bitstring.py

#!/usr/bin/env python
 
r"""
This package defines classes that simplify bit-wise creation, manipulation and
interpretation of data.
 
Classes:
 
Bits -- An immutable container for binary data.
BitArray -- A mutable container for binary data.
ConstBitStream -- An immutable container with streaming methods.
BitStream -- A mutable container with streaming methods.
 
                      Bits (base class)
                     /    \
 + mutating methods /      \ + streaming methods
                   /        \
              BitArray   ConstBitStream
                   \        /
                    \      /
                     \    /
                    BitStream
 
Functions:
 
pack -- Create a BitStream from a format string.
 
Exceptions:
 
Error -- Module exception base class.
CreationError -- Error during creation.
InterpretError -- Inappropriate interpretation of binary data.
ByteAlignError -- Whole byte position or length needed.
ReadError -- Reading or peeking past the end of a bitstring.
 
https://github.com/scott-griffiths/bitstring
"""
 
__licence__ = """
The MIT License
 
Copyright (c) 2006-2016 Scott Griffiths (dr.scottgriffiths@gmail.com)
 
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
 
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
 
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""
 
__version__ = "3.1.5"
 
__author__ = "Scott Griffiths"
 
import numbers
import copy
import sys
import re
import binascii
import mmap
import os
import struct
import operator
import collections
import array
 
byteorder = sys.byteorder
 
bytealigned = False
"""Determines whether a number of methods default to working only on byte boundaries."""
 
# Maximum number of digits to use in __str__ and __repr__.
MAX_CHARS = 250
 
# Maximum size of caches used for speed optimisations.
CACHE_SIZE = 1000
 
 
class Error(Exception):
    """Base class for errors in the bitstring module."""
 
    def __init__(self, *params):
        self.msg = params[0] if params else ''
        self.params = params[1:]
 
    def __str__(self):
        if self.params:
            return self.msg.format(*self.params)
        return self.msg
 
 
class ReadError(Error, IndexError):
    """Reading or peeking past the end of a bitstring."""
 
    def __init__(self, *params):
        Error.__init__(self, *params)
 
 
class InterpretError(Error, ValueError):
    """Inappropriate interpretation of binary data."""
 
    def __init__(self, *params):
        Error.__init__(self, *params)
 
 
class ByteAlignError(Error):
    """Whole-byte position or length needed."""
 
    def __init__(self, *params):
        Error.__init__(self, *params)
 
 
class CreationError(Error, ValueError):
    """Inappropriate argument during bitstring creation."""
 
    def __init__(self, *params):
        Error.__init__(self, *params)
 
 
class ConstByteStore(object):
    """Stores raw bytes together with a bit offset and length.
 
    Used internally - not part of public interface.
    """
 
    __slots__ = ('offset', '_rawarray', 'bitlength')
 
    def __init__(self, data, bitlength=None, offset=None):
        """data is either a bytearray or a MmapByteArray"""
        self._rawarray = data
        if offset is None:
            offset = 0
        if bitlength is None:
            bitlength = 8 * len(data) - offset
        self.offset = offset
        self.bitlength = bitlength
 
    def getbit(self, pos):
        assert 0 <= pos < self.bitlength
        byte, bit = divmod(self.offset + pos, 8)
        return bool(self._rawarray[byte] & (128 >> bit))
 
    def getbyte(self, pos):
        """Direct access to byte data."""
        return self._rawarray[pos]
 
    def getbyteslice(self, start, end):
        """Direct access to byte data."""
        c = self._rawarray[start:end]
        return c
 
    @property
    def bytelength(self):
        if not self.bitlength:
            return 0
        sb = self.offset // 8
        eb = (self.offset + self.bitlength - 1) // 8
        return eb - sb + 1
 
    def __copy__(self):
        return ByteStore(self._rawarray[:], self.bitlength, self.offset)
 
    def _appendstore(self, store):
        """Join another store on to the end of this one."""
        if not store.bitlength:
            return
        # Set new array offset to the number of bits in the final byte of current array.
        store = offsetcopy(store, (self.offset + self.bitlength) % 8)
        if store.offset:
            # first do the byte with the join.
            joinval = (self._rawarray.pop() & (255 ^ (255 >> store.offset)) |
                       (store.getbyte(0) & (255 >> store.offset)))
            self._rawarray.append(joinval)
            self._rawarray.extend(store._rawarray[1:])
        else:
            self._rawarray.extend(store._rawarray)
        self.bitlength += store.bitlength
 
    def _prependstore(self, store):
        """Join another store on to the start of this one."""
        if not store.bitlength:
            return
            # Set the offset of copy of store so that it's final byte
        # ends in a position that matches the offset of self,
        # then join self on to the end of it.
        store = offsetcopy(store, (self.offset - store.bitlength) % 8)
        assert (store.offset + store.bitlength) % 8 == self.offset % 8
        bit_offset = self.offset % 8
        if bit_offset:
            # first do the byte with the join.
            store.setbyte(-1, (store.getbyte(-1) & (255 ^ (255 >> bit_offset)) |
                               (self._rawarray[self.byteoffset] & (255 >> bit_offset))))
            store._rawarray.extend(self._rawarray[self.byteoffset + 1: self.byteoffset + self.bytelength])
        else:
            store._rawarray.extend(self._rawarray[self.byteoffset: self.byteoffset + self.bytelength])
        self._rawarray = store._rawarray
        self.offset = store.offset
        self.bitlength += store.bitlength
 
    @property
    def byteoffset(self):
        return self.offset // 8
 
    @property
    def rawbytes(self):
        return self._rawarray
 
 
class ByteStore(ConstByteStore):
    """Adding mutating methods to ConstByteStore
 
    Used internally - not part of public interface.
    """
    __slots__ = ()
 
    def setbit(self, pos):
        assert 0 <= pos < self.bitlength
        byte, bit = divmod(self.offset + pos, 8)
        self._rawarray[byte] |= (128 >> bit)
 
    def unsetbit(self, pos):
        assert 0 <= pos < self.bitlength
        byte, bit = divmod(self.offset + pos, 8)
        self._rawarray[byte] &= ~(128 >> bit)
 
    def invertbit(self, pos):
        assert 0 <= pos < self.bitlength
        byte, bit = divmod(self.offset + pos, 8)
        self._rawarray[byte] ^= (128 >> bit)
 
    def setbyte(self, pos, value):
        self._rawarray[pos] = value
 
    def setbyteslice(self, start, end, value):
        self._rawarray[start:end] = value
 
 
def offsetcopy(s, newoffset):
    """Return a copy of a ByteStore with the newoffset.
 
    Not part of public interface.
    """
    assert 0 <= newoffset < 8
    if not s.bitlength:
        return copy.copy(s)
    else:
        if newoffset == s.offset % 8:
            return ByteStore(s.getbyteslice(s.byteoffset, s.byteoffset + s.bytelength), s.bitlength, newoffset)
        newdata = []
        d = s._rawarray
        assert newoffset != s.offset % 8
        if newoffset < s.offset % 8:
            # We need to shift everything left
            shiftleft = s.offset % 8 - newoffset
            # First deal with everything except for the final byte
            for x in range(s.byteoffset, s.byteoffset + s.bytelength - 1):
                newdata.append(((d[x] << shiftleft) & 0xff) +
                               (d[x + 1] >> (8 - shiftleft)))
            bits_in_last_byte = (s.offset + s.bitlength) % 8
            if not bits_in_last_byte:
                bits_in_last_byte = 8
            if bits_in_last_byte > shiftleft:
                newdata.append((d[s.byteoffset + s.bytelength - 1] << shiftleft) & 0xff)
        else:  # newoffset > s._offset % 8
            shiftright = newoffset - s.offset % 8
            newdata.append(s.getbyte(0) >> shiftright)
            for x in range(s.byteoffset + 1, s.byteoffset + s.bytelength):
                newdata.append(((d[x - 1] << (8 - shiftright)) & 0xff) +
                               (d[x] >> shiftright))
            bits_in_last_byte = (s.offset + s.bitlength) % 8
            if not bits_in_last_byte:
                bits_in_last_byte = 8
            if bits_in_last_byte + shiftright > 8:
                newdata.append((d[s.byteoffset + s.bytelength - 1] << (8 - shiftright)) & 0xff)
        new_s = ByteStore(bytearray(newdata), s.bitlength, newoffset)
        assert new_s.offset == newoffset
        return new_s
 
 
def equal(a, b):
    """Return True if ByteStores a == b.
 
    Not part of public interface.
    """
    # We want to return False for inequality as soon as possible, which
    # means we get lots of special cases.
    # First the easy one - compare lengths:
    a_bitlength = a.bitlength
    b_bitlength = b.bitlength
    if a_bitlength != b_bitlength:
        return False
    if not a_bitlength:
        assert b_bitlength == 0
        return True
    # Make 'a' the one with the smaller offset
    if (a.offset % 8) > (b.offset % 8):
        a, b = b, a
    # and create some aliases
    a_bitoff = a.offset % 8
    b_bitoff = b.offset % 8
    a_byteoffset = a.byteoffset
    b_byteoffset = b.byteoffset
    a_bytelength = a.bytelength
    b_bytelength = b.bytelength
    da = a._rawarray
    db = b._rawarray
 
    # If they are pointing to the same data, they must be equal
    if da is db and a.offset == b.offset:
        return True
 
    if a_bitoff == b_bitoff:
        bits_spare_in_last_byte = 8 - (a_bitoff + a_bitlength) % 8
        if bits_spare_in_last_byte == 8:
            bits_spare_in_last_byte = 0
        # Special case for a, b contained in a single byte
        if a_bytelength == 1:
            a_val = ((da[a_byteoffset] << a_bitoff) & 0xff) >> (8 - a_bitlength)
            b_val = ((db[b_byteoffset] << b_bitoff) & 0xff) >> (8 - b_bitlength)
            return a_val == b_val
        # Otherwise check first byte
        if da[a_byteoffset] & (0xff >> a_bitoff) != db[b_byteoffset] & (0xff >> b_bitoff):
            return False
        # then everything up to the last
        b_a_offset = b_byteoffset - a_byteoffset
        for x in range(1 + a_byteoffset, a_byteoffset + a_bytelength - 1):
            if da[x] != db[b_a_offset + x]:
                return False
        # and finally the last byte
        return (da[a_byteoffset + a_bytelength - 1] >> bits_spare_in_last_byte ==
                db[b_byteoffset + b_bytelength - 1] >> bits_spare_in_last_byte)
 
    assert a_bitoff != b_bitoff
    # This is how much we need to shift a to the right to compare with b:
    shift = b_bitoff - a_bitoff
    # Special case for b only one byte long
    if b_bytelength == 1:
        assert a_bytelength == 1
        a_val = ((da[a_byteoffset] << a_bitoff) & 0xff) >> (8 - a_bitlength)
        b_val = ((db[b_byteoffset] << b_bitoff) & 0xff) >> (8 - b_bitlength)
        return a_val == b_val
    # Special case for a only one byte long
    if a_bytelength == 1:
        assert b_bytelength == 2
        a_val = ((da[a_byteoffset] << a_bitoff) & 0xff) >> (8 - a_bitlength)
        b_val = ((db[b_byteoffset] << 8) + db[b_byteoffset + 1]) << b_bitoff
        b_val &= 0xffff
        b_val >>= 16 - b_bitlength
        return a_val == b_val
 
    # Compare first byte of b with bits from first byte of a
    if (da[a_byteoffset] & (0xff >> a_bitoff)) >> shift != db[b_byteoffset] & (0xff >> b_bitoff):
        return False
    # Now compare every full byte of b with bits from 2 bytes of a
    for x in range(1, b_bytelength - 1):
        # Construct byte from 2 bytes in a to compare to byte in b
        b_val = db[b_byteoffset + x]
        a_val = ((da[a_byteoffset + x - 1] << 8) + da[a_byteoffset + x]) >> shift
        a_val &= 0xff
        if a_val != b_val:
            return False
 
    # Now check bits in final byte of b
    final_b_bits = (b.offset + b_bitlength) % 8
    if not final_b_bits:
        final_b_bits = 8
    b_val = db[b_byteoffset + b_bytelength - 1] >> (8 - final_b_bits)
    final_a_bits = (a.offset + a_bitlength) % 8
    if not final_a_bits:
        final_a_bits = 8
    if b.bytelength > a_bytelength:
        assert b_bytelength == a_bytelength + 1
        a_val = da[a_byteoffset + a_bytelength - 1] >> (8 - final_a_bits)
        a_val &= 0xff >> (8 - final_b_bits)
        return a_val == b_val
    assert a_bytelength == b_bytelength
    a_val = da[a_byteoffset + a_bytelength - 2] << 8
    a_val += da[a_byteoffset + a_bytelength - 1]
    a_val >>= (8 - final_a_bits)
    a_val &= 0xff >> (8 - final_b_bits)
    return a_val == b_val
 
 
class MmapByteArray(object):
    """Looks like a bytearray, but from an mmap.
 
    Not part of public interface.
    """
 
    __slots__ = ('filemap', 'filelength', 'source', 'byteoffset', 'bytelength')
 
    def __init__(self, source, bytelength=None, byteoffset=None):
        self.source = source
        source.seek(0, os.SEEK_END)
        self.filelength = source.tell()
        if byteoffset is None:
            byteoffset = 0
        if bytelength is None:
            bytelength = self.filelength - byteoffset
        self.byteoffset = byteoffset
        self.bytelength = bytelength
        self.filemap = mmap.mmap(source.fileno(), 0, access=mmap.ACCESS_READ)
 
    def __getitem__(self, key):
        try:
            start = key.start
            stop = key.stop
        except AttributeError:
            try:
                assert 0 <= key < self.bytelength
                return ord(self.filemap[key + self.byteoffset])
            except TypeError:
                # for Python 3
                return self.filemap[key + self.byteoffset]
        else:
            if start is None:
                start = 0
            if stop is None:
                stop = self.bytelength
            assert key.step is None
            assert 0 <= start < self.bytelength
            assert 0 <= stop <= self.bytelength
            s = slice(start + self.byteoffset, stop + self.byteoffset)
            return bytearray(self.filemap.__getitem__(s))
 
    def __len__(self):
        return self.bytelength
 
 
# This creates a dictionary for every possible byte with the value being
# the key with its bits reversed.
BYTE_REVERSAL_DICT = dict()
 
# For Python 2.x/ 3.x coexistence
# Yes this is very very hacky.
try:
    xrange
    for i in range(256):
        BYTE_REVERSAL_DICT[i] = chr(int("{0:08b}".format(i)[::-1], 2))
except NameError:
    for i in range(256):
        BYTE_REVERSAL_DICT[i] = bytes([int("{0:08b}".format(i)[::-1], 2)])
    from io import IOBase as file
    xrange = range
    basestring = str
 
# Python 2.x octals start with '0', in Python 3 it's '0o'
LEADING_OCT_CHARS = len(oct(1)) - 1
 
 
def tidy_input_string(s):
    """Return string made lowercase and with all whitespace removed."""
    s = ''.join(s.split()).lower()
    return s
 
 
INIT_NAMES = ('uint', 'int', 'ue', 'se', 'sie', 'uie', 'hex', 'oct', 'bin', 'bits',
              'uintbe', 'intbe', 'uintle', 'intle', 'uintne', 'intne',
              'float', 'floatbe', 'floatle', 'floatne', 'bytes', 'bool', 'pad')
 
TOKEN_RE = re.compile(r'(?P<name>' + '|'.join(INIT_NAMES) +
                      r')((:(?P<len>[^=]+)))?(=(?P<value>.*))?$', re.IGNORECASE)
DEFAULT_UINT = re.compile(r'(?P<len>[^=]+)?(=(?P<value>.*))?$', re.IGNORECASE)
 
MULTIPLICATIVE_RE = re.compile(r'(?P<factor>.*)\*(?P<token>.+)')
 
# Hex, oct or binary literals
LITERAL_RE = re.compile(r'(?P<name>0(x|o|b))(?P<value>.+)', re.IGNORECASE)
 
# An endianness indicator followed by one or more struct.pack codes
STRUCT_PACK_RE = re.compile(r'(?P<endian><|>|@)?(?P<fmt>(?:\d*[bBhHlLqQfd])+)$')
 
# A number followed by a single character struct.pack code
STRUCT_SPLIT_RE = re.compile(r'\d*[bBhHlLqQfd]')
 
# These replicate the struct.pack codes
# Big-endian
REPLACEMENTS_BE = {'b': 'intbe:8', 'B': 'uintbe:8',
                   'h': 'intbe:16', 'H': 'uintbe:16',
                   'l': 'intbe:32', 'L': 'uintbe:32',
                   'q': 'intbe:64', 'Q': 'uintbe:64',
                   'f': 'floatbe:32', 'd': 'floatbe:64'}
# Little-endian
REPLACEMENTS_LE = {'b': 'intle:8', 'B': 'uintle:8',
                   'h': 'intle:16', 'H': 'uintle:16',
                   'l': 'intle:32', 'L': 'uintle:32',
                   'q': 'intle:64', 'Q': 'uintle:64',
                   'f': 'floatle:32', 'd': 'floatle:64'}
 
# Size in bytes of all the pack codes.
PACK_CODE_SIZE = {'b': 1, 'B': 1, 'h': 2, 'H': 2, 'l': 4, 'L': 4,
                  'q': 8, 'Q': 8, 'f': 4, 'd': 8}
 
_tokenname_to_initialiser = {'hex': 'hex', '0x': 'hex', '0X': 'hex', 'oct': 'oct',
                             '0o': 'oct', '0O': 'oct', 'bin': 'bin', '0b': 'bin',
                             '0B': 'bin', 'bits': 'auto', 'bytes': 'bytes', 'pad': 'pad'}
 
 
def structparser(token):
    """Parse struct-like format string token into sub-token list."""
    m = STRUCT_PACK_RE.match(token)
    if not m:
        return [token]
    else:
        endian = m.group('endian')
        if endian is None:
            return [token]
        # Split the format string into a list of 'q', '4h' etc.
        formatlist = re.findall(STRUCT_SPLIT_RE, m.group('fmt'))
        # Now deal with mulitiplicative factors, 4h -> hhhh etc.
        fmt = ''.join([f[-1] * int(f[:-1]) if len(f) != 1 else
                       f for f in formatlist])
        if endian == '@':
            # Native endianness
            if byteorder == 'little':
                endian = '<'
            else:
                assert byteorder == 'big'
                endian = '>'
        if endian == '<':
            tokens = [REPLACEMENTS_LE[c] for c in fmt]
        else:
            assert endian == '>'
            tokens = [REPLACEMENTS_BE[c] for c in fmt]
    return tokens
 
 
def tokenparser(fmt, keys=None, token_cache=None):
    """Divide the format string into tokens and parse them.
 
    Return stretchy token and list of [initialiser, length, value]
    initialiser is one of: hex, oct, bin, uint, int, se, ue, 0x, 0o, 0b etc.
    length is None if not known, as is value.
 
    If the token is in the keyword dictionary (keys) then it counts as a
    special case and isn't messed with.
 
    tokens must be of the form: [factor*][initialiser][:][length][=value]
 
    """
    if token_cache is None:
        token_cache = {}
    try:
        return token_cache[(fmt, keys)]
    except KeyError:
        token_key = (fmt, keys)
    # Very inefficient expanding of brackets.
    fmt = expand_brackets(fmt)
    # Split tokens by ',' and remove whitespace
    # The meta_tokens can either be ordinary single tokens or multiple
    # struct-format token strings.
    meta_tokens = (''.join(f.split()) for f in fmt.split(','))
    return_values = []
    stretchy_token = False
    for meta_token in meta_tokens:
        # See if it has a multiplicative factor
        m = MULTIPLICATIVE_RE.match(meta_token)
        if not m:
            factor = 1
        else:
            factor = int(m.group('factor'))
            meta_token = m.group('token')
        # See if it's a struct-like format
        tokens = structparser(meta_token)
        ret_vals = []
        for token in tokens:
            if keys and token in keys:
                # Don't bother parsing it, it's a keyword argument
                ret_vals.append([token, None, None])
                continue
            value = length = None
            if token == '':
                continue
            # Match literal tokens of the form 0x... 0o... and 0b...
            m = LITERAL_RE.match(token)
            if m:
                name = m.group('name')
                value = m.group('value')
                ret_vals.append([name, length, value])
                continue
            # Match everything else:
            m1 = TOKEN_RE.match(token)
            if not m1:
                # and if you don't specify a 'name' then the default is 'uint':
                m2 = DEFAULT_UINT.match(token)
                if not m2:
                    raise ValueError("Don't understand token '{0}'.".format(token))
            if m1:
                name = m1.group('name')
                length = m1.group('len')
                if m1.group('value'):
                    value = m1.group('value')
            else:
                assert m2
                name = 'uint'
                length = m2.group('len')
                if m2.group('value'):
                    value = m2.group('value')
            if name == 'bool':
                if length is not None:
                    raise ValueError("You can't specify a length with bool tokens - they are always one bit.")
                length = 1
            if length is None and name not in ('se', 'ue', 'sie', 'uie'):
                stretchy_token = True
            if length is not None:
                # Try converting length to int, otherwise check it's a key.
                try:
                    length = int(length)
                    if length < 0:
                        raise Error
                    # For the 'bytes' token convert length to bits.
                    if name == 'bytes':
                        length *= 8
                except Error:
                    raise ValueError("Can't read a token with a negative length.")
                except ValueError:
                    if not keys or length not in keys:
                        raise ValueError("Don't understand length '{0}' of token.".format(length))
            ret_vals.append([name, length, value])
        # This multiplies by the multiplicative factor, but this means that
        # we can't allow keyword values as multipliers (e.g. n*uint:8).
        # The only way to do this would be to return the factor in some fashion
        # (we can't use the key's value here as it would mean that we couldn't
        # sensibly continue to cache the function's results. (TODO).
        return_values.extend(ret_vals * factor)
    return_values = [tuple(x) for x in return_values]
    if len(token_cache) < CACHE_SIZE:
        token_cache[token_key] = stretchy_token, return_values
    return stretchy_token, return_values
 
 
# Looks for first number*(
BRACKET_RE = re.compile(r'(?P<factor>\d+)\*\‍(')
 
 
def expand_brackets(s):
    """Remove whitespace and expand all brackets."""
    s = ''.join(s.split())
    while True:
        start = s.find('(')
        if start == -1:
            break
        count = 1  # Number of hanging open brackets
        p = start + 1
        while p < len(s):
            if s[p] == '(':
                count += 1
            if s[p] == ')':
                count -= 1
            if not count:
                break
            p += 1
        if count:
            raise ValueError("Unbalanced parenthesis in '{0}'.".format(s))
        if start == 0 or s[start - 1] != '*':
            s = s[0:start] + s[start + 1:p] + s[p + 1:]
        else:
            m = BRACKET_RE.search(s)
            if m:
                factor = int(m.group('factor'))
                matchstart = m.start('factor')
                s = s[0:matchstart] + (factor - 1) * (s[start + 1:p] + ',') + s[start + 1:p] + s[p + 1:]
            else:
                raise ValueError("Failed to parse '{0}'.".format(s))
    return s
 
 
# This converts a single octal digit to 3 bits.
OCT_TO_BITS = ['{0:03b}'.format(i) for i in xrange(8)]
 
# A dictionary of number of 1 bits contained in binary representation of any byte
BIT_COUNT = dict(zip(xrange(256), [bin(i).count('1') for i in xrange(256)]))
 
 
class Bits(object):
    """A container holding an immutable sequence of bits.
 
    For a mutable container use the BitArray class instead.
 
    Methods:
 
    all() -- Check if all specified bits are set to 1 or 0.
    any() -- Check if any of specified bits are set to 1 or 0.
    count() -- Count the number of bits set to 1 or 0.
    cut() -- Create generator of constant sized chunks.
    endswith() -- Return whether the bitstring ends with a sub-string.
    find() -- Find a sub-bitstring in the current bitstring.
    findall() -- Find all occurrences of a sub-bitstring in the current bitstring.
    join() -- Join bitstrings together using current bitstring.
    rfind() -- Seek backwards to find a sub-bitstring.
    split() -- Create generator of chunks split by a delimiter.
    startswith() -- Return whether the bitstring starts with a sub-bitstring.
    tobytes() -- Return bitstring as bytes, padding if needed.
    tofile() -- Write bitstring to file, padding if needed.
    unpack() -- Interpret bits using format string.
 
    Special methods:
 
    Also available are the operators [], ==, !=, +, *, ~, <<, >>, &, |, ^.
 
    Properties:
 
    bin -- The bitstring as a binary string.
    bool -- For single bit bitstrings, interpret as True or False.
    bytes -- The bitstring as a bytes object.
    float -- Interpret as a floating point number.
    floatbe -- Interpret as a big-endian floating point number.
    floatle -- Interpret as a little-endian floating point number.
    floatne -- Interpret as a native-endian floating point number.
    hex -- The bitstring as a hexadecimal string.
    int -- Interpret as a two's complement signed integer.
    intbe -- Interpret as a big-endian signed integer.
    intle -- Interpret as a little-endian signed integer.
    intne -- Interpret as a native-endian signed integer.
    len -- Length of the bitstring in bits.
    oct -- The bitstring as an octal string.
    se -- Interpret as a signed exponential-Golomb code.
    ue -- Interpret as an unsigned exponential-Golomb code.
    sie -- Interpret as a signed interleaved exponential-Golomb code.
    uie -- Interpret as an unsigned interleaved exponential-Golomb code.
    uint -- Interpret as a two's complement unsigned integer.
    uintbe -- Interpret as a big-endian unsigned integer.
    uintle -- Interpret as a little-endian unsigned integer.
    uintne -- Interpret as a native-endian unsigned integer.
 
    """
 
    __slots__ = ('_datastore')
 
    def __init__(self, auto=None, length=None, offset=None, **kwargs):
        """Either specify an 'auto' initialiser:
        auto -- a string of comma separated tokens, an integer, a file object,
                a bytearray, a boolean iterable, an array or another bitstring.
 
        Or initialise via **kwargs with one (and only one) of:
        bytes -- raw data as a string, for example read from a binary file.
        bin -- binary string representation, e.g. '0b001010'.
        hex -- hexadecimal string representation, e.g. '0x2ef'
        oct -- octal string representation, e.g. '0o777'.
        uint -- an unsigned integer.
        int -- a signed integer.
        float -- a floating point number.
        uintbe -- an unsigned big-endian whole byte integer.
        intbe -- a signed big-endian whole byte integer.
        floatbe - a big-endian floating point number.
        uintle -- an unsigned little-endian whole byte integer.
        intle -- a signed little-endian whole byte integer.
        floatle -- a little-endian floating point number.
        uintne -- an unsigned native-endian whole byte integer.
        intne -- a signed native-endian whole byte integer.
        floatne -- a native-endian floating point number.
        se -- a signed exponential-Golomb code.
        ue -- an unsigned exponential-Golomb code.
        sie -- a signed interleaved exponential-Golomb code.
        uie -- an unsigned interleaved exponential-Golomb code.
        bool -- a boolean (True or False).
        filename -- a file which will be opened in binary read-only mode.
 
        Other keyword arguments:
        length -- length of the bitstring in bits, if needed and appropriate.
                  It must be supplied for all integer and float initialisers.
        offset -- bit offset to the data. These offset bits are
                  ignored and this is mainly intended for use when
                  initialising using 'bytes' or 'filename'.
 
        """
 
    def __new__(cls, auto=None, length=None, offset=None, _cache=None, **kwargs):
        # For instances auto-initialised with a string we intern the
        # instance for re-use.
        if _cache is None:
            _cache = {}
        try:
            if isinstance(auto, basestring):
                try:
                    return _cache[auto]
                except KeyError:
                    x = object.__new__(Bits)
                    try:
                        _, tokens = tokenparser(auto)
                    except ValueError as e:
                        raise CreationError(*e.args)
                    x._datastore = ConstByteStore(bytearray(0), 0, 0)
                    for token in tokens:
                        x._datastore._appendstore(Bits._init_with_token(*token)._datastore)
                    assert x._assertsanity()
                    if len(_cache) < CACHE_SIZE:
                        _cache[auto] = x
                    return x
            if isinstance(auto, Bits):
                return auto
        except TypeError:
            pass
        x = super(Bits, cls).__new__(cls)
        x._initialise(auto, length, offset, **kwargs)
        return x
 
    def _initialise(self, auto, length, offset, **kwargs):
        if length is not None and length < 0:
            raise CreationError("bitstring length cannot be negative.")
        if offset is not None and offset < 0:
            raise CreationError("offset must be >= 0.")
        if auto is not None:
            self._initialise_from_auto(auto, length, offset)
            return
        if not kwargs:
            # No initialisers, so initialise with nothing or zero bits
            if length is not None and length != 0:
                data = bytearray((length + 7) // 8)
                self._setbytes_unsafe(data, length, 0)
                return
            self._setbytes_unsafe(bytearray(0), 0, 0)
            return
        k, v = kwargs.popitem()
        try:
            init_without_length_or_offset[k](self, v)
            if length is not None or offset is not None:
                raise CreationError("Cannot use length or offset with this initialiser.")
        except KeyError:
            try:
                init_with_length_only[k](self, v, length)
                if offset is not None:
                    raise CreationError("Cannot use offset with this initialiser.")
            except KeyError:
                if offset is None:
                    offset = 0
                try:
                    init_with_length_and_offset[k](self, v, length, offset)
                except KeyError:
                    raise CreationError("Unrecognised keyword '{0}' used to initialise.", k)
 
    def _initialise_from_auto(self, auto, length, offset):
        if offset is None:
            offset = 0
        self._setauto(auto, length, offset)
        return
 
    def __copy__(self):
        """Return a new copy of the Bits for the copy module."""
        # Note that if you want a new copy (different ID), use _copy instead.
        # The copy can return self as it's immutable.
        return self
 
    def __lt__(self, other):
        raise TypeError("unorderable type: {0}".format(type(self).__name__))
 
    def __gt__(self, other):
        raise TypeError("unorderable type: {0}".format(type(self).__name__))
 
    def __le__(self, other):
        raise TypeError("unorderable type: {0}".format(type(self).__name__))
 
    def __ge__(self, other):
        raise TypeError("unorderable type: {0}".format(type(self).__name__))
 
    def __add__(self, bs):
        """Concatenate bitstrings and return new bitstring.
 
        bs -- the bitstring to append.
 
        """
        bs = Bits(bs)
        if bs.len <= self.len:
            s = self._copy()
            s._append(bs)
        else:
            s = bs._copy()
            s = self.__class__(s)
            s._prepend(self)
        return s
 
    def __radd__(self, bs):
        """Append current bitstring to bs and return new bitstring.
 
        bs -- the string for the 'auto' initialiser that will be appended to.
 
        """
        bs = self._converttobitstring(bs)
        return bs.__add__(self)
 
    def __getitem__(self, key):
        """Return a new bitstring representing a slice of the current bitstring.
 
        Indices are in units of the step parameter (default 1 bit).
        Stepping is used to specify the number of bits in each item.
 
        >>> print BitArray('0b00110')[1:4]
        '0b011'
        >>> print BitArray('0x00112233')[1:3:8]
        '0x1122'
 
        """
        length = self.len
        try:
            step = key.step if key.step is not None else 1
        except AttributeError:
            # single element
            if key < 0:
                key += length
            if not 0 <= key < length:
                raise IndexError("Slice index out of range.")
            # Single bit, return True or False
            return self._datastore.getbit(key)
        else:
            if step != 1:
                # convert to binary string and use string slicing
                bs = self.__class__()
                bs._setbin_unsafe(self._getbin().__getitem__(key))
                return bs
            start, stop = 0, length
            if key.start is not None:
                start = key.start
                if key.start < 0:
                    start += stop
            if key.stop is not None:
                stop = key.stop
                if key.stop < 0:
                    stop += length
            start = max(start, 0)
            stop = min(stop, length)
            if start < stop:
                return self._slice(start, stop)
            else:
                return self.__class__()
 
    def __len__(self):
        """Return the length of the bitstring in bits."""
        return self._getlength()
 
    def __str__(self):
        """Return approximate string representation of bitstring for printing.
 
        Short strings will be given wholly in hexadecimal or binary. Longer
        strings may be part hexadecimal and part binary. Very long strings will
        be truncated with '...'.
 
        """
        length = self.len
        if not length:
            return ''
        if length > MAX_CHARS * 4:
            # Too long for hex. Truncate...
            return ''.join(('0x', self._readhex(MAX_CHARS * 4, 0), '...'))
        # If it's quite short and we can't do hex then use bin
        if length < 32 and length % 4 != 0:
            return '0b' + self.bin
        # If we can use hex then do so
        if not length % 4:
            return '0x' + self.hex
        # Otherwise first we do as much as we can in hex
        # then add on 1, 2 or 3 bits on at the end
        bits_at_end = length % 4
        return ''.join(('0x', self._readhex(length - bits_at_end, 0),
                        ', ', '0b',
                        self._readbin(bits_at_end, length - bits_at_end)))
 
    def __repr__(self):
        """Return representation that could be used to recreate the bitstring.
 
        If the returned string is too long it will be truncated. See __str__().
 
        """
        length = self.len
        if isinstance(self._datastore._rawarray, MmapByteArray):
            offsetstring = ''
            if self._datastore.byteoffset or self._offset:
                offsetstring = ", offset=%d" % (self._datastore._rawarray.byteoffset * 8 + self._offset)
            lengthstring = ", length=%d" % length
            return "{0}(filename='{1}'{2}{3})".format(self.__class__.__name__,
                                                      self._datastore._rawarray.source.name, lengthstring, offsetstring)
        else:
            s = self.__str__()
            lengthstring = ''
            if s.endswith('...'):
                lengthstring = " # length={0}".format(length)
            return "{0}('{1}'){2}".format(self.__class__.__name__, s, lengthstring)
 
    def __eq__(self, bs):
        """Return True if two bitstrings have the same binary representation.
 
        >>> BitArray('0b1110') == '0xe'
        True
 
        """
        try:
            bs = Bits(bs)
        except TypeError:
            return False
        return equal(self._datastore, bs._datastore)
 
    def __ne__(self, bs):
        """Return False if two bitstrings have the same binary representation.
 
        >>> BitArray('0b111') == '0x7'
        False
 
        """
        return not self.__eq__(bs)
 
    def __invert__(self):
        """Return bitstring with every bit inverted.
 
        Raises Error if the bitstring is empty.
 
        """
        if not self.len:
            raise Error("Cannot invert empty bitstring.")
        s = self._copy()
        s._invert_all()
        return s
 
    def __lshift__(self, n):
        """Return bitstring with bits shifted by n to the left.
 
        n -- the number of bits to shift. Must be >= 0.
 
        """
        if n < 0:
            raise ValueError("Cannot shift by a negative amount.")
        if not self.len:
            raise ValueError("Cannot shift an empty bitstring.")
        n = min(n, self.len)
        s = self._slice(n, self.len)
        s._append(Bits(n))
        return s
 
    def __rshift__(self, n):
        """Return bitstring with bits shifted by n to the right.
 
        n -- the number of bits to shift. Must be >= 0.
 
        """
        if n < 0:
            raise ValueError("Cannot shift by a negative amount.")
        if not self.len:
            raise ValueError("Cannot shift an empty bitstring.")
        if not n:
            return self._copy()
        s = self.__class__(length=min(n, self.len))
        s._append(self[:-n])
        return s
 
    def __mul__(self, n):
        """Return bitstring consisting of n concatenations of self.
 
        Called for expression of the form 'a = b*3'.
        n -- The number of concatenations. Must be >= 0.
 
        """
        if n < 0:
            raise ValueError("Cannot multiply by a negative integer.")
        if not n:
            return self.__class__()
        s = self._copy()
        s._imul(n)
        return s
 
    def __rmul__(self, n):
        """Return bitstring consisting of n concatenations of self.
 
        Called for expressions of the form 'a = 3*b'.
        n -- The number of concatenations. Must be >= 0.
 
        """
        return self.__mul__(n)
 
    def __and__(self, bs):
        """Bit-wise 'and' between two bitstrings. Returns new bitstring.
 
        bs -- The bitstring to '&' with.
 
        Raises ValueError if the two bitstrings have differing lengths.
 
        """
        bs = Bits(bs)
        if self.len != bs.len:
            raise ValueError("Bitstrings must have the same length "
                             "for & operator.")
        s = self._copy()
        s._iand(bs)
        return s
 
    def __rand__(self, bs):
        """Bit-wise 'and' between two bitstrings. Returns new bitstring.
 
        bs -- the bitstring to '&' with.
 
        Raises ValueError if the two bitstrings have differing lengths.
 
        """
        return self.__and__(bs)
 
    def __or__(self, bs):
        """Bit-wise 'or' between two bitstrings. Returns new bitstring.
 
        bs -- The bitstring to '|' with.
 
        Raises ValueError if the two bitstrings have differing lengths.
 
        """
        bs = Bits(bs)
        if self.len != bs.len:
            raise ValueError("Bitstrings must have the same length "
                             "for | operator.")
        s = self._copy()
        s._ior(bs)
        return s
 
    def __ror__(self, bs):
        """Bit-wise 'or' between two bitstrings. Returns new bitstring.
 
        bs -- The bitstring to '|' with.
 
        Raises ValueError if the two bitstrings have differing lengths.
 
        """
        return self.__or__(bs)
 
    def __xor__(self, bs):
        """Bit-wise 'xor' between two bitstrings. Returns new bitstring.
 
        bs -- The bitstring to '^' with.
 
        Raises ValueError if the two bitstrings have differing lengths.
 
        """
        bs = Bits(bs)
        if self.len != bs.len:
            raise ValueError("Bitstrings must have the same length "
                             "for ^ operator.")
        s = self._copy()
        s._ixor(bs)
        return s
 
    def __rxor__(self, bs):
        """Bit-wise 'xor' between two bitstrings. Returns new bitstring.
 
        bs -- The bitstring to '^' with.
 
        Raises ValueError if the two bitstrings have differing lengths.
 
        """
        return self.__xor__(bs)
 
    def __contains__(self, bs):
        """Return whether bs is contained in the current bitstring.
 
        bs -- The bitstring to search for.
 
        """
        # Don't want to change pos
        try:
            pos = self._pos
        except AttributeError:
            pass
        found = Bits.find(self, bs, bytealigned=False)
        try:
            self._pos = pos
        except AttributeError:
            pass
        return bool(found)
 
    def __hash__(self):
        """Return an integer hash of the object."""
        # We can't in general hash the whole bitstring (it could take hours!)
        # So instead take some bits from the start and end.
        if self.len <= 160:
            # Use the whole bitstring.
            shorter = self
        else:
            # Take 10 bytes from start and end
            shorter = self[:80] + self[-80:]
        h = 0
        for byte in shorter.tobytes():
            try:
                h = (h << 4) + ord(byte)
            except TypeError:
                # Python 3
                h = (h << 4) + byte
            g = h & 0xf0000000
            if g & (1 << 31):
                h ^= (g >> 24)
                h ^= g
        return h % 1442968193
 
    # This is only used in Python 2.x...
    def __nonzero__(self):
        """Return True if any bits are set to 1, otherwise return False."""
        return self.any(True)
 
    # ...whereas this is used in Python 3.x
    __bool__ = __nonzero__
 
    def _assertsanity(self):
        """Check internal self consistency as a debugging aid."""
        assert self.len >= 0
        assert 0 <= self._offset, "offset={0}".format(self._offset)
        assert (self.len + self._offset + 7) // 8 == self._datastore.bytelength + self._datastore.byteoffset
        return True
 
    @classmethod
    def _init_with_token(cls, name, token_length, value):
        if token_length is not None:
            token_length = int(token_length)
        if token_length == 0:
            return cls()
        # For pad token just return the length in zero bits
        if name == 'pad':
            return cls(token_length)
 
        if value is None:
            if token_length is None:
                error = "Token has no value ({0}=???).".format(name)
            else:
                error = "Token has no value ({0}:{1}=???).".format(name, token_length)
            raise ValueError(error)
        try:
            b = cls(**{_tokenname_to_initialiser[name]: value})
        except KeyError:
            if name in ('se', 'ue', 'sie', 'uie'):
                b = cls(**{name: int(value)})
            elif name in ('uint', 'int', 'uintbe', 'intbe', 'uintle', 'intle', 'uintne', 'intne'):
                b = cls(**{name: int(value), 'length': token_length})
            elif name in ('float', 'floatbe', 'floatle', 'floatne'):
                b = cls(**{name: float(value), 'length': token_length})
            elif name == 'bool':
                if value in (1, 'True', '1'):
                    b = cls(bool=True)
                elif value in (0, 'False', '0'):
                    b = cls(bool=False)
                else:
                    raise CreationError("bool token can only be 'True' or 'False'.")
            else:
                raise CreationError("Can't parse token name {0}.", name)
        if token_length is not None and b.len != token_length:
            msg = "Token with length {0} packed with value of length {1} ({2}:{3}={4})."
            raise CreationError(msg, token_length, b.len, name, token_length, value)
        return b
 
    def _clear(self):
        """Reset the bitstring to an empty state."""
        self._datastore = ByteStore(bytearray(0))
 
    def _setauto(self, s, length, offset):
        """Set bitstring from a bitstring, file, bool, integer, array, iterable or string."""
        # As s can be so many different things it's important to do the checks
        # in the correct order, as some types are also other allowed types.
        # So basestring must be checked before Iterable
        # and bytes/bytearray before Iterable but after basestring!
        if isinstance(s, Bits):
            if length is None:
                length = s.len - offset
            self._setbytes_unsafe(s._datastore.rawbytes, length, s._offset + offset)
            return
        if isinstance(s, file):
            if offset is None:
                offset = 0
            if length is None:
                length = os.path.getsize(s.name) * 8 - offset
            byteoffset, offset = divmod(offset, 8)
            bytelength = (length + byteoffset * 8 + offset + 7) // 8 - byteoffset
            m = MmapByteArray(s, bytelength, byteoffset)
            if length + byteoffset * 8 + offset > m.filelength * 8:
                raise CreationError("File is not long enough for specified "
                                    "length and offset.")
            self._datastore = ConstByteStore(m, length, offset)
            return
        if length is not None:
            raise CreationError("The length keyword isn't applicable to this initialiser.")
        if offset:
            raise CreationError("The offset keyword isn't applicable to this initialiser.")
        if isinstance(s, basestring):
            bs = self._converttobitstring(s)
            assert bs._offset == 0
            self._setbytes_unsafe(bs._datastore.rawbytes, bs.length, 0)
            return
        if isinstance(s, (bytes, bytearray)):
            self._setbytes_unsafe(bytearray(s), len(s) * 8, 0)
            return
        if isinstance(s, array.array):
            b = s.tostring()
            self._setbytes_unsafe(bytearray(b), len(b) * 8, 0)
            return
        if isinstance(s, numbers.Integral):
            # Initialise with s zero bits.
            if s < 0:
                msg = "Can't create bitstring of negative length {0}."
                raise CreationError(msg, s)
            data = bytearray((s + 7) // 8)
            self._datastore = ByteStore(data, s, 0)
            return
        if isinstance(s, collections.abc.Iterable):
            # Evaluate each item as True or False and set bits to 1 or 0.
            self._setbin_unsafe(''.join(str(int(bool(x))) for x in s))
            return
        raise TypeError("Cannot initialise bitstring from {0}.".format(type(s)))
 
    def _setfile(self, filename, length, offset):
        """Use file as source of bits."""
        source = open(filename, 'rb')
        if offset is None:
            offset = 0
        if length is None:
            length = os.path.getsize(source.name) * 8 - offset
        byteoffset, offset = divmod(offset, 8)
        bytelength = (length + byteoffset * 8 + offset + 7) // 8 - byteoffset
        m = MmapByteArray(source, bytelength, byteoffset)
        if length + byteoffset * 8 + offset > m.filelength * 8:
            raise CreationError("File is not long enough for specified "
                                "length and offset.")
        self._datastore = ConstByteStore(m, length, offset)
 
    def _setbytes_safe(self, data, length=None, offset=0):
        """Set the data from a string."""
        data = bytearray(data)
        if length is None:
            # Use to the end of the data
            length = len(data) * 8 - offset
            self._datastore = ByteStore(data, length, offset)
        else:
            if length + offset > len(data) * 8:
                msg = "Not enough data present. Need {0} bits, have {1}."
                raise CreationError(msg, length + offset, len(data) * 8)
            if length == 0:
                self._datastore = ByteStore(bytearray(0))
            else:
                self._datastore = ByteStore(data, length, offset)
 
    def _setbytes_unsafe(self, data, length, offset):
        """Unchecked version of _setbytes_safe."""
        self._datastore = ByteStore(data[:], length, offset)
        assert self._assertsanity()
 
    def _readbytes(self, length, start):
        """Read bytes and return them. Note that length is in bits."""
        assert length % 8 == 0
        assert start + length <= self.len
        if not (start + self._offset) % 8:
            return bytes(self._datastore.getbyteslice((start + self._offset) // 8,
                                                      (start + self._offset + length) // 8))
        return self._slice(start, start + length).tobytes()
 
    def _getbytes(self):
        """Return the data as an ordinary string."""
        if self.len % 8:
            raise InterpretError("Cannot interpret as bytes unambiguously - "
                                 "not multiple of 8 bits.")
        return self._readbytes(self.len, 0)
 
    def _setuint(self, uint, length=None):
        """Reset the bitstring to have given unsigned int interpretation."""
        try:
            if length is None:
                # Use the whole length. Deliberately not using .len here.
                length = self._datastore.bitlength
        except AttributeError:
            # bitstring doesn't have a _datastore as it hasn't been created!
            pass
        # TODO: All this checking code should be hoisted out of here!
        if length is None or length == 0:
            raise CreationError("A non-zero length must be specified with a "
                                "uint initialiser.")
        if uint >= (1 << length):
            msg = "{0} is too large an unsigned integer for a bitstring of length {1}. "\
                  "The allowed range is [0, {2}]."
            raise CreationError(msg, uint, length, (1 << length) - 1)
        if uint < 0:
            raise CreationError("uint cannot be initialsed by a negative number.")
        s = hex(uint)[2:]
        s = s.rstrip('L')
        if len(s) & 1:
            s = '0' + s
        try:
            data = bytes.fromhex(s)
        except AttributeError:
            # the Python 2.x way
            data = binascii.unhexlify(s)
        # Now add bytes as needed to get the right length.
        extrabytes = ((length + 7) // 8) - len(data)
        if extrabytes > 0:
            data = b'\x00' * extrabytes + data
        offset = 8 - (length % 8)
        if offset == 8:
            offset = 0
        self._setbytes_unsafe(bytearray(data), length, offset)
 
    def _readuint(self, length, start):
        """Read bits and interpret as an unsigned int."""
        if not length:
            raise InterpretError("Cannot interpret a zero length bitstring "
                                 "as an integer.")
        offset = self._offset
        startbyte = (start + offset) // 8
        endbyte = (start + offset + length - 1) // 8
 
        b = binascii.hexlify(bytes(self._datastore.getbyteslice(startbyte, endbyte + 1)))
        assert b
        i = int(b, 16)
        final_bits = 8 - ((start + offset + length) % 8)
        if final_bits != 8:
            i >>= final_bits
        i &= (1 << length) - 1
        return i
 
    def _getuint(self):
        """Return data as an unsigned int."""
        return self._readuint(self.len, 0)
 
    def _setint(self, int_, length=None):
        """Reset the bitstring to have given signed int interpretation."""
        # If no length given, and we've previously been given a length, use it.
        if length is None and hasattr(self, 'len') and self.len != 0:
            length = self.len
        if length is None or length == 0:
            raise CreationError("A non-zero length must be specified with an int initialiser.")
        if int_ >= (1 << (length - 1)) or int_ < -(1 << (length - 1)):
            raise CreationError("{0} is too large a signed integer for a bitstring of length {1}. "
                                "The allowed range is [{2}, {3}].", int_, length, -(1 << (length - 1)),
                                (1 << (length - 1)) - 1)
        if int_ >= 0:
            self._setuint(int_, length)
            return
        # TODO: We should decide whether to just use the _setuint, or to do the bit flipping,
        # based upon which will be quicker. If the -ive number is less than half the maximum
        # possible then it's probably quicker to do the bit flipping...
 
        # Do the 2's complement thing. Add one, set to minus number, then flip bits.
        int_ += 1
        self._setuint(-int_, length)
        self._invert_all()
 
    def _readint(self, length, start):
        """Read bits and interpret as a signed int"""
        ui = self._readuint(length, start)
        if not ui >> (length - 1):
            # Top bit not set, number is positive
            return ui
        # Top bit is set, so number is negative
        tmp = (~(ui - 1)) & ((1 << length) - 1)
        return -tmp
 
    def _getint(self):
        """Return data as a two's complement signed int."""
        return self._readint(self.len, 0)
 
    def _setuintbe(self, uintbe, length=None):
        """Set the bitstring to a big-endian unsigned int interpretation."""
        if length is not None and length % 8 != 0:
            raise CreationError("Big-endian integers must be whole-byte. "
                                "Length = {0} bits.", length)
        self._setuint(uintbe, length)
 
    def _readuintbe(self, length, start):
        """Read bits and interpret as a big-endian unsigned int."""
        if length % 8:
            raise InterpretError("Big-endian integers must be whole-byte. "
                                 "Length = {0} bits.", length)
        return self._readuint(length, start)
 
    def _getuintbe(self):
        """Return data as a big-endian two's complement unsigned int."""
        return self._readuintbe(self.len, 0)
 
    def _setintbe(self, intbe, length=None):
        """Set bitstring to a big-endian signed int interpretation."""
        if length is not None and length % 8 != 0:
            raise CreationError("Big-endian integers must be whole-byte. "
                                "Length = {0} bits.", length)
        self._setint(intbe, length)
 
    def _readintbe(self, length, start):
        """Read bits and interpret as a big-endian signed int."""
        if length % 8:
            raise InterpretError("Big-endian integers must be whole-byte. "
                                 "Length = {0} bits.", length)
        return self._readint(length, start)
 
    def _getintbe(self):
        """Return data as a big-endian two's complement signed int."""
        return self._readintbe(self.len, 0)
 
    def _setuintle(self, uintle, length=None):
        if length is not None and length % 8 != 0:
            raise CreationError("Little-endian integers must be whole-byte. "
                                "Length = {0} bits.", length)
        self._setuint(uintle, length)
        self._reversebytes(0, self.len)
 
    def _readuintle(self, length, start):
        """Read bits and interpret as a little-endian unsigned int."""
        if length % 8:
            raise InterpretError("Little-endian integers must be whole-byte. "
                                 "Length = {0} bits.", length)
        assert start + length <= self.len
        absolute_pos = start + self._offset
        startbyte, offset = divmod(absolute_pos, 8)
        val = 0
        if not offset:
            endbyte = (absolute_pos + length - 1) // 8
            chunksize = 4  # for 'L' format
            while endbyte - chunksize + 1 >= startbyte:
                val <<= 8 * chunksize
                val += struct.unpack('<L', bytes(self._datastore.getbyteslice(endbyte + 1 - chunksize, endbyte + 1)))[0]
                endbyte -= chunksize
            for b in xrange(endbyte, startbyte - 1, -1):
                val <<= 8
                val += self._datastore.getbyte(b)
        else:
            data = self._slice(start, start + length)
            assert data.len % 8 == 0
            data._reversebytes(0, self.len)
            for b in bytearray(data.bytes):
                val <<= 8
                val += b
        return val
 
    def _getuintle(self):
        return self._readuintle(self.len, 0)
 
    def _setintle(self, intle, length=None):
        if length is not None and length % 8 != 0:
            raise CreationError("Little-endian integers must be whole-byte. "
                                "Length = {0} bits.", length)
        self._setint(intle, length)
        self._reversebytes(0, self.len)
 
    def _readintle(self, length, start):
        """Read bits and interpret as a little-endian signed int."""
        ui = self._readuintle(length, start)
        if not ui >> (length - 1):
            # Top bit not set, number is positive
            return ui
        # Top bit is set, so number is negative
        tmp = (~(ui - 1)) & ((1 << length) - 1)
        return -tmp
 
    def _getintle(self):
        return self._readintle(self.len, 0)
 
    def _setfloat(self, f, length=None):
        # If no length given, and we've previously been given a length, use it.
        if length is None and hasattr(self, 'len') and self.len != 0:
            length = self.len
        if length is None or length == 0:
            raise CreationError("A non-zero length must be specified with a "
                                "float initialiser.")
        if length == 32:
            b = struct.pack('>f', f)
        elif length == 64:
            b = struct.pack('>d', f)
        else:
            raise CreationError("floats can only be 32 or 64 bits long, "
                                "not {0} bits", length)
        self._setbytes_unsafe(bytearray(b), length, 0)
 
    def _readfloat(self, length, start):
        """Read bits and interpret as a float."""
        if not (start + self._offset) % 8:
            startbyte = (start + self._offset) // 8
            if length == 32:
                f, = struct.unpack('>f', bytes(self._datastore.getbyteslice(startbyte, startbyte + 4)))
            elif length == 64:
                f, = struct.unpack('>d', bytes(self._datastore.getbyteslice(startbyte, startbyte + 8)))
        else:
            if length == 32:
                f, = struct.unpack('>f', self._readbytes(32, start))
            elif length == 64:
                f, = struct.unpack('>d', self._readbytes(64, start))
        try:
            return f
        except NameError:
            raise InterpretError("floats can only be 32 or 64 bits long, not {0} bits", length)
 
    def _getfloat(self):
        """Interpret the whole bitstring as a float."""
        return self._readfloat(self.len, 0)
 
    def _setfloatle(self, f, length=None):
        # If no length given, and we've previously been given a length, use it.
        if length is None and hasattr(self, 'len') and self.len != 0:
            length = self.len
        if length is None or length == 0:
            raise CreationError("A non-zero length must be specified with a "
                                "float initialiser.")
        if length == 32:
            b = struct.pack('<f', f)
        elif length == 64:
            b = struct.pack('<d', f)
        else:
            raise CreationError("floats can only be 32 or 64 bits long, "
                                "not {0} bits", length)
        self._setbytes_unsafe(bytearray(b), length, 0)
 
    def _readfloatle(self, length, start):
        """Read bits and interpret as a little-endian float."""
        startbyte, offset = divmod(start + self._offset, 8)
        if not offset:
            if length == 32:
                f, = struct.unpack('<f', bytes(self._datastore.getbyteslice(startbyte, startbyte + 4)))
            elif length == 64:
                f, = struct.unpack('<d', bytes(self._datastore.getbyteslice(startbyte, startbyte + 8)))
        else:
            if length == 32:
                f, = struct.unpack('<f', self._readbytes(32, start))
            elif length == 64:
                f, = struct.unpack('<d', self._readbytes(64, start))
        try:
            return f
        except NameError:
            raise InterpretError("floats can only be 32 or 64 bits long, "
                                 "not {0} bits", length)
 
    def _getfloatle(self):
        """Interpret the whole bitstring as a little-endian float."""
        return self._readfloatle(self.len, 0)
 
    def _setue(self, i):
        """Initialise bitstring with unsigned exponential-Golomb code for integer i.
 
        Raises CreationError if i < 0.
 
        """
        if i < 0:
            raise CreationError("Cannot use negative initialiser for unsigned "
                                "exponential-Golomb.")
        if not i:
            self._setbin_unsafe('1')
            return
        tmp = i + 1
        leadingzeros = -1
        while tmp > 0:
            tmp >>= 1
            leadingzeros += 1
        remainingpart = i + 1 - (1 << leadingzeros)
        binstring = '0' * leadingzeros + '1' + Bits(uint=remainingpart,
                                                    length=leadingzeros).bin
        self._setbin_unsafe(binstring)
 
    def _readue(self, pos):
        """Return interpretation of next bits as unsigned exponential-Golomb code.
 
        Raises ReadError if the end of the bitstring is encountered while
        reading the code.
 
        """
        oldpos = pos
        try:
            while not self[pos]:
                pos += 1
        except IndexError:
            raise ReadError("Read off end of bitstring trying to read code.")
        leadingzeros = pos - oldpos
        codenum = (1 << leadingzeros) - 1
        if leadingzeros > 0:
            if pos + leadingzeros + 1 > self.len:
                raise ReadError("Read off end of bitstring trying to read code.")
            codenum += self._readuint(leadingzeros, pos + 1)
            pos += leadingzeros + 1
        else:
            assert codenum == 0
            pos += 1
        return codenum, pos
 
    def _getue(self):
        """Return data as unsigned exponential-Golomb code.
 
        Raises InterpretError if bitstring is not a single exponential-Golomb code.
 
        """
        try:
            value, newpos = self._readue(0)
            if value is None or newpos != self.len:
                raise ReadError
        except ReadError:
            raise InterpretError("Bitstring is not a single exponential-Golomb code.")
        return value
 
    def _setse(self, i):
        """Initialise bitstring with signed exponential-Golomb code for integer i."""
        if i > 0:
            u = (i * 2) - 1
        else:
            u = -2 * i
        self._setue(u)
 
    def _getse(self):
        """Return data as signed exponential-Golomb code.
 
        Raises InterpretError if bitstring is not a single exponential-Golomb code.
 
        """
        try:
            value, newpos = self._readse(0)
            if value is None or newpos != self.len:
                raise ReadError
        except ReadError:
            raise InterpretError("Bitstring is not a single exponential-Golomb code.")
        return value
 
    def _readse(self, pos):
        """Return interpretation of next bits as a signed exponential-Golomb code.
 
        Advances position to after the read code.
 
        Raises ReadError if the end of the bitstring is encountered while
        reading the code.
 
        """
        codenum, pos = self._readue(pos)
        m = (codenum + 1) // 2
        if not codenum % 2:
            return -m, pos
        else:
            return m, pos
 
    def _setuie(self, i):
        """Initialise bitstring with unsigned interleaved exponential-Golomb code for integer i.
 
        Raises CreationError if i < 0.
 
        """
        if i < 0:
            raise CreationError("Cannot use negative initialiser for unsigned "
                                "interleaved exponential-Golomb.")
        self._setbin_unsafe('1' if i == 0 else '0' + '0'.join(bin(i + 1)[3:]) + '1')
 
    def _readuie(self, pos):
        """Return interpretation of next bits as unsigned interleaved exponential-Golomb code.
 
        Raises ReadError if the end of the bitstring is encountered while
        reading the code.
 
        """
        try:
            codenum = 1
            while not self[pos]:
                pos += 1
                codenum <<= 1
                codenum += self[pos]
                pos += 1
            pos += 1
        except IndexError:
            raise ReadError("Read off end of bitstring trying to read code.")
        codenum -= 1
        return codenum, pos
 
    def _getuie(self):
        """Return data as unsigned interleaved exponential-Golomb code.
 
        Raises InterpretError if bitstring is not a single exponential-Golomb code.
 
        """
        try:
            value, newpos = self._readuie(0)
            if value is None or newpos != self.len:
                raise ReadError
        except ReadError:
            raise InterpretError("Bitstring is not a single interleaved exponential-Golomb code.")
        return value
 
    def _setsie(self, i):
        """Initialise bitstring with signed interleaved exponential-Golomb code for integer i."""
        if not i:
            self._setbin_unsafe('1')
        else:
            self._setuie(abs(i))
            self._append(Bits([i < 0]))
 
    def _getsie(self):
        """Return data as signed interleaved exponential-Golomb code.
 
        Raises InterpretError if bitstring is not a single exponential-Golomb code.
 
        """
        try:
            value, newpos = self._readsie(0)
            if value is None or newpos != self.len:
                raise ReadError
        except ReadError:
            raise InterpretError("Bitstring is not a single interleaved exponential-Golomb code.")
        return value
 
    def _readsie(self, pos):
        """Return interpretation of next bits as a signed interleaved exponential-Golomb code.
 
        Advances position to after the read code.
 
        Raises ReadError if the end of the bitstring is encountered while
        reading the code.
 
        """
        codenum, pos = self._readuie(pos)
        if not codenum:
            return 0, pos
        try:
            if self[pos]:
                return -codenum, pos + 1
            else:
                return codenum, pos + 1
        except IndexError:
            raise ReadError("Read off end of bitstring trying to read code.")
 
    def _setbool(self, value):
        # We deliberately don't want to have implicit conversions to bool here.
        # If we did then it would be difficult to deal with the 'False' string.
        if value in (1, 'True'):
            self._setbytes_unsafe(bytearray(b'\x80'), 1, 0)
        elif value in (0, 'False'):
            self._setbytes_unsafe(bytearray(b'\x00'), 1, 0)
        else:
            raise CreationError('Cannot initialise boolean with {0}.', value)
 
    def _getbool(self):
        if self.length != 1:
            msg = "For a bool interpretation a bitstring must be 1 bit long, not {0} bits."
            raise InterpretError(msg, self.length)
        return self[0]
 
    def _readbool(self, pos):
        return self[pos], pos + 1
 
    def _setbin_safe(self, binstring):
        """Reset the bitstring to the value given in binstring."""
        binstring = tidy_input_string(binstring)
        # remove any 0b if present
        binstring = binstring.replace('0b', '')
        self._setbin_unsafe(binstring)
 
    def _setbin_unsafe(self, binstring):
        """Same as _setbin_safe, but input isn't sanity checked. binstring mustn't start with '0b'."""
        length = len(binstring)
        # pad with zeros up to byte boundary if needed
        boundary = ((length + 7) // 8) * 8
        padded_binstring = binstring + '0' * (boundary - length)\
            if len(binstring) < boundary else binstring
        try:
            bytelist = [int(padded_binstring[x:x + 8], 2)
                        for x in xrange(0, len(padded_binstring), 8)]
        except ValueError:
            raise CreationError("Invalid character in bin initialiser {0}.", binstring)
        self._setbytes_unsafe(bytearray(bytelist), length, 0)
 
    def _readbin(self, length, start):
        """Read bits and interpret as a binary string."""
        if not length:
            return ''
        # Get the byte slice containing our bit slice
        startbyte, startoffset = divmod(start + self._offset, 8)
        endbyte = (start + self._offset + length - 1) // 8
        b = self._datastore.getbyteslice(startbyte, endbyte + 1)
        # Convert to a string of '0' and '1's (via a hex string an and int!)
        try:
            c = "{:0{}b}".format(int(binascii.hexlify(b), 16), 8 * len(b))
        except TypeError:
            # Hack to get Python 2.6 working
            c = "{0:0{1}b}".format(int(binascii.hexlify(str(b)), 16), 8 * len(b))
        # Finally chop off any extra bits.
        return c[startoffset:startoffset + length]
 
    def _getbin(self):
        """Return interpretation as a binary string."""
        return self._readbin(self.len, 0)
 
    def _setoct(self, octstring):
        """Reset the bitstring to have the value given in octstring."""
        octstring = tidy_input_string(octstring)
        # remove any 0o if present
        octstring = octstring.replace('0o', '')
        binlist = []
        for i in octstring:
            try:
                if not 0 <= int(i) < 8:
                    raise ValueError
                binlist.append(OCT_TO_BITS[int(i)])
            except ValueError:
                raise CreationError("Invalid symbol '{0}' in oct initialiser.", i)
        self._setbin_unsafe(''.join(binlist))
 
    def _readoct(self, length, start):
        """Read bits and interpret as an octal string."""
        if length % 3:
            raise InterpretError("Cannot convert to octal unambiguously - "
                                 "not multiple of 3 bits.")
        if not length:
            return ''
        # Get main octal bit by converting from int.
        # Strip starting 0 or 0o depending on Python version.
        end = oct(self._readuint(length, start))[LEADING_OCT_CHARS:]
        if end.endswith('L'):
            end = end[:-1]
        middle = '0' * (length // 3 - len(end))
        return middle + end
 
    def _getoct(self):
        """Return interpretation as an octal string."""
        return self._readoct(self.len, 0)
 
    def _sethex(self, hexstring):
        """Reset the bitstring to have the value given in hexstring."""
        hexstring = tidy_input_string(hexstring)
        # remove any 0x if present
        hexstring = hexstring.replace('0x', '')
        length = len(hexstring)
        if length % 2:
            hexstring += '0'
        try:
            try:
                data = bytearray.fromhex(hexstring)
            except TypeError:
                # Python 2.6 needs a unicode string (a bug). 2.7 and 3.x work fine.
                data = bytearray.fromhex(unicode(hexstring))  # noqa
        except ValueError:
            raise CreationError("Invalid symbol in hex initialiser.")
        self._setbytes_unsafe(data, length * 4, 0)
 
    def _readhex(self, length, start):
        """Read bits and interpret as a hex string."""
        if length % 4:
            raise InterpretError("Cannot convert to hex unambiguously - "
                                 "not multiple of 4 bits.")
        if not length:
            return ''
        s = self._slice(start, start + length).tobytes()
        try:
            s = s.hex()  # Available in Python 3.5
        except AttributeError:
            # This monstrosity is the only thing I could get to work for both 2.6 and 3.1.
            # TODO: Is utf-8 really what we mean here?
            s = str(binascii.hexlify(s).decode('utf-8'))
        # If there's one nibble too many then cut it off
        return s[:-1] if (length // 4) % 2 else s
 
    def _gethex(self):
        """Return the hexadecimal representation as a string prefixed with '0x'.
 
        Raises an InterpretError if the bitstring's length is not a multiple of 4.
 
        """
        return self._readhex(self.len, 0)
 
    def _getoffset(self):
        return self._datastore.offset
 
    def _getlength(self):
        """Return the length of the bitstring in bits."""
        return self._datastore.bitlength
 
    def _ensureinmemory(self):
        """Ensure the data is held in memory, not in a file."""
        self._setbytes_unsafe(self._datastore.getbyteslice(0, self._datastore.bytelength),
                              self.len, self._offset)
 
    @classmethod
    def _converttobitstring(cls, bs, offset=0, cache=None):
        """Convert bs to a bitstring and return it.
 
        offset gives the suggested bit offset of first significant
        bit, to optimise append etc.
 
        """
        if cache is None:
            cache = {}
        if isinstance(bs, Bits):
            return bs
        try:
            return cache[(bs, offset)]
        except KeyError:
            if isinstance(bs, basestring):
                b = cls()
                try:
                    _, tokens = tokenparser(bs)
                except ValueError as e:
                    raise CreationError(*e.args)
                if tokens:
                    b._append(Bits._init_with_token(*tokens[0]))
                    b._datastore = offsetcopy(b._datastore, offset)
                    for token in tokens[1:]:
                        b._append(Bits._init_with_token(*token))
                assert b._assertsanity()
                assert b.len == 0 or b._offset == offset
                if len(cache) < CACHE_SIZE:
                    cache[(bs, offset)] = b
                return b
        except TypeError:
            # Unhashable type
            pass
        return cls(bs)
 
    def _copy(self):
        """Create and return a new copy of the Bits (always in memory)."""
        s_copy = self.__class__()
        s_copy._setbytes_unsafe(self._datastore.getbyteslice(0, self._datastore.bytelength),
                                self.len, self._offset)
        return s_copy
 
    def _slice(self, start, end):
        """Used internally to get a slice, without error checking."""
        if end == start:
            return self.__class__()
        offset = self._offset
        startbyte, newoffset = divmod(start + offset, 8)
        endbyte = (end + offset - 1) // 8
        bs = self.__class__()
        bs._setbytes_unsafe(self._datastore.getbyteslice(startbyte, endbyte + 1), end - start, newoffset)
        return bs
 
    def _readtoken(self, name, pos, length):
        """Reads a token from the bitstring and returns the result."""
        if length is not None and int(length) > self.length - pos:
            raise ReadError("Reading off the end of the data. "
                            "Tried to read {0} bits when only {1} available.".format(int(length), self.length - pos))
        try:
            val = name_to_read[name](self, length, pos)
            return val, pos + length
        except KeyError:
            if name == 'pad':
                return None, pos + length
            raise ValueError("Can't parse token {0}:{1}".format(name, length))
        except TypeError:
            # This is for the 'ue', 'se' and 'bool' tokens. They will also return the new pos.
            return name_to_read[name](self, pos)
 
    def _append(self, bs):
        """Append a bitstring to the current bitstring."""
        self._datastore._appendstore(bs._datastore)
 
    def _prepend(self, bs):
        """Prepend a bitstring to the current bitstring."""
        self._datastore._prependstore(bs._datastore)
 
    def _reverse(self):
        """Reverse all bits in-place."""
        # Reverse the contents of each byte
        n = [BYTE_REVERSAL_DICT[b] for b in self._datastore.rawbytes]
        # Then reverse the order of the bytes
        n.reverse()
        # The new offset is the number of bits that were unused at the end.
        newoffset = 8 - (self._offset + self.len) % 8
        if newoffset == 8:
            newoffset = 0
        self._setbytes_unsafe(bytearray().join(n), self.length, newoffset)
 
    def _truncatestart(self, bits):
        """Truncate bits from the start of the bitstring."""
        assert 0 <= bits <= self.len
        if not bits:
            return
        if bits == self.len:
            self._clear()
            return
        bytepos, offset = divmod(self._offset + bits, 8)
        self._setbytes_unsafe(self._datastore.getbyteslice(bytepos, self._datastore.bytelength), self.len - bits,
                              offset)
        assert self._assertsanity()
 
    def _truncateend(self, bits):
        """Truncate bits from the end of the bitstring."""
        assert 0 <= bits <= self.len
        if not bits:
            return
        if bits == self.len:
            self._clear()
            return
        newlength_in_bytes = (self._offset + self.len - bits + 7) // 8
        self._setbytes_unsafe(self._datastore.getbyteslice(0, newlength_in_bytes), self.len - bits,
                              self._offset)
        assert self._assertsanity()
 
    def _insert(self, bs, pos):
        """Insert bs at pos."""
        assert 0 <= pos <= self.len
        if pos > self.len // 2:
            # Inserting nearer end, so cut off end.
            end = self._slice(pos, self.len)
            self._truncateend(self.len - pos)
            self._append(bs)
            self._append(end)
        else:
            # Inserting nearer start, so cut off start.
            start = self._slice(0, pos)
            self._truncatestart(pos)
            self._prepend(bs)
            self._prepend(start)
        try:
            self._pos = pos + bs.len
        except AttributeError:
            pass
        assert self._assertsanity()
 
    def _overwrite(self, bs, pos):
        """Overwrite with bs at pos."""
        assert 0 <= pos < self.len
        if bs is self:
            # Just overwriting with self, so do nothing.
            assert pos == 0
            return
        firstbytepos = (self._offset + pos) // 8
        lastbytepos = (self._offset + pos + bs.len - 1) // 8
        bytepos, bitoffset = divmod(self._offset + pos, 8)
        if firstbytepos == lastbytepos:
            mask = ((1 << bs.len) - 1) << (8 - bs.len - bitoffset)
            self._datastore.setbyte(bytepos, self._datastore.getbyte(bytepos) & (~mask))
            d = offsetcopy(bs._datastore, bitoffset)
            self._datastore.setbyte(bytepos, self._datastore.getbyte(bytepos) | (d.getbyte(0) & mask))
        else:
            # Do first byte
            mask = (1 << (8 - bitoffset)) - 1
            self._datastore.setbyte(bytepos, self._datastore.getbyte(bytepos) & (~mask))
            d = offsetcopy(bs._datastore, bitoffset)
            self._datastore.setbyte(bytepos, self._datastore.getbyte(bytepos) | (d.getbyte(0) & mask))
            # Now do all the full bytes
            self._datastore.setbyteslice(firstbytepos + 1, lastbytepos, d.getbyteslice(1, lastbytepos - firstbytepos))
            # and finally the last byte
            bitsleft = (self._offset + pos + bs.len) % 8
            if not bitsleft:
                bitsleft = 8
            mask = (1 << (8 - bitsleft)) - 1
            self._datastore.setbyte(lastbytepos, self._datastore.getbyte(lastbytepos) & mask)
            self._datastore.setbyte(lastbytepos,
                                    self._datastore.getbyte(lastbytepos) | (d.getbyte(d.bytelength - 1) & ~mask))
        assert self._assertsanity()
 
    def _delete(self, bits, pos):
        """Delete bits at pos."""
        assert 0 <= pos <= self.len
        assert pos + bits <= self.len
        if not pos:
            # Cutting bits off at the start.
            self._truncatestart(bits)
            return
        if pos + bits == self.len:
            # Cutting bits off at the end.
            self._truncateend(bits)
            return
        if pos > self.len - pos - bits:
            # More bits before cut point than after it, so do bit shifting
            # on the final bits.
            end = self._slice(pos + bits, self.len)
            assert self.len - pos > 0
            self._truncateend(self.len - pos)
            self._append(end)
            return
        # More bits after the cut point than before it.
        start = self._slice(0, pos)
        self._truncatestart(pos + bits)
        self._prepend(start)
        return
 
    def _reversebytes(self, start, end):
        """Reverse bytes in-place."""
        # Make the start occur on a byte boundary
        # TODO: We could be cleverer here to avoid changing the offset.
        newoffset = 8 - (start % 8)
        if newoffset == 8:
            newoffset = 0
        self._datastore = offsetcopy(self._datastore, newoffset)
        # Now just reverse the byte data
        toreverse = bytearray(self._datastore.getbyteslice((newoffset + start) // 8, (newoffset + end) // 8))
        toreverse.reverse()
        self._datastore.setbyteslice((newoffset + start) // 8, (newoffset + end) // 8, toreverse)
 
    def _set(self, pos):
        """Set bit at pos to 1."""
        assert 0 <= pos < self.len
        self._datastore.setbit(pos)
 
    def _unset(self, pos):
        """Set bit at pos to 0."""
        assert 0 <= pos < self.len
        self._datastore.unsetbit(pos)
 
    def _invert(self, pos):
        """Flip bit at pos 1<->0."""
        assert 0 <= pos < self.len
        self._datastore.invertbit(pos)
 
    def _invert_all(self):
        """Invert every bit."""
        set = self._datastore.setbyte
        get = self._datastore.getbyte
        for p in xrange(self._datastore.byteoffset, self._datastore.byteoffset + self._datastore.bytelength):
            set(p, 256 + ~get(p))
 
    def _ilshift(self, n):
        """Shift bits by n to the left in place. Return self."""
        assert 0 < n <= self.len
        self._append(Bits(n))
        self._truncatestart(n)
        return self
 
    def _irshift(self, n):
        """Shift bits by n to the right in place. Return self."""
        assert 0 < n <= self.len
        self._prepend(Bits(n))
        self._truncateend(n)
        return self
 
    def _imul(self, n):
        """Concatenate n copies of self in place. Return self."""
        assert n >= 0
        if not n:
            self._clear()
            return self
        m = 1
        old_len = self.len
        while m * 2 < n:
            self._append(self)
            m *= 2
        self._append(self[0:(n - m) * old_len])
        return self
 
    def _inplace_logical_helper(self, bs, f):
        """Helper function containing most of the __ior__, __iand__, __ixor__ code."""
        # Give the two bitstrings the same offset (modulo 8)
        self_byteoffset, self_bitoffset = divmod(self._offset, 8)
        bs_byteoffset, bs_bitoffset = divmod(bs._offset, 8)
        if bs_bitoffset != self_bitoffset:
            if not self_bitoffset:
                bs._datastore = offsetcopy(bs._datastore, 0)
            else:
                self._datastore = offsetcopy(self._datastore, bs_bitoffset)
        a = self._datastore.rawbytes
        b = bs._datastore.rawbytes
        for i in xrange(len(a)):
            a[i] = f(a[i + self_byteoffset], b[i + bs_byteoffset])
        return self
 
    def _ior(self, bs):
        return self._inplace_logical_helper(bs, operator.ior)
 
    def _iand(self, bs):
        return self._inplace_logical_helper(bs, operator.iand)
 
    def _ixor(self, bs):
        return self._inplace_logical_helper(bs, operator.xor)
 
    def _readbits(self, length, start):
        """Read some bits from the bitstring and return newly constructed bitstring."""
        return self._slice(start, start + length)
 
    def _validate_slice(self, start, end):
        """Validate start and end and return them as positive bit positions."""
        if start is None:
            start = 0
        elif start < 0:
            start += self.len
        if end is None:
            end = self.len
        elif end < 0:
            end += self.len
        if not 0 <= end <= self.len:
            raise ValueError("end is not a valid position in the bitstring.")
        if not 0 <= start <= self.len:
            raise ValueError("start is not a valid position in the bitstring.")
        if end < start:
            raise ValueError("end must not be less than start.")
        return start, end
 
    def unpack(self, fmt, **kwargs):
        """Interpret the whole bitstring using fmt and return list.
 
        fmt -- A single string or a list of strings with comma separated tokens
               describing how to interpret the bits in the bitstring. Items
               can also be integers, for reading new bitstring of the given length.
        kwargs -- A dictionary or keyword-value pairs - the keywords used in the
                  format string will be replaced with their given value.
 
        Raises ValueError if the format is not understood. If not enough bits
        are available then all bits to the end of the bitstring will be used.
 
        See the docstring for 'read' for token examples.
 
        """
        return self._readlist(fmt, 0, **kwargs)[0]
 
    def _readlist(self, fmt, pos, **kwargs):
        tokens = []
        stretchy_token = None
        if isinstance(fmt, basestring):
            fmt = [fmt]
        # Not very optimal this, but replace integers with 'bits' tokens
        # TODO: optimise
        for i, f in enumerate(fmt):
            if isinstance(f, numbers.Integral):
                fmt[i] = "bits:{0}".format(f)
        for f_item in fmt:
            stretchy, tkns = tokenparser(f_item, tuple(sorted(kwargs.keys())))
            if stretchy:
                if stretchy_token:
                    raise Error("It's not possible to have more than one 'filler' token.")
                stretchy_token = stretchy
            tokens.extend(tkns)
        if not stretchy_token:
            lst = []
            for name, length, _ in tokens:
                if length in kwargs:
                    length = kwargs[length]
                    if name == 'bytes':
                        length *= 8
                if name in kwargs and length is None:
                    # Using default 'uint' - the name is really the length.
                    value, pos = self._readtoken('uint', pos, kwargs[name])
                    lst.append(value)
                    continue
                value, pos = self._readtoken(name, pos, length)
                if value is not None:  # Don't append pad tokens
                    lst.append(value)
            return lst, pos
        stretchy_token = False
        bits_after_stretchy_token = 0
        for token in tokens:
            name, length, _ = token
            if length in kwargs:
                length = kwargs[length]
                if name == 'bytes':
                    length *= 8
            if name in kwargs and length is None:
                # Default 'uint'.
                length = kwargs[name]
            if stretchy_token:
                if name in ('se', 'ue', 'sie', 'uie'):
                    raise Error("It's not possible to parse a variable"
                                "length token after a 'filler' token.")
                else:
                    if length is None:
                        raise Error("It's not possible to have more than "
                                    "one 'filler' token.")
                    bits_after_stretchy_token += length
            if length is None and name not in ('se', 'ue', 'sie', 'uie'):
                assert not stretchy_token
                stretchy_token = token
        bits_left = self.len - pos
        return_values = []
        for token in tokens:
            name, length, _ = token
            if token is stretchy_token:
                # Set length to the remaining bits
                length = max(bits_left - bits_after_stretchy_token, 0)
            if length in kwargs:
                length = kwargs[length]
                if name == 'bytes':
                    length *= 8
            if name in kwargs and length is None:
                # Default 'uint'
                length = kwargs[name]
            if length is not None:
                bits_left -= length
            value, pos = self._readtoken(name, pos, length)
            if value is not None:
                return_values.append(value)
        return return_values, pos
 
    def _findbytes(self, bytes_, start, end, bytealigned):
        """Quicker version of find when everything's whole byte
        and byte aligned.
 
        """
        assert self._datastore.offset == 0
        assert bytealigned is True
        # Extract data bytes from bitstring to be found.
        bytepos = (start + 7) // 8
        found = False
        p = bytepos
        finalpos = end // 8
        increment = max(1024, len(bytes_) * 10)
        buffersize = increment + len(bytes_)
        while p < finalpos:
            # Read in file or from memory in overlapping chunks and search the chunks.
            buf = bytearray(self._datastore.getbyteslice(p, min(p + buffersize, finalpos)))
            pos = buf.find(bytes_)
            if pos != -1:
                found = True
                p += pos
                break
            p += increment
        if not found:
            return ()
        return (p * 8,)
 
    def _findregex(self, reg_ex, start, end, bytealigned):
        """Find first occurrence of a compiled regular expression.
 
        Note that this doesn't support arbitrary regexes, in particular they
        must match a known length.
 
        """
        p = start
        length = len(reg_ex.pattern)
        # We grab overlapping chunks of the binary representation and
        # do an ordinary string search within that.
        increment = max(4096, length * 10)
        buffersize = increment + length
        while p < end:
            buf = self._readbin(min(buffersize, end - p), p)
            # Test using regular expressions...
            m = reg_ex.search(buf)
            if m:
                pos = m.start()
            # pos = buf.find(targetbin)
            # if pos != -1:
                # if bytealigned then we only accept byte aligned positions.
                if not bytealigned or (p + pos) % 8 == 0:
                    return (p + pos,)
                if bytealigned:
                    # Advance to just beyond the non-byte-aligned match and try again...
                    p += pos + 1
                    continue
            p += increment
            # Not found, return empty tuple
        return ()
 
    def find(self, bs, start=None, end=None, bytealigned=None):
        """Find first occurrence of substring bs.
 
        Returns a single item tuple with the bit position if found, or an
        empty tuple if not found. The bit position (pos property) will
        also be set to the start of the substring if it is found.
 
        bs -- The bitstring to find.
        start -- The bit position to start the search. Defaults to 0.
        end -- The bit position one past the last bit to search.
               Defaults to self.len.
        bytealigned -- If True the bitstring will only be
                       found on byte boundaries.
 
        Raises ValueError if bs is empty, if start < 0, if end > self.len or
        if end < start.
 
        >>> BitArray('0xc3e').find('0b1111')
        (6,)
 
        """
        bs = Bits(bs)
        if not bs.len:
            raise ValueError("Cannot find an empty bitstring.")
        start, end = self._validate_slice(start, end)
        if bytealigned is None:
            bytealigned = globals()['bytealigned']
        if bytealigned and not bs.len % 8 and not self._datastore.offset:
            p = self._findbytes(bs.bytes, start, end, bytealigned)
        else:
            p = self._findregex(re.compile(bs._getbin()), start, end, bytealigned)
        # If called from a class that has a pos, set it
        try:
            self._pos = p[0]
        except (AttributeError, IndexError):
            pass
        return p
 
    def findall(self, bs, start=None, end=None, count=None, bytealigned=None):
        """Find all occurrences of bs. Return generator of bit positions.
 
        bs -- The bitstring to find.
        start -- The bit position to start the search. Defaults to 0.
        end -- The bit position one past the last bit to search.
               Defaults to self.len.
        count -- The maximum number of occurrences to find.
        bytealigned -- If True the bitstring will only be found on
                       byte boundaries.
 
        Raises ValueError if bs is empty, if start < 0, if end > self.len or
        if end < start.
 
        Note that all occurrences of bs are found, even if they overlap.
 
        """
        if count is not None and count < 0:
            raise ValueError("In findall, count must be >= 0.")
        bs = Bits(bs)
        start, end = self._validate_slice(start, end)
        if bytealigned is None:
            bytealigned = globals()['bytealigned']
        c = 0
        if bytealigned and not bs.len % 8 and not self._datastore.offset:
            # Use the quick find method
            f = self._findbytes
            x = bs._getbytes()
        else:
            f = self._findregex
            x = re.compile(bs._getbin())
        while True:
 
            p = f(x, start, end, bytealigned)
            if not p:
                break
            if count is not None and c >= count:
                return
            c += 1
            try:
                self._pos = p[0]
            except AttributeError:
                pass
            yield p[0]
            if bytealigned:
                start = p[0] + 8
            else:
                start = p[0] + 1
            if start >= end:
                break
        return
 
    def rfind(self, bs, start=None, end=None, bytealigned=None):
        """Find final occurrence of substring bs.
 
        Returns a single item tuple with the bit position if found, or an
        empty tuple if not found. The bit position (pos property) will
        also be set to the start of the substring if it is found.
 
        bs -- The bitstring to find.
        start -- The bit position to end the reverse search. Defaults to 0.
        end -- The bit position one past the first bit to reverse search.
               Defaults to self.len.
        bytealigned -- If True the bitstring will only be found on byte
                       boundaries.
 
        Raises ValueError if bs is empty, if start < 0, if end > self.len or
        if end < start.
 
        """
        bs = Bits(bs)
        start, end = self._validate_slice(start, end)
        if bytealigned is None:
            bytealigned = globals()['bytealigned']
        if not bs.len:
            raise ValueError("Cannot find an empty bitstring.")
        # Search chunks starting near the end and then moving back
        # until we find bs.
        increment = max(8192, bs.len * 80)
        buffersize = min(increment + bs.len, end - start)
        pos = max(start, end - buffersize)
        while True:
            found = list(self.findall(bs, start=pos, end=pos + buffersize,
                                      bytealigned=bytealigned))
            if not found:
                if pos == start:
                    return ()
                pos = max(start, pos - increment)
                continue
            return (found[-1],)
 
    def cut(self, bits, start=None, end=None, count=None):
        """Return bitstring generator by cutting into bits sized chunks.
 
        bits -- The size in bits of the bitstring chunks to generate.
        start -- The bit position to start the first cut. Defaults to 0.
        end -- The bit position one past the last bit to use in the cut.
               Defaults to self.len.
        count -- If specified then at most count items are generated.
                 Default is to cut as many times as possible.
 
        """
        start, end = self._validate_slice(start, end)
        if count is not None and count < 0:
            raise ValueError("Cannot cut - count must be >= 0.")
        if bits <= 0:
            raise ValueError("Cannot cut - bits must be >= 0.")
        c = 0
        while count is None or c < count:
            c += 1
            nextchunk = self._slice(start, min(start + bits, end))
            if nextchunk.len != bits:
                return
            assert nextchunk._assertsanity()
            yield nextchunk
            start += bits
        return
 
    def split(self, delimiter, start=None, end=None, count=None,
              bytealigned=None):
        """Return bitstring generator by splittling using a delimiter.
 
        The first item returned is the initial bitstring before the delimiter,
        which may be an empty bitstring.
 
        delimiter -- The bitstring used as the divider.
        start -- The bit position to start the split. Defaults to 0.
        end -- The bit position one past the last bit to use in the split.
               Defaults to self.len.
        count -- If specified then at most count items are generated.
                 Default is to split as many times as possible.
        bytealigned -- If True splits will only occur on byte boundaries.
 
        Raises ValueError if the delimiter is empty.
 
        """
        delimiter = Bits(delimiter)
        if not delimiter.len:
            raise ValueError("split delimiter cannot be empty.")
        start, end = self._validate_slice(start, end)
        if bytealigned is None:
            bytealigned = globals()['bytealigned']
        if count is not None and count < 0:
            raise ValueError("Cannot split - count must be >= 0.")
        if count == 0:
            return
        if bytealigned and not delimiter.len % 8 and not self._datastore.offset:
            # Use the quick find method
            f = self._findbytes
            x = delimiter._getbytes()
        else:
            f = self._findregex
            x = re.compile(delimiter._getbin())
        found = f(x, start, end, bytealigned)
        if not found:
            # Initial bits are the whole bitstring being searched
            yield self._slice(start, end)
            return
        # yield the bytes before the first occurrence of the delimiter, even if empty
        yield self._slice(start, found[0])
        startpos = pos = found[0]
        c = 1
        while count is None or c < count:
            pos += delimiter.len
            found = f(x, pos, end, bytealigned)
            if not found:
                # No more occurrences, so return the rest of the bitstring
                yield self._slice(startpos, end)
                return
            c += 1
            yield self._slice(startpos, found[0])
            startpos = pos = found[0]
        # Have generated count bitstrings, so time to quit.
        return
 
    def join(self, sequence):
        """Return concatenation of bitstrings joined by self.
 
        sequence -- A sequence of bitstrings.
 
        """
        s = self.__class__()
        i = iter(sequence)
        try:
            s._append(Bits(next(i)))
            while True:
                n = next(i)
                s._append(self)
                s._append(Bits(n))
        except StopIteration:
            pass
        return s
 
    def tobytes(self):
        """Return the bitstring as bytes, padding with zero bits if needed.
 
        Up to seven zero bits will be added at the end to byte align.
 
        """
        d = offsetcopy(self._datastore, 0).rawbytes
        # Need to ensure that unused bits at end are set to zero
        unusedbits = 8 - self.len % 8
        if unusedbits != 8:
            d[-1] &= (0xff << unusedbits)
        return bytes(d)
 
    def tofile(self, f):
        """Write the bitstring to a file object, padding with zero bits if needed.
 
        Up to seven zero bits will be added at the end to byte align.
 
        """
        # If the bitstring is file based then we don't want to read it all
        # in to memory.
        chunksize = 1024 * 1024  # 1 MB chunks
        if not self._offset:
            a = 0
            bytelen = self._datastore.bytelength
            p = self._datastore.getbyteslice(a, min(a + chunksize, bytelen - 1))
            while len(p) == chunksize:
                f.write(p)
                a += chunksize
                p = self._datastore.getbyteslice(a, min(a + chunksize, bytelen - 1))
            f.write(p)
            # Now the final byte, ensuring that unused bits at end are set to 0.
            bits_in_final_byte = self.len % 8
            if not bits_in_final_byte:
                bits_in_final_byte = 8
            f.write(self[-bits_in_final_byte:].tobytes())
        else:
            # Really quite inefficient...
            a = 0
            b = a + chunksize * 8
            while b <= self.len:
                f.write(self._slice(a, b)._getbytes())
                a += chunksize * 8
                b += chunksize * 8
            if a != self.len:
                f.write(self._slice(a, self.len).tobytes())
 
    def startswith(self, prefix, start=None, end=None):
        """Return whether the current bitstring starts with prefix.
 
        prefix -- The bitstring to search for.
        start -- The bit position to start from. Defaults to 0.
        end -- The bit position to end at. Defaults to self.len.
 
        """
        prefix = Bits(prefix)
        start, end = self._validate_slice(start, end)
        if end < start + prefix.len:
            return False
        end = start + prefix.len
        return self._slice(start, end) == prefix
 
    def endswith(self, suffix, start=None, end=None):
        """Return whether the current bitstring ends with suffix.
 
        suffix -- The bitstring to search for.
        start -- The bit position to start from. Defaults to 0.
        end -- The bit position to end at. Defaults to self.len.
 
        """
        suffix = Bits(suffix)
        start, end = self._validate_slice(start, end)
        if start + suffix.len > end:
            return False
        start = end - suffix.len
        return self._slice(start, end) == suffix
 
    def all(self, value, pos=None):
        """Return True if one or many bits are all set to value.
 
        value -- If value is True then checks for bits set to 1, otherwise
                 checks for bits set to 0.
        pos -- An iterable of bit positions. Negative numbers are treated in
               the same way as slice indices. Defaults to the whole bitstring.
 
        """
        value = bool(value)
        length = self.len
        if pos is None:
            pos = xrange(self.len)
        for p in pos:
            if p < 0:
                p += length
            if not 0 <= p < length:
                raise IndexError("Bit position {0} out of range.".format(p))
            if not self._datastore.getbit(p) is value:
                return False
        return True
 
    def any(self, value, pos=None):
        """Return True if any of one or many bits are set to value.
 
        value -- If value is True then checks for bits set to 1, otherwise
                 checks for bits set to 0.
        pos -- An iterable of bit positions. Negative numbers are treated in
               the same way as slice indices. Defaults to the whole bitstring.
 
        """
        value = bool(value)
        length = self.len
        if pos is None:
            pos = xrange(self.len)
        for p in pos:
            if p < 0:
                p += length
            if not 0 <= p < length:
                raise IndexError("Bit position {0} out of range.".format(p))
            if self._datastore.getbit(p) is value:
                return True
        return False
 
    def count(self, value):
        """Return count of total number of either zero or one bits.
 
        value -- If True then bits set to 1 are counted, otherwise bits set
                 to 0 are counted.
 
        >>> Bits('0xef').count(1)
        7
 
        """
        if not self.len:
            return 0
        # count the number of 1s (from which it's easy to work out the 0s).
        # Don't count the final byte yet.
        count = sum(BIT_COUNT[self._datastore.getbyte(i)] for i in xrange(self._datastore.bytelength - 1))
        # adjust for bits at start that aren't part of the bitstring
        if self._offset:
            count -= BIT_COUNT[self._datastore.getbyte(0) >> (8 - self._offset)]
        # and count the last 1 - 8 bits at the end.
        endbits = self._datastore.bytelength * 8 - (self._offset + self.len)
        count += BIT_COUNT[self._datastore.getbyte(self._datastore.bytelength - 1) >> endbits]
        return count if value else self.len - count
 
    # Create native-endian functions as aliases depending on the byteorder
    if byteorder == 'little':
        _setfloatne = _setfloatle
        _readfloatne = _readfloatle
        _getfloatne = _getfloatle
        _setuintne = _setuintle
        _readuintne = _readuintle
        _getuintne = _getuintle
        _setintne = _setintle
        _readintne = _readintle
        _getintne = _getintle
    else:
        _setfloatne = _setfloat
        _readfloatne = _readfloat
        _getfloatne = _getfloat
        _setuintne = _setuintbe
        _readuintne = _readuintbe
        _getuintne = _getuintbe
        _setintne = _setintbe
        _readintne = _readintbe
        _getintne = _getintbe
 
    _offset = property(_getoffset)
 
    len = property(_getlength,
                   doc="""The length of the bitstring in bits. Read only.
                      """)
    length = property(_getlength,
                      doc="""The length of the bitstring in bits. Read only.
                      """)
    bool = property(_getbool,
                    doc="""The bitstring as a bool (True or False). Read only.
                    """)
    hex = property(_gethex,
                   doc="""The bitstring as a hexadecimal string. Read only.
                   """)
    bin = property(_getbin,
                   doc="""The bitstring as a binary string. Read only.
                   """)
    oct = property(_getoct,
                   doc="""The bitstring as an octal string. Read only.
                   """)
    bytes = property(_getbytes,
                     doc="""The bitstring as a bytes object. Read only.
                      """)
    int = property(_getint,
                   doc="""The bitstring as a two's complement signed int. Read only.
                      """)
    uint = property(_getuint,
                    doc="""The bitstring as a two's complement unsigned int. Read only.
                      """)
    float = property(_getfloat,
                     doc="""The bitstring as a floating point number. Read only.
                      """)
    intbe = property(_getintbe,
                     doc="""The bitstring as a two's complement big-endian signed int. Read only.
                      """)
    uintbe = property(_getuintbe,
                      doc="""The bitstring as a two's complement big-endian unsigned int. Read only.
                      """)
    floatbe = property(_getfloat,
                       doc="""The bitstring as a big-endian floating point number. Read only.
                      """)
    intle = property(_getintle,
                     doc="""The bitstring as a two's complement little-endian signed int. Read only.
                      """)
    uintle = property(_getuintle,
                      doc="""The bitstring as a two's complement little-endian unsigned int. Read only.
                      """)
    floatle = property(_getfloatle,
                       doc="""The bitstring as a little-endian floating point number. Read only.
                      """)
    intne = property(_getintne,
                     doc="""The bitstring as a two's complement native-endian signed int. Read only.
                      """)
    uintne = property(_getuintne,
                      doc="""The bitstring as a two's complement native-endian unsigned int. Read only.
                      """)
    floatne = property(_getfloatne,
                       doc="""The bitstring as a native-endian floating point number. Read only.
                      """)
    ue = property(_getue,
                  doc="""The bitstring as an unsigned exponential-Golomb code. Read only.
                      """)
    se = property(_getse,
                  doc="""The bitstring as a signed exponential-Golomb code. Read only.
                      """)
    uie = property(_getuie,
                   doc="""The bitstring as an unsigned interleaved exponential-Golomb code. Read only.
                      """)
    sie = property(_getsie,
                   doc="""The bitstring as a signed interleaved exponential-Golomb code. Read only.
                      """)
 
 
# Dictionary that maps token names to the function that reads them.
name_to_read = {'uint': Bits._readuint,
                'uintle': Bits._readuintle,
                'uintbe': Bits._readuintbe,
                'uintne': Bits._readuintne,
                'int': Bits._readint,
                'intle': Bits._readintle,
                'intbe': Bits._readintbe,
                'intne': Bits._readintne,
                'float': Bits._readfloat,
                'floatbe': Bits._readfloat,  # floatbe is a synonym for float
                'floatle': Bits._readfloatle,
                'floatne': Bits._readfloatne,
                'hex': Bits._readhex,
                'oct': Bits._readoct,
                'bin': Bits._readbin,
                'bits': Bits._readbits,
                'bytes': Bits._readbytes,
                'ue': Bits._readue,
                'se': Bits._readse,
                'uie': Bits._readuie,
                'sie': Bits._readsie,
                'bool': Bits._readbool,
                }
 
# Dictionaries for mapping init keywords with init functions.
init_with_length_and_offset = {'bytes': Bits._setbytes_safe,
                               'filename': Bits._setfile,
                               }
 
init_with_length_only = {'uint': Bits._setuint,
                         'int': Bits._setint,
                         'float': Bits._setfloat,
                         'uintbe': Bits._setuintbe,
                         'intbe': Bits._setintbe,
                         'floatbe': Bits._setfloat,
                         'uintle': Bits._setuintle,
                         'intle': Bits._setintle,
                         'floatle': Bits._setfloatle,
                         'uintne': Bits._setuintne,
                         'intne': Bits._setintne,
                         'floatne': Bits._setfloatne,
                         }
 
init_without_length_or_offset = {'bin': Bits._setbin_safe,
                                 'hex': Bits._sethex,
                                 'oct': Bits._setoct,
                                 'ue': Bits._setue,
                                 'se': Bits._setse,
                                 'uie': Bits._setuie,
                                 'sie': Bits._setsie,
                                 'bool': Bits._setbool,
                                 }
 
 
class BitArray(Bits):
    """A container holding a mutable sequence of bits.
 
    Subclass of the immutable Bits class. Inherits all of its
    methods (except __hash__) and adds mutating methods.
 
    Mutating methods:
 
    append() -- Append a bitstring.
    byteswap() -- Change byte endianness in-place.
    insert() -- Insert a bitstring.
    invert() -- Flip bit(s) between one and zero.
    overwrite() -- Overwrite a section with a new bitstring.
    prepend() -- Prepend a bitstring.
    replace() -- Replace occurrences of one bitstring with another.
    reverse() -- Reverse bits in-place.
    rol() -- Rotate bits to the left.
    ror() -- Rotate bits to the right.
    set() -- Set bit(s) to 1 or 0.
 
    Methods inherited from Bits:
 
    all() -- Check if all specified bits are set to 1 or 0.
    any() -- Check if any of specified bits are set to 1 or 0.
    count() -- Count the number of bits set to 1 or 0.
    cut() -- Create generator of constant sized chunks.
    endswith() -- Return whether the bitstring ends with a sub-string.
    find() -- Find a sub-bitstring in the current bitstring.
    findall() -- Find all occurrences of a sub-bitstring in the current bitstring.
    join() -- Join bitstrings together using current bitstring.
    rfind() -- Seek backwards to find a sub-bitstring.
    split() -- Create generator of chunks split by a delimiter.
    startswith() -- Return whether the bitstring starts with a sub-bitstring.
    tobytes() -- Return bitstring as bytes, padding if needed.
    tofile() -- Write bitstring to file, padding if needed.
    unpack() -- Interpret bits using format string.
 
    Special methods:
 
    Mutating operators are available: [], <<=, >>=, +=, *=, &=, |= and ^=
    in addition to the inherited [], ==, !=, +, *, ~, <<, >>, &, | and ^.
 
    Properties:
 
    bin -- The bitstring as a binary string.
    bool -- For single bit bitstrings, interpret as True or False.
    bytepos -- The current byte position in the bitstring.
    bytes -- The bitstring as a bytes object.
    float -- Interpret as a floating point number.
    floatbe -- Interpret as a big-endian floating point number.
    floatle -- Interpret as a little-endian floating point number.
    floatne -- Interpret as a native-endian floating point number.
    hex -- The bitstring as a hexadecimal string.
    int -- Interpret as a two's complement signed integer.
    intbe -- Interpret as a big-endian signed integer.
    intle -- Interpret as a little-endian signed integer.
    intne -- Interpret as a native-endian signed integer.
    len -- Length of the bitstring in bits.
    oct -- The bitstring as an octal string.
    pos -- The current bit position in the bitstring.
    se -- Interpret as a signed exponential-Golomb code.
    ue -- Interpret as an unsigned exponential-Golomb code.
    sie -- Interpret as a signed interleaved exponential-Golomb code.
    uie -- Interpret as an unsigned interleaved exponential-Golomb code.
    uint -- Interpret as a two's complement unsigned integer.
    uintbe -- Interpret as a big-endian unsigned integer.
    uintle -- Interpret as a little-endian unsigned integer.
    uintne -- Interpret as a native-endian unsigned integer.
 
    """
 
    __slots__ = ()
 
    # As BitArray objects are mutable, we shouldn't allow them to be hashed.
    __hash__ = None
 
    def __init__(self, auto=None, length=None, offset=None, **kwargs):
        """Either specify an 'auto' initialiser:
        auto -- a string of comma separated tokens, an integer, a file object,
                a bytearray, a boolean iterable or another bitstring.
 
        Or initialise via **kwargs with one (and only one) of:
        bytes -- raw data as a string, for example read from a binary file.
        bin -- binary string representation, e.g. '0b001010'.
        hex -- hexadecimal string representation, e.g. '0x2ef'
        oct -- octal string representation, e.g. '0o777'.
        uint -- an unsigned integer.
        int -- a signed integer.
        float -- a floating point number.
        uintbe -- an unsigned big-endian whole byte integer.
        intbe -- a signed big-endian whole byte integer.
        floatbe - a big-endian floating point number.
        uintle -- an unsigned little-endian whole byte integer.
        intle -- a signed little-endian whole byte integer.
        floatle -- a little-endian floating point number.
        uintne -- an unsigned native-endian whole byte integer.
        intne -- a signed native-endian whole byte integer.
        floatne -- a native-endian floating point number.
        se -- a signed exponential-Golomb code.
        ue -- an unsigned exponential-Golomb code.
        sie -- a signed interleaved exponential-Golomb code.
        uie -- an unsigned interleaved exponential-Golomb code.
        bool -- a boolean (True or False).
        filename -- a file which will be opened in binary read-only mode.
 
        Other keyword arguments:
        length -- length of the bitstring in bits, if needed and appropriate.
                  It must be supplied for all integer and float initialisers.
        offset -- bit offset to the data. These offset bits are
                  ignored and this is intended for use when
                  initialising using 'bytes' or 'filename'.
 
        """
        # For mutable BitArrays we always read in files to memory:
        if not isinstance(self._datastore, ByteStore):
            self._ensureinmemory()
 
    def __new__(cls, auto=None, length=None, offset=None, **kwargs):
        x = super(BitArray, cls).__new__(cls)
        y = Bits.__new__(BitArray, auto, length, offset, **kwargs)
        x._datastore = y._datastore
        return x
 
    def __iadd__(self, bs):
        """Append bs to current bitstring. Return self.
 
        bs -- the bitstring to append.
 
        """
        self.append(bs)
        return self
 
    def __copy__(self):
        """Return a new copy of the BitArray."""
        s_copy = BitArray()
        if not isinstance(self._datastore, ByteStore):
            # Let them both point to the same (invariant) array.
            # If either gets modified then at that point they'll be read into memory.
            s_copy._datastore = self._datastore
        else:
            s_copy._datastore = copy.copy(self._datastore)
        return s_copy
 
    def __setitem__(self, key, value):
        """Set item or range to new value.
 
        Indices are in units of the step parameter (default 1 bit).
        Stepping is used to specify the number of bits in each item.
 
        If the length of the bitstring is changed then pos will be moved
        to after the inserted section, otherwise it will remain unchanged.
 
        >>> s = BitArray('0xff')
        >>> s[0:1:4] = '0xe'
        >>> print s
        '0xef'
        >>> s[4:4] = '0x00'
        >>> print s
        '0xe00f'
 
        """
        try:
            # A slice
            start, step = 0, 1
            if key.step is not None:
                step = key.step
        except AttributeError:
            # single element
            if key < 0:
                key += self.len
            if not 0 <= key < self.len:
                raise IndexError("Slice index out of range.")
            if isinstance(value, numbers.Integral):
                if not value:
                    self._unset(key)
                    return
                if value in (1, -1):
                    self._set(key)
                    return
                raise ValueError("Cannot set a single bit with integer {0}.".format(value))
            value = Bits(value)
            if value.len == 1:
                # TODO: this can't be optimal
                if value[0]:
                    self._set(key)
                else:
                    self._unset(key)
            else:
                self._delete(1, key)
                self._insert(value, key)
            return
        else:
            if step != 1:
                # convert to binary string and use string slicing
                # TODO: Horribly inefficent
                temp = list(self._getbin())
                v = list(Bits(value)._getbin())
                temp.__setitem__(key, v)
                self._setbin_unsafe(''.join(temp))
                return
 
            # If value is an integer then we want to set the slice to that
            # value rather than initialise a new bitstring of that length.
            if not isinstance(value, numbers.Integral):
                try:
                    # TODO: Better way than calling constructor here?
                    value = Bits(value)
                except TypeError:
                    raise TypeError("Bitstring, integer or string expected. "
                                    "Got {0}.".format(type(value)))
            if key.start is not None:
                start = key.start
                if key.start < 0:
                    start += self.len
                if start < 0:
                    start = 0
            stop = self.len
            if key.stop is not None:
                stop = key.stop
                if key.stop < 0:
                    stop += self.len
            if start > stop:
                # The standard behaviour for lists is to just insert at the
                # start position if stop < start and step == 1.
                stop = start
            if isinstance(value, numbers.Integral):
                if value >= 0:
                    value = self.__class__(uint=value, length=stop - start)
                else:
                    value = self.__class__(int=value, length=stop - start)
            stop = min(stop, self.len)
            start = max(start, 0)
            start = min(start, stop)
            if (stop - start) == value.len:
                if not value.len:
                    return
                if step >= 0:
                    self._overwrite(value, start)
                else:
                    self._overwrite(value.__getitem__(slice(None, None, 1)), start)
            else:
                # TODO: A delete then insert is wasteful - it could do unneeded shifts.
                # Could be either overwrite + insert or overwrite + delete.
                self._delete(stop - start, start)
                if step >= 0:
                    self._insert(value, start)
                else:
                    self._insert(value.__getitem__(slice(None, None, 1)), start)
                # pos is now after the inserted piece.
            return
 
    def __delitem__(self, key):
        """Delete item or range.
 
        Indices are in units of the step parameter (default 1 bit).
        Stepping is used to specify the number of bits in each item.
 
        >>> a = BitArray('0x001122')
        >>> del a[1:2:8]
        >>> print a
        0x0022
 
        """
        try:
            # A slice
            start = 0
            step = key.step if key.step is not None else 1
        except AttributeError:
            # single element
            if key < 0:
                key += self.len
            if not 0 <= key < self.len:
                raise IndexError("Slice index out of range.")
            self._delete(1, key)
            return
        else:
            if step != 1:
                # convert to binary string and use string slicing
                # TODO: Horribly inefficent
                temp = list(self._getbin())
                temp.__delitem__(key)
                self._setbin_unsafe(''.join(temp))
                return
            stop = key.stop
            if key.start is not None:
                start = key.start
                if key.start < 0 and stop is None:
                    start += self.len
                if start < 0:
                    start = 0
            if stop is None:
                stop = self.len
            if start > stop:
                return
            stop = min(stop, self.len)
            start = max(start, 0)
            start = min(start, stop)
            self._delete(stop - start, start)
            return
 
    def __ilshift__(self, n):
        """Shift bits by n to the left in place. Return self.
 
        n -- the number of bits to shift. Must be >= 0.
 
        """
        if n < 0:
            raise ValueError("Cannot shift by a negative amount.")
        if not self.len:
            raise ValueError("Cannot shift an empty bitstring.")
        if not n:
            return self
        n = min(n, self.len)
        return self._ilshift(n)
 
    def __irshift__(self, n):
        """Shift bits by n to the right in place. Return self.
 
        n -- the number of bits to shift. Must be >= 0.
 
        """
        if n < 0:
            raise ValueError("Cannot shift by a negative amount.")
        if not self.len:
            raise ValueError("Cannot shift an empty bitstring.")
        if not n:
            return self
        n = min(n, self.len)
        return self._irshift(n)
 
    def __imul__(self, n):
        """Concatenate n copies of self in place. Return self.
 
        Called for expressions of the form 'a *= 3'.
        n -- The number of concatenations. Must be >= 0.
 
        """
        if n < 0:
            raise ValueError("Cannot multiply by a negative integer.")
        return self._imul(n)
 
    def __ior__(self, bs):
        bs = Bits(bs)
        if self.len != bs.len:
            raise ValueError("Bitstrings must have the same length "
                             "for |= operator.")
        return self._ior(bs)
 
    def __iand__(self, bs):
        bs = Bits(bs)
        if self.len != bs.len:
            raise ValueError("Bitstrings must have the same length "
                             "for &= operator.")
        return self._iand(bs)
 
    def __ixor__(self, bs):
        bs = Bits(bs)
        if self.len != bs.len:
            raise ValueError("Bitstrings must have the same length "
                             "for ^= operator.")
        return self._ixor(bs)
 
    def replace(self, old, new, start=None, end=None, count=None,
                bytealigned=None):
        """Replace all occurrences of old with new in place.
 
        Returns number of replacements made.
 
        old -- The bitstring to replace.
        new -- The replacement bitstring.
        start -- Any occurrences that start before this will not be replaced.
                 Defaults to 0.
        end -- Any occurrences that finish after this will not be replaced.
               Defaults to self.len.
        count -- The maximum number of replacements to make. Defaults to
                 replace all occurrences.
        bytealigned -- If True replacements will only be made on byte
                       boundaries.
 
        Raises ValueError if old is empty or if start or end are
        out of range.
 
        """
        old = Bits(old)
        new = Bits(new)
        if not old.len:
            raise ValueError("Empty bitstring cannot be replaced.")
        start, end = self._validate_slice(start, end)
        if bytealigned is None:
            bytealigned = globals()['bytealigned']
        # Adjust count for use in split()
        if count is not None:
            count += 1
        sections = self.split(old, start, end, count, bytealigned)
        lengths = [s.len for s in sections]
        if len(lengths) == 1:
            # Didn't find anything to replace.
            return 0  # no replacements done
        if new is self:
            # Prevent self assignment woes
            new = copy.copy(self)
        positions = [lengths[0] + start]
        for k in lengths[1:-1]:
            # Next position is the previous one plus the length of the next section.
            positions.append(positions[-1] + k)
        # We have all the positions that need replacements. We do them
        # in reverse order so that they won't move around as we replace.
        positions.reverse()
        try:
            # Need to calculate new pos, if this is a bitstream
            newpos = self._pos_pos
            for p in positions:
                self[p:p + old.len] = new
            if old.len != new.len:
                diff = new.len - old.len
                for p in positions:
                    if p >= newpos:
                        continue
                    if p + old.len <= newpos:
                        newpos += diff
                    else:
                        newpos = p
            self._pos_pos = newpos
        except AttributeError:
            for p in positions:
                self[p:p + old.len] = new
        assert self._assertsanity()
        return len(lengths) - 1
 
    def insert(self, bs, pos=None):
        """Insert bs at bit position pos.
 
        bs -- The bitstring to insert.
        pos -- The bit position to insert at.
 
        Raises ValueError if pos < 0 or pos > self.len.
 
        """
        bs = Bits(bs)
        if not bs.len:
            return self
        if bs is self:
            bs = self.__copy____copy__()
        if pos is None:
            try:
                pos = self._pos_pos
            except AttributeError:
                raise TypeError("insert require a bit position for this type.")
        if pos < 0:
            pos += self.len
        if not 0 <= pos <= self.len:
            raise ValueError("Invalid insert position.")
        self._insert(bs, pos)
 
    def overwrite(self, bs, pos=None):
        """Overwrite with bs at bit position pos.
 
        bs -- The bitstring to overwrite with.
        pos -- The bit position to begin overwriting from.
 
        Raises ValueError if pos < 0 or pos + bs.len > self.len
 
        """
        bs = Bits(bs)
        if not bs.len:
            return
        if pos is None:
            try:
                pos = self._pos_pos
            except AttributeError:
                raise TypeError("overwrite require a bit position for this type.")
        if pos < 0:
            pos += self.len
        if pos < 0 or pos + bs.len > self.len:
            raise ValueError("Overwrite exceeds boundary of bitstring.")
        self._overwrite(bs, pos)
        try:
            self._pos_pos = pos + bs.len
        except AttributeError:
            pass
 
    def append(self, bs):
        """Append a bitstring to the current bitstring.
 
        bs -- The bitstring to append.
 
        """
        # The offset is a hint to make bs easily appendable.
        bs = self._converttobitstring(bs, offset=(self.len + self._offset) % 8)
        self._append(bs)
 
    def prepend(self, bs):
        """Prepend a bitstring to the current bitstring.
 
        bs -- The bitstring to prepend.
 
        """
        bs = Bits(bs)
        self._prepend(bs)
 
    def reverse(self, start=None, end=None):
        """Reverse bits in-place.
 
        start -- Position of first bit to reverse. Defaults to 0.
        end -- One past the position of the last bit to reverse.
               Defaults to self.len.
 
        Using on an empty bitstring will have no effect.
 
        Raises ValueError if start < 0, end > self.len or end < start.
 
        """
        start, end = self._validate_slice(start, end)
        if start == 0 and end == self.len:
            self._reverse()
            return
        s = self._slice(start, end)
        s._reverse()
        self[start:end] = s
 
    def set(self, value, pos=None):
        """Set one or many bits to 1 or 0.
 
        value -- If True bits are set to 1, otherwise they are set to 0.
        pos -- Either a single bit position or an iterable of bit positions.
               Negative numbers are treated in the same way as slice indices.
               Defaults to the entire bitstring.
 
        Raises IndexError if pos < -self.len or pos >= self.len.
 
        """
        f = self._set if value else self._unset
        if pos is None:
            pos = xrange(self.len)
        try:
            length = self.len
            for p in pos:
                if p < 0:
                    p += length
                if not 0 <= p < length:
                    raise IndexError("Bit position {0} out of range.".format(p))
                f(p)
        except TypeError:
            # Single pos
            if pos < 0:
                pos += self.len
            if not 0 <= pos < length:
                raise IndexError("Bit position {0} out of range.".format(pos))
            f(pos)
 
    def invert(self, pos=None):
        """Invert one or many bits from 0 to 1 or vice versa.
 
        pos -- Either a single bit position or an iterable of bit positions.
               Negative numbers are treated in the same way as slice indices.
 
        Raises IndexError if pos < -self.len or pos >= self.len.
 
        """
        if pos is None:
            self._invert_all()
            return
        if not isinstance(pos, collections.abc.Iterable):
            pos = (pos,)
        length = self.len
 
        for p in pos:
            if p < 0:
                p += length
            if not 0 <= p < length:
                raise IndexError("Bit position {0} out of range.".format(p))
            self._invert(p)
 
    def ror(self, bits, start=None, end=None):
        """Rotate bits to the right in-place.
 
        bits -- The number of bits to rotate by.
        start -- Start of slice to rotate. Defaults to 0.
        end -- End of slice to rotate. Defaults to self.len.
 
        Raises ValueError if bits < 0.
 
        """
        if not self.len:
            raise Error("Cannot rotate an empty bitstring.")
        if bits < 0:
            raise ValueError("Cannot rotate right by negative amount.")
        start, end = self._validate_slice(start, end)
        bits %= (end - start)
        if not bits:
            return
        rhs = self._slice(end - bits, end)
        self._delete(bits, end - bits)
        self._insert(rhs, start)
 
    def rol(self, bits, start=None, end=None):
        """Rotate bits to the left in-place.
 
        bits -- The number of bits to rotate by.
        start -- Start of slice to rotate. Defaults to 0.
        end -- End of slice to rotate. Defaults to self.len.
 
        Raises ValueError if bits < 0.
 
        """
        if not self.len:
            raise Error("Cannot rotate an empty bitstring.")
        if bits < 0:
            raise ValueError("Cannot rotate left by negative amount.")
        start, end = self._validate_slice(start, end)
        bits %= (end - start)
        if not bits:
            return
        lhs = self._slice(start, start + bits)
        self._delete(bits, start)
        self._insert(lhs, end - bits)
 
    def byteswap(self, fmt=None, start=None, end=None, repeat=True):
        """Change the endianness in-place. Return number of repeats of fmt done.
 
        fmt -- A compact structure string, an integer number of bytes or
               an iterable of integers. Defaults to 0, which byte reverses the
               whole bitstring.
        start -- Start bit position, defaults to 0.
        end -- End bit position, defaults to self.len.
        repeat -- If True (the default) the byte swapping pattern is repeated
                  as much as possible.
 
        """
        start, end = self._validate_slice(start, end)
        if fmt is None or fmt == 0:
            # reverse all of the whole bytes.
            bytesizes = [(end - start) // 8]
        elif isinstance(fmt, numbers.Integral):
            if fmt < 0:
                raise ValueError("Improper byte length {0}.".format(fmt))
            bytesizes = [fmt]
        elif isinstance(fmt, basestring):
            m = STRUCT_PACK_RE.match(fmt)
            if not m:
                raise ValueError("Cannot parse format string {0}.".format(fmt))
            # Split the format string into a list of 'q', '4h' etc.
            formatlist = re.findall(STRUCT_SPLIT_RE, m.group('fmt'))
            # Now deal with multiplicative factors, 4h -> hhhh etc.
            bytesizes = []
            for f in formatlist:
                if len(f) == 1:
                    bytesizes.append(PACK_CODE_SIZE[f])
                else:
                    bytesizes.extend([PACK_CODE_SIZE[f[-1]]] * int(f[:-1]))
        elif isinstance(fmt, collections.abc.Iterable):
            bytesizes = fmt
            for bytesize in bytesizes:
                if not isinstance(bytesize, numbers.Integral) or bytesize < 0:
                    raise ValueError("Improper byte length {0}.".format(bytesize))
        else:
            raise TypeError("Format must be an integer, string or iterable.")
 
        repeats = 0
        totalbitsize = 8 * sum(bytesizes)
        if not totalbitsize:
            return 0
        if repeat:
            # Try to repeat up to the end of the bitstring.
            finalbit = end
        else:
            # Just try one (set of) byteswap(s).
            finalbit = start + totalbitsize
        for patternend in xrange(start + totalbitsize, finalbit + 1, totalbitsize):
            bytestart = patternend - totalbitsize
            for bytesize in bytesizes:
                byteend = bytestart + bytesize * 8
                self._reversebytes(bytestart, byteend)
                bytestart += bytesize * 8
            repeats += 1
        return repeats
 
    def clear(self):
        """Remove all bits, reset to zero length."""
        self._clear()
 
    def copy(self):
        """Return a copy of the bitstring."""
        return self._copy()
 
    int = property(Bits._getint, Bits._setint,
                   doc="""The bitstring as a two's complement signed int. Read and write.
                      """)
    uint = property(Bits._getuint, Bits._setuint,
                    doc="""The bitstring as a two's complement unsigned int. Read and write.
                      """)
    float = property(Bits._getfloat, Bits._setfloat,
                     doc="""The bitstring as a floating point number. Read and write.
                      """)
    intbe = property(Bits._getintbe, Bits._setintbe,
                     doc="""The bitstring as a two's complement big-endian signed int. Read and write.
                      """)
    uintbe = property(Bits._getuintbe, Bits._setuintbe,
                      doc="""The bitstring as a two's complement big-endian unsigned int. Read and write.
                      """)
    floatbe = property(Bits._getfloat, Bits._setfloat,
                       doc="""The bitstring as a big-endian floating point number. Read and write.
                      """)
    intle = property(Bits._getintle, Bits._setintle,
                     doc="""The bitstring as a two's complement little-endian signed int. Read and write.
                      """)
    uintle = property(Bits._getuintle, Bits._setuintle,
                      doc="""The bitstring as a two's complement little-endian unsigned int. Read and write.
                      """)
    floatle = property(Bits._getfloatle, Bits._setfloatle,
                       doc="""The bitstring as a little-endian floating point number. Read and write.
                      """)
    intne = property(Bits._getintne, Bits._setintne,
                     doc="""The bitstring as a two's complement native-endian signed int. Read and write.
                      """)
    uintne = property(Bits._getuintne, Bits._setuintne,
                      doc="""The bitstring as a two's complement native-endian unsigned int. Read and write.
                      """)
    floatne = property(Bits._getfloatne, Bits._setfloatne,
                       doc="""The bitstring as a native-endian floating point number. Read and write.
                      """)
    ue = property(Bits._getue, Bits._setue,
                  doc="""The bitstring as an unsigned exponential-Golomb code. Read and write.
                      """)
    se = property(Bits._getse, Bits._setse,
                  doc="""The bitstring as a signed exponential-Golomb code. Read and write.
                      """)
    uie = property(Bits._getuie, Bits._setuie,
                   doc="""The bitstring as an unsigned interleaved exponential-Golomb code. Read and write.
                      """)
    sie = property(Bits._getsie, Bits._setsie,
                   doc="""The bitstring as a signed interleaved exponential-Golomb code. Read and write.
                      """)
    hex = property(Bits._gethex, Bits._sethex,
                   doc="""The bitstring as a hexadecimal string. Read and write.
                       """)
    bin = property(Bits._getbin, Bits._setbin_safe,
                   doc="""The bitstring as a binary string. Read and write.
                       """)
    oct = property(Bits._getoct, Bits._setoct,
                   doc="""The bitstring as an octal string. Read and write.
                       """)
    bool = property(Bits._getbool, Bits._setbool,
                    doc="""The bitstring as a bool (True or False). Read and write.
                    """)
    bytes = property(Bits._getbytes, Bits._setbytes_safe,
                     doc="""The bitstring as a ordinary string. Read and write.
                      """)
 
 
class ConstBitStream(Bits):
    """A container or stream holding an immutable sequence of bits.
 
    For a mutable container use the BitStream class instead.
 
    Methods inherited from Bits:
 
    all() -- Check if all specified bits are set to 1 or 0.
    any() -- Check if any of specified bits are set to 1 or 0.
    count() -- Count the number of bits set to 1 or 0.
    cut() -- Create generator of constant sized chunks.
    endswith() -- Return whether the bitstring ends with a sub-string.
    find() -- Find a sub-bitstring in the current bitstring.
    findall() -- Find all occurrences of a sub-bitstring in the current bitstring.
    join() -- Join bitstrings together using current bitstring.
    rfind() -- Seek backwards to find a sub-bitstring.
    split() -- Create generator of chunks split by a delimiter.
    startswith() -- Return whether the bitstring starts with a sub-bitstring.
    tobytes() -- Return bitstring as bytes, padding if needed.
    tofile() -- Write bitstring to file, padding if needed.
    unpack() -- Interpret bits using format string.
 
    Other methods:
 
    bytealign() -- Align to next byte boundary.
    peek() -- Peek at and interpret next bits as a single item.
    peeklist() -- Peek at and interpret next bits as a list of items.
    read() -- Read and interpret next bits as a single item.
    readlist() -- Read and interpret next bits as a list of items.
 
    Special methods:
 
    Also available are the operators [], ==, !=, +, *, ~, <<, >>, &, |, ^.
 
    Properties:
 
    bin -- The bitstring as a binary string.
    bool -- For single bit bitstrings, interpret as True or False.
    bytepos -- The current byte position in the bitstring.
    bytes -- The bitstring as a bytes object.
    float -- Interpret as a floating point number.
    floatbe -- Interpret as a big-endian floating point number.
    floatle -- Interpret as a little-endian floating point number.
    floatne -- Interpret as a native-endian floating point number.
    hex -- The bitstring as a hexadecimal string.
    int -- Interpret as a two's complement signed integer.
    intbe -- Interpret as a big-endian signed integer.
    intle -- Interpret as a little-endian signed integer.
    intne -- Interpret as a native-endian signed integer.
    len -- Length of the bitstring in bits.
    oct -- The bitstring as an octal string.
    pos -- The current bit position in the bitstring.
    se -- Interpret as a signed exponential-Golomb code.
    ue -- Interpret as an unsigned exponential-Golomb code.
    sie -- Interpret as a signed interleaved exponential-Golomb code.
    uie -- Interpret as an unsigned interleaved exponential-Golomb code.
    uint -- Interpret as a two's complement unsigned integer.
    uintbe -- Interpret as a big-endian unsigned integer.
    uintle -- Interpret as a little-endian unsigned integer.
    uintne -- Interpret as a native-endian unsigned integer.
 
    """
 
    __slots__ = ('_pos')
 
    def __init__(self, auto=None, length=None, offset=None, **kwargs):
        """Either specify an 'auto' initialiser:
        auto -- a string of comma separated tokens, an integer, a file object,
                a bytearray, a boolean iterable or another bitstring.
 
        Or initialise via **kwargs with one (and only one) of:
        bytes -- raw data as a string, for example read from a binary file.
        bin -- binary string representation, e.g. '0b001010'.
        hex -- hexadecimal string representation, e.g. '0x2ef'
        oct -- octal string representation, e.g. '0o777'.
        uint -- an unsigned integer.
        int -- a signed integer.
        float -- a floating point number.
        uintbe -- an unsigned big-endian whole byte integer.
        intbe -- a signed big-endian whole byte integer.
        floatbe - a big-endian floating point number.
        uintle -- an unsigned little-endian whole byte integer.
        intle -- a signed little-endian whole byte integer.
        floatle -- a little-endian floating point number.
        uintne -- an unsigned native-endian whole byte integer.
        intne -- a signed native-endian whole byte integer.
        floatne -- a native-endian floating point number.
        se -- a signed exponential-Golomb code.
        ue -- an unsigned exponential-Golomb code.
        sie -- a signed interleaved exponential-Golomb code.
        uie -- an unsigned interleaved exponential-Golomb code.
        bool -- a boolean (True or False).
        filename -- a file which will be opened in binary read-only mode.
 
        Other keyword arguments:
        length -- length of the bitstring in bits, if needed and appropriate.
                  It must be supplied for all integer and float initialisers.
        offset -- bit offset to the data. These offset bits are
                  ignored and this is intended for use when
                  initialising using 'bytes' or 'filename'.
 
        """
        self._pos_pos = 0
 
    def __new__(cls, auto=None, length=None, offset=None, **kwargs):
        x = super(ConstBitStream, cls).__new__(cls)
        x._initialise(auto, length, offset, **kwargs)
        return x
 
    def _setbytepos(self, bytepos):
        """Move to absolute byte-aligned position in stream."""
        self._setbitpos(bytepos * 8)
 
    def _getbytepos(self):
        """Return the current position in the stream in bytes. Must be byte aligned."""
        if self._pos_pos % 8:
            raise ByteAlignError("Not byte aligned in _getbytepos().")
        return self._pos_pos // 8
 
    def _setbitpos(self, pos):
        """Move to absolute postion bit in bitstream."""
        if pos < 0:
            raise ValueError("Bit position cannot be negative.")
        if pos > self.len:
            raise ValueError("Cannot seek past the end of the data.")
        self._pos_pos = pos
 
    def _getbitpos(self):
        """Return the current position in the stream in bits."""
        return self._pos_pos
 
    def _clear(self):
        Bits._clear(self)
        self._pos_pos = 0
 
    def __copy__(self):
        """Return a new copy of the ConstBitStream for the copy module."""
        # Note that if you want a new copy (different ID), use _copy instead.
        # The copy can use the same datastore as it's immutable.
        s = ConstBitStream()
        s._datastore = self._datastore
        # Reset the bit position, don't copy it.
        s._pos = 0
        return s
 
    def __add__(self, bs):
        """Concatenate bitstrings and return new bitstring.
 
        bs -- the bitstring to append.
 
        """
        s = Bits.__add__(self, bs)
        s._pos = 0
        return s
 
    def read(self, fmt):
        """Interpret next bits according to the format string and return result.
 
        fmt -- Token string describing how to interpret the next bits.
 
        Token examples: 'int:12'    : 12 bits as a signed integer
                        'uint:8'    : 8 bits as an unsigned integer
                        'float:64'  : 8 bytes as a big-endian float
                        'intbe:16'  : 2 bytes as a big-endian signed integer
                        'uintbe:16' : 2 bytes as a big-endian unsigned integer
                        'intle:32'  : 4 bytes as a little-endian signed integer
                        'uintle:32' : 4 bytes as a little-endian unsigned integer
                        'floatle:64': 8 bytes as a little-endian float
                        'intne:24'  : 3 bytes as a native-endian signed integer
                        'uintne:24' : 3 bytes as a native-endian unsigned integer
                        'floatne:32': 4 bytes as a native-endian float
                        'hex:80'    : 80 bits as a hex string
                        'oct:9'     : 9 bits as an octal string
                        'bin:1'     : single bit binary string
                        'ue'        : next bits as unsigned exp-Golomb code
                        'se'        : next bits as signed exp-Golomb code
                        'uie'       : next bits as unsigned interleaved exp-Golomb code
                        'sie'       : next bits as signed interleaved exp-Golomb code
                        'bits:5'    : 5 bits as a bitstring
                        'bytes:10'  : 10 bytes as a bytes object
                        'bool'      : 1 bit as a bool
                        'pad:3'     : 3 bits of padding to ignore - returns None
 
        fmt may also be an integer, which will be treated like the 'bits' token.
 
        The position in the bitstring is advanced to after the read items.
 
        Raises ReadError if not enough bits are available.
        Raises ValueError if the format is not understood.
 
        """
        if isinstance(fmt, numbers.Integral):
            if fmt < 0:
                raise ValueError("Cannot read negative amount.")
            if fmt > self.len - self._pos_pos:
                raise ReadError("Cannot read {0} bits, only {1} available.",
                                fmt, self.len - self._pos_pos)
            bs = self._slice(self._pos_pos, self._pos_pos + fmt)
            self._pos_pos += fmt
            return bs
        p = self._pos_pos
        _, token = tokenparser(fmt)
        if len(token) != 1:
            self._pos_pos = p
            raise ValueError("Format string should be a single token, not {0} "
                             "tokens - use readlist() instead.".format(len(token)))
        name, length, _ = token[0]
        if length is None:
            length = self.len - self._pos_pos
        value, self._pos_pos = self._readtoken(name, self._pos_pos, length)
        return value
 
    def readlist(self, fmt, **kwargs):
        """Interpret next bits according to format string(s) and return list.
 
        fmt -- A single string or list of strings with comma separated tokens
               describing how to interpret the next bits in the bitstring. Items
               can also be integers, for reading new bitstring of the given length.
        kwargs -- A dictionary or keyword-value pairs - the keywords used in the
                  format string will be replaced with their given value.
 
        The position in the bitstring is advanced to after the read items.
 
        Raises ReadError is not enough bits are available.
        Raises ValueError if the format is not understood.
 
        See the docstring for 'read' for token examples. 'pad' tokens are skipped
        and not added to the returned list.
 
        >>> h, b1, b2 = s.readlist('hex:20, bin:5, bin:3')
        >>> i, bs1, bs2 = s.readlist(['uint:12', 10, 10])
 
        """
        value, self._pos_pos = self._readlist(fmt, self._pos_pos, **kwargs)
        return value
 
    def readto(self, bs, bytealigned=None):
        """Read up to and including next occurrence of bs and return result.
 
        bs -- The bitstring to find. An integer is not permitted.
        bytealigned -- If True the bitstring will only be
                       found on byte boundaries.
 
        Raises ValueError if bs is empty.
        Raises ReadError if bs is not found.
 
        """
        if isinstance(bs, numbers.Integral):
            raise ValueError("Integers cannot be searched for")
        bs = Bits(bs)
        oldpos = self._pos_pos
        p = self.find(bs, self._pos_pos, bytealigned=bytealigned)
        if not p:
            raise ReadError("Substring not found")
        self._pos_pos += bs.len
        return self._slice(oldpos, self._pos_pos)
 
    def peek(self, fmt):
        """Interpret next bits according to format string and return result.
 
        fmt -- Token string describing how to interpret the next bits.
 
        The position in the bitstring is not changed. If not enough bits are
        available then all bits to the end of the bitstring will be used.
 
        Raises ReadError if not enough bits are available.
        Raises ValueError if the format is not understood.
 
        See the docstring for 'read' for token examples.
 
        """
        pos_before = self._pos_pos
        value = self.read(fmt)
        self._pos_pos = pos_before
        return value
 
    def peeklist(self, fmt, **kwargs):
        """Interpret next bits according to format string(s) and return list.
 
        fmt -- One or more strings with comma separated tokens describing
               how to interpret the next bits in the bitstring.
        kwargs -- A dictionary or keyword-value pairs - the keywords used in the
                  format string will be replaced with their given value.
 
        The position in the bitstring is not changed. If not enough bits are
        available then all bits to the end of the bitstring will be used.
 
        Raises ReadError if not enough bits are available.
        Raises ValueError if the format is not understood.
 
        See the docstring for 'read' for token examples.
 
        """
        pos = self._pos_pos
        return_values = self.readlist(fmt, **kwargs)
        self._pos_pos = pos
        return return_values
 
    def bytealign(self):
        """Align to next byte and return number of skipped bits.
 
        Raises ValueError if the end of the bitstring is reached before
        aligning to the next byte.
 
        """
        skipped = (8 - (self._pos_pos % 8)) % 8
        self.pos += self._offset + skipped
        assert self._assertsanity()
        return skipped
 
    pos = property(_getbitpos, _setbitpos,
                   doc="""The position in the bitstring in bits. Read and write.
                      """)
    bitpos = property(_getbitpos, _setbitpos,
                      doc="""The position in the bitstring in bits. Read and write.
                      """)
    bytepos = property(_getbytepos, _setbytepos,
                       doc="""The position in the bitstring in bytes. Read and write.
                      """)
 
 
class BitStream(ConstBitStream, BitArray):
    """A container or stream holding a mutable sequence of bits
 
    Subclass of the ConstBitStream and BitArray classes. Inherits all of
    their methods.
 
    Methods:
 
    all() -- Check if all specified bits are set to 1 or 0.
    any() -- Check if any of specified bits are set to 1 or 0.
    append() -- Append a bitstring.
    bytealign() -- Align to next byte boundary.
    byteswap() -- Change byte endianness in-place.
    count() -- Count the number of bits set to 1 or 0.
    cut() -- Create generator of constant sized chunks.
    endswith() -- Return whether the bitstring ends with a sub-string.
    find() -- Find a sub-bitstring in the current bitstring.
    findall() -- Find all occurrences of a sub-bitstring in the current bitstring.
    insert() -- Insert a bitstring.
    invert() -- Flip bit(s) between one and zero.
    join() -- Join bitstrings together using current bitstring.
    overwrite() -- Overwrite a section with a new bitstring.
    peek() -- Peek at and interpret next bits as a single item.
    peeklist() -- Peek at and interpret next bits as a list of items.
    prepend() -- Prepend a bitstring.
    read() -- Read and interpret next bits as a single item.
    readlist() -- Read and interpret next bits as a list of items.
    replace() -- Replace occurrences of one bitstring with another.
    reverse() -- Reverse bits in-place.
    rfind() -- Seek backwards to find a sub-bitstring.
    rol() -- Rotate bits to the left.
    ror() -- Rotate bits to the right.
    set() -- Set bit(s) to 1 or 0.
    split() -- Create generator of chunks split by a delimiter.
    startswith() -- Return whether the bitstring starts with a sub-bitstring.
    tobytes() -- Return bitstring as bytes, padding if needed.
    tofile() -- Write bitstring to file, padding if needed.
    unpack() -- Interpret bits using format string.
 
    Special methods:
 
    Mutating operators are available: [], <<=, >>=, +=, *=, &=, |= and ^=
    in addition to [], ==, !=, +, *, ~, <<, >>, &, | and ^.
 
    Properties:
 
    bin -- The bitstring as a binary string.
    bool -- For single bit bitstrings, interpret as True or False.
    bytepos -- The current byte position in the bitstring.
    bytes -- The bitstring as a bytes object.
    float -- Interpret as a floating point number.
    floatbe -- Interpret as a big-endian floating point number.
    floatle -- Interpret as a little-endian floating point number.
    floatne -- Interpret as a native-endian floating point number.
    hex -- The bitstring as a hexadecimal string.
    int -- Interpret as a two's complement signed integer.
    intbe -- Interpret as a big-endian signed integer.
    intle -- Interpret as a little-endian signed integer.
    intne -- Interpret as a native-endian signed integer.
    len -- Length of the bitstring in bits.
    oct -- The bitstring as an octal string.
    pos -- The current bit position in the bitstring.
    se -- Interpret as a signed exponential-Golomb code.
    ue -- Interpret as an unsigned exponential-Golomb code.
    sie -- Interpret as a signed interleaved exponential-Golomb code.
    uie -- Interpret as an unsigned interleaved exponential-Golomb code.
    uint -- Interpret as a two's complement unsigned integer.
    uintbe -- Interpret as a big-endian unsigned integer.
    uintle -- Interpret as a little-endian unsigned integer.
    uintne -- Interpret as a native-endian unsigned integer.
 
    """
 
    __slots__ = ()
 
    # As BitStream objects are mutable, we shouldn't allow them to be hashed.
    __hash__ = None
 
    def __init__(self, auto=None, length=None, offset=None, **kwargs):
        """Either specify an 'auto' initialiser:
        auto -- a string of comma separated tokens, an integer, a file object,
                a bytearray, a boolean iterable or another bitstring.
 
        Or initialise via **kwargs with one (and only one) of:
        bytes -- raw data as a string, for example read from a binary file.
        bin -- binary string representation, e.g. '0b001010'.
        hex -- hexadecimal string representation, e.g. '0x2ef'
        oct -- octal string representation, e.g. '0o777'.
        uint -- an unsigned integer.
        int -- a signed integer.
        float -- a floating point number.
        uintbe -- an unsigned big-endian whole byte integer.
        intbe -- a signed big-endian whole byte integer.
        floatbe - a big-endian floating point number.
        uintle -- an unsigned little-endian whole byte integer.
        intle -- a signed little-endian whole byte integer.
        floatle -- a little-endian floating point number.
        uintne -- an unsigned native-endian whole byte integer.
        intne -- a signed native-endian whole byte integer.
        floatne -- a native-endian floating point number.
        se -- a signed exponential-Golomb code.
        ue -- an unsigned exponential-Golomb code.
        sie -- a signed interleaved exponential-Golomb code.
        uie -- an unsigned interleaved exponential-Golomb code.
        bool -- a boolean (True or False).
        filename -- a file which will be opened in binary read-only mode.
 
        Other keyword arguments:
        length -- length of the bitstring in bits, if needed and appropriate.
                  It must be supplied for all integer and float initialisers.
        offset -- bit offset to the data. These offset bits are
                  ignored and this is intended for use when
                  initialising using 'bytes' or 'filename'.
 
        """
        self._pos_pos_pos_pos = 0
        # For mutable BitStreams we always read in files to memory:
        if not isinstance(self._datastore, ByteStore):
            self._ensureinmemory()
 
    def __new__(cls, auto=None, length=None, offset=None, **kwargs):
        x = super(BitStream, cls).__new__(cls)
        x._initialise(auto, length, offset, **kwargs)
        return x
 
    def __copy__(self):
        """Return a new copy of the BitStream."""
        s_copy = BitStream()
        s_copy._pos = 0
        if not isinstance(self._datastore, ByteStore):
            # Let them both point to the same (invariant) array.
            # If either gets modified then at that point they'll be read into memory.
            s_copy._datastore = self._datastore
        else:
            s_copy._datastore = ByteStore(self._datastore._rawarray[:],
                                          self._datastore.bitlength,
                                          self._datastore.offset)
        return s_copy
 
    def prepend(self, bs):
        """Prepend a bitstring to the current bitstring.
 
        bs -- The bitstring to prepend.
 
        """
        bs = self._converttobitstring(bs)
        self._prepend(bs)
        self._pos_pos_pos_pos += bs.len
 
 
def pack(fmt, *values, **kwargs):
    """Pack the values according to the format string and return a new BitStream.
 
    fmt -- A single string or a list of strings with comma separated tokens
           describing how to create the BitStream.
    values -- Zero or more values to pack according to the format.
    kwargs -- A dictionary or keyword-value pairs - the keywords used in the
              format string will be replaced with their given value.
 
    Token examples: 'int:12'    : 12 bits as a signed integer
                    'uint:8'    : 8 bits as an unsigned integer
                    'float:64'  : 8 bytes as a big-endian float
                    'intbe:16'  : 2 bytes as a big-endian signed integer
                    'uintbe:16' : 2 bytes as a big-endian unsigned integer
                    'intle:32'  : 4 bytes as a little-endian signed integer
                    'uintle:32' : 4 bytes as a little-endian unsigned integer
                    'floatle:64': 8 bytes as a little-endian float
                    'intne:24'  : 3 bytes as a native-endian signed integer
                    'uintne:24' : 3 bytes as a native-endian unsigned integer
                    'floatne:32': 4 bytes as a native-endian float
                    'hex:80'    : 80 bits as a hex string
                    'oct:9'     : 9 bits as an octal string
                    'bin:1'     : single bit binary string
                    'ue' / 'uie': next bits as unsigned exp-Golomb code
                    'se' / 'sie': next bits as signed exp-Golomb code
                    'bits:5'    : 5 bits as a bitstring object
                    'bytes:10'  : 10 bytes as a bytes object
                    'bool'      : 1 bit as a bool
                    'pad:3'     : 3 zero bits as padding
 
    >>> s = pack('uint:12, bits', 100, '0xffe')
    >>> t = pack(['bits', 'bin:3'], s, '111')
    >>> u = pack('uint:8=a, uint:8=b, uint:55=a', a=6, b=44)
 
    """
    tokens = []
    if isinstance(fmt, basestring):
        fmt = [fmt]
    try:
        for f_item in fmt:
            _, tkns = tokenparser(f_item, tuple(sorted(kwargs.keys())))
            tokens.extend(tkns)
    except ValueError as e:
        raise CreationError(*e.args)
    value_iter = iter(values)
    s = BitStream()
    try:
        for name, length, value in tokens:
            # If the value is in the kwd dictionary then it takes precedence.
            if value in kwargs:
                value = kwargs[value]
            # If the length is in the kwd dictionary then use that too.
            if length in kwargs:
                length = kwargs[length]
            # Also if we just have a dictionary name then we want to use it
            if name in kwargs and length is None and value is None:
                s.append(kwargs[name])
                continue
            if length is not None:
                length = int(length)
            if value is None and name != 'pad':
                # Take the next value from the ones provided
                value = next(value_iter)
            s._append(BitStream._init_with_token(name, length, value))
    except StopIteration:
        raise CreationError("Not enough parameters present to pack according to the "
                            "format. {0} values are needed.", len(tokens))
    try:
        next(value_iter)
    except StopIteration:
        # Good, we've used up all the *values.
        return s
    raise CreationError("Too many parameters present to pack according to the format.")
 
 
# Aliases for backward compatibility
ConstBitArray = Bits
BitString = BitStream
 
__all__ = ['ConstBitArray', 'ConstBitStream', 'BitStream', 'BitArray',
           'Bits', 'BitString', 'pack', 'Error', 'ReadError',
           'InterpretError', 'ByteAlignError', 'CreationError', 'bytealigned']