Merge branch 'master' into minibatch

.editorconfig

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

.github/workflows/build.yml

@@ -2,16 +2,15 @@ name: build
 on: [push, pull_request]
 jobs:
   build:
-    if: "!contains(github.event.head_commit.message, '[skip ci]')"
     runs-on: ${{ matrix.os }}
     strategy:
       fail-fast: false
       matrix:
         os: [ubuntu-latest]
-        postgres: [13, 12, 11, 10, 9.6]
+        postgres: [14, 13, 12, 11, 10, 9.6]
         include:
         - os: macos-latest
-          postgres: 13
+          postgres: 14
     steps:
     - uses: actions/checkout@v2
     - uses: ankane/setup-postgres@v1
@@ -34,6 +33,6 @@ jobs:
     - if: ${{ startsWith(matrix.os, 'macos') }}
       run: |
         brew install cpanm && cpanm IPC::Run
-        wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_13_2.tar.gz
-        tar xf REL_13_2.tar.gz
-        make prove_installcheck PROVE=prove PERL5LIB=postgres-REL_13_2/src/test/perl
+        wget -q https://github.com/postgres/postgres/archive/refs/tags/REL_14_1.tar.gz
+        tar xf REL_14_1.tar.gz
+        make prove_installcheck PROVE=prove PERL5LIB=postgres-REL_14_1/src/test/perl

CHANGELOG.md

@@ -1,3 +1,36 @@
+## 0.2.6 (unreleased)
+
+- Switched to mini-batch k-means
+- Improved performance of index creation for Postgres < 12
+
+## 0.2.5 (2022-02-11)
+
+- Reduced memory usage during index creation
+- Fixed index creation exceeding `maintenance_work_mem`
+- Fixed error with index creation when lists > 1600
+
+## 0.2.4 (2022-02-06)
+
+- Added support for parallel vacuum
+- Fixed issue with index not reusing space
+
+## 0.2.3 (2022-01-30)
+
+- Added indexing progress for Postgres 12+
+- Improved interrupt handling during index creation
+
+## 0.2.2 (2022-01-15)
+
+- Fixed compilation error on Mac ARM
+
+## 0.2.1 (2022-01-02)
+
+- Fixed `operator is not unique` error
+
+## 0.2.0 (2021-10-03)
+
+- Added support for Postgres 14
+
 ## 0.1.8 (2021-09-07)
 
 - Added cast for `vector` to `real[]`

Dockerfile

@@ -1,9 +1,9 @@
-FROM postgres
+FROM postgres:14
 
 COPY . /tmp/pgvector
 
 RUN apt-get update && \
-		apt-get install -y --no-install-recommends build-essential postgresql-server-dev-13 && \
+		apt-get install -y --no-install-recommends build-essential postgresql-server-dev-14 && \
 		cd /tmp/pgvector && \
 		make clean && \
 		make OPTFLAGS="" && \
@@ -11,6 +11,6 @@ RUN apt-get update && \
 		mkdir /usr/share/doc/pgvector && \
 		cp LICENSE README.md /usr/share/doc/pgvector && \
 		rm -r /tmp/pgvector && \
-		apt-get remove -y build-essential postgresql-server-dev-13 && \
+		apt-get remove -y build-essential postgresql-server-dev-14 && \
 		apt-get autoremove -y && \
 		rm -rf /var/lib/apt/lists/*

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": "0.1.8",
+	"version": "0.2.5",
 	"maintainer": [
 		"Andrew Kane <andrew@ankane.org>"
 	],
@@ -20,18 +20,18 @@
 		"vector": {
 			"file": "sql/vector.sql",
 			"docfile": "README.md",
-			"version": "0.1.8",
+			"version": "0.2.5",
 			"abstract": "Open-source vector similarity search for Postgres"
 		}
 	},
 	"resources": {
-		"homepage": "https://github.com/ankane/pgvector",
+		"homepage": "https://github.com/pgvector/pgvector",
 		"bugtracker": {
-			"web": "https://github.com/ankane/pgvector/issues"
+			"web": "https://github.com/pgvector/pgvector/issues"
 		},
 		"repository": {
-			"url":  "https://github.com/ankane/pgvector.git",
-			"web":  "https://github.com/ankane/pgvector",
+			"url":  "https://github.com/pgvector/pgvector.git",
+			"web":  "https://github.com/pgvector/pgvector",
 			"type": "git"
 		}
 	},

Makefile

@@ -1,5 +1,5 @@
 EXTENSION = vector
-EXTVERSION = 0.1.8
+EXTVERSION = 0.2.5
 
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
@@ -11,10 +11,17 @@ REGRESS_OPTS = --inputdir=test
 
 OPTFLAGS = -march=native
 
+# Mac ARM doesn't support -march=native
+ifeq ($(shell uname -s), Darwin)
+	ifeq ($(shell uname -p), arm)
+		OPTFLAGS =
+	endif
+endif
+
 # For auto-vectorization:
 # - GCC (needs -ftree-vectorize OR -O3) - https://gcc.gnu.org/projects/tree-ssa/vectorization.html
 # - Clang (could use pragma instead) - https://llvm.org/docs/Vectorizers.html
-PG_CFLAGS = $(OPTFLAGS) -ftree-vectorize -fassociative-math -fno-signed-zeros -fno-trapping-math
+PG_CFLAGS += $(OPTFLAGS) -ftree-vectorize -fassociative-math -fno-signed-zeros -fno-trapping-math
 
 # Debug GCC auto-vectorization
 # PG_CFLAGS += -fopt-info-vec
@@ -42,3 +49,8 @@ prove_installcheck:
 dist:
 	mkdir -p dist
 	git archive --format zip --prefix=$(EXTENSION)-$(EXTVERSION)/ --output dist/$(EXTENSION)-$(EXTVERSION).zip master
+
+.PHONY: docker
+
+docker:
+	docker build --pull --no-cache -t ankane/pgvector:latest .

README.md

@@ -4,20 +4,20 @@ Open-source vector similarity search for Postgres
 
 ```sql
 CREATE TABLE table (column vector(3));
-CREATE INDEX ON table USING ivfflat (column);
+CREATE INDEX ON table USING ivfflat (column vector_l2_ops);
 SELECT * FROM table ORDER BY column <-> '[1,2,3]' LIMIT 5;
 ```
 
 Supports L2 distance, inner product, and cosine distance
 
-[![Build Status](https://github.com/ankane/pgvector/workflows/build/badge.svg?branch=master)](https://github.com/ankane/pgvector/actions)
+[![Build Status](https://github.com/pgvector/pgvector/workflows/build/badge.svg?branch=master)](https://github.com/pgvector/pgvector/actions)
 
 ## Installation
 
 Compile and install the extension (supports Postgres 9.6+)
 
 ```sh
-git clone --branch v0.1.8 https://github.com/ankane/pgvector.git
+git clone --branch v0.2.5 https://github.com/pgvector/pgvector.git
 cd pgvector
 make
 make install # may need sudo
@@ -62,7 +62,7 @@ Speed up queries with an approximate index. Add an index for each distance funct
 L2 distance
 
 ```sql
-CREATE INDEX ON table USING ivfflat (column);
+CREATE INDEX ON table USING ivfflat (column vector_l2_ops);
 ```
 
 Inner product
@@ -77,16 +77,18 @@ Cosine distance
 CREATE INDEX ON table USING ivfflat (column vector_cosine_ops);
 ```
 
-Indexes should be created after the table has data for optimal clustering. Also, unlike typical indexes which only affect performance, you may see different results for queries after adding an approximate index.
+Indexes should be created after the table has some data for optimal clustering. Also, unlike typical indexes which only affect performance, you may see different results for queries after adding an approximate index.
 
 ### Index Options
 
 Specify the number of inverted lists (100 by default)
 
 ```sql
-CREATE INDEX ON table USING ivfflat (column) WITH (lists = 100);
+CREATE INDEX ON table USING ivfflat (column opclass) WITH (lists = 100);
 ```
 
+A [good place to start](https://github.com/facebookresearch/faiss/issues/112) is `4 * sqrt(rows)`
+
 ### Query Options
 
 Specify the number of probes (1 by default)
@@ -106,16 +108,47 @@ SELECT ...
 COMMIT;
 ```
 
+### Indexing Progress
+
+Check [indexing progress](https://www.postgresql.org/docs/current/progress-reporting.html#CREATE-INDEX-PROGRESS-REPORTING) with Postgres 12+
+
+```sql
+SELECT phase, tuples_done, tuples_total FROM pg_stat_progress_create_index;
+```
+
+The phases are:
+
+1. `initializing`
+2. `performing k-means`
+3. `sorting tuples`
+4. `loading tuples`
+
+Note: `tuples_done` and `tuples_total` are only populated during the `loading tuples` phase
+
 ### Partial Indexes
 
 Consider [partial indexes](https://www.postgresql.org/docs/current/indexes-partial.html) for queries with a `WHERE` clause
 
 ```sql
-CREATE INDEX ON table USING ivfflat (column) WHERE (other_column = 123);
+CREATE INDEX ON table USING ivfflat (column opclass) WHERE (other_column = 123);
 ```
 
 To index many different values of `other_column`, consider [partitioning](https://www.postgresql.org/docs/current/ddl-partitioning.html) on `other_column`.
 
+## Performance
+
+To speed up queries without an index, increase `max_parallel_workers_per_gather`.
+
+```sql
+SET max_parallel_workers_per_gather = 4;
+```
+
+To speed up queries with an index, increase the number of inverted lists (at the expense of recall).
+
+```sql
+CREATE INDEX ON table USING ivfflat (column opclass) WITH (lists = 1000);
+```
+
 ## Reference
 
 ### Vector Type
@@ -146,17 +179,36 @@ vector_norm(vector) | Euclidean norm
 
 Libraries that use pgvector:
 
-- [pgvector-python](https://github.com/ankane/pgvector-python) (Python)
+- [pgvector-python](https://github.com/pgvector/pgvector-python) (Python)
 - [Neighbor](https://github.com/ankane/neighbor) (Ruby)
-- [pgvector-node](https://github.com/ankane/pgvector-node) (Node.js)
-- [pgvector-go](https://github.com/ankane/pgvector-go) (Go)
-- [pgvector-rust](https://github.com/ankane/pgvector-rust) (Rust)
+- [pgvector-ruby](https://github.com/pgvector/pgvector-ruby) (Ruby)
+- [pgvector-node](https://github.com/pgvector/pgvector-node) (Node.js)
+- [pgvector-go](https://github.com/pgvector/pgvector-go) (Go)
+- [pgvector-rust](https://github.com/pgvector/pgvector-rust) (Rust)
+- [pgvector-cpp](https://github.com/pgvector/pgvector-cpp) (C++)
+
+## Frequently Asked Questions
+
+#### How many vectors can be stored in a single table?
+
+A non-partitioned table has a limit of 32 TB by default in Postgres. A partitioned table can have thousands of partitions of that size.
+
+#### Is replication supported?
+
+Yes, pgvector uses the write-ahead log (WAL), which allows for replication and point-in-time recovery.
+
+#### What if my data has more than 1024 dimensions?
+
+Two things you can try are:
+
+1. use dimensionality reduction
+2. compile Postgres with a larger block size (`./configure --with-blocksize=32`) and edit the limit in `src/vector.h`
 
 ## Additional Installation Methods
 
 ### Docker
 
-Get the [Docker image](https://hub.docker.com/repository/docker/ankane/pgvector) with:
+Get the [Docker image](https://hub.docker.com/r/ankane/pgvector) with:
 
 ```sh
 docker pull ankane/pgvector
@@ -167,7 +219,7 @@ This adds pgvector to the [Postgres image](https://hub.docker.com/_/postgres).
 You can also build the image manually
 
 ```sh
-git clone --branch v0.1.8 https://github.com/ankane/pgvector.git
+git clone --branch v0.2.5 https://github.com/pgvector/pgvector.git
 cd pgvector
 docker build -t pgvector .
 ```
@@ -177,7 +229,7 @@ docker build -t pgvector .
 On Mac with Homebrew Postgres, you can use:
 
 ```sh
-brew install ankane/brew/pgvector
+brew install pgvector/brew/pgvector
 ```
 
 ### PGXN
@@ -194,7 +246,7 @@ Some Postgres providers only support specific extensions. To request a new exten
 
 - Amazon RDS - follow the instructions on [this page](https://aws.amazon.com/rds/postgresql/faqs/)
 - Google Cloud SQL - follow the instructions on [this page](https://cloud.google.com/sql/docs/postgres/extensions#requesting-support-for-a-new-extension)
-- DigitalOcean Managed Databases - follow the instructions on [this page](https://docs.digitalocean.com/products/databases/postgresql/resources/supported-extensions/#supported-extensions)
+- DigitalOcean Managed Databases - vote or comment on [this page](https://ideas.digitalocean.com/app-framework-services/p/pgvector-extension-for-postgresql)
 - Azure Database for PostgreSQL - follow the instructions on [this page](https://docs.microsoft.com/en-us/azure/postgresql/concepts-extensions#next-steps)
 
 ## Upgrading
@@ -211,27 +263,27 @@ Thanks to:
 
 - [PASE: PostgreSQL Ultra-High-Dimensional Approximate Nearest Neighbor Search Extension](https://dl.acm.org/doi/pdf/10.1145/3318464.3386131)
 - [Faiss: A Library for Efficient Similarity Search and Clustering of Dense Vectors](https://github.com/facebookresearch/faiss)
-- [Using the Triangle Inequality to Accelerate k-means](https://www.aaai.org/Papers/ICML/2003/ICML03-022.pdf)
+- [Web-Scale k-means Clustering](https://www.eecs.tufts.edu/~dsculley/papers/fastkmeans.pdf)
 - [k-means++: The Advantage of Careful Seeding](https://theory.stanford.edu/~sergei/papers/kMeansPP-soda.pdf)
 - [Concept Decompositions for Large Sparse Text Data using Clustering](https://www.cs.utexas.edu/users/inderjit/public_papers/concept_mlj.pdf)
 
 ## History
 
-View the [changelog](https://github.com/ankane/pgvector/blob/master/CHANGELOG.md)
+View the [changelog](https://github.com/pgvector/pgvector/blob/master/CHANGELOG.md)
 
 ## Contributing
 
 Everyone is encouraged to help improve this project. Here are a few ways you can help:
 
-- [Report bugs](https://github.com/ankane/pgvector/issues)
-- Fix bugs and [submit pull requests](https://github.com/ankane/pgvector/pulls)
+- [Report bugs](https://github.com/pgvector/pgvector/issues)
+- Fix bugs and [submit pull requests](https://github.com/pgvector/pgvector/pulls)
 - Write, clarify, or fix documentation
 - Suggest or add new features
 
 To get started with development:
 
 ```sh
-git clone https://github.com/ankane/pgvector.git
+git clone https://github.com/pgvector/pgvector.git
 cd pgvector
 make
 make install
@@ -251,6 +303,12 @@ make installcheck REGRESS=functions                    # regression test
 make prove_installcheck PROVE_TESTS=test/t/001_wal.pl  # TAP test
 ```
 
+To enable benchmarking:
+
+```sh
+make clean && PG_CFLAGS=-DIVFFLAT_BENCH make && make install
+```
+
 Resources for contributors
 
 - [Extension Building Infrastructure](https://www.postgresql.org/docs/current/extend-pgxs.html)

sql/vector--0.1.8--0.2.0.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.2.0'" to load this file. \quit

sql/vector--0.2.0--0.2.1.sql

@@ -0,0 +1,19 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.2.1'" to load this file. \quit
+
+DROP CAST (integer[] AS vector);
+DROP CAST (real[] AS vector);
+DROP CAST (double precision[] AS vector);
+DROP CAST (numeric[] AS vector);
+
+CREATE CAST (integer[] AS vector)
+  WITH FUNCTION array_to_vector(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (real[] AS vector)
+  WITH FUNCTION array_to_vector(real[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (double precision[] AS vector)
+  WITH FUNCTION array_to_vector(double precision[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (numeric[] AS vector)
+  WITH FUNCTION array_to_vector(numeric[], integer, boolean) AS ASSIGNMENT;

sql/vector--0.2.1--0.2.2.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.2.2'" to load this file. \quit

sql/vector--0.2.2--0.2.3.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.2.3'" to load this file. \quit

sql/vector--0.2.3--0.2.4.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.2.4'" to load this file. \quit

sql/vector--0.2.4--0.2.5.sql

@@ -0,0 +1,2 @@
+-- complain if script is sourced in psql, rather than via CREATE EXTENSION
+\echo Use "ALTER EXTENSION vector UPDATE TO '0.2.5'" to load this file. \quit

sql/vector.sql

@@ -108,21 +108,21 @@ CREATE FUNCTION vector_to_float4(vector, integer, boolean) RETURNS real[]
 CREATE CAST (vector AS vector)
 	WITH FUNCTION vector(vector, integer, boolean) AS IMPLICIT;
 
-CREATE CAST (integer[] AS vector)
-	WITH FUNCTION array_to_vector(integer[], integer, boolean) AS IMPLICIT;
-
-CREATE CAST (real[] AS vector)
-	WITH FUNCTION array_to_vector(real[], integer, boolean) AS IMPLICIT;
-
-CREATE CAST (double precision[] AS vector)
-	WITH FUNCTION array_to_vector(double precision[], integer, boolean) AS IMPLICIT;
-
-CREATE CAST (numeric[] AS vector)
-	WITH FUNCTION array_to_vector(numeric[], integer, boolean) AS IMPLICIT;
-
 CREATE CAST (vector AS real[])
 	WITH FUNCTION vector_to_float4(vector, integer, boolean) AS IMPLICIT;
 
+CREATE CAST (integer[] AS vector)
+	WITH FUNCTION array_to_vector(integer[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (real[] AS vector)
+	WITH FUNCTION array_to_vector(real[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (double precision[] AS vector)
+	WITH FUNCTION array_to_vector(double precision[], integer, boolean) AS ASSIGNMENT;
+
+CREATE CAST (numeric[] AS vector)
+	WITH FUNCTION array_to_vector(numeric[], integer, boolean) AS ASSIGNMENT;
+
 -- operators
 
 CREATE OPERATOR <-> (

src/ivfbuild.c

@@ -7,8 +7,19 @@
 #include "miscadmin.h"
 #include "storage/bufmgr.h"
 
+#if PG_VERSION_NUM >= 140000
+#include "utils/backend_progress.h"
+#elif PG_VERSION_NUM >= 120000
+#include "pgstat.h"
+#endif
+
 #if PG_VERSION_NUM >= 120000
 #include "access/tableam.h"
+#include "commands/progress.h"
+#else
+#define PROGRESS_CREATEIDX_SUBPHASE 0
+#define PROGRESS_CREATEIDX_TUPLES_TOTAL 0
+#define PROGRESS_CREATEIDX_TUPLES_DONE 0
 #endif
 
 #if PG_VERSION_NUM >= 110000
@@ -25,84 +36,11 @@
 #define CALLBACK_ITEM_POINTER HeapTuple hup
 #endif
 
-/*
- * Callback for sampling
- */
-static void
-SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
-			   bool *isnull, bool tupleIsAlive, void *state)
-{
-	IvfflatBuildState *buildstate = (IvfflatBuildState *) state;
-	VectorArray samples = buildstate->samples;
-	int			targsamples = samples->maxlen;
-	Datum		value = values[0];
-
-	/* Skip nulls */
-	if (isnull[0])
-		return;
-
-	/*
-	 * Normalize with KMEANS_NORM_PROC since spherical distance function
-	 * expects unit vectors
-	 */
-	if (buildstate->kmeansnormprocinfo != NULL)
-	{
-		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->normvec))
-			return;
-	}
-
-	if (samples->length < targsamples)
-	{
-		VectorArraySet(samples, samples->length, DatumGetVector(value));
-		samples->length++;
-	}
-	else
-	{
-		if (buildstate->rowstoskip < 0)
-			buildstate->rowstoskip = reservoir_get_next_S(&buildstate->rstate, samples->length, targsamples);
-
-		if (buildstate->rowstoskip <= 0)
-		{
-			int			k = (int) (targsamples * sampler_random_fract(buildstate->rstate.randstate));
-
-			Assert(k >= 0 && k < targsamples);
-			VectorArraySet(samples, k, DatumGetVector(value));
-		}
-
-		buildstate->rowstoskip -= 1;
-	}
-}
-
-/*
- * Sample rows with same logic as ANALYZE
- */
-static void
-SampleRows(IvfflatBuildState * buildstate)
-{
-	int			targsamples = buildstate->samples->maxlen;
-	BlockNumber totalblocks = RelationGetNumberOfBlocks(buildstate->heap);
-
-	buildstate->rowstoskip = -1;
-
-	BlockSampler_Init(&buildstate->bs, totalblocks, targsamples, random());
-
-	reservoir_init_selection_state(&buildstate->rstate, targsamples);
-	while (BlockSampler_HasMore(&buildstate->bs))
-	{
-		BlockNumber targblock = BlockSampler_Next(&buildstate->bs);
-
 #if PG_VERSION_NUM >= 120000
-		table_index_build_range_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-									 false, true, true, targblock, 1, SampleCallback, (void *) buildstate, NULL);
-#elif PG_VERSION_NUM >= 110000
-		IndexBuildHeapRangeScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-								true, true, targblock, 1, SampleCallback, (void *) buildstate, NULL);
+#define UpdateProgress(index, val) pgstat_progress_update_param(index, val)
 #else
-		IndexBuildHeapRangeScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
-								true, true, targblock, 1, SampleCallback, (void *) buildstate);
+#define UpdateProgress(index, val) ((void)val)
 #endif
-	}
-}
 
 /*
  * Callback for table_index_build_scan
@@ -146,16 +84,20 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 		}
 	}
 
+#ifdef IVFFLAT_KMEANS_DEBUG
+	buildstate->inertia += minDistance;
+	buildstate->listSums[closestCenter] += minDistance;
+	buildstate->listCounts[closestCenter]++;
+#endif
+
 	/* Create a virtual tuple */
 	ExecClearTuple(slot);
 	slot->tts_values[0] = Int32GetDatum(closestCenter);
 	slot->tts_isnull[0] = false;
-	slot->tts_values[1] = Int32GetDatum(ItemPointerGetBlockNumberNoCheck(tid));
+	slot->tts_values[1] = PointerGetDatum(tid);
 	slot->tts_isnull[1] = false;
-	slot->tts_values[2] = Int32GetDatum(ItemPointerGetOffsetNumberNoCheck(tid));
+	slot->tts_values[2] = value;
 	slot->tts_isnull[2] = false;
-	slot->tts_values[3] = value;
-	slot->tts_isnull[3] = false;
 	ExecStoreVirtualTuple(slot);
 
 	/*
@@ -165,6 +107,8 @@ BuildCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
 	 * need not save it.
 	 */
 	tuplesort_puttupleslot(buildstate->sortstate, slot);
+
+	buildstate->indtuples++;
 }
 
 /*
@@ -175,8 +119,6 @@ GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot,
 {
 	Datum		value;
 	bool		isnull;
-	int			tupblk;
-	int			tupoff;
 
 #if PG_VERSION_NUM >= 100000
 	if (tuplesort_gettupleslot(sortstate, true, false, slot, NULL))
@@ -185,13 +127,11 @@ GetNextTuple(Tuplesortstate *sortstate, TupleDesc tupdesc, TupleTableSlot *slot,
 #endif
 	{
 		*list = DatumGetInt32(slot_getattr(slot, 1, &isnull));
-		tupblk = DatumGetInt32(slot_getattr(slot, 2, &isnull));
-		tupoff = DatumGetInt32(slot_getattr(slot, 3, &isnull));
-		value = slot_getattr(slot, 4, &isnull);
+		value = slot_getattr(slot, 3, &isnull);
 
 		/* Form the index tuple */
 		*itup = index_form_tuple(tupdesc, &value, &isnull);
-		ItemPointerSet(&(*itup)->t_tid, tupblk, tupoff);
+		(*itup)->t_tid = *((ItemPointer) DatumGetPointer(slot_getattr(slot, 2, &isnull)));
 	}
 	else
 		*list = -1;
@@ -212,6 +152,7 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 	BlockNumber insertPage = InvalidBlockNumber;
 	Size		itemsz;
 	int			i;
+	int64		inserted = 0;
 
 #if PG_VERSION_NUM >= 120000
 	TupleTableSlot *slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsMinimalTuple);
@@ -220,10 +161,18 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 #endif
 	TupleDesc	tupdesc = RelationGetDescr(index);
 
+	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_LOAD);
+
+	UpdateProgress(PROGRESS_CREATEIDX_TUPLES_TOTAL, buildstate->indtuples);
+
 	GetNextTuple(buildstate->sortstate, tupdesc, slot, &itup, &list);
 
 	for (i = 0; i < buildstate->centers->length; i++)
 	{
+		/* Can take a while, so ensure we can interrupt */
+		/* Needs to be called when no buffer locks are held */
+		CHECK_FOR_INTERRUPTS();
+
 		buf = IvfflatNewBuffer(index, forkNum);
 		IvfflatInitPage(index, &buf, &page, &state);
 
@@ -243,7 +192,7 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 
 			pfree(itup);
 
-			buildstate->indtuples += 1;
+			UpdateProgress(PROGRESS_CREATEIDX_TUPLES_DONE, ++inserted);
 
 			GetNextTuple(buildstate->sortstate, tupdesc, slot, &itup, &list);
 		}
@@ -253,7 +202,7 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 		IvfflatCommitBuffer(buf, state);
 
 		/* Set the start and insert pages */
-		IvfflatUpdateList(index, state, buildstate->listInfo[i], insertPage, startPage, forkNum);
+		IvfflatUpdateList(index, state, buildstate->listInfo[i], insertPage, InvalidBlockNumber, startPage, forkNum);
 	}
 }
 
@@ -283,19 +232,24 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 	buildstate->kmeansnormprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
 	buildstate->collation = index->rd_indcollation[0];
 
+	/* Require more than one dimension for spherical k-means */
+	/* Lists check for backwards compatibility */
+	/* TODO Remove lists check in 0.3.0 */
+	if (buildstate->kmeansnormprocinfo != NULL && buildstate->dimensions == 1 && buildstate->lists > 1)
+		elog(ERROR, "dimensions must be greater than one for this opclass");
+
 	/* Create tuple description for sorting */
 #if PG_VERSION_NUM >= 120000
-	buildstate->tupdesc = CreateTemplateTupleDesc(4);
+	buildstate->tupdesc = CreateTemplateTupleDesc(3);
 #else
-	buildstate->tupdesc = CreateTemplateTupleDesc(4, false);
+	buildstate->tupdesc = CreateTemplateTupleDesc(3, false);
 #endif
 	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 1, "list", INT4OID, -1, 0);
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 2, "blkno", INT4OID, -1, 0);
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 3, "offset", INT4OID, -1, 0);
+	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
 #if PG_VERSION_NUM >= 110000
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 4, "vector", RelationGetDescr(index)->attrs[0].atttypid, -1, 0);
+	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 3, "vector", RelationGetDescr(index)->attrs[0].atttypid, -1, 0);
 #else
-	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 4, "vector", RelationGetDescr(index)->attrs[0]->atttypid, -1, 0);
+	TupleDescInitEntry(buildstate->tupdesc, (AttrNumber) 3, "vector", RelationGetDescr(index)->attrs[0]->atttypid, -1, 0);
 #endif
 
 #if PG_VERSION_NUM >= 120000
@@ -309,6 +263,12 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 
 	/* Reuse for each tuple */
 	buildstate->normvec = InitVector(buildstate->dimensions);
+
+#ifdef IVFFLAT_KMEANS_DEBUG
+	buildstate->inertia = 0;
+	buildstate->listSums = palloc0(sizeof(double) * buildstate->lists);
+	buildstate->listCounts = palloc0(sizeof(int) * buildstate->lists);
+#endif
 }
 
 /*
@@ -320,32 +280,11 @@ FreeBuildState(IvfflatBuildState * buildstate)
 	pfree(buildstate->centers);
 	pfree(buildstate->listInfo);
 	pfree(buildstate->normvec);
-}
 
-/*
- * Compute centers
- */
-static void
-ComputeCenters(IvfflatBuildState * buildstate)
-{
-	int			numSamples;
-
-	/* Target 50 samples per list, with at least 10000 samples */
-	/* The number of samples has a large effect on index build time */
-	numSamples = buildstate->lists * 50;
-	if (numSamples < 10000)
-		numSamples = 10000;
-
-	/* Sample samples */
-	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions);
-	if (buildstate->heap != NULL)
-		SampleRows(buildstate);
-
-	/* Calculate centers */
-	IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers);
-
-	/* Free samples before we allocate more memory */
-	pfree(buildstate->samples);
+#ifdef IVFFLAT_KMEANS_DEBUG
+	pfree(buildstate->listSums);
+	pfree(buildstate->listCounts);
+#endif
 }
 
 /*
@@ -421,6 +360,51 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 	pfree(list);
 }
 
+/*
+ * Print k-means metrics
+ */
+#ifdef IVFFLAT_KMEANS_DEBUG
+static void
+PrintKmeansMetrics(IvfflatBuildState * buildstate)
+{
+	elog(INFO, "inertia: %.3e", buildstate->inertia);
+
+	/* Calculate Davies-Bouldin index */
+	if (buildstate->lists > 1)
+	{
+		double		db = 0.0;
+
+		/* Calculate average distance */
+		for (int i = 0; i < buildstate->lists; i++)
+		{
+			if (buildstate->listCounts[i] > 0)
+				buildstate->listSums[i] /= buildstate->listCounts[i];
+		}
+
+		for (int i = 0; i < buildstate->lists; i++)
+		{
+			double		max = 0.0;
+			double		distance;
+
+			for (int j = 0; j < buildstate->lists; j++)
+			{
+				if (j == i)
+					continue;
+
+				distance = DatumGetFloat8(FunctionCall2Coll(buildstate->procinfo, buildstate->collation, PointerGetDatum(VectorArrayGet(buildstate->centers, i)), PointerGetDatum(VectorArrayGet(buildstate->centers, j))));
+				distance = (buildstate->listSums[i] + buildstate->listSums[j]) / distance;
+
+				if (distance > max)
+					max = distance;
+			}
+			db += max;
+		}
+		db /= buildstate->lists;
+		elog(INFO, "davies-bouldin: %.3f", db);
+	}
+}
+#endif
+
 /*
  * Create entry pages
  */
@@ -432,6 +416,8 @@ CreateEntryPages(IvfflatBuildState * buildstate, ForkNumber forkNum)
 	Oid			sortCollations[] = {InvalidOid};
 	bool		nullsFirstFlags[] = {false};
 
+	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_SORT);
+
 #if PG_VERSION_NUM >= 110000
 	buildstate->sortstate = tuplesort_begin_heap(buildstate->tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, maintenance_work_mem, NULL, false);
 #else
@@ -453,8 +439,14 @@ CreateEntryPages(IvfflatBuildState * buildstate, ForkNumber forkNum)
 #endif
 	}
 
-	/* Sort and insert */
+	/* Sort */
 	tuplesort_performsort(buildstate->sortstate);
+
+#ifdef IVFFLAT_KMEANS_DEBUG
+	PrintKmeansMetrics(buildstate);
+#endif
+
+	/* Insert */
 	InsertTuples(buildstate->index, buildstate, forkNum);
 	tuplesort_end(buildstate->sortstate);
 }
@@ -468,12 +460,14 @@ BuildIndex(Relation heap, Relation index, IndexInfo *indexInfo,
 {
 	InitBuildState(buildstate, heap, index, indexInfo);
 
-	ComputeCenters(buildstate);
+	/* Perform k-means clustering */
+	UpdateProgress(PROGRESS_CREATEIDX_SUBPHASE, PROGRESS_IVFFLAT_PHASE_KMEANS);
+	IvfflatBench("k-means", IvfflatKmeans(buildstate));
 
 	/* Create pages */
 	CreateMetaPage(index, buildstate->dimensions, buildstate->lists, forkNum);
 	CreateListPages(index, buildstate->centers, buildstate->dimensions, buildstate->lists, forkNum, &buildstate->listInfo);
-	CreateEntryPages(buildstate, forkNum);
+	IvfflatBench("CreateEntryPages", CreateEntryPages(buildstate, forkNum));
 
 	FreeBuildState(buildstate);
 }

src/ivfflat.c

@@ -8,6 +8,10 @@
 #include "utils/guc.h"
 #include "utils/selfuncs.h"
 
+#if PG_VERSION_NUM >= 120000
+#include "commands/progress.h"
+#endif
+
 int			ivfflat_probes;
 static relopt_kind ivfflat_relopt_kind;
 
@@ -30,6 +34,29 @@ _PG_init(void)
 							1, 1, IVFFLAT_MAX_LISTS, PGC_USERSET, 0, NULL, NULL, NULL);
 }
 
+/*
+ * Get the name of index build phase
+ */
+#if PG_VERSION_NUM >= 120000
+static char *
+ivfflatbuildphasename(int64 phasenum)
+{
+	switch (phasenum)
+	{
+		case PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE:
+			return "initializing";
+		case PROGRESS_IVFFLAT_PHASE_KMEANS:
+			return "performing k-means";
+		case PROGRESS_IVFFLAT_PHASE_SORT:
+			return "sorting tuples";
+		case PROGRESS_IVFFLAT_PHASE_LOAD:
+			return "loading tuples";
+		default:
+			return NULL;
+	}
+}
+#endif
+
 /*
  * Estimate the cost of an index scan
  */
@@ -130,6 +157,11 @@ ivfflatvalidate(Oid opclassoid)
 	return true;
 }
 
+/*
+ * Define index handler
+ *
+ * See https://www.postgresql.org/docs/current/index-api.html
+ */
 PG_FUNCTION_INFO_V1(ivfflathandler);
 Datum
 ivfflathandler(PG_FUNCTION_ARGS)
@@ -160,23 +192,27 @@ ivfflathandler(PG_FUNCTION_ARGS)
 #endif
 #if PG_VERSION_NUM >= 130000
 	amroutine->amusemaintenanceworkmem = false; /* not used during VACUUM */
-	amroutine->amparallelvacuumoptions = VACUUM_OPTION_NO_PARALLEL; /* TODO support parallel */
+	amroutine->amparallelvacuumoptions = VACUUM_OPTION_PARALLEL_BULKDEL;
 #endif
 	amroutine->amkeytype = InvalidOid;
 
+	/* Interface functions */
 	amroutine->ambuild = ivfflatbuild;
 	amroutine->ambuildempty = ivfflatbuildempty;
 	amroutine->aminsert = ivfflatinsert;
 	amroutine->ambulkdelete = ivfflatbulkdelete;
 	amroutine->amvacuumcleanup = ivfflatvacuumcleanup;
-	amroutine->amcanreturn = NULL;
+	amroutine->amcanreturn = NULL;	/* tuple not included in heapsort */
 	amroutine->amcostestimate = ivfflatcostestimate;
 	amroutine->amoptions = ivfflatoptions;
 	amroutine->amproperty = NULL;	/* TODO AMPROP_DISTANCE_ORDERABLE */
 #if PG_VERSION_NUM >= 120000
-	amroutine->ambuildphasename = NULL;
+	amroutine->ambuildphasename = ivfflatbuildphasename;
 #endif
 	amroutine->amvalidate = ivfflatvalidate;
+#if PG_VERSION_NUM >= 140000
+	amroutine->amadjustmembers = NULL;
+#endif
 	amroutine->ambeginscan = ivfflatbeginscan;
 	amroutine->amrescan = ivfflatrescan;
 	amroutine->amgettuple = ivfflatgettuple;
@@ -184,6 +220,8 @@ ivfflathandler(PG_FUNCTION_ARGS)
 	amroutine->amendscan = ivfflatendscan;
 	amroutine->ammarkpos = NULL;
 	amroutine->amrestrpos = NULL;
+
+	/* Interface functions to support parallel index scans */
 #if PG_VERSION_NUM >= 100000
 	amroutine->amestimateparallelscan = NULL;
 	amroutine->aminitparallelscan = NULL;

src/ivfflat.h

@@ -10,6 +10,14 @@
 #include "utils/tuplesort.h"
 #include "vector.h"
 
+#ifdef IVFFLAT_BENCH
+#include "portability/instr_time.h"
+#endif
+
+#if PG_VERSION_NUM < 90600
+#error "Requires PostgreSQL 9.6+"
+#endif
+
 /* Support functions */
 #define IVFFLAT_DISTANCE_PROC 1
 #define IVFFLAT_NORM_PROC 2
@@ -27,14 +35,30 @@
 #define IVFFLAT_DEFAULT_LISTS	100
 #define IVFFLAT_MAX_LISTS		32768
 
+/* Build phases */
+/* PROGRESS_CREATEIDX_SUBPHASE_INITIALIZE is 1 */
+#define PROGRESS_IVFFLAT_PHASE_KMEANS	2
+#define PROGRESS_IVFFLAT_PHASE_SORT		3
+#define PROGRESS_IVFFLAT_PHASE_LOAD		4
+
 #define IVFFLAT_LIST_SIZE(_dim)	(offsetof(IvfflatListData, center) + VECTOR_SIZE(_dim))
 
 #define IvfflatPageGetOpaque(page)	((IvfflatPageOpaque) PageGetSpecialPointer(page))
 #define IvfflatPageGetMeta(page)	((IvfflatMetaPageData *) PageGetContents(page))
 
-#if PG_VERSION_NUM < 100000
-#define ItemPointerGetBlockNumberNoCheck ItemPointerGetBlockNumber
-#define ItemPointerGetOffsetNumberNoCheck ItemPointerGetOffsetNumber
+#ifdef IVFFLAT_BENCH
+#define IvfflatBench(name, code) \
+	do { \
+		instr_time	start; \
+		instr_time	duration; \
+		INSTR_TIME_SET_CURRENT(start); \
+		(code); \
+		INSTR_TIME_SET_CURRENT(duration); \
+		INSTR_TIME_SUBTRACT(duration, start); \
+		elog(INFO, "%s: %.3f ms", name, INSTR_TIME_GET_MILLISEC(duration)); \
+	} while (0)
+#else
+#define IvfflatBench(name, code) (code)
 #endif
 
 /* Variables */
@@ -90,6 +114,12 @@ typedef struct IvfflatBuildState
 	ListInfo   *listInfo;
 	Vector	   *normvec;
 
+#ifdef IVFFLAT_KMEANS_DEBUG
+	double		inertia;
+	double	   *listSums;
+	int		   *listCounts;
+#endif
+
 	/* Sampling */
 	BlockSamplerData bs;
 	ReservoirStateData rstate;
@@ -131,6 +161,7 @@ typedef IvfflatListData * IvfflatList;
 
 typedef struct IvfflatScanList
 {
+	pairingheap_node ph_node;
 	BlockNumber startPage;
 	double		distance;
 }			IvfflatScanList;
@@ -152,6 +183,8 @@ typedef struct IvfflatScanOpaqueData
 	FmgrInfo   *normprocinfo;
 	Oid			collation;
 
+	/* Lists */
+	pairingheap *listQueue;
 	IvfflatScanList lists[FLEXIBLE_ARRAY_MEMBER];	/* must come last */
 }			IvfflatScanOpaqueData;
 
@@ -166,11 +199,11 @@ typedef IvfflatScanOpaqueData * IvfflatScanOpaque;
 void		_PG_init(void);
 VectorArray VectorArrayInit(int maxlen, int dimensions);
 void		PrintVectorArray(char *msg, VectorArray arr);
-void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
+void		IvfflatKmeans(IvfflatBuildState * buildstate);
 FmgrInfo   *IvfflatOptionalProcInfo(Relation rel, uint16 procnum);
 bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, Vector * result);
 int			IvfflatGetLists(Relation index);
-void		IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo, BlockNumber insertPage, BlockNumber startPage, ForkNumber forkNum);
+void		IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo, BlockNumber insertPage, BlockNumber originalInsertPage, BlockNumber startPage, ForkNumber forkNum);
 void		IvfflatCommitBuffer(Buffer buf, GenericXLogState *state);
 void		IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **state, ForkNumber forkNum);
 Buffer		IvfflatNewBuffer(Relation index, ForkNumber forkNum);
@@ -180,6 +213,9 @@ void		IvfflatInitPage(Relation index, Buffer *buf, Page *page, GenericXLogState
 IndexBuildResult *ivfflatbuild(Relation heap, Relation index, IndexInfo *indexInfo);
 void		ivfflatbuildempty(Relation index);
 bool		ivfflatinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid, Relation heap, IndexUniqueCheck checkUnique
+#if PG_VERSION_NUM >= 140000
+						  ,bool indexUnchanged
+#endif
 #if PG_VERSION_NUM >= 100000
 						  ,IndexInfo *indexInfo
 #endif

src/ivfinsert.c

@@ -77,11 +77,12 @@ InsertTuple(Relation rel, IndexTuple itup, Relation heapRel, Datum *values)
 	Size		itemsz;
 	BlockNumber insertPage = InvalidBlockNumber;
 	ListInfo	listInfo;
-	bool		newPage = false;
+	BlockNumber originalInsertPage;
 
 	/* Find the insert page - sets the page and list info */
 	FindInsertPage(rel, values, &insertPage, &listInfo);
 	Assert(BlockNumberIsValid(insertPage));
+	originalInsertPage = insertPage;
 
 	itemsz = MAXALIGN(IndexTupleSize(itup));
 	Assert(itemsz <= BLCKSZ - MAXALIGN(SizeOfPageHeaderData) - MAXALIGN(sizeof(IvfflatPageOpaqueData)));
@@ -107,7 +108,6 @@ InsertTuple(Relation rel, IndexTuple itup, Relation heapRel, Datum *values)
 			IvfflatAppendPage(rel, &buf, &page, &state, MAIN_FORKNUM);
 
 			insertPage = BufferGetBlockNumber(buf);
-			newPage = true;
 		}
 	}
 
@@ -118,8 +118,8 @@ InsertTuple(Relation rel, IndexTuple itup, Relation heapRel, Datum *values)
 	IvfflatCommitBuffer(buf, state);
 
 	/* Update the insert page */
-	if (newPage)
-		IvfflatUpdateList(rel, state, listInfo, insertPage, InvalidBlockNumber, MAIN_FORKNUM);
+	if (insertPage != originalInsertPage)
+		IvfflatUpdateList(rel, state, listInfo, insertPage, originalInsertPage, InvalidBlockNumber, MAIN_FORKNUM);
 }
 
 /*
@@ -128,6 +128,9 @@ InsertTuple(Relation rel, IndexTuple itup, Relation heapRel, Datum *values)
 bool
 ivfflatinsert(Relation index, Datum *values, bool *isnull, ItemPointer heap_tid,
 			  Relation heap, IndexUniqueCheck checkUnique
+#if PG_VERSION_NUM >= 140000
+			  ,bool indexUnchanged
+#endif
 #if PG_VERSION_NUM >= 100000
 			  ,IndexInfo *indexInfo
 #endif

src/ivfkmeans.c

@@ -2,8 +2,20 @@
 
 #include <float.h>
 
+#include "catalog/index.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
+#include "storage/bufmgr.h"
+
+#if PG_VERSION_NUM >= 120000
+#include "access/tableam.h"
+#endif
+
+#if PG_VERSION_NUM >= 130000
+#define CALLBACK_ITEM_POINTER ItemPointer tid
+#else
+#define CALLBACK_ITEM_POINTER HeapTuple hup
+#endif
 
 /*
  * Initialize with kmeans++
@@ -11,7 +23,7 @@
  * https://theory.stanford.edu/~sergei/papers/kMeansPP-soda.pdf
  */
 static void
-InitCenters(Relation index, VectorArray samples, VectorArray centers, double *lowerBound)
+InitCenters(Relation index, VectorArray samples, VectorArray centers)
 {
 	FmgrInfo   *procinfo;
 	Oid			collation;
@@ -21,7 +33,7 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, double *lo
 	double		sum;
 	double		choice;
 	Vector	   *vec;
-	double	   *weight = palloc(samples->length * sizeof(double));
+	float	   *weight = palloc(samples->length * sizeof(float));
 	int			numCenters = centers->maxlen;
 	int			numSamples = samples->length;
 
@@ -35,7 +47,7 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, double *lo
 	for (j = 0; j < numSamples; j++)
 		weight[j] = DBL_MAX;
 
-	for (i = 0; i < numCenters; i++)
+	for (i = 0; i < numCenters - 1; i++)
 	{
 		CHECK_FOR_INTERRUPTS();
 
@@ -49,9 +61,6 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, double *lo
 			/* TODO Use triangle inequality to reduce distance calculations */
 			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, i))));
 
-			/* Set lower bound */
-			lowerBound[j * numCenters + i] = distance;
-
 			/* Use distance squared for weighted probability distribution */
 			distance *= distance;
 
@@ -61,10 +70,6 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, double *lo
 			sum += weight[j];
 		}
 
-		/* Only compute lower bound on last iteration */
-		if (i + 1 == numCenters)
-			break;
-
 		/* Choose new center using weighted probability distribution. */
 		choice = sum * (((double) random()) / MAX_RANDOM_VALUE);
 		for (j = 0; j < numSamples - 1; j++)
@@ -121,15 +126,18 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	FmgrInfo   *normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
 
 	/* Copy existing vectors while avoiding duplicates */
-	qsort(samples->items, samples->length, VECTOR_SIZE(samples->dim), CompareVectors);
-	for (i = 0; i < samples->length; i++)
+	if (samples->length > 0)
 	{
-		vec = VectorArrayGet(samples, i);
-
-		if (i == 0 || CompareVectors(vec, VectorArrayGet(samples, i - 1)) != 0)
+		qsort(samples->items, samples->length, VECTOR_SIZE(samples->dim), CompareVectors);
+		for (i = 0; i < samples->length; i++)
 		{
-			VectorArraySet(centers, centers->length, vec);
-			centers->length++;
+			vec = VectorArrayGet(samples, i);
+
+			if (i == 0 || CompareVectors(vec, VectorArrayGet(samples, i - 1)) != 0)
+			{
+				VectorArraySet(centers, centers->length, vec);
+				centers->length++;
+			}
 		}
 	}
 
@@ -153,275 +161,202 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 }
 
 /*
- * Use Elkan for performance. This requires distance function to satisfy triangle inequality.
+ * Callback for sampling
+ */
+static void
+SampleCallback(Relation index, CALLBACK_ITEM_POINTER, Datum *values,
+			   bool *isnull, bool tupleIsAlive, void *state)
+{
+	IvfflatBuildState *buildstate = (IvfflatBuildState *) state;
+	VectorArray samples = buildstate->samples;
+	int			targsamples = samples->maxlen;
+	Datum		value = values[0];
+
+	/* Skip nulls */
+	if (isnull[0])
+		return;
+
+	/*
+	 * Normalize with KMEANS_NORM_PROC since spherical distance function
+	 * expects unit vectors
+	 */
+	if (buildstate->kmeansnormprocinfo != NULL)
+	{
+		if (!IvfflatNormValue(buildstate->kmeansnormprocinfo, buildstate->collation, &value, buildstate->normvec))
+			return;
+	}
+
+	if (samples->length < targsamples)
+	{
+		VectorArraySet(samples, samples->length, DatumGetVector(value));
+		samples->length++;
+	}
+	else
+	{
+		if (buildstate->rowstoskip < 0)
+			buildstate->rowstoskip = reservoir_get_next_S(&buildstate->rstate, samples->length, targsamples);
+
+		if (buildstate->rowstoskip <= 0)
+		{
+			int			k = (int) (targsamples * sampler_random_fract(buildstate->rstate.randstate));
+
+			Assert(k >= 0 && k < targsamples);
+			VectorArraySet(samples, k, DatumGetVector(value));
+		}
+
+		buildstate->rowstoskip -= 1;
+	}
+}
+
+/*
+ * Sample rows with same logic as ANALYZE
+ */
+static void
+SampleRows(IvfflatBuildState * buildstate)
+{
+	int			targsamples = buildstate->samples->maxlen;
+	BlockNumber totalblocks = RelationGetNumberOfBlocks(buildstate->heap);
+
+	buildstate->rowstoskip = -1;
+	buildstate->samples->length = 0;
+
+	BlockSampler_Init(&buildstate->bs, totalblocks, targsamples, random());
+
+	reservoir_init_selection_state(&buildstate->rstate, targsamples);
+	while (BlockSampler_HasMore(&buildstate->bs))
+	{
+		BlockNumber targblock = BlockSampler_Next(&buildstate->bs);
+
+#if PG_VERSION_NUM >= 120000
+		table_index_build_range_scan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+									 false, true, false, targblock, 1, SampleCallback, (void *) buildstate, NULL);
+#elif PG_VERSION_NUM >= 110000
+		IndexBuildHeapRangeScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+								false, true, targblock, 1, SampleCallback, (void *) buildstate, NULL);
+#else
+		IndexBuildHeapRangeScan(buildstate->heap, buildstate->index, buildstate->indexInfo,
+								false, true, targblock, 1, SampleCallback, (void *) buildstate);
+#endif
+	}
+}
+
+/*
+ * Use mini-batch k-means
  *
  * We use L2 distance for L2 (not L2 squared like index scan)
  * and angular distance for inner product and cosine distance
  *
- * https://www.aaai.org/Papers/ICML/2003/ICML03-022.pdf
+ * https://www.eecs.tufts.edu/~dsculley/papers/fastkmeans.pdf
  */
 static void
-ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
+MiniBatchKmeans(IvfflatBuildState * buildstate)
 {
-	FmgrInfo   *procinfo;
-	FmgrInfo   *normprocinfo;
-	Oid			collation;
-	Vector	   *vec;
-	Vector	   *newCenter;
-	int			iteration;
-	int			j;
-	int			k;
-	int			dimensions = centers->dim;
-	int			numCenters = centers->maxlen;
-	int			numSamples = samples->length;
-	VectorArray newCenters;
-	int		   *centerCounts;
-	int		   *closestCenters;
-	double	   *lowerBound;
-	double	   *upperBound;
-	double	   *s;
-	double	   *halfcdist;
-	double	   *newcdist;
-	int			changes;
+	VectorArray centers = buildstate->centers;
+	VectorArray m = buildstate->samples;
+	int			b = m->maxlen;
+	int			t = 20;
+	double		distance;
 	double		minDistance;
 	int			closestCenter;
-	double		distance;
-	bool		rj;
-	bool		rjreset;
-	double		dxcx;
-	double		dxc;
+	int			i;
+	int			j;
+	int			k;
+	Vector	   *c;
+	Vector	   *x;
+	int		   *v;
+	int		   *d;
+	double		eta;
 
 	/* Set support functions */
-	procinfo = index_getprocinfo(index, 1, IVFFLAT_KMEANS_DISTANCE_PROC);
-	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
-	collation = index->rd_indcollation[0];
-
-	/* Allocate space */
-	centerCounts = palloc(sizeof(int) * numCenters);
-	closestCenters = palloc(sizeof(int) * numSamples);
-	lowerBound = palloc(sizeof(double) * numSamples * numCenters);
-	upperBound = palloc(sizeof(double) * numSamples);
-	s = palloc(sizeof(double) * numCenters);
-	halfcdist = palloc(sizeof(double) * numCenters * numCenters);
-	newcdist = palloc(sizeof(double) * numCenters);
-
-	newCenters = VectorArrayInit(numCenters, dimensions);
-	for (j = 0; j < numCenters; j++)
-	{
-		vec = VectorArrayGet(newCenters, j);
-		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
-		vec->dim = dimensions;
-	}
+	FmgrInfo   *procinfo = index_getprocinfo(buildstate->index, 1, IVFFLAT_KMEANS_DISTANCE_PROC);
+	FmgrInfo   *normprocinfo = buildstate->kmeansnormprocinfo;
+	Oid			collation = buildstate->index->rd_indcollation[0];
 
 	/* Pick initial centers */
-	InitCenters(index, samples, centers, lowerBound);
+	InitCenters(buildstate->index, buildstate->samples, buildstate->centers);
 
-	/* Assign each x to its closest initial center c(x) = argmin d(x,c) */
-	for (j = 0; j < numSamples; j++)
-	{
-		minDistance = DBL_MAX;
-		closestCenter = -1;
+	v = palloc(sizeof(int) * centers->maxlen);
+	d = palloc(sizeof(int) * b);
 
-		vec = VectorArrayGet(samples, j);
+	for (int i = 0; i < centers->length; i++)
+		v[i] = 0;
 
-		/* Find closest center */
-		for (k = 0; k < numCenters; k++)
-		{
-			/* TODO Use Lemma 1 in k-means++ initialization */
-			distance = lowerBound[j * numCenters + k];
-
-			if (distance < minDistance)
-			{
-				minDistance = distance;
-				closestCenter = k;
-			}
-		}
-
-		upperBound[j] = minDistance;
-		closestCenters[j] = closestCenter;
-	}
-
-	/* Give 500 iterations to converge */
-	for (iteration = 0; iteration < 500; iteration++)
+	for (i = 0; i < t; i++)
 	{
 		/* Can take a while, so ensure we can interrupt */
 		CHECK_FOR_INTERRUPTS();
 
-		changes = 0;
+		/* Get b examples picked randomly from X */
+		SampleRows(buildstate);
 
-		/* Step 1: For all centers, compute distance */
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(centers, j);
-
-			for (k = j + 1; k < numCenters; k++)
-			{
-				distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
-				halfcdist[j * numCenters + k] = distance;
-				halfcdist[k * numCenters + j] = distance;
-			}
-		}
-
-		/* For all centers c, compute s(c) */
-		for (j = 0; j < numCenters; j++)
+		/* Cache nearest center to x */
+		for (j = 0; j < m->length; j++)
 		{
+			/* compute closest */
 			minDistance = DBL_MAX;
+			closestCenter = -1;
 
-			for (k = 0; k < numCenters; k++)
+			x = VectorArrayGet(m, j);
+
+			/* Find closest center */
+			for (k = 0; k < centers->length; k++)
 			{
-				if (j == k)
-					continue;
+				distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(x), PointerGetDatum(VectorArrayGet(centers, k))));
 
-				distance = halfcdist[j * numCenters + k];
 				if (distance < minDistance)
+				{
 					minDistance = distance;
+					closestCenter = k;
+				}
 			}
 
-			s[j] = minDistance;
+			d[j] = closestCenter;
 		}
 
-		rjreset = iteration != 0;
-
-		for (j = 0; j < numSamples; j++)
+		for (j = 0; j < m->length; j++)
 		{
-			/* Step 2: Identify all points x such that u(x) <= s(c(x)) */
-			if (upperBound[j] <= s[closestCenters[j]])
-				continue;
+			x = VectorArrayGet(m, j);
 
-			rj = rjreset;
+			/* Get cached center for this x */
+			c = VectorArrayGet(centers, d[j]);
 
-			for (k = 0; k < numCenters; k++)
+			/* Update per-center counts */
+			v[d[j]]++;
+
+			/* Get per-center learning rate */
+			eta = 1.0 / v[d[j]];
+
+			/* Take gradient step */
+			for (k = 0; k < c->dim; k++)
+				c->x[k] = (1 - eta) * c->x[k] + eta * x->x[k];
+		}
+
+		/* Check for empty centers (likely duplicates) */
+		if (i == 0)
+		{
+			for (j = 0; j < centers->length; j++)
 			{
-				/* Step 3: For all remaining points x and centers c */
-				if (k == closestCenters[j])
-					continue;
-
-				if (upperBound[j] <= lowerBound[j * numCenters + k])
-					continue;
-
-				if (upperBound[j] <= halfcdist[closestCenters[j] * numCenters + k])
-					continue;
-
-				vec = VectorArrayGet(samples, j);
-
-				/* Step 3a */
-				if (rj)
+				if (v[j] == 0)
 				{
-					dxcx = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(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;
-					upperBound[j] = dxcx;
-
-					rj = false;
-				}
-				else
-					dxcx = upperBound[j];
-
-				/* Step 3b */
-				if (dxcx > lowerBound[j * numCenters + k] || dxcx > halfcdist[closestCenters[j] * numCenters + k])
-				{
-					dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
-
-					/* d(x,c) calculated */
-					lowerBound[j * numCenters + k] = dxc;
-
-					if (dxc < dxcx)
-					{
-						closestCenters[j] = k;
-
-						/* c(x) changed */
-						upperBound[j] = dxc;
-
-						changes++;
-					}
+					c = VectorArrayGet(centers, j);
 
+					/* TODO Handle empty centers properly */
+					for (k = 0; k < c->dim; k++)
+						c->x[k] = ((double) random()) / MAX_RANDOM_VALUE;
 				}
 			}
 		}
 
-		/* Step 4: For each center c, let m(c) be mean of all points assigned */
-		for (j = 0; j < numCenters; j++)
+		/* Normalize if needed */
+		if (normprocinfo != NULL)
 		{
-			vec = VectorArrayGet(newCenters, j);
-			for (k = 0; k < dimensions; k++)
-				vec->x[k] = 0.0;
-
-			centerCounts[j] = 0;
+			for (j = 0; j < centers->length; j++)
+				ApplyNorm(normprocinfo, collation, VectorArrayGet(centers, j));
 		}
-
-		for (j = 0; j < numSamples; j++)
-		{
-			vec = VectorArrayGet(samples, j);
-			closestCenter = closestCenters[j];
-
-			/* Increment sum and count of closest center */
-			newCenter = VectorArrayGet(newCenters, closestCenter);
-			for (k = 0; k < dimensions; k++)
-				newCenter->x[k] += vec->x[k];
-
-			centerCounts[closestCenter] += 1;
-		}
-
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-
-			if (centerCounts[j] > 0)
-			{
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] /= centerCounts[j];
-			}
-			else
-			{
-				/* TODO Handle empty centers properly */
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] = ((double) random()) / MAX_RANDOM_VALUE;
-			}
-
-			/* Normalize if needed */
-			if (normprocinfo != NULL)
-				ApplyNorm(normprocinfo, collation, vec);
-		}
-
-		/* Step 5 */
-		for (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 (k = 0; k < numCenters; k++)
-			{
-				distance = lowerBound[j * numCenters + k] - newcdist[k];
-
-				if (distance < 0)
-					distance = 0;
-
-				lowerBound[j * numCenters + k] = distance;
-			}
-		}
-
-		/* Step 6 */
-		/* We reset r(x) before Step 3 in the next iteration */
-		for (j = 0; j < numSamples; j++)
-			upperBound[j] += newcdist[closestCenters[j]];
-
-		/* Step 7 */
-		for (j = 0; j < numCenters; j++)
-			memcpy(VectorArrayGet(centers, j), VectorArrayGet(newCenters, j), VECTOR_SIZE(dimensions));
-
-		if (changes == 0 && iteration != 0)
-			break;
 	}
 
-	pfree(newCenters);
-	pfree(centerCounts);
-	pfree(closestCenters);
-	pfree(lowerBound);
-	pfree(upperBound);
-	pfree(s);
-	pfree(halfcdist);
-	pfree(newcdist);
+	pfree(v);
+	pfree(d);
 }
 
 /*
@@ -464,16 +399,48 @@ CheckCenters(Relation index, VectorArray centers)
 }
 
 /*
- * Perform naive k-means centering
+ * Perform k-means clustering
  * We use spherical k-means for inner product and cosine
  */
 void
-IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers)
+IvfflatKmeans(IvfflatBuildState * buildstate)
 {
-	if (samples->length <= centers->maxlen)
-		QuickCenters(index, samples, centers);
-	else
-		ElkanKmeans(index, samples, centers);
+	int			numSamples;
+	Size		totalSize;
 
-	CheckCenters(index, centers);
+	/* Target 10 samples per list, with at least 10000 samples */
+	/* The number of samples has a large effect on index build time */
+	numSamples = buildstate->lists * 10;
+	if (numSamples < 10000)
+		numSamples = 10000;
+
+	/* Skip samples for unlogged table */
+	if (buildstate->heap == NULL)
+		numSamples = 1;
+
+	/* Calculate total size */
+	totalSize = VECTOR_ARRAY_SIZE(numSamples, buildstate->dimensions);
+
+	/* Check memory requirements */
+	/* Add one to error message to ceil */
+	if (totalSize / 1024 > maintenance_work_mem)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("memory required is %zu MB, maintenance_work_mem is %d MB",
+						totalSize / (1024 * 1024) + 1, maintenance_work_mem / 1024)));
+
+	/* Sample rows */
+	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions);
+	if (buildstate->heap != NULL)
+		SampleRows(buildstate);
+
+	if (buildstate->samples->length <= buildstate->centers->maxlen)
+		QuickCenters(buildstate->index, buildstate->samples, buildstate->centers);
+	else
+		MiniBatchKmeans(buildstate);
+
+	CheckCenters(buildstate->index, buildstate->centers);
+
+	/* Free samples before we allocate more memory */
+	pfree(buildstate->samples);
 }

src/ivfscan.c

@@ -1,5 +1,7 @@
 #include "postgres.h"
 
+#include <float.h>
+
 #include "access/relscan.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
@@ -17,14 +19,12 @@
  * Compare list distances
  */
 static int
-CompareLists(const void *a, const void *b)
+CompareLists(const pairingheap_node *a, const pairingheap_node *b, void *arg)
 {
-	double		diff = (((IvfflatScanList *) a)->distance - ((IvfflatScanList *) b)->distance);
-
-	if (diff > 0)
+	if (((const IvfflatScanList *) a)->distance > ((const IvfflatScanList *) b)->distance)
 		return 1;
 
-	if (diff < 0)
+	if (((const IvfflatScanList *) a)->distance < ((const IvfflatScanList *) b)->distance)
 		return -1;
 
 	return 0;
@@ -45,6 +45,8 @@ GetScanLists(IndexScanDesc scan, Datum value)
 	int			listCount = 0;
 	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
 	double		distance;
+	IvfflatScanList *scanlist;
+	double		maxDistance = DBL_MAX;
 
 	/* Search all list pages */
 	while (BlockNumberIsValid(nextblkno))
@@ -62,21 +64,39 @@ GetScanLists(IndexScanDesc scan, Datum value)
 			/* Use procinfo from the index instead of scan key for performance */
 			distance = DatumGetFloat8(FunctionCall2Coll(so->procinfo, so->collation, PointerGetDatum(&list->center), value));
 
-			so->lists[listCount].startPage = list->startPage;
-			so->lists[listCount].distance = distance;
-			listCount++;
+			if (listCount < so->probes)
+			{
+				scanlist = &so->lists[listCount];
+				scanlist->startPage = list->startPage;
+				scanlist->distance = distance;
+				listCount++;
+
+				/* Add to heap */
+				pairingheap_add(so->listQueue, &scanlist->ph_node);
+
+				/* Calculate max distance */
+				if (listCount == so->probes)
+					maxDistance = ((IvfflatScanList *) pairingheap_first(so->listQueue))->distance;
+			}
+			else if (distance < maxDistance)
+			{
+				/* Remove */
+				scanlist = (IvfflatScanList *) pairingheap_remove_first(so->listQueue);
+
+				/* Reuse */
+				scanlist->startPage = list->startPage;
+				scanlist->distance = distance;
+				pairingheap_add(so->listQueue, &scanlist->ph_node);
+
+				/* Update max distance */
+				maxDistance = ((IvfflatScanList *) pairingheap_first(so->listQueue))->distance;
+			}
 		}
 
 		nextblkno = IvfflatPageGetOpaque(cpage)->nextblkno;
 
 		UnlockReleaseBuffer(cbuf);
 	}
-
-	/* Sort by distance */
-	qsort(so->lists, listCount, sizeof(IvfflatScanList), CompareLists);
-
-	if (so->probes > listCount)
-		so->probes = listCount;
 }
 
 /*
@@ -94,7 +114,6 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	OffsetNumber maxoffno;
 	Datum		datum;
 	bool		isnull;
-	int			i;
 	TupleDesc	tupdesc = RelationGetDescr(scan->indexRelation);
 
 #if PG_VERSION_NUM >= 120000
@@ -111,9 +130,9 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	BufferAccessStrategy bas = GetAccessStrategy(BAS_BULKREAD);
 
 	/* Search closest probes lists */
-	for (i = 0; i < so->probes; i++)
+	while (!pairingheap_is_empty(so->listQueue))
 	{
-		searchPage = so->lists[i].startPage;
+		searchPage = ((IvfflatScanList *) pairingheap_remove_first(so->listQueue))->startPage;
 
 		/* Search all entry pages for list */
 		while (BlockNumberIsValid(searchPage))
@@ -137,12 +156,10 @@ GetScanItems(IndexScanDesc scan, Datum value)
 				ExecClearTuple(slot);
 				slot->tts_values[0] = FunctionCall2Coll(so->procinfo, so->collation, datum, value);
 				slot->tts_isnull[0] = false;
-				slot->tts_values[1] = Int32GetDatum((int) ItemPointerGetBlockNumberNoCheck(&itup->t_tid));
+				slot->tts_values[1] = PointerGetDatum(&itup->t_tid);
 				slot->tts_isnull[1] = false;
-				slot->tts_values[2] = Int32GetDatum((int) ItemPointerGetOffsetNumberNoCheck(&itup->t_tid));
+				slot->tts_values[2] = Int32GetDatum((int) searchPage);
 				slot->tts_isnull[2] = false;
-				slot->tts_values[3] = Int32GetDatum((int) searchPage);
-				slot->tts_isnull[3] = false;
 				ExecStoreVirtualTuple(slot);
 
 				tuplesort_puttupleslot(so->sortstate, slot);
@@ -153,6 +170,8 @@ GetScanItems(IndexScanDesc scan, Datum value)
 			UnlockReleaseBuffer(buf);
 		}
 	}
+
+	tuplesort_performsort(so->sortstate);
 }
 
 /*
@@ -168,13 +187,18 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	Oid			sortOperators[] = {Float8LessOperator};
 	Oid			sortCollations[] = {InvalidOid};
 	bool		nullsFirstFlags[] = {false};
+	int			probes = ivfflat_probes;
 
 	scan = RelationGetIndexScan(index, nkeys, norderbys);
 	lists = IvfflatGetLists(scan->indexRelation);
 
-	so = (IvfflatScanOpaque) palloc(offsetof(IvfflatScanOpaqueData, lists) + lists * sizeof(IvfflatScanList));
+	if (probes > lists)
+		probes = lists;
+
+	so = (IvfflatScanOpaque) palloc(offsetof(IvfflatScanOpaqueData, lists) + probes * sizeof(IvfflatScanList));
 	so->buf = InvalidBuffer;
 	so->first = true;
+	so->probes = probes;
 
 	/* Set support functions */
 	so->procinfo = index_getprocinfo(index, 1, IVFFLAT_DISTANCE_PROC);
@@ -183,14 +207,13 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 
 	/* Create tuple description for sorting */
 #if PG_VERSION_NUM >= 120000
-	so->tupdesc = CreateTemplateTupleDesc(4);
+	so->tupdesc = CreateTemplateTupleDesc(3);
 #else
-	so->tupdesc = CreateTemplateTupleDesc(4, false);
+	so->tupdesc = CreateTemplateTupleDesc(3, false);
 #endif
 	TupleDescInitEntry(so->tupdesc, (AttrNumber) 1, "distance", FLOAT8OID, -1, 0);
-	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "blkno", INT4OID, -1, 0);
-	TupleDescInitEntry(so->tupdesc, (AttrNumber) 3, "offset", INT4OID, -1, 0);
-	TupleDescInitEntry(so->tupdesc, (AttrNumber) 4, "indexblkno", INT4OID, -1, 0);
+	TupleDescInitEntry(so->tupdesc, (AttrNumber) 2, "tid", TIDOID, -1, 0);
+	TupleDescInitEntry(so->tupdesc, (AttrNumber) 3, "indexblkno", INT4OID, -1, 0);
 
 	/* Prep sort */
 #if PG_VERSION_NUM >= 110000
@@ -205,6 +228,8 @@ ivfflatbeginscan(Relation index, int nkeys, int norderbys)
 	so->slot = MakeSingleTupleTableSlot(so->tupdesc);
 #endif
 
+	so->listQueue = pairingheap_allocate(CompareLists, scan);
+
 	scan->opaque = so;
 
 	return scan;
@@ -224,7 +249,7 @@ ivfflatrescan(IndexScanDesc scan, ScanKey keys, int nkeys, ScanKey orderbys, int
 #endif
 
 	so->first = true;
-	so->probes = ivfflat_probes;
+	pairingheap_reset(so->listQueue);
 
 	if (keys && scan->numberOfKeys > 0)
 		memmove(scan->keyData, keys, scan->numberOfKeys * sizeof(ScanKeyData));
@@ -268,9 +293,8 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 				return false;
 		}
 
-		GetScanLists(scan, value);
-		GetScanItems(scan, value);
-		tuplesort_performsort(so->sortstate);
+		IvfflatBench("GetScanLists", GetScanLists(scan, value));
+		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;
 
 		/* Clean up if we allocated a new value */
@@ -284,14 +308,13 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 	if (tuplesort_gettupleslot(so->sortstate, true, so->slot, NULL))
 #endif
 	{
-		BlockNumber blkno = DatumGetInt32(slot_getattr(so->slot, 2, &so->isnull));
-		OffsetNumber offset = DatumGetInt32(slot_getattr(so->slot, 3, &so->isnull));
-		BlockNumber indexblkno = DatumGetInt32(slot_getattr(so->slot, 4, &so->isnull));
+		ItemPointer tid = (ItemPointer) DatumGetPointer(slot_getattr(so->slot, 2, &so->isnull));
+		BlockNumber indexblkno = DatumGetInt32(slot_getattr(so->slot, 3, &so->isnull));
 
 #if PG_VERSION_NUM >= 120000
-		ItemPointerSet(&scan->xs_heaptid, blkno, offset);
+		scan->xs_heaptid = *tid;
 #else
-		ItemPointerSet(&scan->xs_ctup.t_self, blkno, offset);
+		scan->xs_ctup.t_self = *tid;
 #endif
 
 		if (BufferIsValid(so->buf))
@@ -324,6 +347,7 @@ ivfflatendscan(IndexScanDesc scan)
 	if (BufferIsValid(so->buf))
 		ReleaseBuffer(so->buf);
 
+	pairingheap_free(so->listQueue);
 	tuplesort_end(so->sortstate);
 
 	pfree(so);

src/ivfutils.c

@@ -153,11 +153,13 @@ IvfflatAppendPage(Relation index, Buffer *buf, Page *page, GenericXLogState **st
  */
 void
 IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo,
-				  BlockNumber insertPage, BlockNumber startPage, ForkNumber forkNum)
+				  BlockNumber insertPage, BlockNumber originalInsertPage,
+				  BlockNumber startPage, ForkNumber forkNum)
 {
 	Buffer		buf;
 	Page		page;
 	IvfflatList list;
+	bool		changed = false;
 
 	buf = ReadBufferExtended(index, forkNum, listInfo.blkno, RBM_NORMAL, NULL);
 	LockBuffer(buf, BUFFER_LOCK_EXCLUSIVE);
@@ -165,12 +167,29 @@ IvfflatUpdateList(Relation index, GenericXLogState *state, ListInfo listInfo,
 	page = GenericXLogRegisterBuffer(state, buf, 0);
 	list = (IvfflatList) PageGetItem(page, PageGetItemId(page, listInfo.offno));
 
-	if (BlockNumberIsValid(insertPage))
-		list->insertPage = insertPage;
+	if (BlockNumberIsValid(insertPage) && insertPage != list->insertPage)
+	{
+		/* Skip update if insert page is lower than original insert page  */
+		/* This is needed to prevent insert from overwriting vacuum */
+		if (!BlockNumberIsValid(originalInsertPage) || insertPage >= originalInsertPage)
+		{
+			list->insertPage = insertPage;
+			changed = true;
+		}
+	}
 
-	if (BlockNumberIsValid(startPage))
+	if (BlockNumberIsValid(startPage) && startPage != list->startPage)
+	{
 		list->startPage = startPage;
+		changed = true;
+	}
 
-	/* Could only commit if changed, but extra complexity isn't needed */
-	IvfflatCommitBuffer(buf, state);
+	/* Only commit if changed */
+	if (changed)
+		IvfflatCommitBuffer(buf, state);
+	else
+	{
+		GenericXLogAbort(state);
+		UnlockReleaseBuffer(buf);
+	}
 }

src/ivfvacuum.c

@@ -21,7 +21,7 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 	ItemPointer htup;
 	OffsetNumber deletable[MaxOffsetNumber];
 	int			ndeletable;
-	OffsetNumber startPages[MaxOffsetNumber];
+	BlockNumber startPages[MaxOffsetNumber];
 	BlockNumber nextblkno = IVFFLAT_HEAD_BLKNO;
 	BlockNumber searchPage;
 	BlockNumber insertPage;
@@ -98,6 +98,11 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 						stats->num_index_tuples++;
 				}
 
+				/* Set to first free page */
+				/* Must be set before searchPage is updated */
+				if (!BlockNumberIsValid(insertPage) && ndeletable > 0)
+					insertPage = searchPage;
+
 				searchPage = IvfflatPageGetOpaque(page)->nextblkno;
 
 				if (ndeletable > 0)
@@ -106,10 +111,6 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 					PageIndexMultiDelete(page, deletable, ndeletable);
 					MarkBufferDirty(buf);
 					GenericXLogFinish(state);
-
-					/* Set to first free page */
-					if (!BlockNumberIsValid(insertPage))
-						insertPage = searchPage;
 				}
 				else
 					GenericXLogAbort(state);
@@ -123,10 +124,10 @@ ivfflatbulkdelete(IndexVacuumInfo *info, IndexBulkDeleteResult *stats,
 			 * We don't add or delete items from lists pages, so offset won't
 			 * change.
 			 */
-			if (!BlockNumberIsValid(insertPage))
+			if (BlockNumberIsValid(insertPage))
 			{
 				listInfo.offno = coffno;
-				IvfflatUpdateList(index, state, listInfo, insertPage, InvalidBlockNumber, MAIN_FORKNUM);
+				IvfflatUpdateList(index, state, listInfo, insertPage, InvalidBlockNumber, InvalidBlockNumber, MAIN_FORKNUM);
 			}
 		}
 	}

test/expected/cast.out

@@ -42,3 +42,10 @@ SELECT '[1,2,3]'::vector::real[];
 
 SELECT array_agg(n)::vector FROM generate_series(1, 1025) n;
 ERROR:  vector cannot have more than 1024 dimensions
+-- ensure no error
+SELECT ARRAY[1,2,3] = ARRAY[1,2,3];
+ ?column? 
+----------
+ t
+(1 row)
+

test/expected/input.out

@@ -53,3 +53,12 @@ LINE 1: SELECT '[1,]'::vector;
                ^
 SELECT '[1,2,3]'::vector(2);
 ERROR:  expected 2 dimensions, not 3
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
+ unnest  
+---------
+ [1,2,3]
+ [4,5,6]
+(2 rows)
+
+SELECT '{"[1,2,3]"}'::vector(2)[];
+ERROR:  expected 2 dimensions, not 3

test/sql/cast.sql

@@ -12,3 +12,6 @@ SELECT '{-Infinity}'::real[]::vector;
 SELECT '{}'::real[]::vector;
 SELECT '[1,2,3]'::vector::real[];
 SELECT array_agg(n)::vector FROM generate_series(1, 1025) n;
+
+-- ensure no error
+SELECT ARRAY[1,2,3] = ARRAY[1,2,3];

test/sql/input.sql

@@ -13,3 +13,6 @@ SELECT '1,2,3'::vector;
 SELECT '[]'::vector;
 SELECT '[1,]'::vector;
 SELECT '[1,2,3]'::vector(2);
+
+SELECT unnest('{"[1,2,3]", "[4,5,6]"}'::vector[]);
+SELECT '{"[1,2,3]"}'::vector(2)[];

test/t/001_wal.pl

@@ -34,9 +34,10 @@ sub test_index_replay
 	my $r2 = rand();
 	my $r3 = rand();
 
-	my $queries = qq(SET enable_seqscan=off;
-SELECT * FROM tst ORDER BY v <-> '[$r1,$r2,$r3]' LIMIT 10;
-);
+	my $queries = qq(
+		SET enable_seqscan = off;
+		SELECT * FROM tst ORDER BY v <-> '[$r1,$r2,$r3]' LIMIT 10;
+	);
 
 	# Run test queries and compare their result
 	my $primary_result = $node_primary->safe_psql("postgres", $queries);
@@ -65,10 +66,9 @@ $node_replica->start;
 $node_primary->safe_psql("postgres", "CREATE EXTENSION vector;");
 $node_primary->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector(3));");
 $node_primary->safe_psql("postgres",
-	"INSERT INTO tst SELECT i%10, ARRAY[random(), random(), random()] FROM generate_series(1,100000) i;"
+	"INSERT INTO tst SELECT i % 10, ARRAY[random(), random(), random()] FROM generate_series(1, 100000) i;"
 );
-$node_primary->safe_psql("postgres",
-	"CREATE INDEX ON tst USING ivfflat (v);");
+$node_primary->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v);");
 
 # Test that queries give same result
 test_index_replay('initial');
@@ -82,7 +82,7 @@ for my $i (1 .. 10)
 	test_index_replay("vacuum $i");
 	my ($start, $end) = (100001 + ($i - 1) * 10000, 100000 + $i * 10000);
 	$node_primary->safe_psql("postgres",
-		"INSERT INTO tst SELECT i%10, ARRAY[random(), random(), random()] FROM generate_series($start,$end) i;"
+		"INSERT INTO tst SELECT i % 10, ARRAY[random(), random(), random()] FROM generate_series($start, $end) i;"
 	);
 	test_index_replay("insert $i");
 }

test/t/002_vacuum.pl

@@ -0,0 +1,32 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More tests => 1;
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table and index
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector(3));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i % 10, ARRAY[i % 1000, i % 333, i % 55] FROM generate_series(1, 100000) i;"
+);
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v);");
+
+# Get size
+my $size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");
+
+# Delete all, vacuum, and insert same data
+$node->safe_psql("postgres", "DELETE FROM tst;");
+$node->safe_psql("postgres", "VACUUM tst;");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i % 10, ARRAY[i % 1000, i % 333, i % 55] FROM generate_series(1, 100000) i;"
+);
+
+# Check size
+my $new_size = $node->safe_psql("postgres", "SELECT pg_total_relation_size('tst_v_idx');");
+is($size, $new_size, "size does not change");

test/t/003_recall.pl

@@ -0,0 +1,88 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More tests => 9;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($probes, $min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	for my $i (0 .. $#queries) {
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET ivfflat.probes = $probes;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids) {
+			if (exists($actual_set{$_})) {
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector(3));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 100000) i;"
+);
+
+# Generate queries
+for (1..20) {
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "[$r1,$r2,$r3]");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+
+foreach (@operators) {
+	my $operator = $_;
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries) {
+		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
+		push(@expected, $res);
+	}
+
+	# Add index
+	my $opclass;
+	if ($operator == "<->") {
+		$opclass = "vector_l2_ops";
+	} elsif ($operator == "<#>") {
+		$opclass = "vector_ip_ops";
+	} else {
+		$opclass = "vector_cosine_ops";
+	}
+	$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v $opclass);");
+
+	# Test approximate results
+	test_recall(1, 0.75, $operator);
+	test_recall(10, 0.95, $operator);
+	test_recall(100, 1.0, $operator);
+}

test/t/004_centers.pl

@@ -0,0 +1,36 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More tests => 3;
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v vector(3));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, '[1,2,3]' FROM generate_series(1, 10) i;"
+);
+
+sub test_centers
+{
+	my ($lists, $min) = @_;
+
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", "CREATE INDEX ON tst USING ivfflat (v) WITH (lists = $lists);");
+	is($ret, 0, $stderr);
+}
+
+# Test no error for duplicate centers
+test_centers(5);
+test_centers(10);
+
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, '[4,5,6]' FROM generate_series(1, 10) i;"
+);
+
+# Test no error for duplicate centers
+test_centers(10);

test/t/005_query_recall.pl

@@ -0,0 +1,45 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More tests => 60;
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4 primary key, v vector(3));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 100000) i;"
+);
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+foreach (@operators) {
+	my $operator = $_;
+
+	# Add index
+	my $opclass;
+	if ($operator == "<->") {
+		$opclass = "vector_l2_ops";
+	} elsif ($operator == "<#>") {
+		$opclass = "vector_ip_ops";
+	} else {
+		$opclass = "vector_cosine_ops";
+	}
+	$node->safe_psql("postgres", "CREATE INDEX ON tst USING ivfflat (v $opclass);");
+
+	# Test 100% recall
+	for (1..20) {
+		my $i = int(rand() * 100000);
+		my $query = $node->safe_psql("postgres", "SELECT v FROM tst WHERE i = $i;");
+		my $res = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT v FROM tst ORDER BY v <-> '$query' LIMIT 1;
+		));
+		is($res, $query);
+	}
+}

test/t/006_lists.pl

@@ -0,0 +1,31 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More tests => 3;
+
+# Initialize node
+my $node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (v vector(3));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT ARRAY[random(), random(), random()] FROM generate_series(1, 100000) i;"
+);
+
+$node->safe_psql("postgres", "CREATE INDEX lists50 ON tst USING ivfflat (v) WITH (lists = 50);");
+$node->safe_psql("postgres", "CREATE INDEX lists100 ON tst USING ivfflat (v) WITH (lists = 100);");
+
+# Test prefers more lists
+my $res = $node->safe_psql("postgres", "EXPLAIN SELECT v FROM tst ORDER BY v <-> '[0.5,0.5,0.5]' LIMIT 10;");
+like($res, qr/lists100/);
+unlike($res, qr/lists50/);
+
+# Test errors with too much memory
+my ($ret, $stdout, $stderr) = $node->psql("postgres",
+	"CREATE INDEX lists10000 ON tst USING ivfflat (v) WITH (lists = 10000);"
+);
+like($stderr, qr/memory required is/);

vector.control

@@ -1,4 +1,4 @@
 comment = 'vector data type and ivfflat access method'
-default_version = '0.1.8'
+default_version = '0.2.5'
 module_pathname = '$libdir/vector'
 relocatable = true