bloom-filter/bloom_filter_mod.py

'''Bloom Filter: Probabilistic set membership testing for large sets'''

# Shamelessly borrowed (under MIT license) from http://code.activestate.com/recipes/577686-bloom-filter/
# About Bloom Filters: http://en.wikipedia.org/wiki/Bloom_filter

# Tweaked by Daniel Richard Stromberg, mostly to:
# 1) Give it a little nicer __init__ parameters.
# 2) Improve the hash functions to get a much lower rate of false positives
# 3) Make it pass pylint

import os
#mport sys
import math
import array
import random
#mport bufsock
#mport hashlib
#mport numbers
import python2x3

try:
    import mmap as mmap_mod
except ImportError:
    # Jython lacks mmap()
    HAVE_MMAP = False
else:
    HAVE_MMAP = True

# In the literature:
# k is the number of probes - we call this num_probes_k
# m is the number of bits in the filter - we call this num_bits_m
# n is the ideal number of elements to eventually be stored in the filter - we call this ideal_num_elements_n
# p is the desired error rate when full - we call this error_rate_p


def my_range(num_values):
    '''Generate numbers from 0..num_values-1'''

    value = 0
    while value < num_values:
        yield value
        value += 1

# In the abstract, this is what we want &= and |= to do, but especially for disk-based filters, this is extremely slow
#class Backend_set_operations:
#    '''Provide &= and |= for backends'''
#    # pylint: disable=W0232
#    # W0232: We don't need an __init__ method; we're never instantiated directly
#    def __iand__(self, other):
#        assert self.num_bits == other.num_bits
#
#        for bitno in my_range(num_bits):
#            if self.is_set(bitno) and other.is_set(bitno):
#                self[bitno].set()
#            else:
#                self[bitno].clear()
#
#    def __ior__(self, other):
#        assert self.num_bits == other.num_bits
#
#        for bitno in xrange(num_bits):
#            if self[bitno] or other[bitno]:
#                self[bitno].set()
#            else:
#                self[bitno].clear()


if HAVE_MMAP:

    class Mmap_backend(object):
        '''
        Backend storage for our "array of bits" using an mmap'd file.
        Please note that this has only been tested on Linux so far: 2    -11-01.
        '''

        effs = 2 ^ 8 - 1

        def __init__(self, num_bits, filename):
            self.num_bits = num_bits
            self.num_chars = (self.num_bits + 7) // 8
            flags = os.O_RDWR | os.O_CREAT
            if hasattr(os, 'O_BINARY'):
                flags |= getattr(os, 'O_BINARY')
            self.file_ = os.open(filename, flags)
            os.lseek(self.file_, self.num_chars + 1, os.SEEK_SET)
            os.write(self.file_, python2x3.null_byte)
            self.mmap = mmap_mod.mmap(self.file_, self.num_chars)

        def is_set(self, bitno):
            '''Return true iff bit number bitno is set'''
            byteno, bit_within_wordno = divmod(bitno, 8)
            mask = 1 << bit_within_wordno
            char = self.mmap[byteno]
            if isinstance(char, str):
                byte = ord(char)
            else:
                byte = int(char)
            return byte & mask

        def set(self, bitno):
            '''set bit number bitno to true'''

            byteno, bit_within_byteno = divmod(bitno, 8)
            mask = 1 << bit_within_byteno
            char = self.mmap[byteno]
            byte = ord(char)
            byte |= mask
            self.mmap[byteno] = chr(byte)

        def clear(self, bitno):
            '''clear bit number bitno - set it to false'''

            byteno, bit_within_byteno = divmod(bitno, 8)
            mask = 1 << bit_within_byteno
            char = self.mmap[byteno]
            byte = ord(char)
            byte &= Mmap_backend.effs - mask
            self.mmap[byteno] = chr(byte)

        def __iand__(self, other):
            assert self.num_bits == other.num_bits

            for byteno in my_range(self.num_chars):
                self.mmap[byteno] = chr(ord(self.mmap[byteno]) & ord(other.mmap[byteno]))

            return self

        def __ior__(self, other):
            assert self.num_bits == other.num_bits

            for byteno in my_range(self.num_chars):
                self.mmap[byteno] = chr(ord(self.mmap[byteno]) | ord(other.mmap[byteno]))

            return self

        def close(self):
            '''Close the file'''
            os.close(self.file_)


class File_seek_backend(object):
    '''Backend storage for our "array of bits" using a file in which we seek'''

    effs = 2 ^ 8 - 1

    def __init__(self, num_bits, filename):
        self.num_bits = num_bits
        self.num_chars = (self.num_bits + 7) // 8
        flags = os.O_RDWR | os.O_CREAT
        if hasattr(os, 'O_BINARY'):
            flags |= getattr(os, 'O_BINARY')
        self.file_ = os.open(filename, flags)
        os.lseek(self.file_, self.num_chars + 1, os.SEEK_SET)
        os.write(self.file_, python2x3.null_byte)

    def is_set(self, bitno):
        '''Return true iff bit number bitno is set'''
        byteno, bit_within_wordno = divmod(bitno, 8)
        mask = 1 << bit_within_wordno
        os.lseek(self.file_, byteno, os.SEEK_SET)
        char = os.read(self.file_, 1)
        if isinstance(char, str):
            byte = ord(char)
        else:
            byte = char[0]
        return byte & mask

    def set(self, bitno):
        '''set bit number bitno to true'''

        byteno, bit_within_byteno = divmod(bitno, 8)
        mask = 1 << bit_within_byteno
        os.lseek(self.file_, byteno, os.SEEK_SET)
        char = os.read(self.file_, 1)
        if isinstance(char, str):
            byte = ord(char)
            was_char = True
        else:
            byte = char[0]
            was_char = False
        byte |= mask
        os.lseek(self.file_, byteno, os.SEEK_SET)
        if was_char:
            os.write(self.file_, chr(byte))
        else:
            char = python2x3.intlist_to_binary([byte])
            os.write(self.file_, char)

    def clear(self, bitno):
        '''clear bit number bitno - set it to false'''

        byteno, bit_within_byteno = divmod(bitno, 8)
        mask = 1 << bit_within_byteno
        os.lseek(self.file_, byteno, os.SEEK_SET)
        char = os.read(self.file_, 1)
        if isinstance(char, str):
            byte = ord(char)
            was_char = True
        else:
            byte = int(char)
            was_char = False
        byte &= File_seek_backend.effs - mask
        os.lseek(self.file_, byteno, os.SEEK_SET)
        if was_char:
            os.write(chr(byte))
        else:
            char = python2x3.intlist_to_binary([byte])
            os.write(char)

    # These are quite slow ways to do iand and ior, but they should work, and a faster version is going to take more time
    def __iand__(self, other):
        assert self.num_bits == other.num_bits

        for bitno in my_range(self.num_bits):
            if self.is_set(bitno) and other.is_set(bitno):
                self.set(bitno)
            else:
                self.clear(bitno)

        return self

    def __ior__(self, other):
        assert self.num_bits == other.num_bits

        for bitno in my_range(self.num_bits):
            if self.is_set(bitno) or other.is_set(bitno):
                self.set(bitno)
            else:
                self.clear(bitno)

        return self

    def close(self):
        '''Close the file'''
        os.close(self.file_)


class Array_then_file_seek_backend(object):
    # pylint: disable=R0902
    # R0902: We kinda need a bunch of instance attributes
    '''
    Backend storage for our "array of bits" using a python array of integers up to some maximum number of bytes,
    then spilling over to a file.  This is -not- a cache; we instead save the leftmost bits in RAM, and the
    rightmost bits (if necessary) in a file.  On open, we read from the file to RAM.  On close, we write from RAM
    to the file.
    '''

    effs = 2 ** 8 - 1

    def __init__(self, num_bits, filename, max_bytes_in_memory):
        self.num_bits = num_bits
        num_chars = (self.num_bits + 7) // 8
        self.filename = filename
        self.max_bytes_in_memory = max_bytes_in_memory
        self.bits_in_memory = min(num_bits, self.max_bytes_in_memory * 8)
        self.bits_in_file = max(self.num_bits - self.bits_in_memory, 0)
        self.bytes_in_memory = (self.bits_in_memory + 7) // 8
        self.bytes_in_file = (self.bits_in_file + 7) // 8

        self.array_ = array.array('B', [0]) * self.bytes_in_memory
        flags = os.O_RDWR | os.O_CREAT
        if hasattr(os, 'O_BINARY'):
            flags |= getattr(os, 'O_BINARY')
        self.file_ = os.open(filename, flags)
        os.lseek(self.file_, num_chars + 1, os.SEEK_SET)
        os.write(self.file_, python2x3.null_byte)

        os.lseek(self.file_, 0, os.SEEK_SET)
        offset = 0
        intended_block_len = 2 ** 17
        while True:
            if offset + intended_block_len < self.bytes_in_memory:
                block = os.read(self.file_, intended_block_len)
            elif offset < self.bytes_in_memory:
                block = os.read(self.file_, self.bytes_in_memory - offset)
            else:
                break
            for index_in_block, character in enumerate(block):
                self.array_[offset + index_in_block] = ord(character)
            offset += intended_block_len

    def is_set(self, bitno):
        '''Return true iff bit number bitno is set'''
        byteno, bit_within_byteno = divmod(bitno, 8)
        mask = 1 << bit_within_byteno
        if byteno < self.bytes_in_memory:
            return self.array_[byteno] & mask
        else:
            os.lseek(self.file_, byteno, os.SEEK_SET)
            char = os.read(self.file_, 1)
            if isinstance(char, str):
                byte = ord(char)
            else:
                byte = int(char)
            return byte & mask

    def set(self, bitno):
        '''set bit number bitno to true'''
        byteno, bit_within_byteno = divmod(bitno, 8)
        mask = 1 << bit_within_byteno
        if byteno < self.bytes_in_memory:
            self.array_[byteno] |= mask
        else:
            os.lseek(self.file_, byteno, os.SEEK_SET)
            char = os.read(self.file_, 1)
            if isinstance(char, str):
                byte = ord(char)
                was_char = True
            else:
                byte = char
                was_char = False
            byte |= mask
            os.lseek(self.file_, byteno, os.SEEK_SET)
            if was_char:
                os.write(self.file_, chr(byte))
            else:
                os.write(self.file_, byte)

    def clear(self, bitno):
        '''clear bit number bitno - set it to false'''
        byteno, bit_within_byteno = divmod(bitno, 8)
        mask = Array_backend.effs - (1 << bit_within_byteno)
        if byteno < self.bytes_in_memory:
            self.array_[byteno] &= mask
        else:
            os.lseek(self.file_, byteno, os.SEEK_SET)
            char = os.read(self.file_, 1)
            if isinstance(char, str):
                byte = ord(char)
                was_char = True
            else:
                byte = int(char)
                was_char = False
            byte &= File_seek_backend.effs - mask
            os.lseek(self.file_, byteno, os.SEEK_SET)
            if was_char:
                os.write(chr(byte))
            else:
                os.write(byte)

    # These are quite slow ways to do iand and ior, but they should work, and a faster version is going to take more time
    def __iand__(self, other):
        assert self.num_bits == other.num_bits

        for bitno in my_range(self.num_bits):
            if self.is_set(bitno) and other.is_set(bitno):
                self.set(bitno)
            else:
                self.clear(bitno)

        return self

    def __ior__(self, other):
        assert self.num_bits == other.num_bits

        for bitno in my_range(self.num_bits):
            if self.is_set(bitno) or other.is_set(bitno):
                self.set(bitno)
            else:
                self.clear(bitno)

        return self

    def close(self):
        '''Write the in-memory portion to disk, leave the already-on-disk portion unchanged'''

        os.lseek(self.file_, 0, os.SEEK_SET)
        for index in my_range(self.bytes_in_memory):
            self.file_.write(self.array_[index])

        os.close(self.file_)


class Array_backend(object):
    '''Backend storage for our "array of bits" using a python array of integers'''

    # Note that this has now been split out into a bits_mod for the benefit of other projects.
    effs = 2 ** 32 - 1

    def __init__(self, num_bits):
        self.num_bits = num_bits
        self.num_words = (self.num_bits + 31) // 32
        self.array_ = array.array('L', [0]) * self.num_words

    def is_set(self, bitno):
        '''Return true iff bit number bitno is set'''
        wordno, bit_within_wordno = divmod(bitno, 32)
        mask = 1 << bit_within_wordno
        return self.array_[wordno] & mask

    def set(self, bitno):
        '''set bit number bitno to true'''
        wordno, bit_within_wordno = divmod(bitno, 32)
        mask = 1 << bit_within_wordno
        self.array_[wordno] |= mask

    def clear(self, bitno):
        '''clear bit number bitno - set it to false'''
        wordno, bit_within_wordno = divmod(bitno, 32)
        mask = Array_backend.effs - (1 << bit_within_wordno)
        self.array_[wordno] &= mask

    # It'd be nice to do __iand__ and __ior__ in a base class, but that'd be Much slower

    def __iand__(self, other):
        assert self.num_bits == other.num_bits

        for wordno in my_range(self.num_words):
            self.array_[wordno] &= other.array_[wordno]

        return self

    def __ior__(self, other):
        assert self.num_bits == other.num_bits

        for wordno in my_range(self.num_words):
            self.array_[wordno] |= other.array_[wordno]

        return self

    def close(self):
        '''Noop for compatibility with the file+seek backend'''
        pass


def get_bitno_seed_rnd(bloom_filter, key):
    '''Apply num_probes_k hash functions to key.  Generate the array index and bitmask corresponding to each result'''

    # We're using key as a seed to a pseudorandom number generator
    hasher = random.Random(key).randrange
    for dummy in range(bloom_filter.num_probes_k):
        bitno = hasher(bloom_filter.num_bits_m)
        yield bitno % bloom_filter.num_bits_m


MERSENNES1 = [2 ** x - 1 for x in [17, 31, 127]]
MERSENNES2 = [2 ** x - 1 for x in [19, 67, 257]]


def simple_hash(int_list, prime1, prime2, prime3):
    '''Compute a hash value from a list of integers and 3 primes'''
    result = 0
    for integer in int_list:
        result += ((result + integer + prime1) * prime2) % prime3
    return result


def hash1(int_list):
    '''Basic hash function #1'''
    return simple_hash(int_list, MERSENNES1[0], MERSENNES1[1], MERSENNES1[2])


def hash2(int_list):
    '''Basic hash function #2'''
    return simple_hash(int_list, MERSENNES2[0], MERSENNES2[1], MERSENNES2[2])


def get_bitno_lin_comb(bloom_filter, key):
    '''Apply num_probes_k hash functions to key.  Generate the array index and bitmask corresponding to each result'''

    # This one assumes key is either bytes or str (or other list of integers)

    # I'd love to check for long too, but that doesn't exist in 3.2, and 2.5 doesn't have the numbers.Integral base type
    if hasattr(key, '__divmod__'):
        int_list = []
        temp = key
        while temp:
            quotient, remainder = divmod(temp, 256)
            int_list.append(remainder)
            temp = quotient
    elif hasattr(key[0], '__divmod__'):
        int_list = key
    elif isinstance(key[0], str):
        int_list = [ord(char) for char in key]
    else:
        raise TypeError('Sorry, I do not know how to hash this type')

    hash_value1 = hash1(int_list)
    hash_value2 = hash2(int_list)

    # We're using linear combinations of hash_value1 and hash_value2 to obtain num_probes_k hash functions
    for probeno in range(1, bloom_filter.num_probes_k + 1):
        bit_index = hash_value1 + probeno * hash_value2
        yield bit_index % bloom_filter.num_bits_m


def try_unlink(filename):
    '''unlink a file.  Don't complain if it's not there'''
    try:
        os.unlink(filename)
    except OSError:
        pass
    return


class Bloom_filter(object):
    '''Probabilistic set membership testing for large sets'''

    #def __init__(self, ideal_num_elements_n, error_rate_p, probe_offsetter=get_index_bitmask_seed_rnd):
    def __init__(self, ideal_num_elements_n, error_rate_p, probe_bitnoer=get_bitno_lin_comb, filename=None, start_fresh=False):
        # pylint: disable=R0913
        # R0913: We want a few arguments
        if ideal_num_elements_n <= 0:
            raise ValueError('ideal_num_elements_n must be > 0')
        if not (0 < error_rate_p < 1):
            raise ValueError('error_rate_p must be between 0 and 1 exclusive')

        self.error_rate_p = error_rate_p
        # With fewer elements, we should do very well.  With more elements, our error rate "guarantee"
        # drops rapidly.
        self.ideal_num_elements_n = ideal_num_elements_n

        numerator = -1 * self.ideal_num_elements_n * math.log(self.error_rate_p)
        denominator = math.log(2) ** 2
        #self.num_bits_m = - int((self.ideal_num_elements_n * math.log(self.error_rate_p)) / (math.log(2) ** 2))
        real_num_bits_m = numerator / denominator
        self.num_bits_m = int(math.ceil(real_num_bits_m))

        if filename is None:
            self.backend = Array_backend(self.num_bits_m)
        elif isinstance(filename, tuple) and isinstance(filename[1], int):
            if start_fresh:
                try_unlink(filename[0])
            if filename[1] == -1:
                self.backend = Mmap_backend(self.num_bits_m, filename[0])
            else:
                self.backend = Array_then_file_seek_backend(self.num_bits_m, filename[0], filename[1])
        else:
            if start_fresh:
                try_unlink(filename)
            self.backend = File_seek_backend(self.num_bits_m, filename)

        #array.array('L', [0]) * ((self.num_bits_m + 31) // 32)

        # AKA num_offsetters
        # Verified against http://en.wikipedia.org/wiki/Bloom_filter#Probability_of_false_positives
        real_num_probes_k = (self.num_bits_m / self.ideal_num_elements_n) * math.log(2)
        self.num_probes_k = int(math.ceil(real_num_probes_k))

# This comes close, but often isn't the same value
#        alternative_real_num_probes_k = -math.log(self.error_rate_p) / math.log(2)
#
#        if abs(real_num_probes_k - alternative_real_num_probes_k) > 1e-6:
#            sys.stderr.write('real_num_probes_k: %f, alternative_real_num_probes_k: %f\n' %
#                (real_num_probes_k, alternative_real_num_probes_k)
#                )
#            sys.exit(1)

        self.probe_bitnoer = probe_bitnoer

    def __repr__(self):
        return 'Bloom_filter(ideal_num_elements_n=%d, error_rate_p=%f, num_bits_m=%d)' % (
            self.ideal_num_elements_n,
            self.error_rate_p,
            self.num_bits_m,
        )

    def add(self, key):
        '''Add an element to the filter'''
        for bitno in self.probe_bitnoer(self, key):
            self.backend.set(bitno)

    def __iadd__(self, key):
        self.add(key)
        return self

    def _match_template(self, bloom_filter):
        '''Compare a sort of signature for two bloom filters.  Used in preparation for binary operations'''
        return (self.num_bits_m == bloom_filter.num_bits_m
                and self.num_probes_k == bloom_filter.num_probes_k
                and self.probe_bitnoer == bloom_filter.probe_bitnoer)

    def union(self, bloom_filter):
        '''Compute the set union of two bloom filters'''
        self.backend |= bloom_filter.backend

    def __ior__(self, bloom_filter):
        self.union(bloom_filter)
        return self

    def intersection(self, bloom_filter):
        '''Compute the set intersection of two bloom filters'''
        self.backend &= bloom_filter.backend

    def __iand__(self, bloom_filter):
        self.intersection(bloom_filter)
        return self

    def __contains__(self, key):
        for bitno in self.probe_bitnoer(self, key):
            #wordno, bit_within_word = divmod(bitno, 32)
            #mask = 1 << bit_within_word
            #if not (self.array_[wordno] & mask):
            if not self.backend.is_set(bitno):
                return False
        return True

        #return all(self.array_[i] & mask for i, mask in self.probe_bitnoer(self, key))