LCOV - code coverage report
Current view: top level - src/backend/lib - bloomfilter.c (source / functions) Hit Total Coverage
Test: PostgreSQL 17devel Lines: 53 53 100.0 %
Date: 2024-02-22 00:11:39 Functions: 9 9 100.0 %
Legend: Lines: hit not hit

          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) 2018-2024, 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         148 : 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         148 :     bitset_bytes = Min(bloom_work_mem * UINT64CONST(1024), total_elems * 2);
     102         148 :     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         148 :     bloom_power = my_bloom_power(bitset_bytes * BITS_PER_BYTE);
     109         148 :     bitset_bits = UINT64CONST(1) << bloom_power;
     110         148 :     bitset_bytes = bitset_bits / BITS_PER_BYTE;
     111             : 
     112             :     /* Allocate bloom filter with unset bitset */
     113         148 :     filter = palloc0(offsetof(bloom_filter, bitset) +
     114             :                      sizeof(unsigned char) * bitset_bytes);
     115         148 :     filter->k_hash_funcs = optimal_k(bitset_bits, total_elems);
     116         148 :     filter->seed = seed;
     117         148 :     filter->m = bitset_bits;
     118             : 
     119         148 :     return filter;
     120             : }
     121             : 
     122             : /*
     123             :  * Free Bloom filter
     124             :  */
     125             : void
     126         130 : bloom_free(bloom_filter *filter)
     127             : {
     128         130 :     pfree(filter);
     129         130 : }
     130             : 
     131             : /*
     132             :  * Add element to Bloom filter
     133             :  */
     134             : void
     135     2748374 : bloom_add_element(bloom_filter *filter, unsigned char *elem, size_t len)
     136             : {
     137             :     uint32      hashes[MAX_HASH_FUNCS];
     138             :     int         i;
     139             : 
     140     2748374 :     k_hashes(filter, hashes, elem, len);
     141             : 
     142             :     /* Map a bit-wise address to a byte-wise address + bit offset */
     143    25198948 :     for (i = 0; i < filter->k_hash_funcs; i++)
     144             :     {
     145    22450574 :         filter->bitset[hashes[i] >> 3] |= 1 << (hashes[i] & 7);
     146             :     }
     147     2748374 : }
     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     2743556 : bloom_lacks_element(bloom_filter *filter, unsigned char *elem, size_t len)
     158             : {
     159             :     uint32      hashes[MAX_HASH_FUNCS];
     160             :     int         i;
     161             : 
     162     2743556 :     k_hashes(filter, hashes, elem, len);
     163             : 
     164             :     /* Map a bit-wise address to a byte-wise address + bit offset */
     165    15088774 :     for (i = 0; i < filter->k_hash_funcs; i++)
     166             :     {
     167    14009002 :         if (!(filter->bitset[hashes[i] >> 3] & (1 << (hashes[i] & 7))))
     168     1663784 :             return true;
     169             :     }
     170             : 
     171     1079772 :     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           4 : bloom_prop_bits_set(bloom_filter *filter)
     188             : {
     189           4 :     int         bitset_bytes = filter->m / BITS_PER_BYTE;
     190           4 :     uint64      bits_set = pg_popcount((char *) filter->bitset, bitset_bytes);
     191             : 
     192           4 :     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         148 : my_bloom_power(uint64 target_bitset_bits)
     211             : {
     212         148 :     int         bloom_power = -1;
     213             : 
     214        3700 :     while (target_bitset_bits > 0 && bloom_power < 32)
     215             :     {
     216        3552 :         bloom_power++;
     217        3552 :         target_bitset_bits >>= 1;
     218             :     }
     219             : 
     220         148 :     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         148 : optimal_k(uint64 bitset_bits, int64 total_elems)
     230             : {
     231         148 :     int         k = rint(log(2.0) * bitset_bits / total_elems);
     232             : 
     233         148 :     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     5491930 : 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     5491930 :     hash = DatumGetUInt64(hash_any_extended(elem, len, filter->seed));
     260     5491930 :     x = (uint32) hash;
     261     5491930 :     y = (uint32) (hash >> 32);
     262     5491930 :     m = filter->m;
     263             : 
     264     5491930 :     x = mod_m(x, m);
     265     5491930 :     y = mod_m(y, m);
     266             : 
     267             :     /* Accumulate hashes */
     268     5491930 :     hashes[0] = x;
     269    44852968 :     for (i = 1; i < filter->k_hash_funcs; i++)
     270             :     {
     271    39361038 :         x = mod_m(x + y, m);
     272    39361038 :         y = mod_m(y + i, m);
     273             : 
     274    39361038 :         hashes[i] = x;
     275             :     }
     276     5491930 : }
     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    89705936 : mod_m(uint32 val, uint64 m)
     289             : {
     290             :     Assert(m <= PG_UINT32_MAX + UINT64CONST(1));
     291             :     Assert(((m - 1) & m) == 0);
     292             : 
     293    89705936 :     return val & (m - 1);
     294             : }

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