BloomFilter.h

/* -*- 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_ */