TLA Line data Source code
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) 2018-2023, 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 :
44 : struct bloom_filter
45 : {
46 : /* K hash functions are used, seeded by caller's seed */
47 : int k_hash_funcs;
48 : uint64 seed;
49 : /* m is bitset size, in bits. Must be a power of two <= 2^32. */
50 : uint64 m;
51 : unsigned char bitset[FLEXIBLE_ARRAY_MEMBER];
52 : };
53 :
54 : static int my_bloom_power(uint64 target_bitset_bits);
55 : static int optimal_k(uint64 bitset_bits, int64 total_elems);
56 : static void k_hashes(bloom_filter *filter, uint32 *hashes, unsigned char *elem,
57 : size_t len);
58 : static 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 : */
86 : bloom_filter *
87 CBC 57 : bloom_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 57 : bitset_bytes = Min(bloom_work_mem * UINT64CONST(1024), total_elems * 2);
102 57 : 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 57 : bloom_power = my_bloom_power(bitset_bytes * BITS_PER_BYTE);
109 57 : bitset_bits = UINT64CONST(1) << bloom_power;
110 57 : bitset_bytes = bitset_bits / BITS_PER_BYTE;
111 :
112 : /* Allocate bloom filter with unset bitset */
113 57 : filter = palloc0(offsetof(bloom_filter, bitset) +
114 : sizeof(unsigned char) * bitset_bytes);
115 57 : filter->k_hash_funcs = optimal_k(bitset_bits, total_elems);
116 57 : filter->seed = seed;
117 57 : filter->m = bitset_bits;
118 :
119 57 : return filter;
120 : }
121 :
122 : /*
123 : * Free Bloom filter
124 : */
125 : void
126 55 : bloom_free(bloom_filter *filter)
127 : {
128 55 : pfree(filter);
129 55 : }
130 :
131 : /*
132 : * Add element to Bloom filter
133 : */
134 : void
135 1249518 : bloom_add_element(bloom_filter *filter, unsigned char *elem, size_t len)
136 : {
137 : uint32 hashes[MAX_HASH_FUNCS];
138 : int i;
139 :
140 1249518 : k_hashes(filter, hashes, elem, len);
141 :
142 : /* Map a bit-wise address to a byte-wise address + bit offset */
143 11228115 : for (i = 0; i < filter->k_hash_funcs; i++)
144 : {
145 9978597 : filter->bitset[hashes[i] >> 3] |= 1 << (hashes[i] & 7);
146 : }
147 1249518 : }
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 : */
156 : bool
157 1249476 : bloom_lacks_element(bloom_filter *filter, unsigned char *elem, size_t len)
158 : {
159 : uint32 hashes[MAX_HASH_FUNCS];
160 : int i;
161 :
162 1249476 : k_hashes(filter, hashes, elem, len);
163 :
164 : /* Map a bit-wise address to a byte-wise address + bit offset */
165 6200587 : for (i = 0; i < filter->k_hash_funcs; i++)
166 : {
167 5783051 : if (!(filter->bitset[hashes[i] >> 3] & (1 << (hashes[i] & 7))))
168 831940 : return true;
169 : }
170 :
171 417536 : 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 : */
186 : double
187 UBC 0 : bloom_prop_bits_set(bloom_filter *filter)
188 : {
189 0 : int bitset_bytes = filter->m / BITS_PER_BYTE;
190 0 : uint64 bits_set = pg_popcount((char *) filter->bitset, bitset_bytes);
191 :
192 0 : 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 : */
209 : static int
210 CBC 57 : my_bloom_power(uint64 target_bitset_bits)
211 : {
212 57 : int bloom_power = -1;
213 :
214 1425 : while (target_bitset_bits > 0 && bloom_power < 32)
215 : {
216 1368 : bloom_power++;
217 1368 : target_bitset_bits >>= 1;
218 : }
219 :
220 57 : 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 : */
228 : static int
229 57 : optimal_k(uint64 bitset_bits, int64 total_elems)
230 : {
231 57 : int k = rint(log(2.0) * bitset_bits / total_elems);
232 :
233 57 : 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 : */
249 : static void
250 2498994 : k_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 2498994 : hash = DatumGetUInt64(hash_any_extended(elem, len, filter->seed));
260 2498994 : x = (uint32) hash;
261 2498994 : y = (uint32) (hash >> 32);
262 2498994 : m = filter->m;
263 :
264 2498994 : x = mod_m(x, m);
265 2498994 : y = mod_m(y, m);
266 :
267 : /* Accumulate hashes */
268 2498994 : hashes[0] = x;
269 19956774 : for (i = 1; i < filter->k_hash_funcs; i++)
270 : {
271 17457780 : x = mod_m(x + y, m);
272 17457780 : y = mod_m(y + i, m);
273 :
274 17457780 : hashes[i] = x;
275 : }
276 2498994 : }
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 : */
287 : static inline uint32
288 39913548 : mod_m(uint32 val, uint64 m)
289 : {
290 39913548 : Assert(m <= PG_UINT32_MAX + UINT64CONST(1));
291 39913548 : Assert(((m - 1) & m) == 0);
292 :
293 39913548 : return val & (m - 1);
294 : }
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