url去重 --布隆过滤器 bloom filter原理及python实现

# -*- encoding: utf-8 -*-
"""This module implements a bloom filter probabilistic data structure and
an a Scalable Bloom Filter that grows in size as your add more items to it
without increasing the false positive error_rate.

Requires the bitarray library: http://pypi.python.org/pypi/bitarray/

    >>> from pybloom import BloomFilter
    >>> f = BloomFilter(capacity=10000, error_rate=0.001)
    >>> for i in range(0, f.capacity):
    ...     _ = f.add(i)
    ...
    >>> 0 in f
    True
    >>> f.capacity in f
    False
    >>> len(f) <= f.capacity
    True
    >>> abs((len(f) / float(f.capacity)) - 1.0) <= f.error_rate
    True

    >>> from pybloom import ScalableBloomFilter
    >>> sbf = ScalableBloomFilter(mode=ScalableBloomFilter.SMALL_SET_GROWTH)
    >>> count = 10000
    >>> for i in range(0, count):
    ...     _ = sbf.add(i)
    ...
    >>> sbf.capacity > count
    True
    >>> len(sbf) <= count
    True
    >>> abs((len(sbf) / float(count)) - 1.0) <= sbf.error_rate
    True

"""
import math
import hashlib
from struct import unpack, pack, calcsize

try:
    import bitarray
except ImportError:
    raise ImportError(‘pybloom requires bitarray >= 0.3.4‘)

__version__ = ‘1.1‘
__author__  = "Jay Baird <jay@mochimedia.com>, Bob Ippolito <bob@redivi.com>,               Marius Eriksen <marius@monkey.org>,               Alex Brasetvik <alex@brasetvik.com>"

def make_hashfuncs(num_slices, num_bits):
    if num_bits >= (1 << 31):
        fmt_code, chunk_size = ‘Q‘, 8
    elif num_bits >= (1 << 15):
        fmt_code, chunk_size = ‘I‘, 4
    else:
        fmt_code, chunk_size = ‘H‘, 2
    total_hash_bits = 8 * num_slices * chunk_size
    if total_hash_bits > 384:
        hashfn = hashlib.sha512
    elif total_hash_bits > 256:
        hashfn = hashlib.sha384
    elif total_hash_bits > 160:
        hashfn = hashlib.sha256
    elif total_hash_bits > 128:
        hashfn = hashlib.sha1
    else:
        hashfn = hashlib.md5
    fmt = fmt_code * (hashfn().digest_size // chunk_size)
    num_salts, extra = divmod(num_slices, len(fmt))
    if extra:
        num_salts += 1
    salts = [hashfn(hashfn(pack(‘I‘, i)).digest()) for i in range(num_salts)]
    def _make_hashfuncs(key):
        #if isinstance(key, unicode):
        #    key = key.encode(‘utf-8‘)
        #else:
        #    key = str(key)
        key = str(key).encode("utf-8")
        rval = []
        for salt in salts:
            h = salt.copy()
            h.update(key)
            rval.extend(uint % num_bits for uint in unpack(fmt, h.digest()))
        del rval[num_slices:]
        return rval
    return _make_hashfuncs


class BloomFilter(object):
    FILE_FMT = ‘<dQQQQ‘

    def __init__(self, capacity, error_rate=0.001):
        """Implements a space-efficient probabilistic data structure

        capacity
            this BloomFilter must be able to store at least *capacity* elements
            while maintaining no more than *error_rate* chance of false
            positives
        error_rate
            the error_rate of the filter returning false positives. This
            determines the filters capacity. Inserting more than capacity
            elements greatly increases the chance of false positives.

        >>> b = BloomFilter(capacity=100000, error_rate=0.001)
        >>> b.add("test")
        False
        >>> "test" in b
        True

        """
        if not (0 < error_rate < 1):
            raise ValueError("Error_Rate must be between 0 and 1.")
        if not capacity > 0:
            raise ValueError("Capacity must be > 0")
        # given M = num_bits, k = num_slices, p = error_rate, n = capacity
        # solving for m = bits_per_slice
        # n ~= M * ((ln(2) ** 2) / abs(ln(P)))
        # n ~= (k * m) * ((ln(2) ** 2) / abs(ln(P)))
        # m ~= n * abs(ln(P)) / (k * (ln(2) ** 2))
        num_slices = int(math.ceil(math.log(1 / error_rate, 2)))
        # the error_rate constraint assumes a fill rate of 1/2
        # so we double the capacity to simplify the API
        bits_per_slice = int(math.ceil(
            (2 * capacity * abs(math.log(error_rate))) /
            (num_slices * (math.log(2) ** 2))))
        self._setup(error_rate, num_slices, bits_per_slice, capacity, 0)
        self.bitarray = bitarray.bitarray(self.num_bits, endian=‘little‘)
        self.bitarray.setall(False)

    def _setup(self, error_rate, num_slices, bits_per_slice, capacity, count):
        self.error_rate = error_rate
        self.num_slices = num_slices
        self.bits_per_slice = bits_per_slice
        self.capacity = capacity
        self.num_bits = num_slices * bits_per_slice
        self.count = count
        self.make_hashes = make_hashfuncs(self.num_slices, self.bits_per_slice)

    def __contains__(self, key):
        """Tests a key‘s membership in this bloom filter.

        >>> b = BloomFilter(capacity=100)
        >>> b.add("hello")
        False
        >>> "hello" in b
        True

        """
        bits_per_slice = self.bits_per_slice
        bitarray = self.bitarray
        if not isinstance(key, list):
            hashes = self.make_hashes(key)
        else:
            hashes = key
        offset = 0
        for k in hashes:
            if not bitarray[offset + k]:
                return False
            offset += bits_per_slice
        return True

    def __len__(self):
        """Return the number of keys stored by this bloom filter."""
        return self.count

    def add(self, key, skip_check=False):
        """ Adds a key to this bloom filter. If the key already exists in this
        filter it will return True. Otherwise False.

        >>> b = BloomFilter(capacity=100)
        >>> b.add("hello")
        False
        >>> b.add("hello")
        True

        """
        bitarray = self.bitarray
        bits_per_slice = self.bits_per_slice
        hashes = self.make_hashes(key)
        if not skip_check and hashes in self:
            return True
        if self.count > self.capacity:
            raise IndexError("BloomFilter is at capacity")
        offset = 0
        for k in hashes:
            self.bitarray[offset + k] = True
            offset += bits_per_slice
        self.count += 1
        return False

    def copy(self):
        """Return a copy of this bloom filter.
        """
        new_filter = BloomFilter(self.capacity, self.error_rate)
        new_filter.bitarray = self.bitarray.copy()
        return new_filter

    def union(self, other):
        """ Calculates the union of the two underlying bitarrays and returns
        a new bloom filter object."""
        if self.capacity != other.capacity or             self.error_rate != other.error_rate:
            raise ValueError("Unioning filters requires both filters to have both the same capacity and error rate")
        new_bloom = self.copy()
        new_bloom.bitarray = new_bloom.bitarray | other.bitarray
        return new_bloom

    def __or__(self, other):
        return self.union(other)

    def intersection(self, other):
        """ Calculates the union of the two underlying bitarrays and returns
        a new bloom filter object."""
        if self.capacity != other.capacity or             self.error_rate != other.error_rate:
            raise ValueError("Intersecting filters requires both filters to have equal capacity and error rate")
        new_bloom = self.copy()
        new_bloom.bitarray = new_bloom.bitarray & other.bitarray
        return new_bloom

    def __and__(self, other):
        return self.intersection(other)

    def tofile(self, f):
        """Write the bloom filter to file object `f‘. Underlying bits
        are written as machine values. This is much more space
        efficient than pickling the object."""
        f.write(pack(self.FILE_FMT, self.error_rate, self.num_slices,
                     self.bits_per_slice, self.capacity, self.count))
        self.bitarray.tofile(f)

    @classmethod
    def fromfile(cls, f, n=-1):
        """Read a bloom filter from file-object `f‘ serialized with
        ``BloomFilter.tofile‘‘. If `n‘ > 0 read only so many bytes."""
        headerlen = calcsize(cls.FILE_FMT)

        if 0 < n < headerlen:
            raise ValueError(‘n too small!‘)

        filter = cls(1)  # Bogus instantiation, we will `_setup‘.
        filter._setup(*unpack(cls.FILE_FMT, f.read(headerlen)))
        filter.bitarray = bitarray.bitarray(endian=‘little‘)
        if n > 0:
            filter.bitarray.fromfile(f, n - headerlen)
        else:
            filter.bitarray.fromfile(f)
        if filter.num_bits != filter.bitarray.length() and                (filter.num_bits + (8 - filter.num_bits % 8)
                != filter.bitarray.length()):
            raise ValueError(‘Bit length mismatch!‘)

        return filter

    def __getstate__(self):
        d = self.__dict__.copy()
        del d[‘make_hashes‘]
        return d

    def __setstate__(self, d):
        self.__dict__.update(d)
        self.make_hashes = make_hashfuncs(self.num_slices, self.bits_per_slice)

class ScalableBloomFilter(object):
    SMALL_SET_GROWTH = 2 # slower, but takes up less memory
    LARGE_SET_GROWTH = 4 # faster, but takes up more memory faster
    FILE_FMT = ‘<idQd‘

    def __init__(self, initial_capacity=100, error_rate=0.001,
                 mode=SMALL_SET_GROWTH):
        """Implements a space-efficient probabilistic data structure that
        grows as more items are added while maintaining a steady false
        positive rate

        initial_capacity
            the initial capacity of the filter
        error_rate
            the error_rate of the filter returning false positives. This
            determines the filters capacity. Going over capacity greatly
            increases the chance of false positives.
        mode
            can be either ScalableBloomFilter.SMALL_SET_GROWTH or
            ScalableBloomFilter.LARGE_SET_GROWTH. SMALL_SET_GROWTH is slower
            but uses less memory. LARGE_SET_GROWTH is faster but consumes
            memory faster.

        >>> b = ScalableBloomFilter(initial_capacity=512, error_rate=0.001,                                     mode=ScalableBloomFilter.SMALL_SET_GROWTH)
        >>> b.add("test")
        False
        >>> "test" in b
        True
        >>> unicode_string = u‘?‘
        >>> b.add(unicode_string)
        False
        >>> unicode_string in b
        True
        """
        if not error_rate or error_rate < 0:
            raise ValueError("Error_Rate must be a decimal less than 0.")
        self._setup(mode, 0.9, initial_capacity, error_rate)
        self.filters = []

    def _setup(self, mode, ratio, initial_capacity, error_rate):
        self.scale = mode
        self.ratio = ratio
        self.initial_capacity = initial_capacity
        self.error_rate = error_rate

    def __contains__(self, key):
        """Tests a key‘s membership in this bloom filter.

        >>> b = ScalableBloomFilter(initial_capacity=100, error_rate=0.001,                                     mode=ScalableBloomFilter.SMALL_SET_GROWTH)
        >>> b.add("hello")
        False
        >>> "hello" in b
        True

        """
        for f in reversed(self.filters):
            if key in f:
                return True
        return False

    def add(self, key):
        """Adds a key to this bloom filter.
        If the key already exists in this filter it will return True.
        Otherwise False.

        >>> b = ScalableBloomFilter(initial_capacity=100, error_rate=0.001,                                     mode=ScalableBloomFilter.SMALL_SET_GROWTH)
        >>> b.add("hello")
        False
        >>> b.add("hello")
        True

        """
        if key in self:
            return True
        filter = self.filters[-1] if self.filters else None
        if filter is None or filter.count >= filter.capacity:
            num_filters = len(self.filters)
            filter = BloomFilter(
                capacity=self.initial_capacity * (self.scale ** num_filters),
                error_rate=self.error_rate * (self.ratio ** num_filters))
            self.filters.append(filter)
        filter.add(key, skip_check=True)
        return False

    @property
    def capacity(self):
        """Returns the total capacity for all filters in this SBF"""
        return sum([f.capacity for f in self.filters])

    @property
    def count(self):
        return len(self)

    def tofile(self, f):
        """Serialize this ScalableBloomFilter into the file-object
        `f‘."""
        f.write(pack(self.FILE_FMT, self.scale, self.ratio,
                     self.initial_capacity, self.error_rate))

        # Write #-of-filters
        f.write(pack(‘<l‘, len(self.filters)))

        if len(self.filters) > 0:
            # Then each filter directly, with a header describing
            # their lengths.
            headerpos = f.tell()
            headerfmt = ‘<‘ + ‘Q‘*(len(self.filters))
            f.write(‘.‘ * calcsize(headerfmt))
            filter_sizes = []
            for filter in self.filters:
                begin = f.tell()
                filter.tofile(f)
                filter_sizes.append(f.tell() - begin)

            f.seek(headerpos)
            f.write(pack(headerfmt, *filter_sizes))

    @classmethod
    def fromfile(cls, f):
        """Deserialize the ScalableBloomFilter in file object `f‘."""
        filter = cls()
        filter._setup(*unpack(cls.FILE_FMT, f.read(calcsize(cls.FILE_FMT))))
        nfilters, = unpack(‘<l‘, f.read(calcsize(‘<l‘)))
        if nfilters > 0:
            header_fmt = ‘<‘ + ‘Q‘*nfilters
            bytes = f.read(calcsize(header_fmt))
            filter_lengths = unpack(header_fmt, bytes)
            for fl in filter_lengths:
                filter.filters.append(BloomFilter.fromfile(f, fl))
        else:
            filter.filters = []

        return filter

    def __len__(self):
        """Returns the total number of elements stored in this SBF"""
        return sum([f.count for f in self.filters])


if __name__ == "__main__":
    import doctest
    doctest.testmod()