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bloomfilter.c
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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) 2018-2022, 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 */
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 a, 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  */
87 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  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  */
125 void
127 {
128  pfree(filter);
129 }
130 
131 /*
132  * Add element to Bloom filter
133  */
134 void
135 bloom_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  */
156 bool
157 bloom_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  */
186 double
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  */
209 static int
210 my_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  */
228 static int
229 optimal_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  */
249 static void
250 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  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  */
287 static inline uint32
288 mod_m(uint32 val, uint64 m)
289 {
290  Assert(m <= PG_UINT32_MAX + UINT64CONST(1));
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
bloom_filter * bloom_create(int64 total_elems, int bloom_work_mem, uint64 seed)
Definition: bloomfilter.c:87
static int optimal_k(uint64 bitset_bits, int64 total_elems)
Definition: bloomfilter.c:229
double bloom_prop_bits_set(bloom_filter *filter)
Definition: bloomfilter.c:187
static uint32 mod_m(uint32 a, 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
unsigned int uint32
Definition: c.h:441
#define Min(x, y)
Definition: c.h:986
#define offsetof(type, field)
Definition: c.h:727
#define PG_UINT32_MAX
Definition: c.h:525
#define Max(x, y)
Definition: c.h:980
#define FLEXIBLE_ARRAY_MEMBER
Definition: c.h:350
static Datum hash_any_extended(const unsigned char *k, int keylen, uint64 seed)
Definition: hashfn.h:37
long val
Definition: informix.c:664
int y
Definition: isn.c:72
int x
Definition: isn.c:71
int a
Definition: isn.c:69
int i
Definition: isn.c:73
Assert(fmt[strlen(fmt) - 1] !='\n')
void pfree(void *pointer)
Definition: mcxt.c:1175
void * palloc0(Size size)
Definition: mcxt.c:1099
uint64 pg_popcount(const char *buf, int bytes)
Definition: pg_bitutils.c:296
#define BITS_PER_BYTE
const void size_t len
#define DatumGetUInt64(X)
Definition: postgres.h:678
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