PostgreSQL Source Code git master
bloomfilter.c
Go to the documentation of this file.
1/*-------------------------------------------------------------------------
2 *
3 * bloomfilter.c
4 * Space-efficient set membership testing
5 *
6 * A Bloom filter is a probabilistic data structure that is used to test an
7 * element's membership of a set. False positives are possible, but false
8 * negatives are not; a test of membership of the set returns either "possibly
9 * in set" or "definitely not in set". This is typically very space efficient,
10 * which can be a decisive advantage.
11 *
12 * Elements can be added to the set, but not removed. The more elements that
13 * are added, the larger the probability of false positives. Caller must hint
14 * an estimated total size of the set when the Bloom filter is initialized.
15 * This is used to balance the use of memory against the final false positive
16 * rate.
17 *
18 * The implementation is well suited to data synchronization problems between
19 * unordered sets, especially where predictable performance is important and
20 * some false positives are acceptable. It's also well suited to cache
21 * filtering problems where a relatively small and/or low cardinality set is
22 * fingerprinted, especially when many subsequent membership tests end up
23 * indicating that values of interest are not present. That should save the
24 * caller many authoritative lookups, such as expensive probes of a much larger
25 * on-disk structure.
26 *
27 * Copyright (c) 2018-2025, PostgreSQL Global Development Group
28 *
29 * IDENTIFICATION
30 * src/backend/lib/bloomfilter.c
31 *
32 *-------------------------------------------------------------------------
33 */
34#include "postgres.h"
35
36#include <math.h>
37
38#include "common/hashfn.h"
39#include "lib/bloomfilter.h"
40#include "port/pg_bitutils.h"
41
42#define MAX_HASH_FUNCS 10
43
45{
46 /* K hash functions are used, seeded by caller's seed */
49 /* m is bitset size, in bits. Must be a power of two <= 2^32. */
52};
53
54static int my_bloom_power(uint64 target_bitset_bits);
55static int optimal_k(uint64 bitset_bits, int64 total_elems);
56static void k_hashes(bloom_filter *filter, uint32 *hashes, unsigned char *elem,
57 size_t len);
58static inline uint32 mod_m(uint32 val, uint64 m);
59
60/*
61 * Create Bloom filter in caller's memory context. We aim for a false positive
62 * rate of between 1% and 2% when bitset size is not constrained by memory
63 * availability.
64 *
65 * total_elems is an estimate of the final size of the set. It should be
66 * approximately correct, but the implementation can cope well with it being
67 * off by perhaps a factor of five or more. See "Bloom Filters in
68 * Probabilistic Verification" (Dillinger & Manolios, 2004) for details of why
69 * this is the case.
70 *
71 * bloom_work_mem is sized in KB, in line with the general work_mem convention.
72 * This determines the size of the underlying bitset (trivial bookkeeping space
73 * isn't counted). The bitset is always sized as a power of two number of
74 * bits, and the largest possible bitset is 512MB (2^32 bits). The
75 * implementation allocates only enough memory to target its standard false
76 * positive rate, using a simple formula with caller's total_elems estimate as
77 * an input. The bitset might be as small as 1MB, even when bloom_work_mem is
78 * much higher.
79 *
80 * The Bloom filter is seeded using a value provided by the caller. Using a
81 * distinct seed value on every call makes it unlikely that the same false
82 * positives will reoccur when the same set is fingerprinted a second time.
83 * Callers that don't care about this pass a constant as their seed, typically
84 * 0. Callers can also use a pseudo-random seed, eg from pg_prng_uint64().
85 */
87bloom_create(int64 total_elems, int bloom_work_mem, uint64 seed)
88{
89 bloom_filter *filter;
90 int bloom_power;
91 uint64 bitset_bytes;
92 uint64 bitset_bits;
93
94 /*
95 * Aim for two bytes per element; this is sufficient to get a false
96 * positive rate below 1%, independent of the size of the bitset or total
97 * number of elements. Also, if rounding down the size of the bitset to
98 * the next lowest power of two turns out to be a significant drop, the
99 * false positive rate still won't exceed 2% in almost all cases.
100 */
101 bitset_bytes = Min(bloom_work_mem * UINT64CONST(1024), total_elems * 2);
102 bitset_bytes = Max(1024 * 1024, bitset_bytes);
103
104 /*
105 * Size in bits should be the highest power of two <= target. bitset_bits
106 * is uint64 because PG_UINT32_MAX is 2^32 - 1, not 2^32
107 */
108 bloom_power = my_bloom_power(bitset_bytes * BITS_PER_BYTE);
109 bitset_bits = UINT64CONST(1) << bloom_power;
110 bitset_bytes = bitset_bits / BITS_PER_BYTE;
111
112 /* Allocate bloom filter with unset bitset */
113 filter = palloc0(offsetof(bloom_filter, bitset) +
114 sizeof(unsigned char) * bitset_bytes);
115 filter->k_hash_funcs = optimal_k(bitset_bits, total_elems);
116 filter->seed = seed;
117 filter->m = bitset_bits;
118
119 return filter;
120}
121
122/*
123 * Free Bloom filter
124 */
125void
127{
128 pfree(filter);
129}
130
131/*
132 * Add element to Bloom filter
133 */
134void
135bloom_add_element(bloom_filter *filter, unsigned char *elem, size_t len)
136{
137 uint32 hashes[MAX_HASH_FUNCS];
138 int i;
139
140 k_hashes(filter, hashes, elem, len);
141
142 /* Map a bit-wise address to a byte-wise address + bit offset */
143 for (i = 0; i < filter->k_hash_funcs; i++)
144 {
145 filter->bitset[hashes[i] >> 3] |= 1 << (hashes[i] & 7);
146 }
147}
148
149/*
150 * Test if Bloom filter definitely lacks element.
151 *
152 * Returns true if the element is definitely not in the set of elements
153 * observed by bloom_add_element(). Otherwise, returns false, indicating that
154 * element is probably present in set.
155 */
156bool
157bloom_lacks_element(bloom_filter *filter, unsigned char *elem, size_t len)
158{
159 uint32 hashes[MAX_HASH_FUNCS];
160 int i;
161
162 k_hashes(filter, hashes, elem, len);
163
164 /* Map a bit-wise address to a byte-wise address + bit offset */
165 for (i = 0; i < filter->k_hash_funcs; i++)
166 {
167 if (!(filter->bitset[hashes[i] >> 3] & (1 << (hashes[i] & 7))))
168 return true;
169 }
170
171 return false;
172}
173
174/*
175 * What proportion of bits are currently set?
176 *
177 * Returns proportion, expressed as a multiplier of filter size. That should
178 * generally be close to 0.5, even when we have more than enough memory to
179 * ensure a false positive rate within target 1% to 2% band, since more hash
180 * functions are used as more memory is available per element.
181 *
182 * This is the only instrumentation that is low overhead enough to appear in
183 * debug traces. When debugging Bloom filter code, it's likely to be far more
184 * interesting to directly test the false positive rate.
185 */
186double
188{
189 int bitset_bytes = filter->m / BITS_PER_BYTE;
190 uint64 bits_set = pg_popcount((char *) filter->bitset, bitset_bytes);
191
192 return bits_set / (double) filter->m;
193}
194
195/*
196 * Which element in the sequence of powers of two is less than or equal to
197 * target_bitset_bits?
198 *
199 * Value returned here must be generally safe as the basis for actual bitset
200 * size.
201 *
202 * Bitset is never allowed to exceed 2 ^ 32 bits (512MB). This is sufficient
203 * for the needs of all current callers, and allows us to use 32-bit hash
204 * functions. It also makes it easy to stay under the MaxAllocSize restriction
205 * (caller needs to leave room for non-bitset fields that appear before
206 * flexible array member, so a 1GB bitset would use an allocation that just
207 * exceeds MaxAllocSize).
208 */
209static int
210my_bloom_power(uint64 target_bitset_bits)
211{
212 int bloom_power = -1;
213
214 while (target_bitset_bits > 0 && bloom_power < 32)
215 {
216 bloom_power++;
217 target_bitset_bits >>= 1;
218 }
219
220 return bloom_power;
221}
222
223/*
224 * Determine optimal number of hash functions based on size of filter in bits,
225 * and projected total number of elements. The optimal number is the number
226 * that minimizes the false positive rate.
227 */
228static int
229optimal_k(uint64 bitset_bits, int64 total_elems)
230{
231 int k = rint(log(2.0) * bitset_bits / total_elems);
232
233 return Max(1, Min(k, MAX_HASH_FUNCS));
234}
235
236/*
237 * Generate k hash values for element.
238 *
239 * Caller passes array, which is filled-in with k values determined by hashing
240 * caller's element.
241 *
242 * Only 2 real independent hash functions are actually used to support an
243 * interface of up to MAX_HASH_FUNCS hash functions; enhanced double hashing is
244 * used to make this work. The main reason we prefer enhanced double hashing
245 * to classic double hashing is that the latter has an issue with collisions
246 * when using power of two sized bitsets. See Dillinger & Manolios for full
247 * details.
248 */
249static void
250k_hashes(bloom_filter *filter, uint32 *hashes, unsigned char *elem, size_t len)
251{
252 uint64 hash;
253 uint32 x,
254 y;
255 uint64 m;
256 int i;
257
258 /* Use 64-bit hashing to get two independent 32-bit hashes */
259 hash = DatumGetUInt64(hash_any_extended(elem, len, filter->seed));
260 x = (uint32) hash;
261 y = (uint32) (hash >> 32);
262 m = filter->m;
263
264 x = mod_m(x, m);
265 y = mod_m(y, m);
266
267 /* Accumulate hashes */
268 hashes[0] = x;
269 for (i = 1; i < filter->k_hash_funcs; i++)
270 {
271 x = mod_m(x + y, m);
272 y = mod_m(y + i, m);
273
274 hashes[i] = x;
275 }
276}
277
278/*
279 * Calculate "val MOD m" inexpensively.
280 *
281 * Assumes that m (which is bitset size) is a power of two.
282 *
283 * Using a power of two number of bits for bitset size allows us to use bitwise
284 * AND operations to calculate the modulo of a hash value. It's also a simple
285 * way of avoiding the modulo bias effect.
286 */
287static inline uint32
289{
291 Assert(((m - 1) & m) == 0);
292
293 return val & (m - 1);
294}
void bloom_free(bloom_filter *filter)
Definition: bloomfilter.c:126
#define MAX_HASH_FUNCS
Definition: bloomfilter.c:42
static int optimal_k(uint64 bitset_bits, int64 total_elems)
Definition: bloomfilter.c:229
bloom_filter * bloom_create(int64 total_elems, int bloom_work_mem, uint64 seed)
Definition: bloomfilter.c:87
double bloom_prop_bits_set(bloom_filter *filter)
Definition: bloomfilter.c:187
static uint32 mod_m(uint32 val, uint64 m)
Definition: bloomfilter.c:288
bool bloom_lacks_element(bloom_filter *filter, unsigned char *elem, size_t len)
Definition: bloomfilter.c:157
static int my_bloom_power(uint64 target_bitset_bits)
Definition: bloomfilter.c:210
static void k_hashes(bloom_filter *filter, uint32 *hashes, unsigned char *elem, size_t len)
Definition: bloomfilter.c:250
void bloom_add_element(bloom_filter *filter, unsigned char *elem, size_t len)
Definition: bloomfilter.c:135
#define Min(x, y)
Definition: c.h:975
#define PG_UINT32_MAX
Definition: c.h:561
#define Max(x, y)
Definition: c.h:969
int64_t int64
Definition: c.h:499
#define FLEXIBLE_ARRAY_MEMBER
Definition: c.h:434
uint64_t uint64
Definition: c.h:503
uint32_t uint32
Definition: c.h:502
#define UINT64CONST(x)
Definition: c.h:517
static Datum hash_any_extended(const unsigned char *k, int keylen, uint64 seed)
Definition: hashfn.h:37
Assert(PointerIsAligned(start, uint64))
long val
Definition: informix.c:689
int y
Definition: isn.c:73
int x
Definition: isn.c:72
int i
Definition: isn.c:74
void pfree(void *pointer)
Definition: mcxt.c:1524
void * palloc0(Size size)
Definition: mcxt.c:1347
static uint64 pg_popcount(const char *buf, int bytes)
Definition: pg_bitutils.h:337
#define BITS_PER_BYTE
const void size_t len
static uint64 DatumGetUInt64(Datum X)
Definition: postgres.h:424
static unsigned hash(unsigned *uv, int n)
Definition: rege_dfa.c:715
unsigned char bitset[FLEXIBLE_ARRAY_MEMBER]
Definition: bloomfilter.c:51
uint64 seed
Definition: bloomfilter.c:48
int k_hash_funcs
Definition: bloomfilter.c:47