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Improved performance of bit distance functions - #519

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Co-authored-by: Nathan Bossart <nathan@postgresql.org>
Co-authored-by: "Jonathan S. Katz" <jkatz@users.noreply.github.com>
This commit is contained in:
Andrew Kane
2024-04-18 13:45:00 -07:00
parent 0b938f8328
commit fb3c964ac2
8 changed files with 289 additions and 27 deletions
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2
Makefile
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@@ -3,7 +3,7 @@ EXTVERSION = 0.6.2
MODULE_big = vector
DATA = $(wildcard sql/*--*.sql)
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
OBJS = src/bitutils.o 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)

2
Makefile.win
View File

@@ -1,7 +1,7 @@
EXTENSION = vector
EXTVERSION = 0.6.2
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
OBJS = src\bitutils.obj 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_halfvec btree_sparsevec btree_vector 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_halfvec_cosine ivfflat_halfvec_ip ivfflat_halfvec_l2 ivfflat_options ivfflat_unlogged ivfflat_vector_cosine ivfflat_vector_ip ivfflat_vector_l2 sparsevec_functions sparsevec_input vector_functions vector_input

217
src/bitutils.c Normal file
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@@ -0,0 +1,217 @@
#include "postgres.h"
#include "bitutils.h"
#include "port/pg_bitutils.h"
#ifdef BIT_DISPATCH
#include <immintrin.h>
#if defined(HAVE__GET_CPUID)
#include <cpuid.h>
#else
#include <intrin.h>
#endif
#ifdef _MSC_VER
#define TARGET_AVX512_POPCOUNT
#else
#define TARGET_AVX512_POPCOUNT __attribute__((target("avx512f,avx512vpopcntdq")))
#endif
#endif
/* Disable for LLVM due to crash with bitcode generation */
#if defined(USE_TARGET_CLONES) && !defined(__POPCNT__) && !defined(__llvm__)
#define BIT_TARGET_CLONES __attribute__((target_clones("default", "popcnt")))
#else
#define BIT_TARGET_CLONES
#endif
/* Use built-ins when possible for inlining */
#if defined(HAVE__BUILTIN_POPCOUNT) && defined(HAVE_LONG_INT_64)
#define popcount64(x) __builtin_popcountl(x)
#elif defined(HAVE__BUILTIN_POPCOUNT) && defined(HAVE_LONG_LONG_INT_64)
#define popcount64(x) __builtin_popcountll(x)
#elif !defined(_MSC_VER)
/* Fails to resolve with MSVC */
#define popcount64(x) pg_popcount64(x)
#endif
uint64 (*BitHammingDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance);
double (*BitJaccardDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb);
BIT_TARGET_CLONES static uint64
BitHammingDistanceDefault(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance)
{
#ifdef popcount64
for (; bytes >= sizeof(uint64); bytes -= sizeof(uint64))
{
uint64 axs;
uint64 bxs;
/* Ensure aligned */
memcpy(&axs, ax, sizeof(uint64));
memcpy(&bxs, bx, sizeof(uint64));
distance += popcount64(axs ^ bxs);
ax += sizeof(uint64);
bx += sizeof(uint64);
}
#endif
for (uint32 i = 0; i < bytes; i++)
distance += pg_number_of_ones[ax[i] ^ bx[i]];
return distance;
}
#ifdef BIT_DISPATCH
TARGET_AVX512_POPCOUNT static uint64
BitHammingDistanceAvx512Popcount(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance)
{
__m512i dist = _mm512_setzero_si512();
for (; bytes >= sizeof(__m512i); bytes -= sizeof(__m512i))
{
__m512i axs = _mm512_loadu_si512((const __m512i *) ax);
__m512i bxs = _mm512_loadu_si512((const __m512i *) bx);
dist = _mm512_add_epi64(dist, _mm512_popcnt_epi64(_mm512_xor_si512(axs, bxs)));
ax += sizeof(__m512i);
bx += sizeof(__m512i);
}
distance += _mm512_reduce_add_epi64(dist);
return BitHammingDistanceDefault(bytes, ax, bx, distance);
}
#endif
BIT_TARGET_CLONES static double
BitJaccardDistanceDefault(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb)
{
#ifdef popcount64
for (; bytes >= sizeof(uint64); bytes -= sizeof(uint64))
{
uint64 axs;
uint64 bxs;
/* Ensure aligned */
memcpy(&axs, ax, sizeof(uint64));
memcpy(&bxs, bx, sizeof(uint64));
ab += popcount64(axs & bxs);
aa += popcount64(axs);
bb += popcount64(bxs);
ax += sizeof(uint64);
bx += sizeof(uint64);
}
#endif
for (uint32 i = 0; i < bytes; i++)
{
ab += pg_number_of_ones[ax[i] & bx[i]];
aa += pg_number_of_ones[ax[i]];
bb += pg_number_of_ones[bx[i]];
}
if (ab == 0)
return 1;
else
return 1 - (ab / ((double) (aa + bb - ab)));
}
#ifdef BIT_DISPATCH
TARGET_AVX512_POPCOUNT static double
BitJaccardDistanceAvx512Popcount(uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb)
{
__m512i abx = _mm512_setzero_si512();
__m512i aax = _mm512_setzero_si512();
__m512i bbx = _mm512_setzero_si512();
for (; bytes >= sizeof(__m512i); bytes -= sizeof(__m512i))
{
__m512i axs = _mm512_loadu_si512((const __m512i *) ax);
__m512i bxs = _mm512_loadu_si512((const __m512i *) bx);
abx = _mm512_add_epi64(abx, _mm512_popcnt_epi64(_mm512_and_si512(axs, bxs)));
aax = _mm512_add_epi64(aax, _mm512_popcnt_epi64(axs));
bbx = _mm512_add_epi64(bbx, _mm512_popcnt_epi64(bxs));
ax += sizeof(__m512i);
bx += sizeof(__m512i);
}
ab += _mm512_reduce_add_epi64(abx);
aa += _mm512_reduce_add_epi64(aax);
bb += _mm512_reduce_add_epi64(bbx);
return BitJaccardDistanceDefault(bytes, ax, bx, ab, aa, bb);
}
#endif
#ifdef BIT_DISPATCH
#define CPU_FEATURE_OSXSAVE (1 << 27) /* F1 ECX */
#define CPU_FEATURE_AVX512F (1 << 16) /* F7,0 EBX */
#define CPU_FEATURE_AVX512VPOPCNTDQ (1 << 14) /* F7,0 ECX */
#ifdef _MSC_VER
#define TARGET_XSAVE
#else
#define TARGET_XSAVE __attribute__((target("xsave")))
#endif
TARGET_XSAVE static bool
SupportsAvx512Popcount()
{
unsigned int exx[4] = {0, 0, 0, 0};
#if defined(HAVE__GET_CPUID)
__get_cpuid(1, &exx[0], &exx[1], &exx[2], &exx[3]);
#else
__cpuid(exx, 1);
#endif
/* Check OS supports XSAVE */
if ((exx[2] & CPU_FEATURE_OSXSAVE) != CPU_FEATURE_OSXSAVE)
return false;
/* Check XMM, YMM, and ZMM registers are enabled */
if ((_xgetbv(0) & 0xe6) != 0xe6)
return false;
#if defined(HAVE__GET_CPUID)
__get_cpuid_count(7, 0, &exx[0], &exx[1], &exx[2], &exx[3]);
#else
__cpuidex(exx, 7, 0);
#endif
/* Check AVX512F */
if ((exx[1] & CPU_FEATURE_AVX512F) != CPU_FEATURE_AVX512F)
return false;
/* Check AVX512VPOPCNTDQ */
return (exx[2] & CPU_FEATURE_AVX512VPOPCNTDQ) == CPU_FEATURE_AVX512VPOPCNTDQ;
}
#endif
void
BitvecInit(void)
{
/*
* Could skip pointer when single function, but no difference in
* performance
*/
BitHammingDistance = BitHammingDistanceDefault;
BitJaccardDistance = BitJaccardDistanceDefault;
#ifdef BIT_DISPATCH
if (SupportsAvx512Popcount())
{
BitHammingDistance = BitHammingDistanceAvx512Popcount;
BitJaccardDistance = BitJaccardDistanceAvx512Popcount;
}
#endif
}

23
src/bitutils.h Normal file
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@@ -0,0 +1,23 @@
#ifndef BITUTILS_H
#define BITUTILS_H
/* Only enable for more recent compilers */
#if defined(__x86_64__) && defined(__GNUC__) && __GNUC__ >= 8
#define BIT_DISPATCH
#elif defined(__x86_64__) && defined(__clang_major__) && __clang_major__ >= 7
#define BIT_DISPATCH
#elif defined(_M_AMD64) && defined(_MSC_VER) && _MSC_VER >= 1920
#define BIT_DISPATCH
#endif
/* target_clones requires glibc */
#if defined(BIT_DISPATCH) && defined(__gnu_linux__)
#define USE_TARGET_CLONES
#endif
extern uint64 (*BitHammingDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 distance);
extern double (*BitJaccardDistance) (uint32 bytes, unsigned char *ax, unsigned char *bx, uint64 ab, uint64 aa, uint64 bb);
void BitvecInit(void);
#endif

28
src/bitvector.c
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@@ -1,7 +1,7 @@
#include "postgres.h"
#include "bitutils.h"
#include "bitvector.h"
#include "port/pg_bitutils.h"
#include "utils/varbit.h"
#if PG_VERSION_NUM >= 160000
@@ -46,17 +46,10 @@ hamming_distance(PG_FUNCTION_ARGS)
{
VarBit *a = PG_GETARG_VARBIT_P(0);
VarBit *b = PG_GETARG_VARBIT_P(1);
unsigned char *ax = VARBITS(a);
unsigned char *bx = VARBITS(b);
uint64 distance = 0;
CheckDims(a, b);
/* TODO Improve performance */
for (uint32 i = 0; i < VARBITBYTES(a); i++)
distance += pg_number_of_ones[ax[i] ^ bx[i]];
PG_RETURN_FLOAT8((double) distance);
PG_RETURN_FLOAT8((double) BitHammingDistance(VARBITBYTES(a), VARBITS(a), VARBITS(b), 0));
}
/*
@@ -68,23 +61,8 @@ jaccard_distance(PG_FUNCTION_ARGS)
{
VarBit *a = PG_GETARG_VARBIT_P(0);
VarBit *b = PG_GETARG_VARBIT_P(1);
unsigned char *ax = VARBITS(a);
unsigned char *bx = VARBITS(b);
uint64 ab = 0;
uint64 aa;
uint64 bb;
CheckDims(a, b);
/* TODO Improve performance */
for (uint32 i = 0; i < VARBITBYTES(a); i++)
ab += pg_number_of_ones[ax[i] & bx[i]];
if (ab == 0)
PG_RETURN_FLOAT8(1);
aa = pg_popcount((char *) ax, VARBITBYTES(a));
bb = pg_popcount((char *) bx, VARBITBYTES(b));
PG_RETURN_FLOAT8(1 - (ab / ((double) (aa + bb - ab))));
PG_RETURN_FLOAT8(BitJaccardDistance(VARBITBYTES(a), VARBITS(a), VARBITS(b), 0, 0, 0));
}

2
src/vector.c
View File

@@ -2,6 +2,7 @@
#include <math.h>
#include "bitutils.h"
#include "bitvector.h"
#include "catalog/pg_type.h"
#include "common/shortest_dec.h"
@@ -56,6 +57,7 @@ PGDLLEXPORT void _PG_init(void);
void
_PG_init(void)
{
BitvecInit();
HalfvecInit();
HnswInit();
IvfflatInit();

36
test/expected/bit_functions.out
View File

@@ -28,6 +28,24 @@ SELECT hamming_distance('10101010101010101010', '01010101010101010101');
20
(1 row)
SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
hamming_distance
------------------
0
(1 row)
SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
hamming_distance
------------------
513
(1 row)
SELECT hamming_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
hamming_distance
------------------
2
(1 row)
SELECT hamming_distance('', '');
hamming_distance
------------------
@@ -86,6 +104,24 @@ SELECT jaccard_distance('10101010101010101010', '01010101010101010101');
1
(1 row)
SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
jaccard_distance
------------------
0
(1 row)
SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
jaccard_distance
------------------
1
(1 row)
SELECT jaccard_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
jaccard_distance
------------------
0.5
(1 row)
SELECT jaccard_distance('', '');
jaccard_distance
------------------

6
test/sql/bit_functions.sql
View File

@@ -3,6 +3,9 @@ SELECT hamming_distance('111', '110');
SELECT hamming_distance('111', '100');
SELECT hamming_distance('111', '000');
SELECT hamming_distance('10101010101010101010', '01010101010101010101');
SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
SELECT hamming_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
SELECT hamming_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
SELECT hamming_distance('', '');
SELECT hamming_distance('111', '00');
SELECT hamming_distance('111', '000'::varbit(4));
@@ -15,6 +18,9 @@ SELECT jaccard_distance('1111', '1000');
SELECT jaccard_distance('1111', '0000');
SELECT jaccard_distance('1100', '1000');
SELECT jaccard_distance('10101010101010101010', '01010101010101010101');
SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101');
SELECT jaccard_distance('101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101', '010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010');
SELECT jaccard_distance('110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011', '100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001');
SELECT jaccard_distance('', '');
SELECT jaccard_distance('1111', '000');
SELECT jaccard_distance('1111', '0000'::varbit(5));