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/* -*- Mode: C++; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this file,
* You can obtain one at http://mozilla.org/MPL/2.0/. */
/*
* A counting Bloom filter implementation. This allows consumers to
* do fast probabilistic "is item X in set Y?" testing which will
* never answer "no" when the correct answer is "yes" (but might
* incorrectly answer "yes" when the correct answer is "no").
*/
#ifndef mozilla_BloomFilter_h_
#define mozilla_BloomFilter_h_
#include "mozilla/Likely.h"
#include "mozilla/StandardInteger.h"
#include "mozilla/Util.h"
#include <string.h>
namespace mozilla {
/*
* This class implements a counting Bloom filter as described at
* <http://en.wikipedia.org/wiki/Bloom_filter#Counting_filters>, with
* 8-bit counters. This allows quick probabilistic answers to the
* question "is object X in set Y?" where the contents of Y might not
* be time-invariant. The probabilistic nature of the test means that
* sometimes the answer will be "yes" when it should be "no". If the
* answer is "no", then X is guaranteed not to be in Y.
*
* The filter is parametrized on KeySize, which is the size of the key
* generated by each of hash functions used by the filter, in bits,
* and the type of object T being added and removed. T must implement
* a |uint32_t hash() const| method which returns a uint32_t hash key
* that will be used to generate the two separate hash functions for
* the Bloom filter. This hash key MUST be well-distributed for good
* results! KeySize is not allowed to be larger than 16.
*
* The filter uses exactly 2**KeySize bytes of memory. From now on we
* will refer to the memory used by the filter as M.
*
* The expected rate of incorrect "yes" answers depends on M and on
* the number N of objects in set Y. As long as N is small compared
* to M, the rate of such answers is expected to be approximately
* 4*(N/M)**2 for this filter. In practice, if Y has a few hundred
* elements then using a KeySize of 12 gives a reasonably low
* incorrect answer rate. A KeySize of 12 has the additional benefit
* of using exactly one page for the filter in typical hardware
* configurations.
*/
template<unsigned KeySize, class T>
class BloomFilter
{
/*
* A counting Bloom filter with 8-bit counters. For now we assume
* that having two hash functions is enough, but we may revisit that
* decision later.
*
* The filter uses an array with 2**KeySize entries.
*
* Assuming a well-distributed hash function, a Bloom filter with
* array size M containing N elements and
* using k hash function has expected false positive rate exactly
*
* $ (1 - (1 - 1/M)^{kN})^k $
*
* because each array slot has a
*
* $ (1 - 1/M)^{kN} $
*
* chance of being 0, and the expected false positive rate is the
* probability that all of the k hash functions will hit a nonzero
* slot.
*
* For reasonable assumptions (M large, kN large, which should both
* hold if we're worried about false positives) about M and kN this
* becomes approximately
*
* $$ (1 - \exp(-kN/M))^k $$
*
* For our special case of k == 2, that's $(1 - \exp(-2N/M))^2$,
* or in other words
*
* $$ N/M = -0.5 * \ln(1 - \sqrt(r)) $$
*
* where r is the false positive rate. This can be used to compute
* the desired KeySize for a given load N and false positive rate r.
*
* If N/M is assumed small, then the false positive rate can
* further be approximated as 4*N^2/M^2. So increasing KeySize by
* 1, which doubles M, reduces the false positive rate by about a
* factor of 4, and a false positive rate of 1% corresponds to
* about M/N == 20.
*
* What this means in practice is that for a few hundred keys using a
* KeySize of 12 gives false positive rates on the order of 0.25-4%.
*
* Similarly, using a KeySize of 10 would lead to a 4% false
* positive rate for N == 100 and to quite bad false positive
* rates for larger N.
*/
public:
BloomFilter() {
MOZ_STATIC_ASSERT(KeySize <= keyShift, "KeySize too big");
// Should we have a custom operator new using calloc instead and
// require that we're allocated via the operator?
clear();
}
/*
* Clear the filter. This should be done before reusing it, because
* just removing all items doesn't clear counters that hit the upper
* bound.
*/
void clear();
/*
* Add an item to the filter.
*/
void add(const T* t);
/*
* Remove an item from the filter.
*/
void remove(const T* t);
/*
* Check whether the filter might contain an item. This can
* sometimes return true even if the item is not in the filter,
* but will never return false for items that are actually in the
* filter.
*/
bool mightContain(const T* t) const;
/*
* Methods for add/remove/contain when we already have a hash computed
*/
void add(uint32_t hash);
void remove(uint32_t hash);
bool mightContain(uint32_t hash) const;
private:
static const size_t arraySize = (1 << KeySize);
static const uint32_t keyMask = (1 << KeySize) - 1;
static const uint32_t keyShift = 16;
static uint32_t hash1(uint32_t hash) { return hash & keyMask; }
static uint32_t hash2(uint32_t hash) { return (hash >> keyShift) & keyMask; }
uint8_t& firstSlot(uint32_t hash) { return counters[hash1(hash)]; }
uint8_t& secondSlot(uint32_t hash) { return counters[hash2(hash)]; }
const uint8_t& firstSlot(uint32_t hash) const { return counters[hash1(hash)]; }
const uint8_t& secondSlot(uint32_t hash) const { return counters[hash2(hash)]; }
static bool full(const uint8_t& slot) { return slot == UINT8_MAX; }
uint8_t counters[arraySize];
};
template<unsigned KeySize, class T>
inline void
BloomFilter<KeySize, T>::clear()
{
memset(counters, 0, arraySize);
}
template<unsigned KeySize, class T>
inline void
BloomFilter<KeySize, T>::add(uint32_t hash)
{
uint8_t& slot1 = firstSlot(hash);
if (MOZ_LIKELY(!full(slot1)))
++slot1;
uint8_t& slot2 = secondSlot(hash);
if (MOZ_LIKELY(!full(slot2)))
++slot2;
}
template<unsigned KeySize, class T>
MOZ_ALWAYS_INLINE void
BloomFilter<KeySize, T>::add(const T* t)
{
uint32_t hash = t->hash();
return add(hash);
}
template<unsigned KeySize, class T>
inline void
BloomFilter<KeySize, T>::remove(uint32_t hash)
{
// If the slots are full, we don't know whether we bumped them to be
// there when we added or not, so just leave them full.
uint8_t& slot1 = firstSlot(hash);
if (MOZ_LIKELY(!full(slot1)))
--slot1;
uint8_t& slot2 = secondSlot(hash);
if (MOZ_LIKELY(!full(slot2)))
--slot2;
}
template<unsigned KeySize, class T>
MOZ_ALWAYS_INLINE void
BloomFilter<KeySize, T>::remove(const T* t)
{
uint32_t hash = t->hash();
remove(hash);
}
template<unsigned KeySize, class T>
MOZ_ALWAYS_INLINE bool
BloomFilter<KeySize, T>::mightContain(uint32_t hash) const
{
// Check that all the slots for this hash contain something
return firstSlot(hash) && secondSlot(hash);
}
template<unsigned KeySize, class T>
MOZ_ALWAYS_INLINE bool
BloomFilter<KeySize, T>::mightContain(const T* t) const
{
uint32_t hash = t->hash();
return mightContain(hash);
}
} // namespace mozilla
#endif /* mozilla_BloomFilter_h_ */
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