Skip if FMA available [skip ci]

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

.github/workflows/build.yml

@@ -123,6 +123,6 @@ jobs:
       - uses: ankane/setup-postgres-valgrind@v1
         with:
           postgres-version: 16
-      - run: make
+      - run: make OPTFLAGS=""
       - run: sudo --preserve-env=PG_CONFIG make install
       - run: make installcheck

CHANGELOG.md

@@ -7,6 +7,7 @@
 - Added `jaccard_distance` function
 - Added `quantize_binary` function
 - Added `subvector` function
+- Added CPU dispatching for distance functions on Linux x86-64
 - Updated comparison operators to support vectors with different dimensions
 
 ## 0.6.2 (2024-03-18)

Makefile

@@ -3,7 +3,7 @@ EXTVERSION = 0.6.2
 
 MODULE_big = vector
 DATA = $(wildcard sql/*--*.sql)
-OBJS = src/bitvector.o src/halfvec.o src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/sparsevec.o src/vector.o
+OBJS = src/bitvector.o src/halfutils.o src/halfvec.o src/hnsw.o src/hnswbuild.o src/hnswinsert.o src/hnswscan.o src/hnswutils.o src/hnswvacuum.o src/ivfbuild.o src/ivfflat.o src/ivfinsert.o src/ivfkmeans.o src/ivfscan.o src/ivfutils.o src/ivfvacuum.o src/sparsevec.o src/vector.o
 HEADERS = src/halfvec.h src/sparsevec.h src/vector.h
 
 TESTS = $(wildcard test/sql/*.sql)

Makefile.win

@@ -1,7 +1,7 @@
 EXTENSION = vector
 EXTVERSION = 0.6.2
 
-OBJS = src\bitvector.obj src\halfvec.obj src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\sparsevec.obj src\vector.obj
+OBJS = src\bitvector.obj src\halfutils.obj src\halfvec.obj src\hnsw.obj src\hnswbuild.obj src\hnswinsert.obj src\hnswscan.obj src\hnswutils.obj src\hnswvacuum.obj src\ivfbuild.obj src\ivfflat.obj src\ivfinsert.obj src\ivfkmeans.obj src\ivfscan.obj src\ivfutils.obj src\ivfvacuum.obj src\sparsevec.obj src\vector.obj
 HEADERS = src\halfvec.h src\sparsevec.h src\vector.h
 
 REGRESS = bit_functions btree cast copy halfvec_functions halfvec_input hnsw_bit_hamming hnsw_bit_jaccard hnsw_halfvec_cosine hnsw_halfvec_ip hnsw_halfvec_l2 hnsw_options hnsw_sparsevec_cosine hnsw_sparsevec_ip hnsw_sparsevec_l2 hnsw_unlogged hnsw_vector_cosine hnsw_vector_ip hnsw_vector_l2 ivfflat_options ivfflat_unlogged ivfflat_vector_cosine ivfflat_vector_ip ivfflat_vector_l2 sparsevec_functions sparsevec_input vector_functions vector_input

README.md

@@ -346,6 +346,7 @@ CREATE INDEX ON items USING ivfflat (embedding vector_cosine_ops) WITH (lists =
 Supported types are:
 
 - `vector` - up to 2,000 dimensions
+- `halfvec` - up to 4,000 dimensions (unreleased)
 
 ### Query Options
 
@@ -419,6 +420,103 @@ 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 Vectors
+
+*Unreleased*
+
+Use the `halfvec` type to store half-precision vectors
+
+```sql
+CREATE TABLE items (id bigserial PRIMARY KEY, embedding halfvec(3));
+```
+
+## Half Indexing
+
+*Unreleased*
+
+Index vectors at half precision for smaller indexes and faster build times
+
+```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;
+```
+
+## Binary Vectors
+
+Use the `bit` type to store binary vectors ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/hash_image_search.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
+
+```sql
+SELECT * FROM items ORDER BY bit_count(embedding # '101') LIMIT 5;
+```
+
+Or (unreleased)
+
+```sql
+SELECT * FROM items ORDER BY embedding <~> '101' LIMIT 5;
+```
+
+Also supports Jaccard distance (`<%>`)
+
+## Binary Quantization
+
+*Unreleased*
+
+Use expression indexing for binary quantization
+
+```sql
+CREATE INDEX ON items USING hnsw ((quantize_binary(embedding)::bit(3)) bit_hamming_ops);
+```
+
+Get the nearest neighbors by Hamming distance
+
+```sql
+SELECT * FROM items ORDER BY quantize_binary(embedding)::bit(3) <~> quantize_binary('[1,-2,3]') LIMIT 5;
+```
+
+Re-rank by the original vectors for better recall
+
+```sql
+SELECT * FROM (
+    SELECT * FROM items ORDER BY quantize_binary(embedding)::bit(3) <~> quantize_binary('[1,-2,3]') LIMIT 20
+) ORDER BY embedding <=> '[1,-2,3]' LIMIT 5;
+```
+
+## Sparse Vectors
+
+*Unreleased*
+
+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');
+```
+
+Note: 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.
@@ -430,6 +528,30 @@ SELECT id, content FROM items, plainto_tsquery('hello search') query
 
 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.
 
+## Subvector Indexing
+
+*Unreleased*
+
+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
@@ -635,18 +757,6 @@ and query with:
 SELECT * FROM items ORDER BY embedding::vector(3) <-> '[3,1,2]' LIMIT 5;
 ```
 
-#### Are binary vectors supported?
-
-You can store binary vectors and perform exact nearest neighbor search by Hamming distance in Postgres without an extension ([example](https://github.com/pgvector/pgvector-python/blob/master/examples/hash_image_search.py)).
-
-```tsql
-CREATE TABLE items (id bigserial PRIMARY KEY, embedding bit(3));
-INSERT INTO items (embedding) VALUES (B'000'), (B'111');
-SELECT * FROM items ORDER BY bit_count(embedding # B'101') LIMIT 5;
-```
-
-Indexing is not currently supported.
-
 #### Do indexes need to fit into memory?
 
 No, but like other index types, you’ll likely see better performance if they do. You can get the size of an index with:
@@ -801,7 +911,7 @@ jaccard_distance(bit, bit) → double precision | Jaccard distance | unreleased
 
 ### 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 100,000 dimensions.
+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
 

sql/vector--0.6.2--0.7.0.sql

@@ -86,6 +86,9 @@ CREATE FUNCTION halfvec_l2_squared_distance(halfvec, halfvec) RETURNS float8
 CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION halfvec_spherical_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
@@ -137,6 +140,27 @@ CREATE OPERATOR <=> (
 	COMMUTATOR = '<=>'
 );
 
+CREATE OPERATOR CLASS halfvec_l2_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec),
+	FUNCTION 3 l2_distance(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_ip_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_norm(halfvec);
+
+CREATE OPERATOR CLASS halfvec_cosine_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 2 halfvec_norm(halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_norm(halfvec);
+
 CREATE OPERATOR CLASS halfvec_l2_ops
 	FOR TYPE halfvec USING hnsw AS
 	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
@@ -173,6 +197,9 @@ CREATE FUNCTION sparsevec_in(cstring, oid, integer) RETURNS sparsevec
 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;
 
@@ -182,6 +209,7 @@ CREATE FUNCTION sparsevec_send(sparsevec) RETURNS bytea
 CREATE TYPE sparsevec (
 	INPUT     = sparsevec_in,
 	OUTPUT    = sparsevec_out,
+	TYPMOD_IN = sparsevec_typmod_in,
 	RECEIVE   = sparsevec_recv,
 	SEND      = sparsevec_send,
 	STORAGE   = external

sql/vector.sql

@@ -381,6 +381,9 @@ CREATE FUNCTION halfvec_l2_squared_distance(halfvec, halfvec) RETURNS float8
 CREATE FUNCTION halfvec_negative_inner_product(halfvec, halfvec) RETURNS float8
 	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
 
+CREATE FUNCTION halfvec_spherical_distance(halfvec, halfvec) RETURNS float8
+	AS 'MODULE_PATHNAME' LANGUAGE C IMMUTABLE STRICT PARALLEL SAFE;
+
 -- halfvec cast functions
 
 CREATE FUNCTION halfvec(halfvec, integer, boolean) RETURNS halfvec
@@ -440,6 +443,27 @@ CREATE OPERATOR <=> (
 
 -- halfvec opclasses
 
+CREATE OPERATOR CLASS halfvec_l2_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_l2_squared_distance(halfvec, halfvec),
+	FUNCTION 3 l2_distance(halfvec, halfvec);
+
+CREATE OPERATOR CLASS halfvec_ip_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <#> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_norm(halfvec);
+
+CREATE OPERATOR CLASS halfvec_cosine_ops
+	FOR TYPE halfvec USING ivfflat AS
+	OPERATOR 1 <=> (halfvec, halfvec) FOR ORDER BY float_ops,
+	FUNCTION 1 halfvec_negative_inner_product(halfvec, halfvec),
+	FUNCTION 2 halfvec_norm(halfvec),
+	FUNCTION 3 halfvec_spherical_distance(halfvec, halfvec),
+	FUNCTION 4 halfvec_norm(halfvec);
+
 CREATE OPERATOR CLASS halfvec_l2_ops
 	FOR TYPE halfvec USING hnsw AS
 	OPERATOR 1 <-> (halfvec, halfvec) FOR ORDER BY float_ops,
@@ -480,6 +504,9 @@ CREATE FUNCTION sparsevec_in(cstring, oid, integer) RETURNS sparsevec
 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;
 
@@ -489,6 +516,7 @@ CREATE FUNCTION sparsevec_send(sparsevec) RETURNS bytea
 CREATE TYPE sparsevec (
 	INPUT     = sparsevec_in,
 	OUTPUT    = sparsevec_out,
+	TYPMOD_IN = sparsevec_typmod_in,
 	RECEIVE   = sparsevec_recv,
 	SEND      = sparsevec_send,
 	STORAGE   = external

src/halfutils.c

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

src/halfutils.h

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

src/halfvec.c

@@ -6,6 +6,7 @@
 #include "catalog/pg_type.h"
 #include "common/shortest_dec.h"
 #include "fmgr.h"
+#include "halfutils.h"
 #include "halfvec.h"
 #include "lib/stringinfo.h"
 #include "libpq/pqformat.h"
@@ -22,45 +23,6 @@
 #define TYPALIGN_INT 'i'
 #endif
 
-/*
- * 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
-}
-
 /*
  * Get a half from a message buffer
  */
@@ -93,207 +55,6 @@ pq_sendhalf(StringInfo buf, half h)
 	pq_sendint16(buf, swap.i);
 }
 
-/*
- * Convert a half to a float4
- */
-float
-HalfToFloat4(half num)
-{
-#ifdef FLT16_SUPPORT
-	return (float) num;
-#else
-	/* TODO Improve performance */
-
-	/* Assumes same endianness for floats and integers */
-	union
-	{
-		float		f;
-		uint32		i;
-	}			swapfloat;
-
-	union
-	{
-		half		h;
-		uint16		i;
-	}			swaphalf;
-
-	uint16		bin;
-	uint32		exponent;
-	uint32		mantissa;
-	uint32		result;
-
-	swaphalf.h = num;
-	bin = swaphalf.i;
-	exponent = (bin & 0x7C00) >> 10;
-	mantissa = bin & 0x03FF;
-
-	/* Sign */
-	result = (bin & 0x8000) << 16;
-
-	if (exponent == 31)
-	{
-		if (mantissa == 0)
-		{
-			/* Infinite */
-			result |= 0x7F800000;
-		}
-		else
-		{
-			/* NaN */
-			result |= 0x7FC00000;
-			result |= mantissa << 13;
-		}
-	}
-	else if (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;
-			result |= mantissa << 13;
-		}
-	}
-	else
-	{
-		/* Normal */
-		result |= (exponent - 15 + 127) << 23;
-		result |= mantissa << 13;
-	}
-
-	swapfloat.i = result;
-	return swapfloat.f;
-#endif
-}
-
-/*
- * Convert a float4 to a half
- */
-half
-Float4ToHalfUnchecked(float num)
-{
-#ifdef FLT16_SUPPORT
-	return (_Float16) num;
-#else
-	/* TODO Improve performance */
-
-	/* Assumes same endianness for floats and integers */
-	union
-	{
-		float		f;
-		uint32		i;
-	}			swapfloat;
-
-	union
-	{
-		half		h;
-		uint16		i;
-	}			swaphalf;
-
-	uint32		bin;
-	int			exponent;
-	int			mantissa;
-	uint16		result;
-
-	swapfloat.f = num;
-	bin = swapfloat.i;
-	exponent = (bin & 0x7F800000) >> 23;
-	mantissa = bin & 0x007FFFFF;
-
-	/* Sign */
-	result = (bin & 0x80000000) >> 16;
-
-	if (isinf(num))
-	{
-		/* Infinite */
-		result |= 0x7C00;
-	}
-	else if (isnan(num))
-	{
-		/* NaN */
-		result |= 0x7E00;
-		result |= mantissa >> 13;
-	}
-	else if (exponent > 98)
-	{
-		int			m;
-		int			gr;
-		int			s;
-
-		exponent -= 127;
-		s = mantissa & 0x00000FFF;
-
-		/* Subnormal */
-		if (exponent < -14)
-		{
-			int			diff = -exponent - 14;
-
-			mantissa >>= diff;
-			mantissa += 1 << (23 - diff);
-			s |= mantissa & 0x00000FFF;
-		}
-
-		m = mantissa >> 13;
-
-		/* Round */
-		gr = (mantissa >> 12) % 4;
-		if (gr == 3 || (gr == 1 && s != 0))
-			m += 1;
-
-		if (m == 1024)
-		{
-			m = 0;
-			exponent += 1;
-		}
-
-		if (exponent > 15)
-		{
-			/* Infinite */
-			result |= 0x7C00;
-		}
-		else
-		{
-			if (exponent >= -14)
-				result |= (exponent + 15) << 10;
-
-			result |= m;
-		}
-	}
-
-	swaphalf.i = result;
-	return swaphalf.h;
-#endif
-}
-
-/*
- * Convert a float4 to a half
- */
-half
-Float4ToHalf(float num)
-{
-	half		result = Float4ToHalfUnchecked(num);
-
-	if (unlikely(HalfIsInf(result)) && !isinf(num))
-		float_overflow_error();
-	if (unlikely(HalfIsZero(result)) && num != 0.0)
-		float_underflow_error();
-
-	return result;
-}
-
 /*
  * Ensure same dimensions
  */
@@ -385,24 +146,6 @@ halfvec_isspace(char ch)
 	return false;
 }
 
-#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
  */
@@ -414,27 +157,33 @@ halfvec_in(PG_FUNCTION_ARGS)
 	int32		typmod = PG_GETARG_INT32(2);
 	half		x[HALFVEC_MAX_DIM];
 	int			dim = 0;
-	char	   *pt;
-	char	   *stringEnd;
+	char	   *pt = lit;
 	HalfVector *result;
-	char	   *litcopy = pstrdup(lit);
-	char	   *str = litcopy;
 
-	while (halfvec_isspace(*str))
-		str++;
+	while (halfvec_isspace(*pt))
+		pt++;
 
-	if (*str != '[')
+	if (*pt != '[')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed halfvec literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type halfvec: \"%s\"", lit),
 				 errdetail("Vector contents must start with \"[\".")));
 
-	str++;
-	pt = strtok(str, ",");
-	stringEnd = pt;
+	pt++;
 
-	while (pt != NULL && *stringEnd != ']')
+	while (halfvec_isspace(*pt))
+		pt++;
+
+	if (*pt == ']')
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("halfvec must have at least 1 dimension")));
+
+	for (;;)
 	{
+		float		val;
+		char	   *stringEnd;
+
 		if (dim == HALFVEC_MAX_DIM)
 			ereport(ERROR,
 					(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
@@ -449,61 +198,56 @@ halfvec_in(PG_FUNCTION_ARGS)
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
 
-		/* Use strtof like float4in to avoid a double-rounding problem */
-		x[dim] = Float4ToHalf(strtof(pt, &stringEnd));
-		CheckElement(x[dim]);
-		dim++;
+		errno = 0;
+
+		/* Postgres sets LC_NUMERIC to C on startup */
+		val = strtof(pt, &stringEnd);
 
 		if (stringEnd == pt)
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
 
-		while (halfvec_isspace(*stringEnd))
-			stringEnd++;
+		x[dim] = Float4ToHalfUnchecked(val);
 
-		if (*stringEnd != '\0' && *stringEnd != ']')
+		/* Check for range error like float4in */
+		if ((errno == ERANGE && isinf(val)) || (HalfIsInf(x[dim]) && !isinf(val)))
+			ereport(ERROR,
+					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+					 errmsg("\"%s\" is out of range for type halfvec", pnstrdup(pt, stringEnd - pt))));
+
+		CheckElement(x[dim]);
+		dim++;
+
+		pt = stringEnd;
+
+		while (halfvec_isspace(*pt))
+			pt++;
+
+		if (*pt == ',')
+			pt++;
+		else if (*pt == ']')
+		{
+			pt++;
+			break;
+		}
+		else
 			ereport(ERROR,
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type halfvec: \"%s\"", lit)));
-
-		pt = strtok(NULL, ",");
 	}
 
-	if (stringEnd == NULL || *stringEnd != ']')
-		ereport(ERROR,
-				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed halfvec literal: \"%s\"", lit),
-				 errdetail("Unexpected end of input.")));
-
-	stringEnd++;
-
 	/* Only whitespace is allowed after the closing brace */
-	while (halfvec_isspace(*stringEnd))
-		stringEnd++;
+	while (halfvec_isspace(*pt))
+		pt++;
 
-	if (*stringEnd != '\0')
+	if (*pt != '\0')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed halfvec literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type halfvec: \"%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 halfvec literal: \"%s\"", lit)));
-	}
-
-	if (dim < 1)
-		ereport(ERROR,
-				(errcode(ERRCODE_DATA_EXCEPTION),
-				 errmsg("halfvec must have at least 1 dimension")));
-
-	pfree(litcopy);
-
+	CheckDim(dim);
 	CheckExpectedDim(typmod, dim);
 
 	result = InitHalfVector(dim);
@@ -773,11 +517,7 @@ vector_to_halfvec(PG_FUNCTION_ARGS)
 	result = InitHalfVector(vec->dim);
 
 	for (int i = 0; i < vec->dim; i++)
-	{
-		result->x[i] = Float4ToHalfUnchecked(vec->x[i]);
-		/* TODO Better error for overflow */
-		CheckElement(result->x[i]);
-	}
+		result->x[i] = Float4ToHalf(vec->x[i]);
 
 	PG_RETURN_POINTER(result);
 }
@@ -791,21 +531,10 @@ halfvec_l2_distance(PG_FUNCTION_ARGS)
 {
 	HalfVector *a = PG_GETARG_HALFVEC_P(0);
 	HalfVector *b = PG_GETARG_HALFVEC_P(1);
-	half	   *ax = a->x;
-	half	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
-
-		distance += diff * diff;
-	}
-
-	PG_RETURN_FLOAT8(sqrt((double) distance));
+	PG_RETURN_FLOAT8(sqrt((double) HalfvecL2SquaredDistance(a->dim, a->x, b->x)));
 }
 
 /*
@@ -817,21 +546,10 @@ halfvec_l2_squared_distance(PG_FUNCTION_ARGS)
 {
 	HalfVector *a = PG_GETARG_HALFVEC_P(0);
 	HalfVector *b = PG_GETARG_HALFVEC_P(1);
-	half	   *ax = a->x;
-	half	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		float		diff = HalfToFloat4(ax[i]) - HalfToFloat4(bx[i]);
-
-		distance += diff * diff;
-	}
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) HalfvecL2SquaredDistance(a->dim, a->x, b->x));
 }
 
 /*
@@ -843,17 +561,10 @@ halfvec_inner_product(PG_FUNCTION_ARGS)
 {
 	HalfVector *a = PG_GETARG_HALFVEC_P(0);
 	HalfVector *b = PG_GETARG_HALFVEC_P(1);
-	half	   *ax = a->x;
-	half	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) HalfvecInnerProduct(a->dim, a->x, b->x));
 }
 
 /*
@@ -865,17 +576,10 @@ halfvec_negative_inner_product(PG_FUNCTION_ARGS)
 {
 	HalfVector *a = PG_GETARG_HALFVEC_P(0);
 	HalfVector *b = PG_GETARG_HALFVEC_P(1);
-	half	   *ax = a->x;
-	half	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += HalfToFloat4(ax[i]) * HalfToFloat4(bx[i]);
-
-	PG_RETURN_FLOAT8((double) distance * -1);
+	PG_RETURN_FLOAT8((double) -HalfvecInnerProduct(a->dim, a->x, b->x));
 }
 
 /*
@@ -925,6 +629,32 @@ halfvec_cosine_distance(PG_FUNCTION_ARGS)
 	PG_RETURN_FLOAT8(1 - similarity);
 }
 
+/*
+ * Get the distance for spherical k-means
+ * Currently uses angular distance since needs to satisfy triangle inequality
+ * Assumes inputs are unit vectors (skips norm)
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(halfvec_spherical_distance);
+Datum
+halfvec_spherical_distance(PG_FUNCTION_ARGS)
+{
+	HalfVector *a = PG_GETARG_HALFVEC_P(0);
+	HalfVector *b = PG_GETARG_HALFVEC_P(1);
+	double		distance;
+
+	CheckDims(a, b);
+
+	distance = (double) HalfvecInnerProduct(a->dim, a->x, b->x);
+
+	/* Prevent NaN with acos with loss of precision */
+	if (distance > 1)
+		distance = 1;
+	else if (distance < -1)
+		distance = -1;
+
+	PG_RETURN_FLOAT8(acos(distance) / M_PI);
+}
+
 /*
  * Get the L1 distance between two half vectors
  */
@@ -1018,3 +748,30 @@ halfvec_subvector(PG_FUNCTION_ARGS)
 
 	PG_RETURN_POINTER(result);
 }
+
+/*
+ * Internal helper to compare half vectors
+ */
+int
+halfvec_cmp_internal(HalfVector * a, HalfVector * b)
+{
+	int			dim = Min(a->dim, b->dim);
+
+	/* Check values before dimensions to be consistent with Postgres arrays */
+	for (int i = 0; i < dim; i++)
+	{
+		if (HalfToFloat4(a->x[i]) < HalfToFloat4(b->x[i]))
+			return -1;
+
+		if (HalfToFloat4(a->x[i]) > HalfToFloat4(b->x[i]))
+			return 1;
+	}
+
+	if (a->dim < b->dim)
+		return -1;
+
+	if (a->dim > b->dim)
+		return 1;
+
+	return 0;
+}

src/halfvec.h

@@ -7,7 +7,14 @@
 
 #include "vector.h"
 
-#ifdef __FLT16_MAX__
+#if defined(__x86_64__) || defined(_M_AMD64)
+#define HALFVEC_DISPATCH
+#endif
+
+/* F16C has better performance than _Float16 (on x86-64) */
+#if defined(__F16C__)
+#define F16C_SUPPORT
+#elif defined(__FLT16_MAX__) && !defined(HALFVEC_DISPATCH)
 #define FLT16_SUPPORT
 #endif
 
@@ -15,7 +22,6 @@
 #define half _Float16
 #define HALF_MAX FLT16_MAX
 #else
-/* TODO #pragma message("")? */
 #define half uint16
 #define HALF_MAX 65504
 #endif
@@ -36,8 +42,6 @@ typedef struct HalfVector
 }			HalfVector;
 
 HalfVector *InitHalfVector(int dim);
-float		HalfToFloat4(half num);
-half		Float4ToHalf(float num);
-half		Float4ToHalfUnchecked(float num);
+int			halfvec_cmp_internal(HalfVector * a, HalfVector * b);
 
 #endif

src/hnswbuild.c

@@ -681,6 +681,8 @@ GetMaxDimensions(HnswType type)
 		maxDimensions *= 2;
 	else if (type == HNSW_TYPE_BIT)
 		maxDimensions *= 32;
+	else if (type == HNSW_TYPE_SPARSEVEC)
+		maxDimensions = INT_MAX;
 
 	return maxDimensions;
 }
@@ -691,6 +693,8 @@ GetMaxDimensions(HnswType type)
 static void
 InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, IndexInfo *indexInfo, ForkNumber forkNum)
 {
+	int			maxDimensions;
+
 	buildstate->heap = heap;
 	buildstate->index = index;
 	buildstate->indexInfo = indexInfo;
@@ -701,17 +705,14 @@ InitBuildState(HnswBuildState * buildstate, Relation heap, Relation index, Index
 	buildstate->efConstruction = HnswGetEfConstruction(index);
 	buildstate->dimensions = TupleDescAttr(index->rd_att, 0)->atttypmod;
 
+	maxDimensions = GetMaxDimensions(buildstate->type);
 
-	if (buildstate->type != HNSW_TYPE_SPARSEVEC)
-	{
-		int			maxDimensions = GetMaxDimensions(buildstate->type);
+	/* Require column to have dimensions to be indexed */
+	if (buildstate->dimensions < 0)
+		elog(ERROR, "column does not have dimensions");
 
-		if (buildstate->dimensions < 0)
-			elog(ERROR, "column does not have dimensions");
-
-		if (buildstate->dimensions > maxDimensions)
-			elog(ERROR, "column cannot have more than %d dimensions for hnsw index", maxDimensions);
-	}
+	if (buildstate->dimensions > maxDimensions)
+		elog(ERROR, "column cannot have more than %d dimensions for hnsw index", maxDimensions);
 
 	if (buildstate->efConstruction < 2 * buildstate->m)
 		elog(ERROR, "ef_construction must be greater than or equal to 2 * m");

src/hnswscan.c

@@ -158,6 +158,10 @@ hnswgettuple(IndexScanDesc scan, ScanDirection dir)
 		UnlockPage(scan->indexRelation, HNSW_SCAN_LOCK, ShareLock);
 
 		so->first = false;
+
+#if defined(HNSW_MEMORY) && PG_VERSION_NUM >= 130000
+		elog(INFO, "memory: %zu MB", MemoryContextMemAllocated(so->tmpCtx, false) / (1024 * 1024));
+#endif
 	}
 
 	while (list_length(so->w) > 0)

src/hnswutils.c

@@ -5,6 +5,7 @@
 #include "access/generic_xlog.h"
 #include "catalog/pg_type.h"
 #include "catalog/pg_type_d.h"
+#include "halfutils.h"
 #include "halfvec.h"
 #include "hnsw.h"
 #include "lib/pairingheap.h"
@@ -163,9 +164,9 @@ HnswGetType(Relation index)
 	Oid			typid = TupleDescAttr(index->rd_att, 0)->atttypid;
 	HeapTuple	tuple;
 	Form_pg_type type;
-	int			result;
+	HnswType	result;
 
-	if (typid == BITOID || typid == VARBITOID)
+	if (typid == BITOID)
 		return HNSW_TYPE_BIT;
 
 	tuple = SearchSysCache1(TYPEOID, ObjectIdGetDatum(typid));
@@ -180,7 +181,10 @@ HnswGetType(Relation index)
 	else if (strcmp(NameStr(type->typname), "sparsevec") == 0)
 		result = HNSW_TYPE_SPARSEVEC;
 	else
-		elog(ERROR, "Unsupported type");
+	{
+		ReleaseSysCache(tuple);
+		elog(ERROR, "type not supported for hnsw index");
+	}
 
 	ReleaseSysCache(tuple);
 
@@ -219,17 +223,14 @@ HnswNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, HnswType type)
 			HalfVector *result = InitHalfVector(v->dim);
 
 			for (int i = 0; i < v->dim; i++)
-			{
-				/* TODO Fix */
 				result->x[i] = Float4ToHalfUnchecked(HalfToFloat4(v->x[i]) / norm);
-			}
 
 			*value = PointerGetDatum(result);
 		}
 		else if (type == HNSW_TYPE_SPARSEVEC)
 		{
 			SparseVector *v = DatumGetSparseVector(*value);
-			SparseVector *result = InitSparseVector(v->nnz);
+			SparseVector *result = InitSparseVector(v->dim, v->nnz);
 			float	   *vx = SPARSEVEC_VALUES(v);
 			float	   *rx = SPARSEVEC_VALUES(result);
 

src/ivfbuild.c

@@ -10,12 +10,14 @@
 #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"
@@ -63,7 +65,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 
 	if (samples->length < targsamples)
 	{
-		VectorArraySet(samples, samples->length, DatumGetVector(value));
+		VectorArraySet(samples, samples->length, DatumGetPointer(value));
 		samples->length++;
 	}
 	else
@@ -80,7 +82,7 @@ AddSample(Datum *values, IvfflatBuildState * buildstate)
 #endif
 
 			Assert(k >= 0 && k < targsamples);
-			VectorArraySet(samples, k, DatumGetVector(value));
+			VectorArraySet(samples, k, DatumGetPointer(value));
 		}
 
 		buildstate->rowstoskip -= 1;
@@ -318,7 +320,26 @@ InsertTuples(Relation index, IvfflatBuildState * buildstate, ForkNumber forkNum)
 static int
 GetMaxDimensions(IvfflatType type)
 {
-	return IVFFLAT_MAX_DIM;
+	int			maxDimensions = IVFFLAT_MAX_DIM;
+
+	if (type == IVFFLAT_TYPE_HALFVEC)
+		maxDimensions *= 2;
+
+	return maxDimensions;
+}
+
+/*
+ * Get item size
+ */
+static Size
+GetItemSize(IvfflatType type, int dimensions)
+{
+	if (type == IVFFLAT_TYPE_VECTOR)
+		return VECTOR_SIZE(dimensions);
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+		return HALFVEC_SIZE(dimensions);
+	else
+		elog(ERROR, "Unsupported type");
 }
 
 /*
@@ -367,7 +388,7 @@ InitBuildState(IvfflatBuildState * buildstate, Relation heap, Relation index, In
 
 	buildstate->slot = MakeSingleTupleTableSlot(buildstate->tupdesc, &TTSOpsVirtual);
 
-	buildstate->centers = VectorArrayInit(buildstate->lists, buildstate->dimensions);
+	buildstate->centers = VectorArrayInit(buildstate->lists, buildstate->dimensions, GetItemSize(buildstate->type, buildstate->dimensions));
 	buildstate->listInfo = palloc(sizeof(ListInfo) * buildstate->lists);
 
 	buildstate->tmpCtx = AllocSetContextCreate(CurrentMemoryContext,
@@ -422,7 +443,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 
 	/* Sample rows */
 	/* TODO Ensure within maintenance_work_mem */
-	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions);
+	buildstate->samples = VectorArrayInit(numSamples, buildstate->dimensions, buildstate->centers->itemsize);
 	if (buildstate->heap != NULL)
 	{
 		SampleRows(buildstate);
@@ -437,7 +458,7 @@ ComputeCenters(IvfflatBuildState * buildstate)
 	}
 
 	/* Calculate centers */
-	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers));
+	IvfflatBench("k-means", IvfflatKmeans(buildstate->index, buildstate->samples, buildstate->centers, buildstate->type));
 
 	/* Free samples before we allocate more memory */
 	VectorArrayFree(buildstate->samples);
@@ -482,7 +503,7 @@ 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);
@@ -495,7 +516,7 @@ CreateListPages(Relation index, VectorArray centers, int dimensions,
 		/* Load list */
 		list->startPage = InvalidBlockNumber;
 		list->insertPage = InvalidBlockNumber;
-		memcpy(&list->center, VectorArrayGet(centers, i), VECTOR_SIZE(dimensions));
+		memcpy(&list->center, VectorArrayGet(centers, i), centers->itemsize);
 
 		/* Ensure free space */
 		if (PageGetFreeSpace(page) < listSize)
@@ -600,7 +621,7 @@ 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;
@@ -624,7 +645,7 @@ IvfflatParallelScanAndSort(IvfflatSpool * ivfspool, IvfflatShared * ivfshared, S
 	indexInfo = BuildIndexInfo(ivfspool->index);
 	indexInfo->ii_Concurrent = ivfshared->isconcurrent;
 	InitBuildState(&buildstate, ivfspool->heap, ivfspool->index, indexInfo);
-	memcpy(buildstate.centers->items, ivfcenters, VECTOR_SIZE(buildstate.centers->dim) * buildstate.centers->maxlen);
+	memcpy(buildstate.centers->items, ivfcenters, buildstate.centers->itemsize * buildstate.centers->maxlen);
 	buildstate.centers->length = buildstate.centers->maxlen;
 	ivfspool->sortstate = tuplesort_begin_heap(buildstate.tupdesc, 1, attNums, sortOperators, sortCollations, nullsFirstFlags, sortmem, coordinate, false);
 	buildstate.sortstate = ivfspool->sortstate;
@@ -672,7 +693,7 @@ IvfflatParallelBuildMain(dsm_segment *seg, shm_toc *toc)
 	IvfflatSpool *ivfspool;
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 	Relation	heapRel;
 	Relation	indexRel;
 	LOCKMODE	heapLockmode;
@@ -786,7 +807,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	Size		estcenters;
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 	IvfflatLeader *ivfleader = (IvfflatLeader *) palloc0(sizeof(IvfflatLeader));
 	bool		leaderparticipates = true;
 	int			querylen;
@@ -813,7 +834,7 @@ IvfflatBeginParallel(IvfflatBuildState * buildstate, bool isconcurrent, int requ
 	shm_toc_estimate_chunk(&pcxt->estimator, estivfshared);
 	estsort = tuplesort_estimate_shared(scantuplesortstates);
 	shm_toc_estimate_chunk(&pcxt->estimator, estsort);
-	estcenters = VECTOR_SIZE(buildstate->dimensions) * buildstate->lists;
+	estcenters = buildstate->centers->itemsize * buildstate->centers->maxlen;
 	shm_toc_estimate_chunk(&pcxt->estimator, estcenters);
 	shm_toc_estimate_keys(&pcxt->estimator, 3);
 
@@ -865,7 +886,7 @@ 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);

src/ivfflat.h

@@ -45,7 +45,8 @@
 
 typedef enum IvfflatType
 {
-	IVFFLAT_TYPE_VECTOR
+	IVFFLAT_TYPE_VECTOR,
+	IVFFLAT_TYPE_HALFVEC
 }			IvfflatType;
 
 /* Build phases */
@@ -54,7 +55,7 @@ typedef enum IvfflatType
 #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))
@@ -90,7 +91,8 @@ typedef struct VectorArrayData
 	int			length;
 	int			maxlen;
 	int			dim;
-	Vector	   *items;
+	Size		itemsize;
+	char	   *items;
 }			VectorArrayData;
 
 typedef VectorArrayData * VectorArray;
@@ -149,7 +151,7 @@ typedef struct IvfflatLeader
 	IvfflatShared *ivfshared;
 	Sharedsort *sharedsort;
 	Snapshot	snapshot;
-	Vector	   *ivfcenters;
+	char	   *ivfcenters;
 }			IvfflatLeader;
 
 typedef struct IvfflatBuildState
@@ -261,16 +263,15 @@ typedef struct IvfflatScanOpaqueData
 
 typedef IvfflatScanOpaqueData * IvfflatScanOpaque;
 
-#define VECTOR_ARRAY_SIZE(_length, _dim) (sizeof(VectorArrayData) + (_length) * VECTOR_SIZE(_dim))
-#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * VECTOR_SIZE((_arr)->dim))
-#define VectorArrayGet(_arr, _offset) ((Vector *) VECTOR_ARRAY_OFFSET(_arr, _offset))
-#define VectorArraySet(_arr, _offset, _val) memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, VECTOR_SIZE((_arr)->dim))
+#define VECTOR_ARRAY_SIZE(_length, _size) (sizeof(VectorArrayData) + (_length) * _size)
+#define VECTOR_ARRAY_OFFSET(_arr, _offset) ((char*) (_arr)->items + (_offset) * (_arr)->itemsize)
+#define VectorArrayGet(_arr, _offset) VECTOR_ARRAY_OFFSET(_arr, _offset)
+#define VectorArraySet(_arr, _offset, _val) memcpy(VECTOR_ARRAY_OFFSET(_arr, _offset), _val, (_arr)->itemsize)
 
 /* Methods */
-VectorArray VectorArrayInit(int maxlen, int dimensions);
+VectorArray VectorArrayInit(int maxlen, int dimensions, Size itemsize);
 void		VectorArrayFree(VectorArray arr);
-void		PrintVectorArray(char *msg, VectorArray arr);
-void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers);
+void		IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatType type);
 FmgrInfo   *IvfflatOptionalProcInfo(Relation index, uint16 procnum);
 IvfflatType IvfflatGetType(Relation index);
 bool		IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, IvfflatType type);

src/ivfkmeans.c

@@ -3,12 +3,13 @@
 #include <float.h>
 #include <math.h>
 
+#include "halfutils.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
-
-#ifdef IVFFLAT_MEMORY
+#include "utils/datum.h"
 #include "utils/memutils.h"
-#endif
+#include "vector.h"
 
 /*
  * Initialize with kmeans++
@@ -46,12 +47,12 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
 
 		for (j = 0; j < numSamples; j++)
 		{
-			Vector	   *vec = VectorArrayGet(samples, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, j));
 			double		distance;
 
 			/* Only need to compute distance for new center */
 			/* TODO Use triangle inequality to reduce distance calculations */
-			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, i))));
+			distance = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, i))));
 
 			/* Set lower bound */
 			lowerBound[j * numCenters + i] = distance;
@@ -89,15 +90,29 @@ InitCenters(Relation index, VectorArray samples, VectorArray centers, float *low
  * Apply norm to vector
  */
 static inline void
-ApplyNorm(FmgrInfo *normprocinfo, Oid collation, Vector * vec)
+ApplyNorm(FmgrInfo *normprocinfo, Oid collation, Datum value, IvfflatType type)
 {
-	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, PointerGetDatum(vec)));
+	double		norm = DatumGetFloat8(FunctionCall1Coll(normprocinfo, collation, value));
 
 	/* TODO Handle zero norm */
 	if (norm > 0)
 	{
-		for (int i = 0; i < vec->dim; i++)
-			vec->x[i] /= norm;
+		if (type == IVFFLAT_TYPE_VECTOR)
+		{
+			Vector	   *vec = DatumGetVector(value);
+
+			for (int i = 0; i < vec->dim; i++)
+				vec->x[i] /= norm;
+		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *vec = DatumGetHalfVector(value);
+
+			for (int i = 0; i < vec->dim; i++)
+				vec->x[i] = Float4ToHalfUnchecked(HalfToFloat4(vec->x[i]) / norm);
+		}
+		else
+			elog(ERROR, "Unsupported type");
 	}
 }
 
@@ -110,11 +125,20 @@ CompareVectors(const void *a, const void *b)
 	return vector_cmp_internal((Vector *) a, (Vector *) b);
 }
 
+/*
+ * Compare half vectors
+ */
+static int
+CompareHalfVectors(const void *a, const void *b)
+{
+	return halfvec_cmp_internal((HalfVector *) a, (HalfVector *) b);
+}
+
 /*
  * Quick approach if we have little data
  */
 static void
-QuickCenters(Relation index, VectorArray samples, VectorArray centers)
+QuickCenters(Relation index, VectorArray samples, VectorArray centers, IvfflatType type)
 {
 	int			dimensions = centers->dim;
 	Oid			collation = index->rd_indcollation[0];
@@ -123,14 +147,20 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	/* Copy existing vectors while avoiding duplicates */
 	if (samples->length > 0)
 	{
-		qsort(samples->items, samples->length, VECTOR_SIZE(samples->dim), CompareVectors);
+		if (type == IVFFLAT_TYPE_VECTOR)
+			qsort(samples->items, samples->length, samples->itemsize, CompareVectors);
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+			qsort(samples->items, samples->length, samples->itemsize, CompareHalfVectors);
+		else
+			elog(ERROR, "Unsupported type");
+
 		for (int i = 0; i < samples->length; i++)
 		{
-			Vector	   *vec = VectorArrayGet(samples, i);
+			Datum		vec = PointerGetDatum(VectorArrayGet(samples, i));
 
-			if (i == 0 || CompareVectors(vec, VectorArrayGet(samples, i - 1)) != 0)
+			if (i == 0 || !datumIsEqual(vec, PointerGetDatum(VectorArrayGet(samples, i - 1)), false, -1))
 			{
-				VectorArraySet(centers, centers->length, vec);
+				VectorArraySet(centers, centers->length, DatumGetPointer(vec));
 				centers->length++;
 			}
 		}
@@ -139,17 +169,34 @@ QuickCenters(Relation index, VectorArray samples, VectorArray centers)
 	/* Fill remaining with random data */
 	while (centers->length < centers->maxlen)
 	{
-		Vector	   *vec = VectorArrayGet(centers, centers->length);
+		Datum		center = PointerGetDatum(VectorArrayGet(centers, centers->length));
 
-		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
-		vec->dim = dimensions;
+		if (type == IVFFLAT_TYPE_VECTOR)
+		{
+			Vector	   *vec = DatumGetVector(center);
 
-		for (int j = 0; j < dimensions; j++)
-			vec->x[j] = RandomDouble();
+			SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
+			vec->dim = dimensions;
+
+			for (int j = 0; j < dimensions; j++)
+				vec->x[j] = RandomDouble();
+		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *vec = DatumGetHalfVector(center);
+
+			SET_VARSIZE(vec, HALFVEC_SIZE(dimensions));
+			vec->dim = dimensions;
+
+			for (int j = 0; j < dimensions; j++)
+				vec->x[j] = Float4ToHalfUnchecked((float) RandomDouble());
+		}
+		else
+			elog(ERROR, "Unsupported type");
 
 		/* Normalize if needed (only needed for random centers) */
 		if (normprocinfo != NULL)
-			ApplyNorm(normprocinfo, collation, vec);
+			ApplyNorm(normprocinfo, collation, center, type);
 
 		centers->length++;
 	}
@@ -160,18 +207,120 @@ 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));
+		 MemoryContextMemAllocated(context, true) / (1024 * 1024));
 #else
-	MemoryContextStats(CurrentMemoryContext);
+	MemoryContextStats(context);
 #endif
 	elog(INFO, "estimated memory: %zu MB", estimatedSize / (1024 * 1024));
 }
 #endif
 
+/*
+ * Compute new centers
+ */
+static void
+ComputeNewCenters(VectorArray samples, VectorArray aggCenters, VectorArray newCenters, int *centerCounts, int *closestCenters, FmgrInfo *normprocinfo, Oid collation, IvfflatType type)
+{
+	int			dimensions = aggCenters->dim;
+	int			numCenters = aggCenters->maxlen;
+	int			numSamples = samples->length;
+
+	/* Reset sum and count */
+	for (int j = 0; j < numCenters; j++)
+	{
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
+		for (int k = 0; k < dimensions; k++)
+			vec->x[k] = 0.0;
+
+		centerCounts[j] = 0;
+	}
+
+	/* Increment sum of closest center */
+	if (type == IVFFLAT_TYPE_VECTOR)
+	{
+		for (int j = 0; j < numSamples; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, closestCenters[j]);
+			Vector	   *vec = (Vector *) VectorArrayGet(samples, j);
+
+			for (int k = 0; k < dimensions; k++)
+				aggCenter->x[k] += vec->x[k];
+		}
+	}
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		for (int j = 0; j < numSamples; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, closestCenters[j]);
+			HalfVector *vec = (HalfVector *) VectorArrayGet(samples, j);
+
+			for (int k = 0; k < dimensions; k++)
+				aggCenter->x[k] += HalfToFloat4(vec->x[k]);
+		}
+	}
+	else
+		elog(ERROR, "Unsupported type");
+
+	/* Increment count of closest center */
+	for (int j = 0; j < numSamples; j++)
+		centerCounts[closestCenters[j]] += 1;
+
+	/* Divide sum by count */
+	for (int j = 0; j < numCenters; j++)
+	{
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
+		if (centerCounts[j] > 0)
+		{
+			/* Double avoids overflow, but requires more memory */
+			/* TODO Update bounds */
+			for (int k = 0; k < dimensions; k++)
+			{
+				if (isinf(vec->x[k]))
+					vec->x[k] = vec->x[k] > 0 ? FLT_MAX : -FLT_MAX;
+			}
+
+			for (int k = 0; k < dimensions; k++)
+				vec->x[k] /= centerCounts[j];
+		}
+		else
+		{
+			/* TODO Handle empty centers properly */
+			for (int k = 0; k < dimensions; k++)
+				vec->x[k] = RandomDouble();
+		}
+	}
+
+	/* Set new centers if different from agg centers */
+	if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		for (int j = 0; j < numCenters; j++)
+		{
+			Vector	   *aggCenter = (Vector *) VectorArrayGet(aggCenters, j);
+			HalfVector *newCenter = (HalfVector *) VectorArrayGet(newCenters, j);
+
+			for (int k = 0; k < dimensions; k++)
+				newCenter->x[k] = Float4ToHalfUnchecked(aggCenter->x[k]);
+		}
+	}
+
+	/* Normalize if needed */
+	if (normprocinfo != NULL)
+	{
+		for (int j = 0; j < numCenters; j++)
+		{
+			Datum		newCenter = PointerGetDatum(VectorArrayGet(newCenters, j));
+
+			ApplyNorm(normprocinfo, collation, newCenter, type);
+		}
+	}
+}
+
 /*
  * Use Elkan for performance. This requires distance function to satisfy triangle inequality.
  *
@@ -181,19 +330,16 @@ 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, IvfflatType type)
 {
 	FmgrInfo   *procinfo;
 	FmgrInfo   *normprocinfo;
 	Oid			collation;
-	Vector	   *vec;
-	Vector	   *newCenter;
-	int64		j;
-	int64		k;
 	int			dimensions = centers->dim;
 	int			numCenters = centers->maxlen;
 	int			numSamples = samples->length;
 	VectorArray newCenters;
+	VectorArray aggCenters;
 	int		   *centerCounts;
 	int		   *closestCenters;
 	float	   *lowerBound;
@@ -201,11 +347,14 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	float	   *s;
 	float	   *halfcdist;
 	float	   *newcdist;
+	MemoryContext kmeansCtx;
+	MemoryContext oldCtx;
 
 	/* Calculate allocation sizes */
-	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->dim);
-	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->dim);
-	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, dimensions);
+	Size		samplesSize = VECTOR_ARRAY_SIZE(samples->maxlen, samples->itemsize);
+	Size		centersSize = VECTOR_ARRAY_SIZE(centers->maxlen, centers->itemsize);
+	Size		newCentersSize = VECTOR_ARRAY_SIZE(numCenters, centers->itemsize);
+	Size		aggCentersSize = type == IVFFLAT_TYPE_VECTOR ? 0 : VECTOR_ARRAY_SIZE(numCenters, VECTOR_SIZE(dimensions));
 	Size		centerCountsSize = sizeof(int) * numCenters;
 	Size		closestCentersSize = sizeof(int) * numSamples;
 	Size		lowerBoundSize = sizeof(float) * numSamples * numCenters;
@@ -215,7 +364,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	Size		newcdistSize = sizeof(float) * numCenters;
 
 	/* Calculate total size */
-	Size		totalSize = samplesSize + centersSize + newCentersSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
+	Size		totalSize = samplesSize + centersSize + newCentersSize + aggCentersSize + centerCountsSize + closestCentersSize + lowerBoundSize + upperBoundSize + sSize + halfcdistSize + newcdistSize;
 
 	/* Check memory requirements */
 	/* Add one to error message to ceil */
@@ -234,6 +383,12 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	normprocinfo = IvfflatOptionalProcInfo(index, IVFFLAT_KMEANS_NORM_PROC);
 	collation = index->rd_indcollation[0];
 
+	/* Use memory context */
+	kmeansCtx = AllocSetContextCreate(CurrentMemoryContext,
+									  "Ivfflat kmeans temporary context",
+									  ALLOCSET_DEFAULT_SIZES);
+	oldCtx = MemoryContextSwitchTo(kmeansCtx);
+
 	/* Allocate space */
 	/* Use float instead of double to save memory */
 	centerCounts = palloc(centerCountsSize);
@@ -244,29 +399,50 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 	halfcdist = palloc_extended(halfcdistSize, MCXT_ALLOC_HUGE);
 	newcdist = palloc(newcdistSize);
 
-	newCenters = VectorArrayInit(numCenters, dimensions);
-	for (j = 0; j < numCenters; j++)
+	aggCenters = VectorArrayInit(numCenters, dimensions, VECTOR_SIZE(dimensions));
+	for (int j = 0; j < numCenters; j++)
 	{
-		vec = VectorArrayGet(newCenters, j);
+		Vector	   *vec = (Vector *) VectorArrayGet(aggCenters, j);
+
 		SET_VARSIZE(vec, VECTOR_SIZE(dimensions));
 		vec->dim = dimensions;
 	}
 
+	if (type == IVFFLAT_TYPE_VECTOR)
+	{
+		/* Use same centers to save memory */
+		newCenters = aggCenters;
+	}
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+	{
+		newCenters = VectorArrayInit(numCenters, dimensions, centers->itemsize);
+
+		for (int j = 0; j < numCenters; j++)
+		{
+			HalfVector *vec = (HalfVector *) VectorArrayGet(newCenters, j);
+
+			SET_VARSIZE(vec, HALFVEC_SIZE(dimensions));
+			vec->dim = dimensions;
+		}
+	}
+	else
+		elog(ERROR, "Unsupported type");
+
 #ifdef IVFFLAT_MEMORY
-	ShowMemoryUsage(totalSize);
+	ShowMemoryUsage(oldCtx, totalSize);
 #endif
 
 	/* Pick initial centers */
 	InitCenters(index, samples, centers, lowerBound);
 
 	/* Assign each x to its closest initial center c(x) = argmin d(x,c) */
-	for (j = 0; j < numSamples; j++)
+	for (int64 j = 0; j < numSamples; j++)
 	{
 		float		minDistance = FLT_MAX;
 		int			closestCenter = 0;
 
 		/* Find closest center */
-		for (k = 0; k < numCenters; k++)
+		for (int64 k = 0; k < numCenters; k++)
 		{
 			/* TODO Use Lemma 1 in k-means++ initialization */
 			float		distance = lowerBound[j * numCenters + k];
@@ -292,13 +468,13 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		CHECK_FOR_INTERRUPTS();
 
 		/* Step 1: For all centers, compute distance */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
-			vec = VectorArrayGet(centers, j);
+			Datum		vec = PointerGetDatum(VectorArrayGet(centers, j));
 
-			for (k = j + 1; k < numCenters; k++)
+			for (int64 k = j + 1; k < numCenters; k++)
 			{
-				float		distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
+				float		distance = 0.5 * DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, k))));
 
 				halfcdist[j * numCenters + k] = distance;
 				halfcdist[k * numCenters + j] = distance;
@@ -306,11 +482,11 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		}
 
 		/* For all centers c, compute s(c) */
-		for (j = 0; j < numCenters; j++)
+		for (int64 j = 0; j < numCenters; j++)
 		{
 			float		minDistance = FLT_MAX;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
 				float		distance;
 
@@ -327,7 +503,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 		rjreset = iteration != 0;
 
-		for (j = 0; j < numSamples; j++)
+		for (int64 j = 0; j < numSamples; j++)
 		{
 			bool		rj;
 
@@ -337,8 +513,9 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 			rj = rjreset;
 
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
+				Datum		vec;
 				float		dxcx;
 
 				/* Step 3: For all remaining points x and centers c */
@@ -351,12 +528,12 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 				if (upperBound[j] <= halfcdist[closestCenters[j] * numCenters + k])
 					continue;
 
-				vec = VectorArrayGet(samples, j);
+				vec = PointerGetDatum(VectorArrayGet(samples, j));
 
 				/* Step 3a */
 				if (rj)
 				{
-					dxcx = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, closestCenters[j]))));
+					dxcx = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, closestCenters[j]))));
 
 					/* d(x,c(x)) computed, which is a form of d(x,c) */
 					lowerBound[j * numCenters + closestCenters[j]] = dxcx;
@@ -370,7 +547,7 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 				/* Step 3b */
 				if (dxcx > lowerBound[j * numCenters + k] || dxcx > halfcdist[closestCenters[j] * numCenters + k])
 				{
-					float		dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(vec), PointerGetDatum(VectorArrayGet(centers, k))));
+					float		dxc = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, vec, PointerGetDatum(VectorArrayGet(centers, k))));
 
 					/* d(x,c) calculated */
 					lowerBound[j * numCenters + k] = dxc;
@@ -389,66 +566,15 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 		}
 
 		/* Step 4: For each center c, let m(c) be mean of all points assigned */
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-			for (k = 0; k < dimensions; k++)
-				vec->x[k] = 0.0;
-
-			centerCounts[j] = 0;
-		}
-
-		for (j = 0; j < numSamples; j++)
-		{
-			int			closestCenter;
-
-			vec = VectorArrayGet(samples, j);
-			closestCenter = closestCenters[j];
-
-			/* Increment sum and count of closest center */
-			newCenter = VectorArrayGet(newCenters, closestCenter);
-			for (k = 0; k < dimensions; k++)
-				newCenter->x[k] += vec->x[k];
-
-			centerCounts[closestCenter] += 1;
-		}
-
-		for (j = 0; j < numCenters; j++)
-		{
-			vec = VectorArrayGet(newCenters, j);
-
-			if (centerCounts[j] > 0)
-			{
-				/* Double avoids overflow, but requires more memory */
-				/* TODO Update bounds */
-				for (k = 0; k < dimensions; k++)
-				{
-					if (isinf(vec->x[k]))
-						vec->x[k] = vec->x[k] > 0 ? FLT_MAX : -FLT_MAX;
-				}
-
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] /= centerCounts[j];
-			}
-			else
-			{
-				/* TODO Handle empty centers properly */
-				for (k = 0; k < dimensions; k++)
-					vec->x[k] = RandomDouble();
-			}
-
-			/* Normalize if needed */
-			if (normprocinfo != NULL)
-				ApplyNorm(normprocinfo, collation, vec);
-		}
+		ComputeNewCenters(samples, aggCenters, newCenters, centerCounts, closestCenters, normprocinfo, collation, type);
 
 		/* Step 5 */
-		for (j = 0; j < numCenters; j++)
+		for (int j = 0; j < numCenters; j++)
 			newcdist[j] = DatumGetFloat8(FunctionCall2Coll(procinfo, collation, PointerGetDatum(VectorArrayGet(centers, j)), PointerGetDatum(VectorArrayGet(newCenters, j))));
 
-		for (j = 0; j < numSamples; j++)
+		for (int64 j = 0; j < numSamples; j++)
 		{
-			for (k = 0; k < numCenters; k++)
+			for (int64 k = 0; k < numCenters; k++)
 			{
 				float		distance = lowerBound[j * numCenters + k] - newcdist[k];
 
@@ -461,32 +587,26 @@ ElkanKmeans(Relation index, VectorArray samples, VectorArray centers)
 
 		/* Step 6 */
 		/* We reset r(x) before Step 3 in the next iteration */
-		for (j = 0; j < numSamples; j++)
+		for (int j = 0; j < numSamples; j++)
 			upperBound[j] += newcdist[closestCenters[j]];
 
 		/* Step 7 */
-		for (j = 0; j < numCenters; j++)
+		for (int j = 0; j < numCenters; j++)
 			VectorArraySet(centers, j, VectorArrayGet(newCenters, j));
 
 		if (changes == 0 && iteration != 0)
 			break;
 	}
 
-	VectorArrayFree(newCenters);
-	pfree(centerCounts);
-	pfree(closestCenters);
-	pfree(lowerBound);
-	pfree(upperBound);
-	pfree(s);
-	pfree(halfcdist);
-	pfree(newcdist);
+	MemoryContextSwitchTo(oldCtx);
+	MemoryContextDelete(kmeansCtx);
 }
 
 /*
  * Detect issues with centers
  */
 static void
-CheckCenters(Relation index, VectorArray centers)
+CheckCenters(Relation index, VectorArray centers, IvfflatType type)
 {
 	FmgrInfo   *normprocinfo;
 
@@ -496,24 +616,48 @@ CheckCenters(Relation index, VectorArray centers)
 	/* Ensure no NaN or infinite values */
 	for (int i = 0; i < centers->length; i++)
 	{
-		Vector	   *vec = VectorArrayGet(centers, i);
-
-		for (int j = 0; j < vec->dim; j++)
+		if (type == IVFFLAT_TYPE_VECTOR)
 		{
-			if (isnan(vec->x[j]))
-				elog(ERROR, "NaN detected. Please report a bug.");
+			Vector	   *vec = (Vector *) VectorArrayGet(centers, i);
 
-			if (isinf(vec->x[j]))
-				elog(ERROR, "Infinite value detected. Please report a bug.");
+			for (int j = 0; j < vec->dim; j++)
+			{
+				if (isnan(vec->x[j]))
+					elog(ERROR, "NaN detected. Please report a bug.");
+
+				if (isinf(vec->x[j]))
+					elog(ERROR, "Infinite value detected. Please report a bug.");
+			}
 		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *vec = (HalfVector *) VectorArrayGet(centers, i);
+
+			for (int j = 0; j < vec->dim; j++)
+			{
+				if (HalfIsNan(vec->x[j]))
+					elog(ERROR, "NaN detected. Please report a bug.");
+
+				if (HalfIsInf(vec->x[j]))
+					elog(ERROR, "Infinite value detected. Please report a bug.");
+			}
+		}
+		else
+			elog(ERROR, "Unsupported type");
 	}
 
 	/* Ensure no duplicate centers */
 	/* Fine to sort in-place */
-	qsort(centers->items, centers->length, VECTOR_SIZE(centers->dim), CompareVectors);
+	if (type == IVFFLAT_TYPE_VECTOR)
+		qsort(centers->items, centers->length, centers->itemsize, CompareVectors);
+	else if (type == IVFFLAT_TYPE_HALFVEC)
+		qsort(centers->items, centers->length, centers->itemsize, CompareHalfVectors);
+	else
+		elog(ERROR, "Unsupported type");
+
 	for (int i = 1; i < centers->length; i++)
 	{
-		if (CompareVectors(VectorArrayGet(centers, i), VectorArrayGet(centers, i - 1)) == 0)
+		if (datumIsEqual(PointerGetDatum(VectorArrayGet(centers, i)), PointerGetDatum(VectorArrayGet(centers, i - 1)), false, -1))
 			elog(ERROR, "Duplicate centers detected. Please report a bug.");
 	}
 
@@ -539,12 +683,12 @@ CheckCenters(Relation index, VectorArray centers)
  * We use spherical k-means for inner product and cosine
  */
 void
-IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers)
+IvfflatKmeans(Relation index, VectorArray samples, VectorArray centers, IvfflatType type)
 {
 	if (samples->length <= centers->maxlen)
-		QuickCenters(index, samples, centers);
+		QuickCenters(index, samples, centers, type);
 	else
-		ElkanKmeans(index, samples, centers);
+		ElkanKmeans(index, samples, centers, type);
 
-	CheckCenters(index, centers);
+	CheckCenters(index, centers, type);
 }

src/ivfscan.c

@@ -5,6 +5,7 @@
 #include "access/relscan.h"
 #include "catalog/pg_operator_d.h"
 #include "catalog/pg_type_d.h"
+#include "halfvec.h"
 #include "lib/pairingheap.h"
 #include "ivfflat.h"
 #include "miscadmin.h"
@@ -177,6 +178,42 @@ GetScanItems(IndexScanDesc scan, Datum value)
 	tuplesort_performsort(so->sortstate);
 }
 
+/*
+ * Get scan value
+ */
+static Datum
+GetScanValue(IndexScanDesc scan)
+{
+	IvfflatScanOpaque so = (IvfflatScanOpaque) scan->opaque;
+	Datum		value;
+
+	if (scan->orderByData->sk_flags & SK_ISNULL)
+	{
+		IvfflatType type = IvfflatGetType(scan->indexRelation);
+
+		if (type == IVFFLAT_TYPE_VECTOR)
+			value = PointerGetDatum(InitVector(so->dimensions));
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+			value = PointerGetDatum(InitHalfVector(so->dimensions));
+		else
+			elog(ERROR, "Unsupported type");
+	}
+	else
+	{
+		value = scan->orderByData->sk_argument;
+
+		/* Value should not be compressed or toasted */
+		Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
+		Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
+
+		/* Fine if normalization fails */
+		if (so->normprocinfo != NULL)
+			IvfflatNormValue(so->normprocinfo, so->collation, &value, IvfflatGetType(scan->indexRelation));
+	}
+
+	return value;
+}
+
 /*
  * Prepare for an index scan
  */
@@ -268,7 +305,6 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 	if (so->first)
 	{
 		Datum		value;
-		IvfflatType type = IvfflatGetType(scan->indexRelation);
 
 		/* Count index scan for stats */
 		pgstat_count_index_scan(scan->indexRelation);
@@ -282,26 +318,7 @@ ivfflatgettuple(IndexScanDesc scan, ScanDirection dir)
 		if (!IsMVCCSnapshot(scan->xs_snapshot))
 			elog(ERROR, "non-MVCC snapshots are not supported with ivfflat");
 
-		if (scan->orderByData->sk_flags & SK_ISNULL)
-		{
-			if (type == IVFFLAT_TYPE_VECTOR)
-				value = PointerGetDatum(InitVector(so->dimensions));
-			else
-				elog(ERROR, "Unsupported type");
-		}
-		else
-		{
-			value = scan->orderByData->sk_argument;
-
-			/* Value should not be compressed or toasted */
-			Assert(!VARATT_IS_COMPRESSED(DatumGetPointer(value)));
-			Assert(!VARATT_IS_EXTENDED(DatumGetPointer(value)));
-
-			/* Fine if normalization fails */
-			if (so->normprocinfo != NULL)
-				IvfflatNormValue(so->normprocinfo, so->collation, &value, type);
-		}
-
+		value = GetScanValue(scan);
 		IvfflatBench("GetScanLists", GetScanLists(scan, value));
 		IvfflatBench("GetScanItems", GetScanItems(scan, value));
 		so->first = false;

src/ivfutils.c

@@ -1,22 +1,27 @@
 #include "postgres.h"
 
 #include "access/generic_xlog.h"
+#include "catalog/pg_type.h"
+#include "halfutils.h"
+#include "halfvec.h"
 #include "ivfflat.h"
 #include "storage/bufmgr.h"
 #include "vector.h"
+#include "utils/syscache.h"
 
 /*
  * Allocate a vector array
  */
 VectorArray
-VectorArrayInit(int maxlen, int dimensions)
+VectorArrayInit(int maxlen, int dimensions, Size itemsize)
 {
 	VectorArray res = palloc(sizeof(VectorArrayData));
 
 	res->length = 0;
 	res->maxlen = maxlen;
 	res->dim = dimensions;
-	res->items = palloc_extended(maxlen * VECTOR_SIZE(dimensions), MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
+	res->itemsize = itemsize;
+	res->items = palloc_extended(maxlen * itemsize, MCXT_ALLOC_ZERO | MCXT_ALLOC_HUGE);
 	return res;
 }
 
@@ -30,16 +35,6 @@ VectorArrayFree(VectorArray arr)
 	pfree(arr);
 }
 
-/*
- * Print vector array - useful for debugging
- */
-void
-PrintVectorArray(char *msg, VectorArray arr)
-{
-	for (int i = 0; i < arr->length; i++)
-		PrintVector(msg, VectorArrayGet(arr, i));
-}
-
 /*
  * Get the number of lists in the index
  */
@@ -72,7 +67,29 @@ IvfflatOptionalProcInfo(Relation index, uint16 procnum)
 IvfflatType
 IvfflatGetType(Relation index)
 {
-	return IVFFLAT_TYPE_VECTOR;
+	Oid			typid = TupleDescAttr(index->rd_att, 0)->atttypid;
+	HeapTuple	tuple;
+	Form_pg_type type;
+	IvfflatType result;
+
+	tuple = SearchSysCache1(TYPEOID, ObjectIdGetDatum(typid));
+	if (!HeapTupleIsValid(tuple))
+		elog(ERROR, "cache lookup failed for type %u", typid);
+
+	type = (Form_pg_type) GETSTRUCT(tuple);
+	if (strcmp(NameStr(type->typname), "vector") == 0)
+		result = IVFFLAT_TYPE_VECTOR;
+	else if (strcmp(NameStr(type->typname), "halfvec") == 0)
+		result = IVFFLAT_TYPE_HALFVEC;
+	else
+	{
+		ReleaseSysCache(tuple);
+		elog(ERROR, "type not supported for ivfflat index");
+	}
+
+	ReleaseSysCache(tuple);
+
+	return result;
 }
 
 /*
@@ -100,6 +117,16 @@ IvfflatNormValue(FmgrInfo *procinfo, Oid collation, Datum *value, IvfflatType ty
 
 			*value = PointerGetDatum(result);
 		}
+		else if (type == IVFFLAT_TYPE_HALFVEC)
+		{
+			HalfVector *v = DatumGetHalfVector(*value);
+			HalfVector *result = InitHalfVector(v->dim);
+
+			for (int i = 0; i < v->dim; i++)
+				result->x[i] = Float4ToHalfUnchecked(HalfToFloat4(v->x[i]) / norm);
+
+			*value = PointerGetDatum(result);
+		}
 		else
 			elog(ERROR, "Unsupported type");
 

src/sparsevec.c

@@ -18,35 +18,86 @@
 #include "utils/builtins.h"
 #endif
 
+/*
+ * Ensure same dimensions
+ */
+static inline void
+CheckDims(SparseVector * a, SparseVector * b)
+{
+	if (a->dim != b->dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("different sparsevec dimensions %d and %d", a->dim, b->dim)));
+}
+
+/*
+ * Ensure expected dimensions
+ */
+static inline void
+CheckExpectedDim(int32 typmod, int dim)
+{
+	if (typmod != -1 && typmod != dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("expected %d dimensions, not %d", typmod, dim)));
+}
+
+/*
+ * Ensure valid dimensions
+ */
+static inline void
+CheckDim(int dim)
+{
+	if (dim < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("sparsevec must have at least 1 dimension")));
+
+	if (dim > SPARSEVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("sparsevec cannot have more than %d dimensions", SPARSEVEC_MAX_DIM)));
+}
+
 /*
  * Ensure valid nnz
  */
 static inline void
-CheckNnz(int nnz)
+CheckNnz(int nnz, int dim)
 {
 	if (nnz < 0)
 		ereport(ERROR,
 				(errcode(ERRCODE_DATA_EXCEPTION),
-				 errmsg("sparsevec must have at least one element")));
+				 errmsg("sparsevec cannot have negative number of elements")));
 
 	if (nnz > SPARSEVEC_MAX_NNZ)
 		ereport(ERROR,
 				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
-				 errmsg("sparsevec cannot have more elements than non-zero elements")));
+				 errmsg("sparsevec cannot have more than %d non-zero elements", SPARSEVEC_MAX_NNZ)));
+
+	if (nnz > dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_PROGRAM_LIMIT_EXCEEDED),
+				 errmsg("sparsevec cannot have more elements than dimensions")));
 }
 
 /*
  * Ensure valid index
  */
 static inline void
-CheckIndex(int32 *indices, int i)
+CheckIndex(int32 *indices, int i, int dim)
 {
 	int32		index = indices[i];
 
-	if (index < 0)
+	if (index < 1)
 		ereport(ERROR,
 				(errcode(ERRCODE_DATA_EXCEPTION),
-				 errmsg("index must not be negative")));
+				 errmsg("index must be greater than zero")));
+
+	if (index > dim)
+		ereport(ERROR,
+				(errcode(ERRCODE_DATA_EXCEPTION),
+				 errmsg("index must be less than or equal to dimensions")));
 
 	if (i > 0)
 	{
@@ -83,7 +134,7 @@ CheckElement(float value)
  * Allocate and initialize a new sparse vector
  */
 SparseVector *
-InitSparseVector(int nnz)
+InitSparseVector(int dim, int nnz)
 {
 	SparseVector *result;
 	int			size;
@@ -91,6 +142,7 @@ InitSparseVector(int nnz)
 	size = SPARSEVEC_SIZE(nnz);
 	result = (SparseVector *) palloc0(size);
 	SET_VARSIZE(result, size);
+	result->dim = dim;
 	result->nnz = nnz;
 
 	return result;
@@ -120,19 +172,18 @@ Datum
 sparsevec_in(PG_FUNCTION_ARGS)
 {
 	char	   *lit = PG_GETARG_CSTRING(0);
-	char	   *pt;
+	int32		typmod = PG_GETARG_INT32(2);
+	int			dim;
+	char	   *pt = lit;
 	char	   *stringEnd;
 	SparseVector *result;
 	float	   *rvalues;
-	char	   *litcopy = pstrdup(lit);
-	char	   *str = litcopy;
 	int32	   *indices;
 	float	   *values;
 	int			maxNnz;
 	int			nnz = 0;
 
 	maxNnz = 1;
-	pt = str;
 	while (*pt != '\0')
 	{
 		if (*pt == ',')
@@ -149,131 +200,167 @@ sparsevec_in(PG_FUNCTION_ARGS)
 	indices = palloc(maxNnz * sizeof(int32));
 	values = palloc(maxNnz * sizeof(float));
 
-	while (sparsevec_isspace(*str))
-		str++;
+	pt = lit;
 
-	if (*str != '{')
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '{')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed sparsevec literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
 				 errdetail("Vector contents must start with \"{\".")));
 
-	str++;
-	pt = strtok(str, ",");
-	stringEnd = pt;
+	pt++;
 
-	while (pt != NULL && *stringEnd != '}')
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt == '}')
+		pt++;
+	else
 	{
-		long		index;
-		float		value;
+		for (;;)
+		{
+			long		index;
+			float		value;
 
-		/* TODO Better error */
-		if (nnz == maxNnz)
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("ran out of buffer: \"%s\"", lit)));
+			/* TODO Better error */
+			if (nnz == maxNnz)
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("ran out of buffer: \"%s\"", lit)));
+
+			while (sparsevec_isspace(*pt))
+				pt++;
+
+			/* Check for empty string like float4in */
+			if (*pt == '\0')
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+
+			/* Use similar logic as int2vectorin */
+			errno = 0;
+			index = strtol(pt, &stringEnd, 10);
+
+			if (stringEnd == pt)
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+
+			if (errno == ERANGE || index < 1 || index > INT_MAX)
+				ereport(ERROR,
+						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+						 errmsg("index \"%ld\" is out of range for type sparsevec", index)));
+
+			pt = stringEnd;
+
+			while (sparsevec_isspace(*pt))
+				pt++;
+
+			if (*pt != ':')
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
 
-		while (sparsevec_isspace(*pt))
 			pt++;
 
-		/* Check for empty string like float4in */
-		if (*pt == '\0')
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+			while (sparsevec_isspace(*pt))
+				pt++;
 
-		/* Use similar logic as int2vectorin */
-		errno = 0;
-		index = strtol(pt, &stringEnd, 10);
+			errno = 0;
 
-		if (stringEnd == pt)
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+			/* Use strtof like float4in to avoid a double-rounding problem */
+			/* Postgres sets LC_NUMERIC to C on startup */
+			value = strtof(pt, &stringEnd);
 
-		if (errno == ERANGE || index < 0 || index > INT_MAX)
-			ereport(ERROR,
-					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-					 errmsg("index \"%ld\" is out of range for type sparsevec", index)));
+			if (stringEnd == pt)
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
 
-		if (stringEnd == pt)
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+			/* Check for range error like float4in */
+			if (errno == ERANGE && (value == 0 || isinf(value)))
+				ereport(ERROR,
+						(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
+						 errmsg("\"%s\" is out of range for type sparsevec", pnstrdup(pt, stringEnd - pt))));
 
-		while (sparsevec_isspace(*stringEnd))
-			stringEnd++;
+			CheckElement(value);
 
-		if (*stringEnd != ':')
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
+			/* Do not store zero values */
+			if (value != 0)
+			{
+				indices[nnz] = index;
+				values[nnz] = value;
+				nnz++;
+			}
 
-		stringEnd++;
+			pt = stringEnd;
 
-		while (sparsevec_isspace(*stringEnd))
-			stringEnd++;
+			while (sparsevec_isspace(*pt))
+				pt++;
 
-		errno = 0;
-		pt = stringEnd;
-		value = strtof(pt, &stringEnd);
-
-		if (stringEnd == pt)
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
-
-		/* Check for range error like float4in */
-		if (errno == ERANGE && (value == 0 || isinf(value)))
-			ereport(ERROR,
-					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-					 errmsg("\"%s\" is out of range for type sparsevec", pt)));
-
-		/* TODO Decide whether to store zero values */
-		if (value != 0)
-		{
-			indices[nnz] = index;
-			values[nnz] = value;
-			nnz++;
+			if (*pt == ',')
+				pt++;
+			else if (*pt == '}')
+			{
+				pt++;
+				break;
+			}
+			else
+				ereport(ERROR,
+						(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+						 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
 		}
-
-		if (*stringEnd != '\0' && *stringEnd != '}')
-			ereport(ERROR,
-					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-					 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
-
-		pt = strtok(NULL, ",");
 	}
 
-	if (stringEnd == NULL || *stringEnd != '}')
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '/')
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed sparsevec literal: \"%s\"", lit),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
 				 errdetail("Unexpected end of input.")));
 
-	stringEnd++;
+	pt++;
 
-	/* Only whitespace is allowed after the closing brace */
-	while (sparsevec_isspace(*stringEnd))
-		stringEnd++;
+	while (sparsevec_isspace(*pt))
+		pt++;
 
-	if (*stringEnd != '\0')
+	/* Use similar logic as int2vectorin */
+	errno = 0;
+	dim = strtol(pt, &stringEnd, 10);
+
+	if (stringEnd == pt)
 		ereport(ERROR,
 				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
-				 errmsg("malformed sparsevec literal: \"%s\"", lit),
-				 errdetail("Junk after closing right brace.")));
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit)));
 
-	pfree(litcopy);
+	pt = stringEnd;
 
-	result = InitSparseVector(nnz);
+	/* Only whitespace is allowed after the closing brace */
+	while (sparsevec_isspace(*pt))
+		pt++;
+
+	if (*pt != '\0')
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
+				 errmsg("invalid input syntax for type sparsevec: \"%s\"", lit),
+				 errdetail("Junk after closing.")));
+
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
+	result = InitSparseVector(dim, nnz);
 	rvalues = SPARSEVEC_VALUES(result);
 	for (int i = 0; i < nnz; i++)
 	{
 		result->indices[i] = indices[i];
 		rvalues[i] = values[i];
 
-		CheckIndex(result->indices, i);
-		CheckElement(rvalues[i]);
+		CheckIndex(result->indices, i, dim);
 	}
 
 	PG_RETURN_POINTER(result);
@@ -317,9 +404,11 @@ sparsevec_out(PG_FUNCTION_ARGS)
 	 *
 	 * nnz - 1 bytes for ,
 	 *
-	 * 3 bytes for {, }, and \0
+	 * 10 bytes for dimensions
+	 *
+	 * 4 bytes for {, }, /, and \0
 	 */
-	buf = (char *) palloc((11 + FLOAT_SHORTEST_DECIMAL_LEN) * sparsevec->nnz + 2);
+	buf = (char *) palloc((11 + FLOAT_SHORTEST_DECIMAL_LEN) * sparsevec->nnz + 13);
 	ptr = buf;
 
 	AppendChar(ptr, '{');
@@ -335,12 +424,45 @@ sparsevec_out(PG_FUNCTION_ARGS)
 	}
 
 	AppendChar(ptr, '}');
+	AppendChar(ptr, '/');
+	AppendInt(ptr, sparsevec->dim);
 	*ptr = '\0';
 
 	PG_FREE_IF_COPY(sparsevec, 0);
 	PG_RETURN_CSTRING(buf);
 }
 
+/*
+ * Convert type modifier
+ */
+PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec_typmod_in);
+Datum
+sparsevec_typmod_in(PG_FUNCTION_ARGS)
+{
+	ArrayType  *ta = PG_GETARG_ARRAYTYPE_P(0);
+	int32	   *tl;
+	int			n;
+
+	tl = ArrayGetIntegerTypmods(ta, &n);
+
+	if (n != 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("invalid type modifier")));
+
+	if (*tl < 1)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type sparsevec must be at least 1")));
+
+	if (*tl > SPARSEVEC_MAX_DIM)
+		ereport(ERROR,
+				(errcode(ERRCODE_INVALID_PARAMETER_VALUE),
+				 errmsg("dimensions for type sparsevec cannot exceed %d", SPARSEVEC_MAX_DIM)));
+
+	PG_RETURN_INT32(*tl);
+}
+
 /*
  * Convert external binary representation to internal representation
  */
@@ -349,30 +471,33 @@ Datum
 sparsevec_recv(PG_FUNCTION_ARGS)
 {
 	StringInfo	buf = (StringInfo) PG_GETARG_POINTER(0);
+	int32		typmod = PG_GETARG_INT32(2);
 	SparseVector *result;
+	int32		dim;
 	int32		nnz;
 	int32		unused;
-	int32		unused2;
 	float	   *values;
 
+	dim = pq_getmsgint(buf, sizeof(int32));
 	nnz = pq_getmsgint(buf, sizeof(int32));
 	unused = pq_getmsgint(buf, sizeof(int32));
-	unused2 = pq_getmsgint(buf, sizeof(int32));
 
-	CheckNnz(nnz);
+	CheckDim(dim);
+	CheckNnz(nnz, dim);
+	CheckExpectedDim(typmod, dim);
 
-	if (unused != 0 || unused2 != 0)
+	if (unused != 0)
 		ereport(ERROR,
 				(errcode(ERRCODE_DATA_EXCEPTION),
 				 errmsg("expected unused to be 0, not %d", unused)));
 
-	result = InitSparseVector(nnz);
+	result = InitSparseVector(dim, nnz);
 	values = SPARSEVEC_VALUES(result);
 
 	for (int i = 0; i < nnz; i++)
 	{
 		result->indices[i] = pq_getmsgint(buf, sizeof(int32));
-		CheckIndex(result->indices, i);
+		CheckIndex(result->indices, i, dim);
 	}
 
 	for (int i = 0; i < nnz; i++)
@@ -396,9 +521,9 @@ sparsevec_send(PG_FUNCTION_ARGS)
 	StringInfoData buf;
 
 	pq_begintypsend(&buf);
+	pq_sendint(&buf, svec->dim, sizeof(int32));
 	pq_sendint(&buf, svec->nnz, sizeof(int32));
 	pq_sendint(&buf, svec->unused, sizeof(int32));
-	pq_sendint(&buf, svec->unused2, sizeof(int32));
 	for (int i = 0; i < svec->nnz; i++)
 		pq_sendint(&buf, svec->indices[i], sizeof(int32));
 	for (int i = 0; i < svec->nnz; i++)
@@ -409,12 +534,16 @@ sparsevec_send(PG_FUNCTION_ARGS)
 
 /*
  * Convert sparse vector to sparse vector
+ * This is needed to check the type modifier
  */
 PGDLLEXPORT PG_FUNCTION_INFO_V1(sparsevec);
 Datum
 sparsevec(PG_FUNCTION_ARGS)
 {
 	SparseVector *svec = PG_GETARG_SPARSEVEC_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
+
+	CheckExpectedDim(typmod, svec->dim);
 
 	PG_RETURN_POINTER(svec);
 }
@@ -427,20 +556,23 @@ Datum
 vector_to_sparsevec(PG_FUNCTION_ARGS)
 {
 	Vector	   *vec = PG_GETARG_VECTOR_P(0);
+	int32		typmod = PG_GETARG_INT32(1);
 	SparseVector *result;
 	int			dim = vec->dim;
 	int			nnz = 0;
 	float	   *values;
 	int			j = 0;
 
+	CheckDim(dim);
+	CheckExpectedDim(typmod, dim);
+
 	for (int i = 0; i < dim; i++)
 	{
 		if (vec->x[i] != 0)
 			nnz++;
 	}
 
-	CheckNnz(nnz);
-	result = InitSparseVector(nnz);
+	result = InitSparseVector(dim, nnz);
 	values = SPARSEVEC_VALUES(result);
 	for (int i = 0; i < dim; i++)
 	{
@@ -450,7 +582,7 @@ vector_to_sparsevec(PG_FUNCTION_ARGS)
 			if (j == nnz)
 				elog(ERROR, "safety check failed");
 
-			result->indices[j] = i;
+			result->indices[j] = i + 1;
 			values[j] = vec->x[i];
 			j++;
 		}
@@ -460,10 +592,10 @@ vector_to_sparsevec(PG_FUNCTION_ARGS)
 }
 
 /*
- *  Get the L2 squared distance between sparse vectors
+ * Get the L2 squared distance between sparse vectors
  */
 static double
-l2_distance_squared_internal(SparseVector * a, SparseVector * b)
+SparsevecL2SquaredDistance(SparseVector * a, SparseVector * b)
 {
 	float	   *ax = SPARSEVEC_VALUES(a);
 	float	   *bx = SPARSEVEC_VALUES(b);
@@ -517,7 +649,9 @@ sparsevec_l2_distance(PG_FUNCTION_ARGS)
 	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
 	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
 
-	PG_RETURN_FLOAT8(sqrt(l2_distance_squared_internal(a, b)));
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(sqrt(SparsevecL2SquaredDistance(a, b)));
 }
 
 /*
@@ -531,14 +665,16 @@ sparsevec_l2_squared_distance(PG_FUNCTION_ARGS)
 	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
 	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
 
-	PG_RETURN_FLOAT8(l2_distance_squared_internal(a, b));
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(SparsevecL2SquaredDistance(a, b));
 }
 
 /*
  * Get the inner product of two sparse vectors
  */
 static double
-inner_product_internal(SparseVector * a, SparseVector * b)
+SparsevecInnerProduct(SparseVector * a, SparseVector * b)
 {
 	float	   *ax = SPARSEVEC_VALUES(a);
 	float	   *bx = SPARSEVEC_VALUES(b);
@@ -580,7 +716,9 @@ sparsevec_inner_product(PG_FUNCTION_ARGS)
 	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
 	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
 
-	PG_RETURN_FLOAT8(inner_product_internal(a, b));
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(SparsevecInnerProduct(a, b));
 }
 
 /*
@@ -593,7 +731,9 @@ sparsevec_negative_inner_product(PG_FUNCTION_ARGS)
 	SparseVector *a = PG_GETARG_SPARSEVEC_P(0);
 	SparseVector *b = PG_GETARG_SPARSEVEC_P(1);
 
-	PG_RETURN_FLOAT8(-inner_product_internal(a, b));
+	CheckDims(a, b);
+
+	PG_RETURN_FLOAT8(-SparsevecInnerProduct(a, b));
 }
 
 /*
@@ -611,7 +751,9 @@ sparsevec_cosine_distance(PG_FUNCTION_ARGS)
 	float		normb = 0.0;
 	double		similarity;
 
-	similarity = inner_product_internal(a, b);
+	CheckDims(a, b);
+
+	similarity = SparsevecInnerProduct(a, b);
 
 	/* Auto-vectorized */
 	for (int i = 0; i < a->nnz; i++)

src/sparsevec.h

@@ -1,7 +1,8 @@
 #ifndef SPARSEVEC_H
 #define SPARSEVEC_H
 
-#define SPARSEVEC_MAX_NNZ 100000
+#define SPARSEVEC_MAX_DIM 100000
+#define SPARSEVEC_MAX_NNZ 16000
 
 /* Ensure values are aligned */
 #define SPARSEVEC_SIZE(_nnz)		(offsetof(SparseVector, indices) + MAXALIGN((_nnz) * sizeof(int32)) + (_nnz * sizeof(float)))
@@ -13,12 +14,12 @@
 typedef struct SparseVector
 {
 	int32		vl_len_;		/* varlena header (do not touch directly!) */
+	int32		dim;			/* number of dimensions */
 	int32		nnz;
 	int32		unused;
-	int32		unused2;
 	int32		indices[FLEXIBLE_ARRAY_MEMBER];
 }			SparseVector;
 
-SparseVector *InitSparseVector(int nnz);
+SparseVector *InitSparseVector(int dim, int nnz);
 
 #endif

src/vector.c

@@ -6,6 +6,7 @@
 #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"
@@ -32,6 +33,13 @@
 #define STATE_DIMS(x) (ARR_DIMS(x)[0] - 1)
 #define CreateStateDatums(dim) palloc(sizeof(Datum) * (dim + 1))
 
+/* target_clones requires glibc */
+#if defined(__x86_64__) && defined(__gnu_linux__) && defined(__has_attribute) && __has_attribute(target_clones) && !defined(__FMA__)
+#define VECTOR_DISPATCH __attribute__((target_clones("default", "fma")))
+#else
+#define VECTOR_DISPATCH
+#endif
+
 PG_MODULE_MAGIC;
 
 /*
@@ -41,6 +49,7 @@ PGDLLEXPORT void _PG_init(void);
 void
 _PG_init(void)
 {
+	HalfvecInit();
 	HnswInit();
 	IvfflatInit();
 }
@@ -179,28 +188,32 @@ 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,
@@ -216,8 +229,10 @@ vector_in(PG_FUNCTION_ARGS)
 					(errcode(ERRCODE_INVALID_TEXT_REPRESENTATION),
 					 errmsg("invalid input syntax for type vector: \"%s\"", lit)));
 
-		/* Use strtof like float4in to avoid a double-rounding problem */
 		errno = 0;
+
+		/* Use strtof like float4in to avoid a double-rounding problem */
+		/* Postgres sets LC_NUMERIC to C on startup */
 		val = strtof(pt, &stringEnd);
 
 		if (stringEnd == pt)
@@ -229,56 +244,40 @@ vector_in(PG_FUNCTION_ARGS)
 		if (errno == ERANGE && isinf(val))
 			ereport(ERROR,
 					(errcode(ERRCODE_NUMERIC_VALUE_OUT_OF_RANGE),
-					 errmsg("\"%s\" is out of range for type vector", pt)));
+					 errmsg("\"%s\" is out of range for type vector", pnstrdup(pt, stringEnd - pt))));
 
 		CheckElement(val);
 		x[dim++] = val;
 
-		while (vector_isspace(*stringEnd))
-			stringEnd++;
+		pt = stringEnd;
 
-		if (*stringEnd != '\0' && *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);
@@ -565,6 +564,22 @@ halfvec_to_vector(PG_FUNCTION_ARGS)
 	PG_RETURN_POINTER(result);
 }
 
+VECTOR_DISPATCH static float
+VectorL2SquaredDistance(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+	{
+		float		diff = ax[i] - bx[i];
+
+		distance += diff * diff;
+	}
+
+	return distance;
+}
+
 /*
  * Get the L2 distance between vectors
  */
@@ -574,21 +589,10 @@ l2_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
-	float		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
-
-	PG_RETURN_FLOAT8(sqrt((double) distance));
+	PG_RETURN_FLOAT8(sqrt((double) VectorL2SquaredDistance(a->dim, a->x, b->x)));
 }
 
 /*
@@ -601,21 +605,22 @@ vector_l2_squared_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
-	float		diff;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-	{
-		diff = ax[i] - bx[i];
-		distance += diff * diff;
-	}
+	PG_RETURN_FLOAT8((double) VectorL2SquaredDistance(a->dim, a->x, b->x));
+}
 
-	PG_RETURN_FLOAT8((double) distance);
+VECTOR_DISPATCH static float
+VectorInnerProduct(int dim, float *ax, float *bx)
+{
+	float		distance = 0.0;
+
+	/* Auto-vectorized */
+	for (int i = 0; i < dim; i++)
+		distance += ax[i] * bx[i];
+
+	return distance;
 }
 
 /*
@@ -627,17 +632,10 @@ inner_product(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8((double) distance);
+	PG_RETURN_FLOAT8((double) VectorInnerProduct(a->dim, a->x, b->x));
 }
 
 /*
@@ -649,17 +647,10 @@ vector_negative_inner_product(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		distance = 0.0;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		distance += ax[i] * bx[i];
-
-	PG_RETURN_FLOAT8((double) distance * -1);
+	PG_RETURN_FLOAT8((double) -VectorInnerProduct(a->dim, a->x, b->x));
 }
 
 /*
@@ -717,18 +708,11 @@ vector_spherical_distance(PG_FUNCTION_ARGS)
 {
 	Vector	   *a = PG_GETARG_VECTOR_P(0);
 	Vector	   *b = PG_GETARG_VECTOR_P(1);
-	float	   *ax = a->x;
-	float	   *bx = b->x;
-	float		dp = 0.0;
 	double		distance;
 
 	CheckDims(a, b);
 
-	/* Auto-vectorized */
-	for (int i = 0; i < a->dim; i++)
-		dp += ax[i] * bx[i];
-
-	distance = (double) dp;
+	distance = (double) VectorInnerProduct(a->dim, a->x, b->x);
 
 	/* Prevent NaN with acos with loss of precision */
 	if (distance > 1)
@@ -1236,23 +1220,15 @@ sparsevec_to_vector(PG_FUNCTION_ARGS)
 	SparseVector *svec = PG_GETARG_SPARSEVEC_P(0);
 	int32		typmod = PG_GETARG_INT32(1);
 	Vector	   *result;
-	int			dim;
+	int			dim = svec->dim;
 	float	   *values = SPARSEVEC_VALUES(svec);
-	int			maxIndex = svec->nnz == 0 ? -1 : svec->indices[svec->nnz - 1];
-
-	if (typmod == -1)
-		dim = maxIndex + 1;
-	else
-		dim = typmod;
 
 	CheckDim(dim);
-
-	if (dim < maxIndex + 1)
-		elog(ERROR, "Vector must have at least %d dimensions", maxIndex + 1);
+	CheckExpectedDim(typmod, dim);
 
 	result = InitVector(dim);
 	for (int i = 0; i < svec->nnz; i++)
-		result->x[svec->indices[i]] = values[i];
+		result->x[svec->indices[i] - 1] = values[i];
 
 	PG_RETURN_POINTER(result);
 }

test/expected/bit_functions.out

@@ -1,64 +1,104 @@
-SELECT hamming_distance(B'111', B'111');
+SELECT hamming_distance('111', '111');
  hamming_distance 
 ------------------
                 0
 (1 row)
 
-SELECT hamming_distance(B'111', B'110');
+SELECT hamming_distance('111', '110');
  hamming_distance 
 ------------------
                 1
 (1 row)
 
-SELECT hamming_distance(B'111', B'100');
+SELECT hamming_distance('111', '100');
  hamming_distance 
 ------------------
                 2
 (1 row)
 
-SELECT hamming_distance(B'111', B'000');
+SELECT hamming_distance('111', '000');
  hamming_distance 
 ------------------
                 3
 (1 row)
 
-SELECT hamming_distance(B'111', B'00');
+SELECT hamming_distance('10101010101010101010', '01010101010101010101');
+ hamming_distance 
+------------------
+               20
+(1 row)
+
+SELECT hamming_distance('', '');
+ hamming_distance 
+------------------
+                0
+(1 row)
+
+SELECT hamming_distance('111', '00');
 ERROR:  different bit lengths 3 and 2
-SELECT jaccard_distance(B'1111', B'1111');
+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(B'1111', B'1110');
+SELECT jaccard_distance('1111', '1110');
  jaccard_distance 
 ------------------
              0.25
 (1 row)
 
-SELECT jaccard_distance(B'1111', B'1100');
+SELECT jaccard_distance('1111', '1100');
  jaccard_distance 
 ------------------
               0.5
 (1 row)
 
-SELECT jaccard_distance(B'1111', B'1000');
+SELECT jaccard_distance('1111', '1000');
  jaccard_distance 
 ------------------
              0.75
 (1 row)
 
-SELECT jaccard_distance(B'1111', B'0000');
+SELECT jaccard_distance('1111', '0000');
  jaccard_distance 
 ------------------
                 1
 (1 row)
 
-SELECT jaccard_distance(B'1100', B'1000');
+SELECT jaccard_distance('1100', '1000');
  jaccard_distance 
 ------------------
               0.5
 (1 row)
 
-SELECT jaccard_distance(B'1111', B'000');
+SELECT jaccard_distance('10101010101010101010', '01010101010101010101');
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('', '');
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('1111', '000');
 ERROR:  different bit lengths 4 and 3
+SELECT jaccard_distance('1111', '0000'::varbit(5));
+ jaccard_distance 
+------------------
+                1
+(1 row)
+
+SELECT jaccard_distance('1111', '00000'::varbit(5));
+ERROR:  different bit lengths 4 and 5

test/expected/cast.out

@@ -28,6 +28,26 @@ SELECT ARRAY[1,2,3]::numeric[]::vector;
  [1,2,3]
 (1 row)
 
+SELECT '[1,2,3]'::vector::real[];
+ float4  
+---------
+ {1,2,3}
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::vector(2);
+ERROR:  expected 2 dimensions, not 3
 SELECT '{NULL}'::real[]::vector;
 ERROR:  array must not contain nulls
 SELECT '{NaN}'::real[]::vector;
@@ -40,10 +60,26 @@ SELECT '{}'::real[]::vector;
 ERROR:  vector must have at least 1 dimension
 SELECT '{{1}}'::real[]::vector;
 ERROR:  array must be 1-D
-SELECT '[1,2,3]'::vector::real[];
- float4  
+SELECT '{1,2,3}'::double precision[]::vector;
+ vector  
 ---------
- {1,2,3}
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::double precision[]::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::double precision[]::vector(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{4e38,-4e38}'::double precision[]::vector;
+ERROR:  infinite value not allowed in vector
+SELECT '{1e-46,-1e-46}'::double precision[]::vector;
+ vector 
+--------
+ [0,-0]
 (1 row)
 
 SELECT '[1,2,3]'::vector::halfvec;
@@ -52,24 +88,88 @@ SELECT '[1,2,3]'::vector::halfvec;
  [1,2,3]
 (1 row)
 
-SELECT '[1,2,3]'::halfvec::vector;
- vector  
+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 '[1,2,3]'::halfvec::vector(2);
-ERROR:  expected 2 dimensions, not 3
 SELECT '[65520]'::vector::halfvec;
-ERROR:  infinite value not allowed in halfvec
+ERROR:  "65520" is out of range for type halfvec
 SELECT '[1e-8]'::vector::halfvec;
  halfvec 
 ---------
  [0]
 (1 row)
 
+SELECT '[1,2,3]'::halfvec::vector;
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector(3);
+ vector  
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '[1,2,3]'::halfvec::vector(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{1,2,3}'::real[]::halfvec;
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::halfvec(3);
+ halfvec 
+---------
+ [1,2,3]
+(1 row)
+
+SELECT '{1,2,3}'::real[]::halfvec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{65520,-65520}'::real[]::halfvec;
+ERROR:  "65520" is out of range for type halfvec
+SELECT '{1e-8,-1e-8}'::real[]::halfvec;
+ halfvec 
+---------
+ [0,-0]
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(5);
+    sparsevec    
+-----------------
+ {2:1.5,4:3.5}/5
+(1 row)
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector;
+     vector      
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(5);
+     vector      
+-----------------
+ [0,1.5,0,3.5,0]
+(1 row)
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(4);
+ERROR:  expected 4 dimensions, not 5
+SELECT '{}/16001'::sparsevec::vector;
+ERROR:  vector cannot have more than 16000 dimensions
 SELECT array_agg(n)::vector FROM generate_series(1, 16001) n;
 ERROR:  vector cannot have more than 16000 dimensions
 SELECT array_to_vector(array_agg(n), 16001, false) FROM generate_series(1, 16001) n;

test/expected/copy.out

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

test/expected/halfvec_functions.out

@@ -1,3 +1,21 @@
+SELECT round(halfvec_norm('[1,1]')::numeric, 5);
+  round  
+---------
+ 1.41421
+(1 row)
+
+SELECT halfvec_norm('[3,4]');
+ halfvec_norm 
+--------------
+            5
+(1 row)
+
+SELECT halfvec_norm('[0,1]');
+ halfvec_norm 
+--------------
+            1
+(1 row)
+
 SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
  l2_distance 
 -------------
@@ -12,6 +30,12 @@ SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
 
 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? 
 ----------
@@ -32,6 +56,12 @@ SELECT inner_product('[65504]'::halfvec, '[65504]');
     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? 
 ----------

test/expected/halfvec_input.out

@@ -51,51 +51,68 @@ SELECT '[65519,-65519]'::halfvec;
 (1 row)
 
 SELECT '[65520,-65520]'::halfvec;
-ERROR:  value out of range: overflow
+ERROR:  "65520" is out of range for type halfvec
 LINE 1: SELECT '[65520,-65520]'::halfvec;
                ^
 SELECT '[1e-8,-1e-8]'::halfvec;
-ERROR:  value out of range: underflow
-LINE 1: SELECT '[1e-8,-1e-8]'::halfvec;
-               ^
+ halfvec 
+---------
+ [0,-0]
+(1 row)
+
 SELECT '[4e38,1]'::halfvec;
-ERROR:  infinite value not allowed in 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:  malformed halfvec literal: "[1,2,3"
+ERROR:  invalid input syntax for type halfvec: "[1,2,3"
 LINE 1: SELECT '[1,2,3'::halfvec;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[1,2,3]9'::halfvec;
-ERROR:  malformed halfvec literal: "[1,2,3]9"
+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:  malformed halfvec literal: "1,2,3"
+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:  malformed halfvec literal: ""
+ERROR:  invalid input syntax for type halfvec: ""
 LINE 1: SELECT ''::halfvec;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT '['::halfvec;
-ERROR:  malformed halfvec literal: "["
+ERROR:  invalid input syntax for type halfvec: "["
 LINE 1: SELECT '['::halfvec;
                ^
-DETAIL:  Unexpected end of input.
+SELECT '[ '::halfvec;
+ERROR:  invalid input syntax for type halfvec: "[ "
+LINE 1: SELECT '[ '::halfvec;
+               ^
 SELECT '[,'::halfvec;
-ERROR:  malformed halfvec literal: "[,"
+ERROR:  invalid input syntax for type halfvec: "[,"
 LINE 1: SELECT '[,'::halfvec;
                ^
-DETAIL:  Unexpected end of input.
 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;
@@ -105,7 +122,7 @@ ERROR:  invalid input syntax for type halfvec: "[1a]"
 LINE 1: SELECT '[1a]'::halfvec;
                ^
 SELECT '[1,,3]'::halfvec;
-ERROR:  malformed halfvec literal: "[1,,3]"
+ERROR:  invalid input syntax for type halfvec: "[1,,3]"
 LINE 1: SELECT '[1,,3]'::halfvec;
                ^
 SELECT '[1, ,3]'::halfvec;

test/expected/hnsw_bit_hamming.out

@@ -19,3 +19,11 @@ SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <~> (SELECT NULL::bit)) t2;
 (1 row)
 
 DROP TABLE t;
+-- TODO move
+CREATE TABLE t (val varbit(3));
+CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
+ERROR:  type not supported for hnsw index
+CREATE INDEX ON t USING hnsw ((val::bit(3)) bit_hamming_ops);
+CREATE INDEX ON t USING hnsw ((val::bit(64001)) bit_hamming_ops);
+ERROR:  column cannot have more than 64000 dimensions for hnsw index
+DROP TABLE t;

test/expected/hnsw_sparsevec_cosine.out

@@ -1,17 +1,17 @@
 SET enable_seqscan = off;
-CREATE TABLE t (val sparsevec);
-INSERT INTO t (val) VALUES ('{}'), ('{0:1,1:2,2:3}'), ('{0:1,1:1,2:1}'), (NULL);
+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 ('{0:1,1:2,2:4}');
-SELECT * FROM t ORDER BY val <=> '{0:3,1:3,2:3}';
-      val      
----------------
- {0:1,1:1,2:1}
- {0:1,1:2,2:3}
- {0:1,1:2,2:4}
+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 <=> '{}') t2;
+SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <=> '{}/3') t2;
  count 
 -------
      3

test/expected/hnsw_sparsevec_ip.out

@@ -1,15 +1,15 @@
 SET enable_seqscan = off;
-CREATE TABLE t (val sparsevec);
-INSERT INTO t (val) VALUES ('{}'), ('{0:1,1:2,2:3}'), ('{0:1,1:1,2:1}'), (NULL);
+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 ('{0:1,1:2,2:4}');
-SELECT * FROM t ORDER BY val <#> '{0:3,1:3,2:3}';
-      val      
----------------
- {0:1,1:2,2:4}
- {0:1,1:2,2:3}
- {0:1,1:1,2:1}
- {}
+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;

test/expected/hnsw_sparsevec_l2.out

@@ -1,15 +1,15 @@
 SET enable_seqscan = off;
-CREATE TABLE t (val sparsevec);
-INSERT INTO t (val) VALUES ('{}'), ('{0:1,1:2,2:3}'), ('{0:1,1:1,2:1}'), (NULL);
+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 ('{0:1,1:2,2:4}');
-SELECT * FROM t ORDER BY val <-> '{0:3,1:3,2:3}';
-      val      
----------------
- {0:1,1:2,2:3}
- {0:1,1:2,2:4}
- {0:1,1:1,2:1}
- {}
+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;
@@ -25,14 +25,14 @@ SELECT COUNT(*) FROM t;
 (1 row)
 
 TRUNCATE t;
-SELECT * FROM t ORDER BY val <-> '{0:3,1:3,2:3}';
+SELECT * FROM t ORDER BY val <-> '{1:3,2:3,3:3}/3';
  val 
 -----
 (0 rows)
 
 DROP TABLE t;
 -- TODO move
-CREATE TABLE t (val sparsevec);
+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

test/expected/ivfflat_halfvec_cosine.out

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

test/expected/ivfflat_halfvec_ip.out

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

test/expected/ivfflat_halfvec_l2.out

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

test/expected/ivfflat_vector_l2.out

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

test/expected/sparsevec_functions.out

@@ -1,60 +1,86 @@
-SELECT l2_distance('{}'::sparsevec, '{0:3,1:4}');
+SELECT round(sparsevec_norm('{1:1,2:1}/2')::numeric, 5);
+  round  
+---------
+ 1.41421
+(1 row)
+
+SELECT sparsevec_norm('{1:3,2:4}/2');
+ sparsevec_norm 
+----------------
+              5
+(1 row)
+
+SELECT sparsevec_norm('{2:1}/2');
+ sparsevec_norm 
+----------------
+              1
+(1 row)
+
+SELECT sparsevec_norm('{1:3e37,2:4e37}/2')::real;
+ sparsevec_norm 
+----------------
+          5e+37
+(1 row)
+
+SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
  l2_distance 
 -------------
            5
 (1 row)
 
-SELECT l2_distance('{}'::sparsevec, '{1:1}');
+SELECT l2_distance('{}/2'::sparsevec, '{2:1}/2');
  l2_distance 
 -------------
            1
 (1 row)
 
-SELECT '{}'::sparsevec <-> '{0:3,1:4}';
+SELECT '{}/2'::sparsevec <-> '{1:3,2:4}/2';
  ?column? 
 ----------
         5
 (1 row)
 
-SELECT inner_product('{0:1,1:2}'::sparsevec, '{0:2,1:4}');
+SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
  inner_product 
 ---------------
             10
 (1 row)
 
-SELECT sparsevec_negative_inner_product('{0:1,1:2}', '{0:2,1:4}');
+SELECT sparsevec_negative_inner_product('{1:1,2:2}/2', '{1:2,2:4}/2');
  sparsevec_negative_inner_product 
 ----------------------------------
                               -10
 (1 row)
 
-SELECT cosine_distance('{0:1,1:2}'::sparsevec, '{0:2,1:4}');
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
  cosine_distance 
 -----------------
                0
 (1 row)
 
-SELECT cosine_distance('{0:1,1:2}'::sparsevec, '{}');
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{}/2');
  cosine_distance 
 -----------------
              NaN
 (1 row)
 
-SELECT cosine_distance('{0:1,1:1}'::sparsevec, '{0:-1,1:-1}');
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1,2:-1}/2');
  cosine_distance 
 -----------------
                2
 (1 row)
 
-SELECT cosine_distance('{0:1}'::sparsevec, '{1:2}');
+SELECT cosine_distance('{1:2}/2'::sparsevec, '{2:2}/2');
  cosine_distance 
 -----------------
                1
 (1 row)
 
-SELECT cosine_distance('{}'::sparsevec, '{}');
+SELECT cosine_distance('{}/1'::sparsevec, '{}/1');
  cosine_distance 
 -----------------
              NaN
 (1 row)
 
+SELECT cosine_distance('{1:2}/2'::sparsevec, '{1:1}/3');
+ERROR:  different sparsevec dimensions 2 and 3

test/expected/sparsevec_input.out

@@ -1,64 +1,215 @@
-SELECT '{0:1.5,2:3.5}'::sparsevec;
-   sparsevec   
----------------
- {0:1.5,2:3.5}
-(1 row)
-
-SELECT '{0:1.5,2:3.5}'::sparsevec::vector;
-   vector    
--------------
- [1.5,0,3.5]
-(1 row)
-
-SELECT '{0:1.5,2:3.5}'::sparsevec::vector(5);
-     vector      
+SELECT '{1:1.5,3:3.5}/5'::sparsevec;
+    sparsevec    
 -----------------
- [1.5,0,3.5,0,0]
+ {1:1.5,3:3.5}/5
 (1 row)
 
-SELECT '{0:1.5,2:3.5}'::sparsevec::vector(4);
-    vector     
----------------
- [1.5,0,3.5,0]
-(1 row)
-
-SELECT '{0:1.5,2:3.5}'::sparsevec::vector(2);
-ERROR:  Vector must have at least 3 dimensions
-SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
+SELECT '{1:-2,3:-4}/5'::sparsevec;
    sparsevec   
 ---------------
- {1:1.5,3:3.5}
+ {1:-2,3:-4}/5
 (1 row)
 
-SELECT '{0:0,1:1,2:0}'::sparsevec;
- sparsevec 
------------
- {1:1}
+SELECT '{1:2.,3:4.}/5'::sparsevec;
+  sparsevec  
+-------------
+ {1:2,3:4}/5
 (1 row)
 
-SELECT '{1:1,0:1}'::sparsevec;
-ERROR:  indexes must be in ascending order
-LINE 1: SELECT '{1:1,0:1}'::sparsevec;
+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;
- sparsevec 
------------
- {}
-(1 row)
-
-SELECT '{}'::sparsevec::vector;
-ERROR:  vector must have at least 1 dimension
-SELECT '{-1:1}'::sparsevec;
-ERROR:  index "-1" is out of range for type sparsevec
-LINE 1: SELECT '{-1:1}'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{}"
+LINE 1: SELECT '{}'::sparsevec;
                ^
-SELECT '{1:1}'::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}
+ {}/1
 (1 row)
 
-SELECT '{}'::sparsevec(2);
-ERROR:  type modifier is not allowed for type "sparsevec"
-LINE 1: SELECT '{}'::sparsevec(2);
-                     ^
+SELECT '{}/1a'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{}/1a"
+LINE 1: SELECT '{}/1a'::sparsevec;
+               ^
+DETAIL:  Junk after closing.
+SELECT '{ }/1'::sparsevec;
+ sparsevec 
+-----------
+ {}/1
+(1 row)
+
+SELECT '{:}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{:}/1"
+LINE 1: SELECT '{:}/1'::sparsevec;
+               ^
+SELECT '{,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{,}/1"
+LINE 1: SELECT '{,}/1'::sparsevec;
+               ^
+SELECT '{1,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1,}/1"
+LINE 1: SELECT '{1,}/1'::sparsevec;
+               ^
+SELECT '{:1}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{:1}/1"
+LINE 1: SELECT '{:1}/1'::sparsevec;
+               ^
+SELECT '{1:}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:}/1"
+LINE 1: SELECT '{1:}/1'::sparsevec;
+               ^
+SELECT '{1a:1}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1a:1}/1"
+LINE 1: SELECT '{1a:1}/1'::sparsevec;
+               ^
+SELECT '{1:1a}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:1a}/1"
+LINE 1: SELECT '{1:1a}/1'::sparsevec;
+               ^
+SELECT '{1:1,}/1'::sparsevec;
+ERROR:  invalid input syntax for type sparsevec: "{1:1,}/1"
+LINE 1: SELECT '{1:1,}/1'::sparsevec;
+               ^
+SELECT '{1:0,2:1,3:0}/3'::sparsevec;
+ sparsevec 
+-----------
+ {2:1}/3
+(1 row)
+
+SELECT '{2:1,1:1}/2'::sparsevec;
+ERROR:  indexes must be in ascending order
+LINE 1: SELECT '{2:1,1:1}/2'::sparsevec;
+               ^
+SELECT '{}/5'::sparsevec;
+ sparsevec 
+-----------
+ {}/5
+(1 row)
+
+SELECT '{}/-1'::sparsevec;
+ERROR:  sparsevec must have at least 1 dimension
+LINE 1: SELECT '{}/-1'::sparsevec;
+               ^
+SELECT '{}/100001'::sparsevec;
+ERROR:  sparsevec cannot have more than 100000 dimensions
+LINE 1: SELECT '{}/100001'::sparsevec;
+               ^
+SELECT '{0:1}/1'::sparsevec;
+ERROR:  index "0" is out of range for type sparsevec
+LINE 1: SELECT '{0:1}/1'::sparsevec;
+               ^
+SELECT '{2:1}/1'::sparsevec;
+ERROR:  index must be less than or equal to dimensions
+LINE 1: SELECT '{2:1}/1'::sparsevec;
+               ^
+SELECT '{}/3'::sparsevec(3);
+ sparsevec 
+-----------
+ {}/3
+(1 row)
+
+SELECT '{}/3'::sparsevec(2);
+ERROR:  expected 2 dimensions, not 3
+SELECT '{}/3'::sparsevec(3, 2);
+ERROR:  invalid type modifier
+LINE 1: SELECT '{}/3'::sparsevec(3, 2);
+                       ^
+SELECT '{}/3'::sparsevec('a');
+ERROR:  invalid input syntax for type integer: "a"
+LINE 1: SELECT '{}/3'::sparsevec('a');
+                       ^
+SELECT '{}/3'::sparsevec(0);
+ERROR:  dimensions for type sparsevec must be at least 1
+LINE 1: SELECT '{}/3'::sparsevec(0);
+                       ^
+SELECT '{}/3'::sparsevec(100001);
+ERROR:  dimensions for type sparsevec cannot exceed 100000
+LINE 1: SELECT '{}/3'::sparsevec(100001);
+                       ^

test/expected/vector_input.out

@@ -83,39 +83,48 @@ SELECT '[-1e-46,1]'::vector;
 (1 row)
 
 SELECT '[1,2,3'::vector;
-ERROR:  malformed vector literal: "[1,2,3"
+ERROR:  invalid input syntax for type vector: "[1,2,3"
 LINE 1: SELECT '[1,2,3'::vector;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[1,2,3]9'::vector;
-ERROR:  malformed vector literal: "[1,2,3]9"
+ERROR:  invalid input syntax for type vector: "[1,2,3]9"
 LINE 1: SELECT '[1,2,3]9'::vector;
                ^
 DETAIL:  Junk after closing right brace.
 SELECT '1,2,3'::vector;
-ERROR:  malformed vector literal: "1,2,3"
+ERROR:  invalid input syntax for type vector: "1,2,3"
 LINE 1: SELECT '1,2,3'::vector;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT ''::vector;
-ERROR:  malformed vector literal: ""
+ERROR:  invalid input syntax for type vector: ""
 LINE 1: SELECT ''::vector;
                ^
 DETAIL:  Vector contents must start with "[".
 SELECT '['::vector;
-ERROR:  malformed vector literal: "["
+ERROR:  invalid input syntax for type vector: "["
 LINE 1: SELECT '['::vector;
                ^
-DETAIL:  Unexpected end of input.
+SELECT '[ '::vector;
+ERROR:  invalid input syntax for type vector: "[ "
+LINE 1: SELECT '[ '::vector;
+               ^
 SELECT '[,'::vector;
-ERROR:  malformed vector literal: "[,"
+ERROR:  invalid input syntax for type vector: "[,"
 LINE 1: SELECT '[,'::vector;
                ^
-DETAIL:  Unexpected end of input.
 SELECT '[]'::vector;
 ERROR:  vector must have at least 1 dimension
 LINE 1: SELECT '[]'::vector;
                ^
+SELECT '[ ]'::vector;
+ERROR:  vector must have at least 1 dimension
+LINE 1: SELECT '[ ]'::vector;
+               ^
+SELECT '[,]'::vector;
+ERROR:  invalid input syntax for type vector: "[,]"
+LINE 1: SELECT '[,]'::vector;
+               ^
 SELECT '[1,]'::vector;
 ERROR:  invalid input syntax for type vector: "[1,]"
 LINE 1: SELECT '[1,]'::vector;
@@ -125,7 +134,7 @@ ERROR:  invalid input syntax for type vector: "[1a]"
 LINE 1: SELECT '[1a]'::vector;
                ^
 SELECT '[1,,3]'::vector;
-ERROR:  malformed vector literal: "[1,,3]"
+ERROR:  invalid input syntax for type vector: "[1,,3]"
 LINE 1: SELECT '[1,,3]'::vector;
                ^
 SELECT '[1, ,3]'::vector;

test/sql/bit_functions.sql

@@ -1,13 +1,21 @@
-SELECT hamming_distance(B'111', B'111');
-SELECT hamming_distance(B'111', B'110');
-SELECT hamming_distance(B'111', B'100');
-SELECT hamming_distance(B'111', B'000');
-SELECT hamming_distance(B'111', B'00');
+SELECT hamming_distance('111', '111');
+SELECT hamming_distance('111', '110');
+SELECT hamming_distance('111', '100');
+SELECT hamming_distance('111', '000');
+SELECT hamming_distance('10101010101010101010', '01010101010101010101');
+SELECT hamming_distance('', '');
+SELECT hamming_distance('111', '00');
+SELECT hamming_distance('111', '000'::varbit(4));
+SELECT hamming_distance('111', '0000'::varbit(4));
 
-SELECT jaccard_distance(B'1111', B'1111');
-SELECT jaccard_distance(B'1111', B'1110');
-SELECT jaccard_distance(B'1111', B'1100');
-SELECT jaccard_distance(B'1111', B'1000');
-SELECT jaccard_distance(B'1111', B'0000');
-SELECT jaccard_distance(B'1100', B'1000');
-SELECT jaccard_distance(B'1111', B'000');
+SELECT jaccard_distance('1111', '1111');
+SELECT jaccard_distance('1111', '1110');
+SELECT jaccard_distance('1111', '1100');
+SELECT jaccard_distance('1111', '1000');
+SELECT jaccard_distance('1111', '0000');
+SELECT jaccard_distance('1100', '1000');
+SELECT jaccard_distance('10101010101010101010', '01010101010101010101');
+SELECT jaccard_distance('', '');
+SELECT jaccard_distance('1111', '000');
+SELECT jaccard_distance('1111', '0000'::varbit(5));
+SELECT jaccard_distance('1111', '00000'::varbit(5));

test/sql/cast.sql

@@ -3,19 +3,50 @@ SELECT ARRAY[1.0,2.0,3.0]::vector;
 SELECT ARRAY[1,2,3]::float4[]::vector;
 SELECT ARRAY[1,2,3]::float8[]::vector;
 SELECT ARRAY[1,2,3]::numeric[]::vector;
+
+SELECT '[1,2,3]'::vector::real[];
+
+SELECT '{1,2,3}'::real[]::vector;
+SELECT '{1,2,3}'::real[]::vector(3);
+SELECT '{1,2,3}'::real[]::vector(2);
 SELECT '{NULL}'::real[]::vector;
 SELECT '{NaN}'::real[]::vector;
 SELECT '{Infinity}'::real[]::vector;
 SELECT '{-Infinity}'::real[]::vector;
 SELECT '{}'::real[]::vector;
 SELECT '{{1}}'::real[]::vector;
-SELECT '[1,2,3]'::vector::real[];
+
+SELECT '{1,2,3}'::double precision[]::vector;
+SELECT '{1,2,3}'::double precision[]::vector(3);
+SELECT '{1,2,3}'::double precision[]::vector(2);
+SELECT '{4e38,-4e38}'::double precision[]::vector;
+SELECT '{1e-46,-1e-46}'::double precision[]::vector;
+
 SELECT '[1,2,3]'::vector::halfvec;
-SELECT '[1,2,3]'::halfvec::vector;
+SELECT '[1,2,3]'::vector::halfvec(3);
 SELECT '[1,2,3]'::vector::halfvec(2);
-SELECT '[1,2,3]'::halfvec::vector(2);
 SELECT '[65520]'::vector::halfvec;
 SELECT '[1e-8]'::vector::halfvec;
+
+SELECT '[1,2,3]'::halfvec::vector;
+SELECT '[1,2,3]'::halfvec::vector(3);
+SELECT '[1,2,3]'::halfvec::vector(2);
+
+SELECT '{1,2,3}'::real[]::halfvec;
+SELECT '{1,2,3}'::real[]::halfvec(3);
+SELECT '{1,2,3}'::real[]::halfvec(2);
+SELECT '{65520,-65520}'::real[]::halfvec;
+SELECT '{1e-8,-1e-8}'::real[]::halfvec;
+
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(5);
+SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec(4);
+
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector;
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(5);
+SELECT '{2:1.5,4:3.5}/5'::sparsevec::vector(4);
+SELECT '{}/16001'::sparsevec::vector;
+
 SELECT array_agg(n)::vector FROM generate_series(1, 16001) n;
 SELECT array_to_vector(array_agg(n), 16001, false) FROM generate_series(1, 16001) n;
 

test/sql/copy.sql

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

test/sql/halfvec_functions.sql

@@ -1,11 +1,17 @@
+SELECT round(halfvec_norm('[1,1]')::numeric, 5);
+SELECT halfvec_norm('[3,4]');
+SELECT halfvec_norm('[0,1]');
+
 SELECT l2_distance('[0,0]'::halfvec, '[3,4]');
 SELECT l2_distance('[0,0]'::halfvec, '[0,1]');
 SELECT l2_distance('[1,2]'::halfvec, '[3]');
+SELECT l2_distance('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,1,1,1,1,1,1,4,5]');
 SELECT '[0,0]'::halfvec <-> '[3,4]';
 
 SELECT inner_product('[1,2]'::halfvec, '[3,4]');
 SELECT inner_product('[1,2]'::halfvec, '[3]');
 SELECT inner_product('[65504]'::halfvec, '[65504]');
+SELECT inner_product('[1,1,1,1,1,1,1,1,1]'::halfvec, '[1,2,3,4,5,6,7,8,9]');
 SELECT '[1,2]'::halfvec <#> '[3,4]';
 
 SELECT cosine_distance('[1,2]'::halfvec, '[2,4]');

test/sql/halfvec_input.sql

@@ -11,13 +11,17 @@ 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;

test/sql/hnsw_bit_hamming.sql

@@ -10,3 +10,10 @@ SELECT * FROM t ORDER BY val <~> B'111';
 SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <~> (SELECT NULL::bit)) t2;
 
 DROP TABLE t;
+
+-- TODO move
+CREATE TABLE t (val varbit(3));
+CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
+CREATE INDEX ON t USING hnsw ((val::bit(3)) bit_hamming_ops);
+CREATE INDEX ON t USING hnsw ((val::bit(64001)) bit_hamming_ops);
+DROP TABLE t;

test/sql/hnsw_sparsevec_cosine.sql

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

test/sql/hnsw_sparsevec_ip.sql

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

test/sql/hnsw_sparsevec_l2.sql

@@ -1,22 +1,22 @@
 SET enable_seqscan = off;
 
-CREATE TABLE t (val sparsevec);
-INSERT INTO t (val) VALUES ('{}'), ('{0:1,1:2,2:3}'), ('{0:1,1:1,2:1}'), (NULL);
+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 ('{0:1,1:2,2:4}');
+INSERT INTO t (val) VALUES ('{1:1,2:2,3:4}/3');
 
-SELECT * FROM t ORDER BY val <-> '{0:3,1:3,2:3}';
+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 <-> '{0:3,1:3,2:3}';
+SELECT * FROM t ORDER BY val <-> '{1:3,2:3,3:3}/3';
 
 DROP TABLE t;
 
 -- TODO move
-CREATE TABLE t (val sparsevec);
+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;

test/sql/ivfflat_halfvec_cosine.sql

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

test/sql/ivfflat_halfvec_ip.sql

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

test/sql/ivfflat_halfvec_l2.sql

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

test/sql/ivfflat_vector_l2.sql

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

test/sql/sparsevec_functions.sql

@@ -1,12 +1,18 @@
-SELECT l2_distance('{}'::sparsevec, '{0:3,1:4}');
-SELECT l2_distance('{}'::sparsevec, '{1:1}');
-SELECT '{}'::sparsevec <-> '{0:3,1:4}';
+SELECT round(sparsevec_norm('{1:1,2:1}/2')::numeric, 5);
+SELECT sparsevec_norm('{1:3,2:4}/2');
+SELECT sparsevec_norm('{2:1}/2');
+SELECT sparsevec_norm('{1:3e37,2:4e37}/2')::real;
 
-SELECT inner_product('{0:1,1:2}'::sparsevec, '{0:2,1:4}');
-SELECT sparsevec_negative_inner_product('{0:1,1:2}', '{0:2,1:4}');
+SELECT l2_distance('{}/2'::sparsevec, '{1:3,2:4}/2');
+SELECT l2_distance('{}/2'::sparsevec, '{2:1}/2');
+SELECT '{}/2'::sparsevec <-> '{1:3,2:4}/2';
 
-SELECT cosine_distance('{0:1,1:2}'::sparsevec, '{0:2,1:4}');
-SELECT cosine_distance('{0:1,1:2}'::sparsevec, '{}');
-SELECT cosine_distance('{0:1,1:1}'::sparsevec, '{0:-1,1:-1}');
-SELECT cosine_distance('{0:1}'::sparsevec, '{1:2}');
-SELECT cosine_distance('{}'::sparsevec, '{}');
+SELECT inner_product('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
+SELECT sparsevec_negative_inner_product('{1:1,2:2}/2', '{1:2,2:4}/2');
+
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{1:2,2:4}/2');
+SELECT cosine_distance('{1:1,2:2}/2'::sparsevec, '{}/2');
+SELECT cosine_distance('{1:1,2:1}/2'::sparsevec, '{1:-1,2:-1}/2');
+SELECT cosine_distance('{1:2}/2'::sparsevec, '{2:2}/2');
+SELECT cosine_distance('{}/1'::sparsevec, '{}/1');
+SELECT cosine_distance('{1:2}/2'::sparsevec, '{1:1}/3');

test/sql/sparsevec_input.sql

@@ -1,18 +1,48 @@
-SELECT '{0:1.5,2:3.5}'::sparsevec;
-SELECT '{0:1.5,2:3.5}'::sparsevec::vector;
-SELECT '{0:1.5,2:3.5}'::sparsevec::vector(5);
-SELECT '{0:1.5,2:3.5}'::sparsevec::vector(4);
-SELECT '{0:1.5,2:3.5}'::sparsevec::vector(2);
-SELECT '[0,1.5,0,3.5,0]'::vector::sparsevec;
-
-SELECT '{0:0,1:1,2:0}'::sparsevec;
-
-SELECT '{1:1,0:1}'::sparsevec;
-
+SELECT '{1:1.5,3:3.5}/5'::sparsevec;
+SELECT '{1:-2,3:-4}/5'::sparsevec;
+SELECT '{1:2.,3:4.}/5'::sparsevec;
+SELECT ' { 1 : 1.5 ,  3  :  3.5  } / 5 '::sparsevec;
+SELECT '{1:1.23456}/1'::sparsevec;
+SELECT '{1:hello,2:1}/2'::sparsevec;
+SELECT '{1:NaN,2:1}/2'::sparsevec;
+SELECT '{1:Infinity,2:1}/2'::sparsevec;
+SELECT '{1:-Infinity,2:1}/2'::sparsevec;
+SELECT '{1:1.5e38,2:-1.5e38}/2'::sparsevec;
+SELECT '{1:1.5e+38,2:-1.5e+38}/2'::sparsevec;
+SELECT '{1:1.5e-38,2:-1.5e-38}/2'::sparsevec;
+SELECT '{1:4e38,2:1}/2'::sparsevec;
+SELECT '{1:-4e38,2:1}/2'::sparsevec;
+SELECT '{1:1e-46,2:1}/2'::sparsevec;
+SELECT '{1:-1e-46,2:1}/2'::sparsevec;
+SELECT ''::sparsevec;
+SELECT '{'::sparsevec;
+SELECT '{ '::sparsevec;
+SELECT '{:'::sparsevec;
+SELECT '{,'::sparsevec;
 SELECT '{}'::sparsevec;
-SELECT '{}'::sparsevec::vector;
+SELECT '{}/'::sparsevec;
+SELECT '{}/1'::sparsevec;
+SELECT '{}/1a'::sparsevec;
+SELECT '{ }/1'::sparsevec;
+SELECT '{:}/1'::sparsevec;
+SELECT '{,}/1'::sparsevec;
+SELECT '{1,}/1'::sparsevec;
+SELECT '{:1}/1'::sparsevec;
+SELECT '{1:}/1'::sparsevec;
+SELECT '{1a:1}/1'::sparsevec;
+SELECT '{1:1a}/1'::sparsevec;
+SELECT '{1:1,}/1'::sparsevec;
+SELECT '{1:0,2:1,3:0}/3'::sparsevec;
+SELECT '{2:1,1:1}/2'::sparsevec;
+SELECT '{}/5'::sparsevec;
+SELECT '{}/-1'::sparsevec;
+SELECT '{}/100001'::sparsevec;
+SELECT '{0:1}/1'::sparsevec;
+SELECT '{2:1}/1'::sparsevec;
 
-SELECT '{-1:1}'::sparsevec;
-SELECT '{1:1}'::sparsevec;
-
-SELECT '{}'::sparsevec(2);
+SELECT '{}/3'::sparsevec(3);
+SELECT '{}/3'::sparsevec(2);
+SELECT '{}/3'::sparsevec(3, 2);
+SELECT '{}/3'::sparsevec('a');
+SELECT '{}/3'::sparsevec(0);
+SELECT '{}/3'::sparsevec(100001);

test/sql/vector_input.sql

@@ -19,8 +19,11 @@ SELECT '[1,2,3]9'::vector;
 SELECT '1,2,3'::vector;
 SELECT ''::vector;
 SELECT '['::vector;
+SELECT '[ '::vector;
 SELECT '[,'::vector;
 SELECT '[]'::vector;
+SELECT '[ ]'::vector;
+SELECT '[,]'::vector;
 SELECT '[1,]'::vector;
 SELECT '[1a]'::vector;
 SELECT '[1,,3]'::vector;

test/t/003_ivfflat_build_recall.pl

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

test/t/013_hnsw_insert_recall.pl

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

test/t/016_hnsw_vacuum_recall.pl

@@ -86,7 +86,7 @@ foreach (@queries)
 	push(@expected, $res);
 }
 
-test_recall(0.19, $limit, "before vacuum");
+test_recall(0.18, $limit, "before vacuum");
 test_recall(0.95, 100, "before vacuum");
 
 # TODO Test concurrent inserts with vacuum

test/t/020_hnsw_bit_build_recall.pl

@@ -85,7 +85,7 @@ for my $i (0 .. $#operators)
 		# Handle ties
 		my $res = $node->safe_psql("postgres", qq(
 			WITH top AS (
-				SELECT v $operator $_ AS distance FROM tst ORDER BY v $operator $_ LIMIT $limit
+				SELECT v $operator $_ AS distance FROM tst ORDER BY distance LIMIT $limit
 			)
 			SELECT i FROM tst WHERE (v $operator $_) <= (SELECT MAX(distance) FROM top)
 		));
@@ -99,7 +99,7 @@ for my $i (0 .. $#operators)
 	));
 
 	# Test approximate results
-	my $min = $operator eq "<\%>" ? 0.96 : 0.98;
+	my $min = $operator eq "<\%>" ? 0.95 : 0.98;
 	test_recall($min, $operator);
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");

test/t/021_hnsw_halfvec_build_recall.pl

@@ -94,7 +94,7 @@ for my $i (0 .. $#operators)
 	));
 
 	# Test approximate results
-	my $min = $operator eq "<#>" ? 0.95 : 0.98;
+	my $min = $operator eq "<#>" ? 0.93 : 0.98;
 	test_recall($min, $operator);
 
 	$node->safe_psql("postgres", "DROP INDEX idx;");

test/t/022_hnsw_sparsevec_build_recall.pl

@@ -0,0 +1,128 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v sparsevec(3));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()]::vector::sparsevec FROM generate_series(1, 10000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "{1:$r1,2:$r2,3:$r3}/3");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+my @opclasses = ("sparsevec_l2_ops", "sparsevec_ip_ops", "sparsevec_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", "SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;");
+		push(@expected, $res);
+	}
+
+	# Build index serially
+	$node->safe_psql("postgres", qq(
+		SET max_parallel_maintenance_workers = 0;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+
+	# Test approximate results
+	my $min = $operator eq "<#>" ? 0.80 : 0.99;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel in memory
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		SET client_min_messages = DEBUG;
+		SET min_parallel_table_scan_size = 1;
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel on disk
+	# Set parallel_workers on table to use workers with low maintenance_work_mem
+	($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		ALTER TABLE tst SET (parallel_workers = 2);
+		SET client_min_messages = DEBUG;
+		SET maintenance_work_mem = '4MB';
+		CREATE INDEX idx ON tst USING hnsw (v $opclass);
+		ALTER TABLE tst RESET (parallel_workers);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+	like($stderr, qr/hnsw graph no longer fits into maintenance_work_mem/);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();

test/t/023_hnsw_bit_insert_recall.pl

@@ -0,0 +1,116 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 52;
+my $max = 2**$dim;
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 100;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator $queries[0] LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = 100;
+			SELECT i FROM tst ORDER BY v $operator $queries[$i] LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+
+		my @expected_ids = split("\n", $expected[$i]);
+		my %expected_set = map { $_ => 1 } @expected_ids;
+
+		foreach (@actual_ids)
+		{
+			if (exists($expected_set{$_}))
+			{
+				$correct++;
+			}
+		}
+
+		$total += $limit;
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i serial, v bit($dim));");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r = int(rand() * $max);
+	push(@queries, "${r}::bigint::bit($dim)");
+}
+
+# Check each index type
+my @operators = ("<~>", "<\%>");
+my @opclasses = ("bit_hamming_ops", "bit_jaccard_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Add index
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v $opclass);");
+
+	# Use concurrent inserts
+	$node->pgbench(
+		"--no-vacuum --client=10 --transactions=1000",
+		0,
+		[qr{actually processed}],
+		[qr{^$}],
+		"concurrent INSERTs",
+		{
+			"023_hnsw_bit_insert_recall_$opclass" => "INSERT INTO tst (v) VALUES ((random() * $max)::bigint::bit($dim));"
+		}
+	);
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		# Handle ties
+		my $res = $node->safe_psql("postgres", qq(
+			SET enable_indexscan = off;
+			WITH top AS (
+				SELECT v $operator $_ AS distance FROM tst ORDER BY distance LIMIT $limit
+			)
+			SELECT i FROM tst WHERE (v $operator $_) <= (SELECT MAX(distance) FROM top)
+		));
+		push(@expected, $res);
+	}
+
+	# Test approximate results
+	my $min = $operator eq "<\%>" ? 0.95 : 0.98;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres", "TRUNCATE tst;");
+}
+
+done_testing();

test/t/024_hnsw_halfvec_insert_recall.pl

@@ -0,0 +1,113 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 10;
+my $array_sql = join(",", ('random()') x $dim);
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i serial, v halfvec($dim));");
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Add index
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v $opclass);");
+
+	# Use concurrent inserts
+	$node->pgbench(
+		"--no-vacuum --client=10 --transactions=1000",
+		0,
+		[qr{actually processed}],
+		[qr{^$}],
+		"concurrent INSERTs",
+		{
+			"024_hnsw_halfvec_insert_recall_$opclass" => "INSERT INTO tst (v) VALUES (ARRAY[$array_sql]);"
+		}
+	);
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", qq(
+			SET enable_indexscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;
+		));
+		push(@expected, $res);
+	}
+
+	# Test approximate results
+	my $min = $operator eq "<#>" ? 0.94 : 0.98;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres", "TRUNCATE tst;");
+}
+
+done_testing();

test/t/025_hnsw_sparsevec_insert_recall.pl

@@ -0,0 +1,109 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$queries[$i]' LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+		my %actual_set = map { $_ => 1 } @actual_ids;
+
+		my @expected_ids = split("\n", $expected[$i]);
+
+		foreach (@expected_ids)
+		{
+			if (exists($actual_set{$_}))
+			{
+				$correct++;
+			}
+			$total++;
+		}
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i serial, v sparsevec(3));");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "{1:$r1,2:$r2,3:$r3}/3");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+my @opclasses = ("sparsevec_l2_ops", "sparsevec_ip_ops", "sparsevec_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Add index
+	$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v $opclass);");
+
+	# Use concurrent inserts
+	$node->pgbench(
+		"--no-vacuum --client=10 --transactions=1000",
+		0,
+		[qr{actually processed}],
+		[qr{^$}],
+		"concurrent INSERTs",
+		{
+			"025_hnsw_sparsevec_insert_recall_$opclass" => "INSERT INTO tst (v) VALUES (ARRAY[random(), random(), random()]::vector::sparsevec);"
+		}
+	);
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", qq(
+			SET enable_indexscan = off;
+			SELECT i FROM tst ORDER BY v $operator '$_' LIMIT $limit;
+		));
+		push(@expected, $res);
+	}
+
+	# Test approximate results
+	my $min = $operator eq "<#>" ? 0.80 : 0.99;
+	test_recall($min, $operator);
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+	$node->safe_psql("postgres", "TRUNCATE tst;");
+}
+
+done_testing();

test/t/026_hnsw_bit_duplicates.pl

@@ -0,0 +1,58 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+# 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 bit(3));");
+
+sub insert_vectors
+{
+	for my $i (1 .. 20)
+	{
+		$node->safe_psql("postgres", "INSERT INTO tst VALUES ('111');");
+	}
+}
+
+sub test_duplicates
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 1;
+		SELECT COUNT(*) FROM (SELECT * FROM tst ORDER BY v <~> '111') t;
+	));
+	is($res, 10);
+}
+
+# Test duplicates with build
+insert_vectors();
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v bit_hamming_ops);");
+test_duplicates();
+
+# Reset
+$node->safe_psql("postgres", "TRUNCATE tst;");
+
+# Test duplicates with inserts
+insert_vectors();
+test_duplicates();
+
+# Test fallback path for inserts
+$node->pgbench(
+	"--no-vacuum --client=5 --transactions=100",
+	0,
+	[qr{actually processed}],
+	[qr{^$}],
+	"concurrent INSERTs",
+	{
+		"026_hnsw_bit_duplicates" => "INSERT INTO tst VALUES ('111');"
+	}
+);
+
+done_testing();

test/t/027_hnsw_halfvec_duplicates.pl

@@ -0,0 +1,58 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+# 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 halfvec(3));");
+
+sub insert_vectors
+{
+	for my $i (1 .. 20)
+	{
+		$node->safe_psql("postgres", "INSERT INTO tst VALUES ('[1,1,1]');");
+	}
+}
+
+sub test_duplicates
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 1;
+		SELECT COUNT(*) FROM (SELECT * FROM tst ORDER BY v <-> '[1,1,1]') t;
+	));
+	is($res, 10);
+}
+
+# Test duplicates with build
+insert_vectors();
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v halfvec_l2_ops);");
+test_duplicates();
+
+# Reset
+$node->safe_psql("postgres", "TRUNCATE tst;");
+
+# Test duplicates with inserts
+insert_vectors();
+test_duplicates();
+
+# Test fallback path for inserts
+$node->pgbench(
+	"--no-vacuum --client=5 --transactions=100",
+	0,
+	[qr{actually processed}],
+	[qr{^$}],
+	"concurrent INSERTs",
+	{
+		"027_hnsw_halfvec_duplicates" => "INSERT INTO tst VALUES ('[1,1,1]');"
+	}
+);
+
+done_testing();

test/t/028_hnsw_sparsevec_duplicates.pl

@@ -0,0 +1,58 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+# 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 sparsevec(3));");
+
+sub insert_vectors
+{
+	for my $i (1 .. 20)
+	{
+		$node->safe_psql("postgres", "INSERT INTO tst VALUES ('{1:1,2:1,3:1}/3');");
+	}
+}
+
+sub test_duplicates
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = 1;
+		SELECT COUNT(*) FROM (SELECT * FROM tst ORDER BY v <-> '{1:1,2:1,3:1}/3') t;
+	));
+	is($res, 10);
+}
+
+# Test duplicates with build
+insert_vectors();
+$node->safe_psql("postgres", "CREATE INDEX idx ON tst USING hnsw (v sparsevec_l2_ops);");
+test_duplicates();
+
+# Reset
+$node->safe_psql("postgres", "TRUNCATE tst;");
+
+# Test duplicates with inserts
+insert_vectors();
+test_duplicates();
+
+# Test fallback path for inserts
+$node->pgbench(
+	"--no-vacuum --client=5 --transactions=100",
+	0,
+	[qr{actually processed}],
+	[qr{^$}],
+	"concurrent INSERTs",
+	{
+		"028_hnsw_sparsevec_duplicates" => "INSERT INTO tst VALUES ('{1:1,2:1,3:1}/3');"
+	}
+);
+
+done_testing();

test/t/029_hnsw_bit_vacuum_recall.pl

@@ -0,0 +1,100 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 52;
+my $max = 2**$dim;
+
+sub test_recall
+{
+	my ($min, $ef_search, $test_name) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = $ef_search;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <~> $queries[0] LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = $ef_search;
+			SELECT i FROM tst ORDER BY v <~> $queries[$i] LIMIT $limit;
+		));
+		my @actual_ids = split("\n", $actual);
+
+		my @expected_ids = split("\n", $expected[$i]);
+		my %expected_set = map { $_ => 1 } @expected_ids;
+
+		foreach (@actual_ids)
+		{
+			if (exists($expected_set{$_}))
+			{
+				$correct++;
+			}
+		}
+
+		$total += $limit;
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $test_name);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v bit($dim));");
+$node->safe_psql("postgres", "ALTER TABLE tst SET (autovacuum_enabled = false);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, (random() * $max)::bigint::bit($dim) FROM generate_series(1, 10000) i;"
+);
+
+# Add index
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v bit_hamming_ops) WITH (m = 4, ef_construction = 8);");
+
+# Delete data
+$node->safe_psql("postgres", "DELETE FROM tst WHERE i > 2500;");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r = int(rand() * $max);
+	push(@queries, "${r}::bigint::bit($dim)");
+}
+
+# Get exact results
+@expected = ();
+foreach (@queries)
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_indexscan = off;
+		WITH top AS (
+			SELECT v <~> $_ AS distance FROM tst ORDER BY distance LIMIT $limit
+		)
+		SELECT i FROM tst WHERE (v <~> $_) <= (SELECT MAX(distance) FROM top)
+	));
+	push(@expected, $res);
+}
+
+test_recall(0.35, 100, "before vacuum");
+
+# TODO Test concurrent inserts with vacuum
+$node->safe_psql("postgres", "VACUUM tst;");
+
+test_recall(0.80, 100, "after vacuum");
+
+done_testing();

test/t/030_hnsw_halfvec_vacuum_recall.pl

@@ -0,0 +1,97 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($min, $ef_search, $test_name) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = $ef_search;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = $ef_search;
+			SELECT i FROM tst ORDER BY v <-> '$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, $test_name);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v halfvec(3));");
+$node->safe_psql("postgres", "ALTER TABLE tst SET (autovacuum_enabled = false);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()] FROM generate_series(1, 10000) i;"
+);
+
+# Add index
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v halfvec_l2_ops) WITH (m = 4, ef_construction = 8);");
+
+# Delete data
+$node->safe_psql("postgres", "DELETE FROM tst WHERE i > 2500;");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "[$r1,$r2,$r3]");
+}
+
+# Get exact results
+@expected = ();
+foreach (@queries)
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_indexscan = off;
+		SELECT i FROM tst ORDER BY v <-> '$_' LIMIT $limit;
+	));
+	push(@expected, $res);
+}
+
+test_recall(0.18, $limit, "before vacuum");
+test_recall(0.95, 100, "before vacuum");
+
+# TODO Test concurrent inserts with vacuum
+$node->safe_psql("postgres", "VACUUM tst;");
+
+test_recall(0.95, $limit, "after vacuum");
+
+done_testing();

test/t/031_hnsw_sparsevec_vacuum_recall.pl

@@ -0,0 +1,97 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+
+sub test_recall
+{
+	my ($min, $ef_search, $test_name) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET hnsw.ef_search = $ef_search;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v <-> '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan/);
+
+	for my $i (0 .. $#queries)
+	{
+		my $actual = $node->safe_psql("postgres", qq(
+			SET enable_seqscan = off;
+			SET hnsw.ef_search = $ef_search;
+			SELECT i FROM tst ORDER BY v <-> '$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, $test_name);
+}
+
+# Initialize node
+$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 sparsevec(3));");
+$node->safe_psql("postgres", "ALTER TABLE tst SET (autovacuum_enabled = false);");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[random(), random(), random()]::vector::sparsevec(3) FROM generate_series(1, 10000) i;"
+);
+
+# Add index
+$node->safe_psql("postgres", "CREATE INDEX ON tst USING hnsw (v sparsevec_l2_ops) WITH (m = 4, ef_construction = 8);");
+
+# Delete data
+$node->safe_psql("postgres", "DELETE FROM tst WHERE i > 2500;");
+
+# Generate queries
+for (1 .. 20)
+{
+	my $r1 = rand();
+	my $r2 = rand();
+	my $r3 = rand();
+	push(@queries, "{1:$r1,2:$r2,3:$r3}/3");
+}
+
+# Get exact results
+@expected = ();
+foreach (@queries)
+{
+	my $res = $node->safe_psql("postgres", qq(
+		SET enable_indexscan = off;
+		SELECT i FROM tst ORDER BY v <-> '$_' LIMIT $limit;
+	));
+	push(@expected, $res);
+}
+
+test_recall(0.18, $limit, "before vacuum");
+test_recall(0.95, 100, "before vacuum");
+
+# TODO Test concurrent inserts with vacuum
+$node->safe_psql("postgres", "VACUUM tst;");
+
+test_recall(0.95, $limit, "after vacuum");
+
+done_testing();

test/t/032_ivfflat_halfvec_build_recall.pl

@@ -0,0 +1,154 @@
+use strict;
+use warnings;
+use PostgresNode;
+use TestLib;
+use Test::More;
+
+my $node;
+my @queries = ();
+my @expected;
+my $limit = 20;
+my $dim = 10;
+my $array_sql = join(",", ('random()') x $dim);
+
+sub test_recall
+{
+	my ($probes, $min, $operator) = @_;
+	my $correct = 0;
+	my $total = 0;
+
+	my $explain = $node->safe_psql("postgres", qq(
+		SET enable_seqscan = off;
+		SET ivfflat.probes = $probes;
+		EXPLAIN ANALYZE SELECT i FROM tst ORDER BY v $operator '$queries[0]' LIMIT $limit;
+	));
+	like($explain, qr/Index Scan using idx on tst/);
+
+	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 @expected_ids = split("\n", $expected[$i]);
+		my %expected_set = map { $_ => 1 } @expected_ids;
+
+		foreach (@actual_ids)
+		{
+			if (exists($expected_set{$_}))
+			{
+				$correct++;
+			}
+		}
+
+		$total += $limit;
+	}
+
+	cmp_ok($correct / $total, ">=", $min, $operator);
+}
+
+# Initialize node
+$node = get_new_node('node');
+$node->init;
+$node->start;
+
+# Create table
+$node->safe_psql("postgres", "CREATE EXTENSION vector;");
+$node->safe_psql("postgres", "CREATE TABLE tst (i int4, v halfvec($dim));");
+$node->safe_psql("postgres",
+	"INSERT INTO tst SELECT i, ARRAY[$array_sql] FROM generate_series(1, 100000) i;"
+);
+
+# Generate queries
+for (1 .. 20)
+{
+	my @r = ();
+	for (1 .. $dim)
+	{
+		push(@r, rand());
+	}
+	push(@queries, "[" . join(",", @r) . "]");
+}
+
+# Check each index type
+my @operators = ("<->", "<#>", "<=>");
+my @opclasses = ("halfvec_l2_ops", "halfvec_ip_ops", "halfvec_cosine_ops");
+
+for my $i (0 .. $#operators)
+{
+	my $operator = $operators[$i];
+	my $opclass = $opclasses[$i];
+
+	# Get exact results
+	@expected = ();
+	foreach (@queries)
+	{
+		my $res = $node->safe_psql("postgres", qq(
+			WITH top AS (
+				SELECT v $operator '$_' AS distance FROM tst ORDER BY distance LIMIT $limit
+			)
+			SELECT i FROM tst WHERE (v $operator '$_') <= (SELECT MAX(distance) FROM top)
+		));
+		push(@expected, $res);
+	}
+
+	# Build index serially
+	$node->safe_psql("postgres", qq(
+		SET max_parallel_maintenance_workers = 0;
+		CREATE INDEX idx ON tst USING ivfflat (v $opclass);
+	));
+
+	# Test approximate results
+	if ($operator ne "<#>")
+	{
+		# TODO Fix test (uniform random vectors all have similar inner product)
+		test_recall(1, 0.35, $operator);
+		test_recall(10, 0.95, $operator);
+	}
+
+	# Test probes equals lists
+	if ($operator eq "<=>")
+	{
+		test_recall(100, 0.98, $operator);
+	}
+	else
+	{
+		test_recall(100, 1.00, $operator);
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+
+	# Build index in parallel
+	my ($ret, $stdout, $stderr) = $node->psql("postgres", qq(
+		SET client_min_messages = DEBUG;
+		SET min_parallel_table_scan_size = 1;
+		CREATE INDEX idx ON tst USING ivfflat (v $opclass);
+	));
+	is($ret, 0, $stderr);
+	like($stderr, qr/using \d+ parallel workers/);
+
+	# Test approximate results
+	if ($operator ne "<#>")
+	{
+		# TODO Fix test (uniform random vectors all have similar inner product)
+		test_recall(1, 0.35, $operator);
+		test_recall(10, 0.95, $operator);
+	}
+
+	# Test probes equals lists
+	if ($operator eq "<=>")
+	{
+		test_recall(100, 0.98, $operator);
+	}
+	else
+	{
+		test_recall(100, 1.00, $operator);
+	}
+
+	$node->safe_psql("postgres", "DROP INDEX idx;");
+}
+
+done_testing();