,7 +499,7 @@ array_to_vector(PG_FUNCTION_ARGS)
 /*
  * Convert vector to float4[]
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_to_float4);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_to_float4);
 Datum
 vector_to_float4(PG_FUNCTION_ARGS)
 {
@@ -532,131 +520,150 @@ vector_to_float4(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+/*
+ * Convert half vector to vector
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(halfvec_to_vector);
+Datum
+halfvec_to_vector(PG_FUNCTION_ARGS)
+{
+	HalfVector *vec = PG_GETARG_HALFVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	Vector	   *result;
+
+	CheckDim(vec->dim);
+	CheckExpectedDim(typmod, vec->dim);
+
+	result = InitVector(vec->dim);
+
+	for (int i = 0; i < vec->dim; i++)
+		result->x[i] = HalfToFloat4(vec->x[i]);
+
+	PG_RETURN_POINTER(result);
+}
+
+VECTOR_TARGET_CLONES static float
+VectorL2SquaredDistance(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		diff = ax[i] - bx[i];
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+
 /*
  * Get the L2 distance between vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(l2_distance);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(l2_distance);
 Datum
 l2_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
-	float		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
-
-	PG_RETURN_FLOAT8(sqrt((double) distance));
+	PG_RETURN_FLOAT8(sqrt((double) VectorL2SquaredDistance(a->dim, a->x, b->x)));
 }
 
 /*
  * Get the L2 squared distance between vectors
  * This saves a sqrt calculation
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_l2_squared_distance);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_l2_squared_distance);
 Datum
 vector_l2_squared_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
-	float		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
+	PG_RETURN_FLOAT8((double) VectorL2SquaredDistance(a->dim, a->x, b->x));
+}
 
-	PG_RETURN_FLOAT8((double) distance);
+VECTOR_TARGET_CLONES static float
+VectorInnerProduct(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += ax[i] * bx[i];
+
+	return distance;
 }
 
 /*
  * Get the inner product of two vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(inner_product);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(inner_product);
 Datum
 inner_product(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) VectorInnerProduct(a->dim, a->x, b->x));
 }
 
 /*
  * Get the negative inner product of two vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_negative_inner_product);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_negative_inner_product);
 Datum
 vector_negative_inner_product(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8((double) distance * -1);
+	PG_RETURN_FLOAT8((double) -VectorInnerProduct(a->dim, a->x, b->x));
 }
 
-/*
- * Get the cosine distance between two vectors
- */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(cosine_distance);
-Datum
-cosine_distance(PG_FUNCTION_ARGS)
+VECTOR_TARGET_CLONES static double
+VectorCosineSimilarity(int dim, float *ax, float *bx)
 {
-	Vector	   *a = PG_GETARG_VECTOR_P(0);
-	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
+	float		similarity = 0.0;
 	float		norma = 0.0;
 	float		normb = 0.0;
-	double		similarity;
-
-	CheckDims(a, b);
 
 	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
+	for (int i = 0; i < dim; i++)
 	{
-		distance += ax[i] * bx[i];
+		similarity += ax[i] * bx[i];
 		norma += ax[i] * ax[i];
 		normb += bx[i] * bx[i];
 	}
 
 	/* Use sqrt(a * b) over sqrt(a) * sqrt(b) */
-	similarity = (double) distance / sqrt((double) norma * (double) normb);
+	return (double) similarity / sqrt((double) norma * (double) normb);
+}
+
+/*
+ * Get the cosine distance between two vectors
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(cosine_distance);
+Datum
+cosine_distance(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
+	double		similarity;
+
+	CheckDims(a, b);
+
+	similarity = VectorCosineSimilarity(a->dim, a->x, b->x);
 
 #ifdef _MSC_VER
 	/* /fp:fast may not propagate NaN */
@@ -678,24 +685,17 @@ cosine_distance(PG_FUNCTION_ARGS)
  * Currently uses angular distance since needs to satisfy triangle inequality
  * Assumes inputs are unit vectors (skips norm)
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_spherical_distance);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_spherical_distance);
 Datum
 vector_spherical_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		dp = 0.0;
 	double		distance;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		dp += ax[i] * bx[i];
-
-	distance = (double) dp;
+	distance = (double) VectorInnerProduct(a->dim, a->x, b->x);
 
 	/* Prevent NaN with acos with loss of precision */
 	if (distance > 1)
@@ -706,32 +706,38 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(acos(distance) / M_PI);
 }
 
+/* Does not require FMA, but keep logic simple */
+VECTOR_TARGET_CLONES static float
+VectorL1Distance(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += fabsf(ax[i] - bx[i]);
+
+	return distance;
+}
+
 /*
  * Get the L1 distance between two vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(l1_distance);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(l1_distance);
 Datum
 l1_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += fabsf(ax[i] - bx[i]);
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) VectorL1Distance(a->dim, a->x, b->x));
 }
 
 /*
  * Get the dimensions of a vector
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_dims);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_dims);
 Datum
 vector_dims(PG_FUNCTION_ARGS)
 {
@@ -743,7 +749,7 @@ vector_dims(PG_FUNCTION_ARGS)
 /*
  * Get the L2 norm of a vector
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_norm);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_norm);
 Datum
 vector_norm(PG_FUNCTION_ARGS)
 {
@@ -758,10 +764,49 @@ vector_norm(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(sqrt(norm));
 }
 
+/*
+ * Normalize a vector with the L2 norm
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(l2_normalize);
+Datum
+l2_normalize(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	float	   *ax = a->x;
+	double		norm = 0;
+	Vector	   *result;
+	float	   *rx;
+
+	result = InitVector(a->dim);
+	rx = result->x;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < a->dim; i++)
+		norm += (double) ax[i] * (double) ax[i];
+
+	norm = sqrt(norm);
+
+	/* Return zero vector for zero norm */
+	if (norm > 0)
+	{
+		for (int i = 0; i < a->dim; i++)
+			rx[i] = ax[i] / norm;
+
+		/* Check for overflow */
+		for (int i = 0; i < a->dim; i++)
+		{
+			if (isinf(rx[i]))
+				float_overflow_error();
+		}
+	}
+
+	PG_RETURN_POINTER(result);
+}
+
 /*
  * Add vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_add);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_add);
 Datum
 vector_add(PG_FUNCTION_ARGS)
 {
@@ -794,7 +839,7 @@ vector_add(PG_FUNCTION_ARGS)
 /*
  * Subtract vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_sub);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_sub);
 Datum
 vector_sub(PG_FUNCTION_ARGS)
 {
@@ -827,7 +872,7 @@ vector_sub(PG_FUNCTION_ARGS)
 /*
  * Multiply vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_mul);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_mul);
 Datum
 vector_mul(PG_FUNCTION_ARGS)
 {
@@ -860,6 +905,95 @@ vector_mul(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+/*
+ * Concatenate vectors
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_concat);
+Datum
+vector_concat(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	Vector	   *b = PG_GETARG_VECTOR_P(1);
+	Vector	   *result;
+	int			dim = a->dim + b->dim;
+
+	CheckDim(dim);
+	result = InitVector(dim);
+
+	for (int i = 0; i < a->dim; i++)
+		result->x[i] = a->x[i];
+
+	for (int i = 0; i < b->dim; i++)
+		result->x[i + a->dim] = b->x[i];
+
+	PG_RETURN_POINTER(result);
+}
+
+/*
+ * Quantize a vector
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(binary_quantize);
+Datum
+binary_quantize(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	float	   *ax = a->x;
+	VarBit	   *result = InitBitVector(a->dim);
+	unsigned char *rx = VARBITS(result);
+
+	for (int i = 0; i < a->dim; i++)
+		rx[i / 8] |= (ax[i] > 0) << (7 - (i % 8));
+
+	PG_RETURN_VARBIT_P(result);
+}
+
+/*
+ * Get a subvector
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(subvector);
+Datum
+subvector(PG_FUNCTION_ARGS)
+{
+	Vector	   *a = PG_GETARG_VECTOR_P(0);
+	int32		start = PG_GETARG_INT32(1);
+	int32		count = PG_GETARG_INT32(2);
+	int32		end;
+	float	   *ax = a->x;
+	Vector	   *result;
+	int			dim;
+
+	if (count < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("vector must have at least 1 dimension")));
+
+	/*
+	 * Check if (start + count > a->dim), avoiding integer overflow. a->dim
+	 * and count are both positive, so a->dim - count won't overflow.
+	 */
+	if (start > a->dim - count)
+		end = a->dim + 1;
+	else
+		end = start + count;
+
+	/* Indexing starts at 1, like substring */
+	if (start < 1)
+		start = 1;
+	else if (start > a->dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("vector must have at least 1 dimension")));
+
+	dim = end - start;
+	CheckDim(dim);
+	result = InitVector(dim);
+
+	for (int i = 0; i < dim; i++)
+		result->x[i] = ax[start - 1 + i];
+
+	PG_RETURN_POINTER(result);
+}
+
 /*
  * Internal helper to compare vectors
  */
@@ -890,103 +1024,85 @@ vector_cmp_internal(Vector * a, Vector * b)
 /*
  * Less than
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_lt);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_lt);
 Datum
 vector_lt(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
-	/* TODO Remove in 0.7.0 */
-	CheckDims(a, b);
-
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) < 0);
 }
 
 /*
  * Less than or equal
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_le);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_le);
 Datum
 vector_le(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
-	/* TODO Remove in 0.7.0 */
-	CheckDims(a, b);
-
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) <= 0);
 }
 
 /*
  * Equal
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_eq);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_eq);
 Datum
 vector_eq(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
-	/* TODO Remove in 0.7.0 */
-	CheckDims(a, b);
-
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) == 0);
 }
 
 /*
  * Not equal
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_ne);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_ne);
 Datum
 vector_ne(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
-	/* TODO Remove in 0.7.0 */
-	CheckDims(a, b);
-
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) != 0);
 }
 
 /*
  * Greater than or equal
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_ge);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_ge);
 Datum
 vector_ge(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
-	/* TODO Remove in 0.7.0 */
-	CheckDims(a, b);
-
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) >= 0);
 }
 
 /*
  * Greater than
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_gt);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_gt);
 Datum
 vector_gt(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
 
-	/* TODO Remove in 0.7.0 */
-	CheckDims(a, b);
-
 	PG_RETURN_BOOL(vector_cmp_internal(a, b) > 0);
 }
 
 /*
  * Compare vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_cmp);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_cmp);
 Datum
 vector_cmp(PG_FUNCTION_ARGS)
 {
@@ -999,7 +1115,7 @@ vector_cmp(PG_FUNCTION_ARGS)
 /*
  * Accumulate vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_accum);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_accum);
 Datum
 vector_accum(PG_FUNCTION_ARGS)
 {
@@ -1058,12 +1174,13 @@ vector_accum(PG_FUNCTION_ARGS)
 }
 
 /*
- * Combine vectors
+ * Combine vectors or half vectors (also used for halfvec_combine)
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_combine);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_combine);
 Datum
 vector_combine(PG_FUNCTION_ARGS)
 {
+	/* Must also update parameters of halfvec_combine if modifying */
 	ArrayType  *statearray1 = PG_GETARG_ARRAYTYPE_P(0);
 	ArrayType  *statearray2 = PG_GETARG_ARRAYTYPE_P(1);
 	float8	   *statevalues1;
@@ -1130,7 +1247,7 @@ vector_combine(PG_FUNCTION_ARGS)
 /*
  * Average vectors
  */
-PGDLLEXPORT PG_FUNCTION_INFO_V1(vector_avg);
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(vector_avg);
 Datum
 vector_avg(PG_FUNCTION_ARGS)
 {
@@ -1160,3 +1277,26 @@ vector_avg(PG_FUNCTION_ARGS)
 
 	PG_RETURN_POINTER(result);
 }
+
+/*
+ * Convert sparse vector to dense vector
+ */
+FUNCTION_PREFIX PG_FUNCTION_INFO_V1(sparsevec_to_vector);
+Datum
+sparsevec_to_vector(PG_FUNCTION_ARGS)
+{
+	SparseVector *svec = PG_GETARG_SPARSEVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+	Vector	   *result;
+	int			dim = svec->dim;
+	float	   *values = SPARSEVEC_VALUES(svec);
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	result = InitVector(dim);
+	for (int i = 0; i < svec->nnz; i++)
+		result->x[svec->indices[i]] = values[i];
+
+	PG_RETURN_POINTER(result);
+}

src/vector.h

@@ -12,7 +12,7 @@ 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;
 
@@ -20,4 +20,11 @@ Vector	   *InitVector(int dim);
 void		PrintVector(char *msg, Vector * vector);
 int			vector_cmp_internal(Vector * a, Vector * b);
 
+/* 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

@@ -1,4 +1,5 @@
 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);
@@ -8,10 +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

@@ -28,6 +28,26 @@ SELECT ARRAY[1,2,3]::numeric[]::vector;
  [1,2,3]
 (1 row)
 
+SELECT '[1,2,3]'::vector::real[];
+ float4  
+---------
+ {1,2,3}
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector(2);
+ERROR:  expected 2 dimensions, not 3
 SELECT '{NULL}'::real[]::vector;
 ERROR:  array must not contain nulls
 SELECT '{NaN}'::real[]::vector;
@@ -40,12 +60,238 @@ SELECT '{}'::real[]::vector;
 ERROR:  vector must have at least 1 dimension
 SELECT '{{1}}'::real[]::vector;
 ERROR:  array must be 1-D
-SELECT '[1,2,3]'::vector::real[];
- float4  
+SELECT '{1,2,3}'::double precision[]::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::double precision[]::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::double precision[]::vector(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{4e38,-4e38}'::double precision[]::vector;
+ERROR:  infinite value not allowed in vector
+SELECT '{1e-46,-1e-46}'::double precision[]::vector;
+ vector 
+--------
+ [0,-0]
+(1 row)
+
+SELECT '[1,2,3]'::vector::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::vector::halfvec(3);
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::vector::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '[65520]'::vector::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '[1e-8]'::vector::halfvec;
+ halfvec 
+---------
+ [0]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{1,2,3}'::real[]::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::halfvec(3);
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{65520,-65520}'::real[]::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '{1e-8,-1e-8}'::real[]::halfvec;
+ halfvec 
+---------
+ [0,-0]
+(1 row)
+
+SELECT '[1,2,3]'::intvec::integer[];
+  int4   
 ---------
  {1,2,3}
 (1 row)
 
+SELECT '{1,2,3}'::integer[]::intvec;
+ intvec  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::integer[]::intvec(3);
+ intvec  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::integer[]::intvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{127,-128}'::integer[]::intvec;
+   intvec   
+------------
+ [127,-128]
+(1 row)
+
+SELECT '{128,-129}'::integer[]::intvec;
+ERROR:  value "128" is out of range for type intvec
+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;

test/expected/copy.out

@@ -1,8 +1,9 @@
+-- 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 'results/data.bin' WITH (FORMAT binary)
-\copy t2 FROM 'results/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   
 ---------
@@ -14,3 +15,54 @@ 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;
+-- intvec
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE TABLE t2 (val intvec(3));
+\copy t TO 'results/intvec.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/intvec.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

@@ -1,260 +0,0 @@
-SELECT '[1,2,3]'::vector + '[4,5,6]';
- ?column? 
-----------
- [5,7,9]
-(1 row)
-
-SELECT '[3e38]'::vector + '[3e38]';
-ERROR:  value out of range: overflow
-SELECT '[1,2,3]'::vector - '[4,5,6]';
-  ?column?  
-------------
- [-3,-3,-3]
-(1 row)
-
-SELECT '[-3e38]'::vector - '[3e38]';
-ERROR:  value out of range: overflow
-SELECT '[1,2,3]'::vector * '[4,5,6]';
- ?column?  
------------
- [4,10,18]
-(1 row)
-
-SELECT '[1e37]'::vector * '[1e37]';
-ERROR:  value out of range: overflow
-SELECT '[1e-37]'::vector * '[1e-37]';
-ERROR:  value out of range: underflow
-SELECT '[1,2,3]'::vector = '[1,2,3]';
- ?column? 
-----------
- t
-(1 row)
-
-SELECT '[1,2,3]'::vector = '[1,2]';
-ERROR:  different vector dimensions 3 and 2
-SELECT vector_cmp('[1,2,3]', '[1,2,3]');
- vector_cmp 
-------------
-          0
-(1 row)
-
-SELECT vector_cmp('[1,2,3]', '[0,0,0]');
- vector_cmp 
-------------
-          1
-(1 row)
-
-SELECT vector_cmp('[0,0,0]', '[1,2,3]');
- vector_cmp 
-------------
-         -1
-(1 row)
-
-SELECT vector_cmp('[1,2]', '[1,2,3]');
- vector_cmp 
-------------
-         -1
-(1 row)
-
-SELECT vector_cmp('[1,2,3]', '[1,2]');
- vector_cmp 
-------------
-          1
-(1 row)
-
-SELECT vector_cmp('[1,2]', '[2,3,4]');
- vector_cmp 
-------------
-         -1
-(1 row)
-
-SELECT vector_cmp('[2,3]', '[1,2,3]');
- vector_cmp 
-------------
-          1
-(1 row)
-
-SELECT vector_dims('[1,2,3]');
- vector_dims 
--------------
-           3
-(1 row)
-
-SELECT round(vector_norm('[1,1]')::numeric, 5);
-  round  
----------
- 1.41421
-(1 row)
-
-SELECT vector_norm('[3,4]');
- vector_norm 
--------------
-           5
-(1 row)
-
-SELECT vector_norm('[0,1]');
- vector_norm 
--------------
-           1
-(1 row)
-
-SELECT vector_norm('[3e37,4e37]')::real;
- vector_norm 
--------------
-       5e+37
-(1 row)
-
-SELECT l2_distance('[0,0]', '[3,4]');
- l2_distance 
--------------
-           5
-(1 row)
-
-SELECT l2_distance('[0,0]', '[0,1]');
- l2_distance 
--------------
-           1
-(1 row)
-
-SELECT l2_distance('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-SELECT l2_distance('[3e38]', '[-3e38]');
- l2_distance 
--------------
-    Infinity
-(1 row)
-
-SELECT inner_product('[1,2]', '[3,4]');
- inner_product 
----------------
-            11
-(1 row)
-
-SELECT inner_product('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-SELECT inner_product('[3e38]', '[3e38]');
- inner_product 
----------------
-      Infinity
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[2,4]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[0,0]');
- cosine_distance 
------------------
-             NaN
-(1 row)
-
-SELECT cosine_distance('[1,1]', '[1,1]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,0]', '[0,2]');
- cosine_distance 
------------------
-               1
-(1 row)
-
-SELECT cosine_distance('[1,1]', '[-1,-1]');
- cosine_distance 
------------------
-               2
-(1 row)
-
-SELECT cosine_distance('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-SELECT cosine_distance('[1,1]', '[1.1,1.1]');
- cosine_distance 
------------------
-               0
-(1 row)
-
-SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
- cosine_distance 
------------------
-               2
-(1 row)
-
-SELECT cosine_distance('[3e38]', '[3e38]');
- cosine_distance 
------------------
-             NaN
-(1 row)
-
-SELECT l1_distance('[0,0]', '[3,4]');
- l1_distance 
--------------
-           7
-(1 row)
-
-SELECT l1_distance('[0,0]', '[0,1]');
- l1_distance 
--------------
-           1
-(1 row)
-
-SELECT l1_distance('[1,2]', '[3]');
-ERROR:  different vector dimensions 2 and 1
-SELECT l1_distance('[3e38]', '[-3e38]');
- l1_distance 
--------------
-    Infinity
-(1 row)
-
-SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
-    avg    
------------
- [2,3.5,5]
-(1 row)
-
-SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
-    avg    
------------
- [2,3.5,5]
-(1 row)
-
-SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
- avg 
------
- 
-(1 row)
-
-SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
-ERROR:  expected 2 dimensions, not 1
-SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
-   avg   
----------
- [3e+38]
-(1 row)
-
-SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
-ERROR:  vector cannot have more than 16000 dimensions
-SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
-   sum    
-----------
- [4,7,10]
-(1 row)
-
-SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
-   sum    
-----------
- [4,7,10]
-(1 row)
-
-SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
- sum 
------
- 
-(1 row)
-
-SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
-ERROR:  different vector dimensions 2 and 1
-SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
-ERROR:  value out of range: overflow

test/expected/halfvec.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_cosine.out

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

test/expected/hnsw_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_intvec.out

@@ -0,0 +1,102 @@
+SET enable_seqscan = off;
+-- L2
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) 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 intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;
+-- cosine
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) t2;
+ count 
+-------
+     3
+(1 row)
+
+DROP TABLE t;
+-- L1
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) t2;
+ count 
+-------
+     4
+(1 row)
+
+DROP TABLE t;

test/expected/hnsw_ip.out

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

test/expected/hnsw_l2.out

@@ -1,36 +0,0 @@
-SET enable_seqscan = off;
-CREATE TABLE t (val vector(3));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE INDEX ON t USING hnsw (val vector_l2_ops);
-INSERT INTO t (val) VALUES ('[1,2,4]');
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-   val   
----------
- [1,2,3]
- [1,2,4]
- [1,1,1]
- [0,0,0]
-(4 rows)
-
-SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
-   val   
----------
- [0,0,0]
- [1,1,1]
- [1,2,3]
- [1,2,4]
-(4 rows)
-
-SELECT COUNT(*) FROM t;
- count 
--------
-     5
-(1 row)
-
-TRUNCATE t;
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
- val 
------
-(0 rows)
-
-DROP TABLE t;

test/expected/hnsw_options.out

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

test/expected/hnsw_sparsevec.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_unlogged.out

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

test/expected/hnsw_vector.out

@@ -0,0 +1,185 @@
+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;
+-- iterative
+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);
+SET hnsw.iterative_search = strict_order;
+SET hnsw.ef_search = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+SET hnsw.iterative_search = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+RESET hnsw.iterative_search;
+RESET hnsw.ef_search;
+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)
+SHOW hnsw.iterative_search;
+ hnsw.iterative_search 
+-----------------------
+ off
+(1 row)
+
+SET hnsw.iterative_search = on;
+ERROR:  invalid value for parameter "hnsw.iterative_search": "on"
+HINT:  Available values: off, relaxed_order, strict_order.
+SHOW hnsw.max_search_tuples;
+ hnsw.max_search_tuples 
+------------------------
+ -1
+(1 row)
+
+SET hnsw.max_search_tuples = -2;
+ERROR:  -2 is outside the valid range for parameter "hnsw.max_search_tuples" (-1 .. 2147483647)
+DROP TABLE t;

test/expected/input.out

@@ -1,129 +0,0 @@
-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:  infinite value not allowed in vector
-LINE 1: SELECT '[4e38,1]'::vector;
-               ^
-SELECT '[1,2,3'::vector;
-ERROR:  malformed vector literal: "[1,2,3"
-LINE 1: SELECT '[1,2,3'::vector;
-               ^
-DETAIL:  Unexpected end of input.
-SELECT '[1,2,3]9'::vector;
-ERROR:  malformed vector literal: "[1,2,3]9"
-LINE 1: SELECT '[1,2,3]9'::vector;
-               ^
-DETAIL:  Junk after closing right brace.
-SELECT '1,2,3'::vector;
-ERROR:  malformed vector literal: "1,2,3"
-LINE 1: SELECT '1,2,3'::vector;
-               ^
-DETAIL:  Vector contents must start with "[".
-SELECT ''::vector;
-ERROR:  malformed vector literal: ""
-LINE 1: SELECT ''::vector;
-               ^
-DETAIL:  Vector contents must start with "[".
-SELECT '['::vector;
-ERROR:  malformed vector literal: "["
-LINE 1: SELECT '['::vector;
-               ^
-DETAIL:  Unexpected end of input.
-SELECT '[,'::vector;
-ERROR:  malformed vector literal: "[,"
-LINE 1: SELECT '[,'::vector;
-               ^
-DETAIL:  Unexpected end of input.
-SELECT '[]'::vector;
-ERROR:  vector must have at least 1 dimension
-LINE 1: SELECT '[]'::vector;
-               ^
-SELECT '[1,]'::vector;
-ERROR:  invalid input syntax for type vector: "[1,]"
-LINE 1: SELECT '[1,]'::vector;
-               ^
-SELECT '[1a]'::vector;
-ERROR:  invalid input syntax for type vector: "[1a]"
-LINE 1: SELECT '[1a]'::vector;
-               ^
-SELECT '[1,,3]'::vector;
-ERROR:  malformed vector literal: "[1,,3]"
-LINE 1: SELECT '[1,,3]'::vector;
-               ^
-SELECT '[1, ,3]'::vector;
-ERROR:  invalid input syntax for type vector: "[1, ,3]"
-LINE 1: SELECT '[1, ,3]'::vector;
-               ^
-SELECT '[1,2,3]'::vector(2);
-ERROR:  expected 2 dimensions, not 3
-SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
- unnest  
----------
- [1,2,3]
- [4,5,6]
-(2 rows)
-
-SELECT '{"[1,2,3]"}'::vector(2)[];
-ERROR:  expected 2 dimensions, not 3

test/expected/intvec.out

@@ -0,0 +1,328 @@
+SELECT '[1,2,3]'::intvec;
+ intvec  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[-1,-2,-3]'::intvec;
+   intvec   
+------------
+ [-1,-2,-3]
+(1 row)
+
+SELECT ' [ 1,  2 ,    3  ] '::intvec;
+ intvec  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1.23456]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1.23456]"
+LINE 1: SELECT '[1.23456]'::intvec;
+               ^
+SELECT '[hello,1]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[hello,1]"
+LINE 1: SELECT '[hello,1]'::intvec;
+               ^
+SELECT '[127,-128]'::intvec;
+   intvec   
+------------
+ [127,-128]
+(1 row)
+
+SELECT '[128,-129]'::intvec;
+ERROR:  "128" is out of range for type intvec
+LINE 1: SELECT '[128,-129]'::intvec;
+               ^
+SELECT '[1,2,3'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1,2,3"
+LINE 1: SELECT '[1,2,3'::intvec;
+               ^
+SELECT '[1,2,3]9'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1,2,3]9"
+LINE 1: SELECT '[1,2,3]9'::intvec;
+               ^
+DETAIL:  Junk after closing right brace.
+SELECT '1,2,3'::intvec;
+ERROR:  invalid input syntax for type intvec: "1,2,3"
+LINE 1: SELECT '1,2,3'::intvec;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT ''::intvec;
+ERROR:  invalid input syntax for type intvec: ""
+LINE 1: SELECT ''::intvec;
+               ^
+DETAIL:  Vector contents must start with "[".
+SELECT '['::intvec;
+ERROR:  invalid input syntax for type intvec: "["
+LINE 1: SELECT '['::intvec;
+               ^
+SELECT '[,'::intvec;
+ERROR:  invalid input syntax for type intvec: "[,"
+LINE 1: SELECT '[,'::intvec;
+               ^
+SELECT '[]'::intvec;
+ERROR:  intvec must have at least 1 dimension
+LINE 1: SELECT '[]'::intvec;
+               ^
+SELECT '[1,]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1,]"
+LINE 1: SELECT '[1,]'::intvec;
+               ^
+SELECT '[1a]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1a]"
+LINE 1: SELECT '[1a]'::intvec;
+               ^
+SELECT '[1,,3]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1,,3]"
+LINE 1: SELECT '[1,,3]'::intvec;
+               ^
+SELECT '[1, ,3]'::intvec;
+ERROR:  invalid input syntax for type intvec: "[1, ,3]"
+LINE 1: SELECT '[1, ,3]'::intvec;
+               ^
+SELECT '[1,2,3]'::intvec(3);
+ intvec  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::intvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::intvec(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '[1,2,3]'::intvec(3, 2);
+                          ^
+SELECT '[1,2,3]'::intvec('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '[1,2,3]'::intvec('a');
+                          ^
+SELECT '[1,2,3]'::intvec(0);
+ERROR:  dimensions for type intvec must be at least 1
+LINE 1: SELECT '[1,2,3]'::intvec(0);
+                          ^
+SELECT '[1,2,3]'::intvec(16001);
+ERROR:  dimensions for type intvec cannot exceed 16000
+LINE 1: SELECT '[1,2,3]'::intvec(16001);
+                          ^
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::intvec[]);
+ unnest  
+---------
+ [1,2,3]
+ [4,5,6]
+(2 rows)
+
+SELECT '{"[1,2,3]"}'::intvec(2)[];
+ERROR:  expected 2 dimensions, not 3
+SELECT '[1,2,3]'::intvec < '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec < '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec <= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec <= '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec = '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec = '[1,2]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec != '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec != '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec >= '[1,2,3]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec >= '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT '[1,2,3]'::intvec > '[1,2,3]';
+ ?column? 
+----------
+ f
+(1 row)
+
+SELECT '[1,2,3]'::intvec > '[1,2]';
+ ?column? 
+----------
+ t
+(1 row)
+
+SELECT intvec_cmp('[1,2,3]', '[1,2,3]');
+ intvec_cmp 
+------------
+          0
+(1 row)
+
+SELECT intvec_cmp('[1,2,3]', '[0,0,0]');
+ intvec_cmp 
+------------
+          1
+(1 row)
+
+SELECT intvec_cmp('[0,0,0]', '[1,2,3]');
+ intvec_cmp 
+------------
+         -1
+(1 row)
+
+SELECT intvec_cmp('[1,2]', '[1,2,3]');
+ intvec_cmp 
+------------
+         -1
+(1 row)
+
+SELECT intvec_cmp('[1,2,3]', '[1,2]');
+ intvec_cmp 
+------------
+          1
+(1 row)
+
+SELECT intvec_cmp('[1,2]', '[2,3,4]');
+ intvec_cmp 
+------------
+         -1
+(1 row)
+
+SELECT intvec_cmp('[2,3]', '[1,2,3]');
+ intvec_cmp 
+------------
+          1
+(1 row)
+
+SELECT vector_dims('[1,2,3]'::intvec);
+ vector_dims 
+-------------
+           3
+(1 row)
+
+SELECT l2_distance('[0,0]'::intvec, '[3,4]');
+ l2_distance 
+-------------
+           5
+(1 row)
+
+SELECT l2_distance('[0,0]'::intvec, '[0,1]');
+ l2_distance 
+-------------
+           1
+(1 row)
+
+SELECT l2_distance('[1,2]'::intvec, '[3]');
+ERROR:  different intvec dimensions 2 and 1
+SELECT '[0,0]'::intvec <-> '[3,4]';
+ ?column? 
+----------
+        5
+(1 row)
+
+SELECT inner_product('[1,2]'::intvec, '[3,4]');
+ inner_product 
+---------------
+            11
+(1 row)
+
+SELECT inner_product('[1,2]'::intvec, '[3]');
+ERROR:  different intvec dimensions 2 and 1
+SELECT inner_product('[127]'::intvec, '[127]');
+ inner_product 
+---------------
+         16129
+(1 row)
+
+SELECT '[1,2]'::intvec <#> '[3,4]';
+ ?column? 
+----------
+      -11
+(1 row)
+
+SELECT cosine_distance('[1,2]'::intvec, '[2,4]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,2]'::intvec, '[0,0]');
+ cosine_distance 
+-----------------
+             NaN
+(1 row)
+
+SELECT cosine_distance('[1,1]'::intvec, '[1,1]');
+ cosine_distance 
+-----------------
+               0
+(1 row)
+
+SELECT cosine_distance('[1,0]'::intvec, '[0,2]');
+ cosine_distance 
+-----------------
+               1
+(1 row)
+
+SELECT cosine_distance('[1,1]'::intvec, '[-1,-1]');
+ cosine_distance 
+-----------------
+               2
+(1 row)
+
+SELECT cosine_distance('[1,2]'::intvec, '[3]');
+ERROR:  different intvec dimensions 2 and 1
+SELECT '[1,2]'::intvec <=> '[2,4]';
+ ?column? 
+----------
+        0
+(1 row)
+
+SELECT l1_distance('[0,0]'::intvec, '[3,4]');
+ l1_distance 
+-------------
+           7
+(1 row)
+
+SELECT l1_distance('[0,0]'::intvec, '[0,1]');
+ l1_distance 
+-------------
+           1
+(1 row)
+
+SELECT l1_distance('[1,2]'::intvec, '[3]');
+ERROR:  different intvec dimensions 2 and 1

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

@@ -1,26 +0,0 @@
-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 COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
- count 
--------
-     3
-(1 row)
-
-SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2;
- count 
--------
-     3
-(1 row)
-
-DROP TABLE t;

test/expected/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

@@ -1,21 +0,0 @@
-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 COUNT(*) FROM (SELECT * FROM t ORDER BY val <#> (SELECT NULL::vector)) t2;
- count 
--------
-     4
-(1 row)
-
-DROP TABLE t;

test/expected/ivfflat_l2.out

@@ -1,39 +0,0 @@
-SET enable_seqscan = off;
-CREATE TABLE t (val vector(3));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 1);
-INSERT INTO t (val) VALUES ('[1,2,4]');
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-   val   
----------
- [1,2,3]
- [1,2,4]
- [1,1,1]
- [0,0,0]
-(4 rows)
-
-SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
-   val   
----------
- [0,0,0]
- [1,1,1]
- [1,2,3]
- [1,2,4]
-(4 rows)
-
-SELECT COUNT(*) FROM t;
- count 
--------
-     5
-(1 row)
-
-TRUNCATE t;
-NOTICE:  ivfflat index created with little data
-DETAIL:  This will cause low recall.
-HINT:  Drop the index until the table has more data.
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
- val 
------
-(0 rows)
-
-DROP TABLE t;

test/expected/ivfflat_options.out

@@ -1,14 +0,0 @@
-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/ivfflat_unlogged.out

@@ -1,13 +0,0 @@
-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 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;

test/expected/ivfflat_vector.out

@@ -0,0 +1,173 @@
+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;
+-- iterative
+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 = 3);
+SET ivfflat.iterative_search = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+ [0,0,0]
+(3 rows)
+
+SET ivfflat.max_probes = 0;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+(1 row)
+
+SET ivfflat.max_probes = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+(1 row)
+
+SET ivfflat.max_probes = 2;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+   val   
+---------
+ [1,2,3]
+ [1,1,1]
+(2 rows)
+
+RESET ivfflat.iterative_search;
+RESET ivfflat.max_probes;
+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)
+
+SET ivfflat.probes = 0;
+ERROR:  0 is outside the valid range for parameter "ivfflat.probes" (1 .. 32768)
+SET ivfflat.probes = 32769;
+ERROR:  32769 is outside the valid range for parameter "ivfflat.probes" (1 .. 32768)
+SHOW ivfflat.iterative_search;
+ ivfflat.iterative_search 
+--------------------------
+ off
+(1 row)
+
+SET ivfflat.iterative_search = on;
+ERROR:  invalid value for parameter "ivfflat.iterative_search": "on"
+HINT:  Available values: off, relaxed_order.
+SHOW ivfflat.max_probes;
+ ivfflat.max_probes 
+--------------------
+ -1
+(1 row)
+
+SET ivfflat.max_probes = -2;
+ERROR:  -2 is outside the valid range for parameter "ivfflat.max_probes" (-1 .. 32768)
+SET ivfflat.max_probes = 32769;
+ERROR:  32769 is outside the valid range for parameter "ivfflat.max_probes" (-1 .. 32768)
+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

@@ -1,10 +1,34 @@
 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

@@ -3,13 +3,85 @@ SELECT ARRAY[1.0,2.0,3.0]::vector;
 SELECT ARRAY[1,2,3]::float4[]::vector;
 SELECT ARRAY[1,2,3]::float8[]::vector;
 SELECT ARRAY[1,2,3]::numeric[]::vector;
+
+SELECT '[1,2,3]'::vector::real[];
+
+SELECT '{1,2,3}'::real[]::vector;
+SELECT '{1,2,3}'::real[]::vector(3);
+SELECT '{1,2,3}'::real[]::vector(2);
 SELECT '{NULL}'::real[]::vector;
 SELECT '{NaN}'::real[]::vector;
 SELECT '{Infinity}'::real[]::vector;
 SELECT '{-Infinity}'::real[]::vector;
 SELECT '{}'::real[]::vector;
 SELECT '{{1}}'::real[]::vector;
-SELECT '[1,2,3]'::vector::real[];
+
+SELECT '{1,2,3}'::double precision[]::vector;
+SELECT '{1,2,3}'::double precision[]::vector(3);
+SELECT '{1,2,3}'::double precision[]::vector(2);
+SELECT '{4e38,-4e38}'::double precision[]::vector;
+SELECT '{1e-46,-1e-46}'::double precision[]::vector;
+
+SELECT '[1,2,3]'::vector::halfvec;
+SELECT '[1,2,3]'::vector::halfvec(3);
+SELECT '[1,2,3]'::vector::halfvec(2);
+SELECT '[65520]'::vector::halfvec;
+SELECT '[1e-8]'::vector::halfvec;
+
+SELECT '[1,2,3]'::halfvec::vector;
+SELECT '[1,2,3]'::halfvec::vector(3);
+SELECT '[1,2,3]'::halfvec::vector(2);
+
+SELECT '{1,2,3}'::real[]::halfvec;
+SELECT '{1,2,3}'::real[]::halfvec(3);
+SELECT '{1,2,3}'::real[]::halfvec(2);
+SELECT '{65520,-65520}'::real[]::halfvec;
+SELECT '{1e-8,-1e-8}'::real[]::halfvec;
+
+SELECT '[1,2,3]'::intvec::integer[];
+
+SELECT '{1,2,3}'::integer[]::intvec;
+SELECT '{1,2,3}'::integer[]::intvec(3);
+SELECT '{1,2,3}'::integer[]::intvec(2);
+SELECT '{127,-128}'::integer[]::intvec;
+SELECT '{128,-129}'::integer[]::intvec;
+
+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;
 

test/sql/copy.sql

@@ -1,10 +1,57 @@
+-- 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 'results/data.bin' WITH (FORMAT binary)
-\copy t2 FROM 'results/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;
+
+-- intvec
+
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+
+CREATE TABLE t2 (val intvec(3));
+
+\copy t TO 'results/intvec.bin' WITH (FORMAT binary)
+\copy t2 FROM 'results/intvec.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

@@ -1,62 +0,0 @@
-SELECT '[1,2,3]'::vector + '[4,5,6]';
-SELECT '[3e38]'::vector + '[3e38]';
-SELECT '[1,2,3]'::vector - '[4,5,6]';
-SELECT '[-3e38]'::vector - '[3e38]';
-SELECT '[1,2,3]'::vector * '[4,5,6]';
-SELECT '[1e37]'::vector * '[1e37]';
-SELECT '[1e-37]'::vector * '[1e-37]';
-
-SELECT '[1,2,3]'::vector = '[1,2,3]';
-SELECT '[1,2,3]'::vector = '[1,2]';
-
-SELECT vector_cmp('[1,2,3]', '[1,2,3]');
-SELECT vector_cmp('[1,2,3]', '[0,0,0]');
-SELECT vector_cmp('[0,0,0]', '[1,2,3]');
-SELECT vector_cmp('[1,2]', '[1,2,3]');
-SELECT vector_cmp('[1,2,3]', '[1,2]');
-SELECT vector_cmp('[1,2]', '[2,3,4]');
-SELECT vector_cmp('[2,3]', '[1,2,3]');
-
-SELECT vector_dims('[1,2,3]');
-
-SELECT round(vector_norm('[1,1]')::numeric, 5);
-SELECT vector_norm('[3,4]');
-SELECT vector_norm('[0,1]');
-SELECT vector_norm('[3e37,4e37]')::real;
-
-SELECT l2_distance('[0,0]', '[3,4]');
-SELECT l2_distance('[0,0]', '[0,1]');
-SELECT l2_distance('[1,2]', '[3]');
-SELECT l2_distance('[3e38]', '[-3e38]');
-
-SELECT inner_product('[1,2]', '[3,4]');
-SELECT inner_product('[1,2]', '[3]');
-SELECT inner_product('[3e38]', '[3e38]');
-
-SELECT cosine_distance('[1,2]', '[2,4]');
-SELECT cosine_distance('[1,2]', '[0,0]');
-SELECT cosine_distance('[1,1]', '[1,1]');
-SELECT cosine_distance('[1,0]', '[0,2]');
-SELECT cosine_distance('[1,1]', '[-1,-1]');
-SELECT cosine_distance('[1,2]', '[3]');
-SELECT cosine_distance('[1,1]', '[1.1,1.1]');
-SELECT cosine_distance('[1,1]', '[-1.1,-1.1]');
-SELECT cosine_distance('[3e38]', '[3e38]');
-
-SELECT l1_distance('[0,0]', '[3,4]');
-SELECT l1_distance('[0,0]', '[0,1]');
-SELECT l1_distance('[1,2]', '[3]');
-SELECT l1_distance('[3e38]', '[-3e38]');
-
-SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
-SELECT avg(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
-SELECT avg(v) FROM unnest(ARRAY[]::vector[]) v;
-SELECT avg(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
-SELECT avg(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;
-SELECT vector_avg(array_agg(n)) FROM generate_series(1, 16002) n;
-
-SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]']) v;
-SELECT sum(v) FROM unnest(ARRAY['[1,2,3]'::vector, '[3,5,7]', NULL]) v;
-SELECT sum(v) FROM unnest(ARRAY[]::vector[]) v;
-SELECT sum(v) FROM unnest(ARRAY['[1,2]'::vector, '[3]']) v;
-SELECT sum(v) FROM unnest(ARRAY['[3e38]'::vector, '[3e38]']) v;

test/sql/halfvec.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_cosine.sql

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

test/sql/hnsw_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_intvec.sql

@@ -0,0 +1,58 @@
+SET enable_seqscan = off;
+
+-- L2
+
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) 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 intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) t2;
+
+DROP TABLE t;
+
+-- cosine
+
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) t2;
+
+DROP TABLE t;
+
+-- L1
+
+CREATE TABLE t (val intvec(3));
+INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
+CREATE INDEX ON t USING hnsw (val intvec_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::intvec)) t2;
+
+DROP TABLE t;

test/sql/hnsw_ip.sql

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

test/sql/hnsw_l2.sql

@@ -1,16 +0,0 @@
-SET enable_seqscan = off;
-
-CREATE TABLE t (val vector(3));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE INDEX ON t USING hnsw (val vector_l2_ops);
-
-INSERT INTO t (val) VALUES ('[1,2,4]');
-
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
-SELECT COUNT(*) FROM t;
-
-TRUNCATE t;
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-
-DROP TABLE t;

test/sql/hnsw_options.sql

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

test/sql/hnsw_sparsevec.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_unlogged.sql

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

test/sql/hnsw_vector.sql

@@ -0,0 +1,109 @@
+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;
+
+-- iterative
+
+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);
+
+SET hnsw.iterative_search = strict_order;
+SET hnsw.ef_search = 1;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+SET hnsw.iterative_search = relaxed_order;
+SELECT * FROM t ORDER BY val <-> '[3,3,3]';
+
+RESET hnsw.iterative_search;
+RESET hnsw.ef_search;
+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;
+
+SHOW hnsw.iterative_search;
+
+SET hnsw.iterative_search = on;
+
+SHOW hnsw.max_search_tuples;
+
+SET hnsw.max_search_tuples = -2;
+
+DROP TABLE t;

test/sql/input.sql

@@ -1,28 +0,0 @@
-SELECT '[1,2,3]'::vector;
-SELECT '[-1,-2,-3]'::vector;
-SELECT '[1.,2.,3.]'::vector;
-SELECT ' [ 1,  2 ,    3  ] '::vector;
-SELECT '[1.23456]'::vector;
-SELECT '[hello,1]'::vector;
-SELECT '[NaN,1]'::vector;
-SELECT '[Infinity,1]'::vector;
-SELECT '[-Infinity,1]'::vector;
-SELECT '[1.5e38,-1.5e38]'::vector;
-SELECT '[1.5e+38,-1.5e+38]'::vector;
-SELECT '[1.5e-38,-1.5e-38]'::vector;
-SELECT '[4e38,1]'::vector;
-SELECT '[1,2,3'::vector;
-SELECT '[1,2,3]9'::vector;
-SELECT '1,2,3'::vector;
-SELECT ''::vector;
-SELECT '['::vector;
-SELECT '[,'::vector;
-SELECT '[]'::vector;
-SELECT '[1,]'::vector;
-SELECT '[1a]'::vector;
-SELECT '[1,,3]'::vector;
-SELECT '[1, ,3]'::vector;
-SELECT '[1,2,3]'::vector(2);
-
-SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
-SELECT '{"[1,2,3]"}'::vector(2)[];

test/sql/intvec.sql

@@ -0,0 +1,73 @@
+SELECT '[1,2,3]'::intvec;
+SELECT '[-1,-2,-3]'::intvec;
+SELECT ' [ 1,  2 ,    3  ] '::intvec;
+SELECT '[1.23456]'::intvec;
+SELECT '[hello,1]'::intvec;
+SELECT '[127,-128]'::intvec;
+SELECT '[128,-129]'::intvec;
+SELECT '[1,2,3'::intvec;
+SELECT '[1,2,3]9'::intvec;
+SELECT '1,2,3'::intvec;
+SELECT ''::intvec;
+SELECT '['::intvec;
+SELECT '[,'::intvec;
+SELECT '[]'::intvec;
+SELECT '[1,]'::intvec;
+SELECT '[1a]'::intvec;
+SELECT '[1,,3]'::intvec;
+SELECT '[1, ,3]'::intvec;
+
+SELECT '[1,2,3]'::intvec(3);
+SELECT '[1,2,3]'::intvec(2);
+SELECT '[1,2,3]'::intvec(3, 2);
+SELECT '[1,2,3]'::intvec('a');
+SELECT '[1,2,3]'::intvec(0);
+SELECT '[1,2,3]'::intvec(16001);
+
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::intvec[]);
+SELECT '{"[1,2,3]"}'::intvec(2)[];
+
+SELECT '[1,2,3]'::intvec < '[1,2,3]';
+SELECT '[1,2,3]'::intvec < '[1,2]';
+SELECT '[1,2,3]'::intvec <= '[1,2,3]';
+SELECT '[1,2,3]'::intvec <= '[1,2]';
+SELECT '[1,2,3]'::intvec = '[1,2,3]';
+SELECT '[1,2,3]'::intvec = '[1,2]';
+SELECT '[1,2,3]'::intvec != '[1,2,3]';
+SELECT '[1,2,3]'::intvec != '[1,2]';
+SELECT '[1,2,3]'::intvec >= '[1,2,3]';
+SELECT '[1,2,3]'::intvec >= '[1,2]';
+SELECT '[1,2,3]'::intvec > '[1,2,3]';
+SELECT '[1,2,3]'::intvec > '[1,2]';
+
+SELECT intvec_cmp('[1,2,3]', '[1,2,3]');
+SELECT intvec_cmp('[1,2,3]', '[0,0,0]');
+SELECT intvec_cmp('[0,0,0]', '[1,2,3]');
+SELECT intvec_cmp('[1,2]', '[1,2,3]');
+SELECT intvec_cmp('[1,2,3]', '[1,2]');
+SELECT intvec_cmp('[1,2]', '[2,3,4]');
+SELECT intvec_cmp('[2,3]', '[1,2,3]');
+
+SELECT vector_dims('[1,2,3]'::intvec);
+
+SELECT l2_distance('[0,0]'::intvec, '[3,4]');
+SELECT l2_distance('[0,0]'::intvec, '[0,1]');
+SELECT l2_distance('[1,2]'::intvec, '[3]');
+SELECT '[0,0]'::intvec <-> '[3,4]';
+
+SELECT inner_product('[1,2]'::intvec, '[3,4]');
+SELECT inner_product('[1,2]'::intvec, '[3]');
+SELECT inner_product('[127]'::intvec, '[127]');
+SELECT '[1,2]'::intvec <#> '[3,4]';
+
+SELECT cosine_distance('[1,2]'::intvec, '[2,4]');
+SELECT cosine_distance('[1,2]'::intvec, '[0,0]');
+SELECT cosine_distance('[1,1]'::intvec, '[1,1]');
+SELECT cosine_distance('[1,0]'::intvec, '[0,2]');
+SELECT cosine_distance('[1,1]'::intvec, '[-1,-1]');
+SELECT cosine_distance('[1,2]'::intvec, '[3]');
+SELECT '[1,2]'::intvec <=> '[2,4]';
+
+SELECT l1_distance('[0,0]'::intvec, '[3,4]');
+SELECT l1_distance('[0,0]'::intvec, '[0,1]');
+SELECT l1_distance('[1,2]'::intvec, '[3]');

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

@@ -1,13 +0,0 @@
-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 COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '[0,0,0]') t2;
-SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> (SELECT NULL::vector)) t2;
-
-DROP TABLE t;

test/sql/ivfflat_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

@@ -1,12 +0,0 @@
-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 COUNT(*) FROM (SELECT * FROM t ORDER BY val <#> (SELECT NULL::vector)) t2;
-
-DROP TABLE t;

test/sql/ivfflat_l2.sql

@@ -1,16 +0,0 @@
-SET enable_seqscan = off;
-
-CREATE TABLE t (val vector(3));
-INSERT INTO t (val) VALUES ('[0,0,0]'), ('[1,2,3]'), ('[1,1,1]'), (NULL);
-CREATE INDEX ON t USING ivfflat (val vector_l2_ops) WITH (lists = 1);
-
-INSERT INTO t (val) VALUES ('[1,2,4]');
-
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-SELECT * FROM t ORDER BY val <-> (SELECT NULL::vector);
-SELECT COUNT(*) FROM t;
-
-TRUNCATE t;
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-
-DROP TABLE t;

test/sql/ivfflat_options.sql

@@ -1,7 +0,0 @@
-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/ivfflat_unlogged.sql

@@ -1,9 +0,0 @@
-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 vector_l2_ops) WITH (lists = 1);
-
-SELECT * FROM t ORDER BY val <-> '[3,3,3]';
-
-DROP TABLE t;