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help / color / mirror / Atom feedFrom: Tomas Vondra <[email protected]>
Subject: [PATCH 6/8] use one-hash bloom variant
Date: Mon, 2 Nov 2020 23:55:28 +0100
one-hash tweaks
tweak generation of primes
---
src/backend/access/brin/brin_bloom.c | 179 ++++++++++++++++++++++++---
1 file changed, 159 insertions(+), 20 deletions(-)
diff --git a/src/backend/access/brin/brin_bloom.c b/src/backend/access/brin/brin_bloom.c
index f7b405f76f..87a3d5598a 100644
--- a/src/backend/access/brin/brin_bloom.c
+++ b/src/backend/access/brin/brin_bloom.c
@@ -208,6 +208,9 @@ typedef struct BloomOptions
#define BLOOM_DEFAULT_FALSE_POSITIVE_RATE 0.01 /* 1% fp rate */
#define BLOOM_DEFAULT_SORT_MODE true /* start in sort */
+/* With the minimum allowed false positive rate of 0.001, we need up to 10 hashes */
+#define BLOOM_MAX_NUM_PARTITIONS 10
+
#define BloomGetNDistinctPerRange(opts) \
((opts) && (((BloomOptions *) (opts))->nDistinctPerRange != 0) ? \
(((BloomOptions *) (opts))->nDistinctPerRange) : \
@@ -279,6 +282,7 @@ typedef struct BloomFilter
uint8 nhashes; /* number of hash functions */
uint32 nbits; /* number of bits in the bitmap (size) */
uint32 nbits_set; /* number of bits set to 1 */
+ uint32 partlens[BLOOM_MAX_NUM_PARTITIONS]; /* partition lengths */
/* data of the bloom filter (used both for sorted and hashed phase) */
char data[FLEXIBLE_ARRAY_MEMBER];
@@ -288,6 +292,127 @@ typedef struct BloomFilter
static BloomFilter *bloom_switch_to_hashing(BloomFilter *filter);
+/*
+ * generate_primes
+ * returns array of all primes less than limit
+ *
+ * WIP: very naive prime sieve; could be optimized using segmented ranges
+ */
+static uint32 *
+generate_primes(int limit)
+{
+ /* upper bound of number of primes below limit */
+ /* WIP: reference for this number */
+ int numprimes = 1.26 * limit / log(limit);
+
+ bool *is_composite = (bool *) palloc0(limit * sizeof(bool));
+ uint32 *primes = (uint32 *) palloc0(numprimes * sizeof(uint32));
+
+ int maxfactor = floor(sqrt(limit));
+ int factor = 2; /* first prime */
+
+ /* mark the sieve where the index is composite */
+ while (factor < maxfactor)
+ {
+ for (int i = factor * factor; i < limit; i += factor)
+ is_composite[i] = true;
+ do { factor++; } while (is_composite[factor]);
+ }
+
+ /* the unmarked numbers are prime, so copy over */
+ for (int i = 2, j = 0; i < limit && j < numprimes; i++)
+ {
+ if (!is_composite[i])
+ primes[j++] = i;
+ }
+
+ /* there should still be some zeroes at the end, but make sure */
+ primes[numprimes - 1] = 0;
+
+ /* pretty large, so free it now (segmented ranges would make it smaller) */
+ pfree(is_composite);
+ return primes;
+}
+
+/*
+ * set_bloom_partitions
+ * Calculate k moduli for one-hashing bloom filter.
+ *
+ * Find consecutive primes whose sum is close to nbits and
+ * return the sum. Copy the primes to the filter to use as
+ * partition lengths.
+ * WIP: one-hashing bf paper ref somewhere
+ */
+static uint32
+set_bloom_partitions(int nbits, uint8 nhashes, uint32 *partlens)
+{
+ int min, diff, incr;
+ int pidx = 0;
+ int sum = 0;
+
+ /* we want partitions roughly with this length */
+ int target_partlen = nbits / nhashes;
+ uint32 *primes;
+
+ /*
+ * Generate primes up to a maximum value, based on the target length.
+ * How much higher it needs to be is based on gaps between primes,
+ * as shown at: https://primes.utm.edu/notes/gaps.html
+ *
+ * The largest possible filter is 32kB (the largest page size), i.e.
+ * ~262kb. Assuming a single partition of this length, the maximum
+ * gap is 95. With more partitions the gaps would be smaller, so we
+ * just use this as an upper boundary, and multiply it with the max
+ * number of partitions.
+ *
+ * Note: This is an overkill, but the impact on CPU time is minimal,
+ * particularly with "regular" filter sizes. If needed, we can make
+ * this more efficient in the future.
+ */
+ primes = generate_primes(target_partlen + BLOOM_MAX_NUM_PARTITIONS * 100);
+
+ /*
+ * In our array of primes, find a sequence of length nhashes, whose
+ * last item is close to our target partition length. The end of the
+ * array will be filled with zeros, so we need to guard against that.
+ */
+ while (primes[pidx + nhashes - 1] <= target_partlen &&
+ primes[pidx + nhashes] > 0)
+ pidx++;
+
+ for (int i = 0; i < nhashes; i++)
+ sum += primes[pidx + i];
+
+ /*
+ * Since all the primes are less than or equal the desired partition
+ * length, the sum is somewhat less than nbits. Increment the starting
+ * point until we find the sequence of primes whose sum is closest to
+ * nbits. It doesn't matter whether it's higher or lower.
+ */
+ min = abs(nbits - sum);
+ for (;;)
+ {
+ incr = primes[pidx + nhashes] - primes[pidx];
+ diff = abs(nbits - (sum + incr));
+ if (diff >= min)
+ break;
+
+ min = diff;
+ sum += incr;
+ pidx++;
+ }
+
+ memcpy(partlens, &primes[pidx], nhashes * sizeof(uint32));
+
+ /* WIP: assuming it's not important to pfree primes */
+
+ /*
+ * The actual filter length will be the sum of the partition lengths
+ * rounded up to the nearest byte.
+ */
+ return (uint32) ((sum + 7) / 8) * 8;
+}
+
/*
* bloom_init
* Initialize the Bloom Filter, allocate all the memory.
@@ -319,6 +444,7 @@ bloom_init(bool sort_mode, int ndistinct, double false_positive_rate)
*/
k = log(2.0) * m / ndistinct;
k = (k - floor(k) >= 0.5) ? ceil(k) : floor(k);
+ k = Min(k, BLOOM_MAX_NUM_PARTITIONS);
/*
* When sort phase is enabled, start with a small filter which we grow
@@ -338,7 +464,9 @@ bloom_init(bool sort_mode, int ndistinct, double false_positive_rate)
filter->flags = 0;
filter->nhashes = (int) k;
- filter->nbits = m;
+
+ /* calculate the partition lengths and adjust m to match */
+ filter->nbits = set_bloom_partitions(m, k, filter->partlens);
if (!sort_mode)
filter->flags |= BLOOM_FLAG_PHASE_HASH;
@@ -463,7 +591,7 @@ static BloomFilter *
bloom_add_value(BloomFilter *filter, uint32 value, bool *updated)
{
int i;
- uint32 h1, h2;
+ int part_boundary = 0;
/* assume 'not updated' by default */
Assert(filter);
@@ -532,17 +660,16 @@ bloom_add_value(BloomFilter *filter, uint32 value, bool *updated)
/* we better be in the hashing phase */
Assert(BLOOM_IS_HASHED(filter));
- /* compute the hashes, used for the bloom filter */
- h1 = hash_uint32_extended(value, 0x71d924af) % filter->nbits;
- h2 = hash_uint32_extended(value, 0xba48b314) % filter->nbits;
-
/* compute the requested number of hashes */
for (i = 0; i < filter->nhashes; i++)
{
- /* h1 + h2 + f(i) */
- uint32 h = (h1 + i * h2) % filter->nbits;
- uint32 byte = (h / 8);
- uint32 bit = (h % 8);
+ int partlen = filter->partlens[i];
+ int bitloc = part_boundary + (value % partlen);
+
+ int byte = (bitloc / 8);
+ int bit = (bitloc % 8);
+
+ Assert(bitloc < filter->nbits);
/* if the bit is not set, set it and remember we did that */
if (! (filter->data[byte] & (0x01 << bit)))
@@ -552,6 +679,9 @@ bloom_add_value(BloomFilter *filter, uint32 value, bool *updated)
if (updated)
*updated = true;
}
+
+ /* next bit */
+ part_boundary += partlen;
}
return filter;
@@ -581,6 +711,7 @@ bloom_switch_to_hashing(BloomFilter *filter)
newfilter->nhashes = filter->nhashes;
newfilter->nbits = filter->nbits;
+ memcpy(newfilter->partlens, filter->partlens, filter->nhashes * sizeof(uint32));
newfilter->flags |= BLOOM_FLAG_PHASE_HASH;
SET_VARSIZE(newfilter, len);
@@ -605,7 +736,7 @@ static bool
bloom_contains_value(BloomFilter *filter, uint32 value)
{
int i;
- uint32 h1, h2;
+ int part_boundary = 0;
Assert(filter);
@@ -634,21 +765,23 @@ bloom_contains_value(BloomFilter *filter, uint32 value)
/* now the regular hashing mode */
Assert(BLOOM_IS_HASHED(filter));
- /* calculate the two hashes */
- h1 = hash_uint32_extended(value, 0x71d924af) % filter->nbits;
- h2 = hash_uint32_extended(value, 0xba48b314) % filter->nbits;
-
/* compute the requested number of hashes */
for (i = 0; i < filter->nhashes; i++)
{
- /* h1 + h2 + f(i) */
- uint32 h = (h1 + i * h2) % filter->nbits;
- uint32 byte = (h / 8);
- uint32 bit = (h % 8);
+ int partlen = filter->partlens[i];
+ int bitloc = part_boundary + (value % partlen);
+
+ int byte = (bitloc / 8);
+ int bit = (bitloc % 8);
+
+ Assert(bitloc < filter->nbits);
/* if the bit is not set, the value is not there */
if (! (filter->data[byte] & (0x01 << bit)))
return false;
+
+ /* next bit */
+ part_boundary += partlen;
}
/* all hashes found in bloom filter */
@@ -1081,8 +1214,14 @@ brin_bloom_summary_out(PG_FUNCTION_ARGS)
if (BLOOM_IS_HASHED(filter))
{
- appendStringInfo(&str, "mode: hashed nhashes: %u nbits: %u nbits_set: %u",
+ appendStringInfo(&str,
+ "mode: hashed nhashes: %u nbits: %u nbits_set: %u partition lengths: [",
filter->nhashes, filter->nbits, filter->nbits_set);
+ for (int i = 0; i < filter->nhashes - 1; i++)
+ {
+ appendStringInfo(&str, "%u, ", filter->partlens[i]);
+ }
+ appendStringInfo(&str, "%u]", filter->partlens[filter->nhashes - 1]);
}
else
{
--
2.26.2
--------------45196B023835614BDFCBD16D
Content-Type: text/x-patch; charset=UTF-8;
name="0005-use-two-independent-hashes-20201220.patch"
Content-Transfer-Encoding: 7bit
Content-Disposition: attachment;
filename="0005-use-two-independent-hashes-20201220.patch"
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