/*
 * Copyright (C) 2014 Freie Universität Berlin
 *
 * This file is subject to the terms and conditions of the GNU Lesser
 * General Public License v2.1. See the file LICENSE in the top level
 * directory for more details.
 */

/*
 * bloom.c
 *
 * Bloom filters
 *
 * HISTORY
 *                                                   {x,  y,  z}
 * A Bloom filter is a probibalistic                  :   :   :
 * data structure with several interesting           /|\ /|\ /|\
 * properties, such as low memory usage,            / | X | X | \
 * asymmetric query confidence, and a very         /  |/ \|/ \|  \
 * speedy O(k) membership test.                   /   |   |   \   \
 *                                               /   /|  /|\  |\   \
 * Because a Bloom filter can                   .   . . . . . . .   .
 * accept any input that can be       00000000001000101010101010100010000000000
 * hashed effectively (such as                       "    "    "
 * strings), that membership test                     \   |   /
 * tends to draw a crowd. TNSTAAFL, but                \  |  /
 * as caveats go, the Bloom filters' are                \ | /
 * more interesting than incapacitating.                 \|/
 *                                                        :
 * Most notably, it can tell you with certainty          {w}
 * that an item 'i' is *not* a member of set 's',
 * but it can only tell you with some finite
 * probability whether an item 'i' *is* a member
 * of set 's'.
 *
 * Still, along with the intriguing possibility of using bitwise AND and OR
 * to compute the logical union and intersection of two filters, the cheap
 * cost of adding elements to the filter set, and the low memory requirements,
 * the Bloom filter is a good choice for many applications.
 *
 * NOTES
 *
 * Let's look more closely at the probability values.
 *
 * Assume that a hash function selects each array position with equal
 * probability. If m is the number of bits in the array, and k is the number
 * of hash functions, then the probability that a certain bit is not set
 * to 1 by a certain hash function during the insertion of an element is
 *
 *      1-(1/m).
 *
 * The probability that it is not set to 1 by any of the hash functions is
 *
 *      (1-(1/m))^k.
 *
 * If we have inserted n elements, the probability that a certain bit is
 * set 0 is
 *
 *      (1-(1/m))^kn,
 *
 * Meaning that the probability said bit is set to 1 is therefore
 *
 *      1-([1-(1/m)]^kn).
 *
 * Now test membership of an element that is not in the set. Each of the k
 * array positions computed by the hash functions is 1 with a probability
 * as above. The probability of all of them being 1, which would cause the
 * algorithm to erroneously claim that the element is in the set, is often
 * given as
 *
 *      (1-[1-(1/m)]^kn)^k ~~ (1 - e^(-kn/m))^k.
 *
 * This is not strictly correct as it assumes independence for the
 * probabilities of each bit being set. However, assuming it is a close
 * approximation we have that the probability of false positives descreases
 * as m (the number of bits in the array) increases, and increases as n
 * (the number of inserted elements) increases. For a given m and n, the
 * value of k (the number of hash functions) that minimizes the probability
 * is
 *
 *      (m/n)ln(2) ~~ 0.7(m/n),
 *
 * which gives the false positive probability of
 *
 *      2^-k ~~ 0.6185^(m/n).
 *
 * The required number of bits m, given n and a desired false positive
 * probability p (and assuming the optimal value of k is used) can be
 * computed by substituting the optimal value of k in the probability
 * expression above:
 *
 *      p = (1 - e^(-(((m/n)ln(2))*(n/m))))^((m/n)ln(2)),
 *
 * which simplifies to
 *
 *      ln(p) = -(m/n) * (ln2)^2.
 *
 * This results in the equation
 *
 *      m = -((n*ln(p)) / ((ln(2))^2))
 *
 * The classic filter uses
 *
 *       1.44*log2(1/eta)
 *
 * bits of space per inserted key, where eta is the false positive rate of
 * the Bloom filter.
 *
 */

/**
 * @defgroup    sys_bloom Bloom filter
 * @ingroup     sys
 * @brief       Bloom filter library
 * @{
 *
 * @file
 * @brief       Bloom filter API
 *
 * @author Christian Mehlis <mehlis@inf.fu-berlin.de>
 */

#ifndef BLOOM_H
#define BLOOM_H

#include <stdlib.h>
#include <stdbool.h>
#include <stdint.h>

#ifdef __cplusplus
extern "C" {
#endif

/**
 * @brief hash function to use in thee filter
 */
typedef uint32_t (*hashfp_t)(const uint8_t *, int len);

/**
 * @brief bloom_t bloom filter object
 */
typedef struct {
    /** number of bits in the bloom array */
    size_t m;
    /** number of hash functions */
    size_t k;
    /** the bloom array */
    uint8_t *a;
    /** the hash functions */
    hashfp_t *hash;
} bloom_t;

/**
 * @brief Initialize a Bloom Filter.
 *
 * @note For best results, make 'size' a power of 2.
 *
 * @param bloom             bloom_t to initialize
 * @param size              size of the bloom filter in bits
 * @param bitfield          underlying bitfield of the bloom filter
 * @param hashes            array of hashes
 * @param hashes_numof      number of elements in hashes
 *
 * @pre     @p bitfield MUST be large enough to hold @p size bits.
 */
void bloom_init(bloom_t *bloom, size_t size, uint8_t *bitfield, hashfp_t *hashes, int hashes_numof);

/**
 * @brief Delete a Bloom filter.
 *
 * @param bloom The condemned
 * @return nothing
 *
 */
void bloom_del(bloom_t *bloom);

/**
 * @brief Add a string to a Bloom filter.
 *
 * CAVEAT
 * Once a string has been added to the filter, it cannot be "removed"!
 *
 * @param bloom  Bloom filter
 * @param buf    string to add
 * @param len    the length of the string @p buf
 * @return       nothing
 *
 */
void bloom_add(bloom_t *bloom, const uint8_t *buf, size_t len);

/**
 * @brief Determine if a string is in the Bloom filter.
 *
 * The string 's' is hashed once for each of the 'k' hash functions, as
 * though we were planning to add it to the filter. Instead of adding it
 * however, we examine the bit that we *would* have set, and consider its
 * value.
 *
 * If the bit is 1 (set), the string we are hashing may be in the filter,
 * since it would have set this bit when it was originally hashed. However,
 * it may also be that another string just happened to produce a hash value
 * that would also set this bit. That would be a false positive. This is why
 * we have k > 1, so we can minimize the likelihood of false positives
 * occuring.
 *
 * If every bit corresponding to every one of the k hashes of our query
 * string is set, we can say with some probability of being correct that
 * the string we are holding is indeed "in" the filter. However, we can
 * never be sure.
 *
 * If, however, as we hash our string and peek at the resulting bit in the
 * filter, we find the bit is 0 (not set)... well now, that's different.
 * In this case, we can say with absolute certainty that the string we are
 * holding is *not* in the filter, because if it were, this bit would have
 * to be set.
 *
 * In this way, the Bloom filter can answer NO with absolute surety, but
 * can only speak a qualified YES.
 *
 * @param bloom  Bloom filter
 * @param buf    string to check
 * @param len    the length of the string @p buf
 *
 *
 * @return       false if string does not exist in the filter
 * @return       true if string is may be in the filter
 *
 */
bool bloom_check(bloom_t *bloom, const uint8_t *buf, size_t len);

#ifdef __cplusplus
}
#endif

/** @} */
#endif /* BLOOM_H */