# Bitarray module

This module provides an object type which efficiently represents an array of booleans. Bitarrays are sequence types and behave very much like usual lists. Eight bits are represented by one byte in contiguous block of memory. The user can select between two representations; little-endian and big-endian. Most of the functionality is implemented in C. Methods for accessing the machine representation are provided. This can be useful when bit level access to binary files is required, such as portable bitmap image files (.pbm). Also, when dealing with compressed data which uses variable bit length encoding, you may find this module useful.

Requires Python 2.5 or greater, see PEP 353.

## Key features

• On 32bit machines, a bitarray object can contain up to 2^34 elements, that is 16 Gbits (on 64bit machines up to 2^63 elements in theory).
• All functionality implemented in C.
• Bitarray objects behave very much like a list object, in particular slicing (including slice assignment and deletion) is supported.
• The bit endianness can be specified for each bitarray object, see below.
• Packing and unpacking to other binary data formats, e.g. numpy.ndarray, is possible.
• Fast methods for encoding and decoding variable bit length prefix codes
• Sequential search
• Bitwise operations: &, |, ^, &=, |=, ^=, ~
• Pickling and unpickling of bitarray objects possible.

## Installation

bitarray can be installed from source:

$tar xzf bitarray-0.3.5.tar.gz$ cd bitarray-0.3.5
$python setup.py install On Unix systems, the latter command may have to be executed with root privileges. If you have setuptools installed, you can easy_install bitarray. Once you have installed the package, you may want to test it:$ python -c 'import bitarray; bitarray.test()'
bitarray is installed in: /usr/local/lib/python2.5/site-packages/bitarray
bitarray version: 0.3.5
2.5.2 (r252:60911, Jul 17 2008, 10:38:24)
[GCC 4.2.1 (SUSE Linux)]
.........................................................................
..........
----------------------------------------------------------------------
Ran 90 tests in 2.420s

OK

You can always import the function test, and test().wasSuccessful() will return True when the test went OK.

## Using the module

As mentioned above, bitarray objects behave very much like lists, so there is not too new to learn. The biggest difference to list objects is the ability to access the machine representation of the object. When doing so, the bit endianness is of importance, this issue is explained in detail in the section below. Here, we demonstrate the basic usage of bitarray objects:

>>> from bitarray import bitarray
>>> a = bitarray()            # create empty bitarray
>>> a.append(True)
>>> a.extend([False, True, True])
>>> a
bitarray('1011')

Bitarray objects can be instantiated in different ways:

>>> a = bitarray(2**20)       # bitarray of length 1048576 (uninitialized)
>>> bitarray('1001011')       # from a string
bitarray('1001011')
>>> lst = [True, False, False, True, False, True, True]
>>> bitarray(lst)             # from list, tuple, iterable
bitarray('1001011')

Bits can be assigned from any Python object, if the value can be interpreted as a truth value. You can think of this as Python's built-in function bool() being applied, whenever casting an object:

>>> a = bitarray([42, '', True, {}, 'foo', None])
>>> a
bitarray('101010')
>>> a.append(a)      # note that bool(a) is True
>>> a.count(42)      # counts occurrences of True (not 42)
4L
>>> a.remove('')     # removes first occurrence of False
>>> a
bitarray('110101')

Like lists, bitarray objects support slice assignment and deletion:

>>> a = bitarray(50)
>>> a.setall(False)
>>> a[11:37:3] = 9 * bitarray([True])
>>> a
bitarray('00000000000100100100100100100100100100000000000000')
>>> del a[12::3]
>>> a
bitarray('0000000000010101010101010101000000000')
>>> a[-6:] = bitarray('10011')
>>> a
bitarray('000000000001010101010101010100010011')
>>> a += bitarray('000111')
>>> a[9:]
bitarray('001010101010101010100010011000111')

In addition, slices can be assigned to booleans, which is easier (and faster) than assigning to a bitarray in which all values are the same:

>>> a = 20 * bitarray('0')
>>> a[1:15:3] = True
>>> a
bitarray('01001001001001000000')

This is easier and faster than:

>>> a = 20 * bitarray('0')
>>> a[1:15:3] = 5 * bitarray('1')
>>> a
bitarray('01001001001001000000')

Note that in the latter we have to create a temporary bitarray whose length must be known or calculated.

## Bit endianness

Since a bitarray allows addressing of individual bits, where the machine represents 8 bits in one byte, there two obvious choices for this mapping; little- and big-endian. When creating a new bitarray object, the endianness can always be specified explicitly:

>>> a = bitarray(endian='little')
>>> a.fromstring('A')
>>> a
bitarray('10000010')
>>> b = bitarray('11000010', endian='little')
>>> b.tostring()
'C'

Here the low-bit comes first because little-endian means that increasing numeric significance corresponds to an increasing address (or index). So a[0] is the lowest and least significant bit, and a[7] is the highest and most significant bit.

>>> a = bitarray(endian='big')
>>> a.fromstring('A')
>>> a
bitarray('01000001')
>>> a[6] = 1
>>> a.tostring()
'C'

Here the high-bit comes first because big-endian means "most-significant first". So a[0] is now the lowest and most significant bit, and a[7] is the highest and least significant bit.

The bit endianness is a property attached to each bitarray object. When comparing bitarray objects, the endianness (and hence the machine representation) is irrelevant; what matters is the mapping from indices to bits:

>>> bitarray('11001', endian='big') == bitarray('11001', endian='little')
True

Bitwise operations (&, |, ^, &=, |=, ^=, ~) are implemented efficiently using the corresponding byte operations in C, i.e. the operators act on the machine representation of the bitarray objects. Therefore, one has to be cautious when applying the operation to bitarrays with different endianness.

When converting to and from machine representation, using the tostring, fromstring, tofile and fromfile methods, the endianness matters:

>>> a = bitarray(endian='little')
>>> a.fromstring('\x01')
>>> a
bitarray('10000000')
>>> b = bitarray(endian='big')
>>> b.fromstring('\x80')
>>> b
bitarray('10000000')
>>> a == b
True
>>> a.tostring() == b.tostring()
False

The endianness can not be changed once an object is created. However, since creating a bitarray from another bitarray just copies the memory representing the data, you can create a new bitarray with different endianness:

>>> a = bitarray('11100000', endian='little')
>>> a
bitarray('11100000')
>>> b = bitarray(a, endian='big')
>>> b
bitarray('00000111')
>>> a == b
False
>>> a.tostring() == b.tostring()
True

The default bit endianness is currently big-endian, however this may change in the future, and when dealing with the machine representation of bitarray objects, it is recommended to always explicitly specify the endianness.

Unless, explicitly converting to machine representation, using the tostring, fromstring, tofile and fromfile methods, the bit endianness will have no effect on any computation, and you can safely ignore setting the endianness, and other details of this section.

## Variable bit length prefix codes

The method encode takes a dictionary mapping symbols to bitarrays and an iterable, and extends the bitarray object with the encoded symbols found while iterating. For example:

>>> d = {'H':bitarray('111'), 'e':bitarray('0'),
...      'l':bitarray('110'), 'o':bitarray('10')}
...
>>> a = bitarray()
>>> a.encode(d, 'Hello')
>>> a
bitarray('111011011010')

Note that the string 'Hello' is an iterable, but the symbols are not limited to characters, any hashable Python object can be a symbol. Taking the same dictionary, we can apply the decode method which will return a list of the symbols:

>>> a.decode(d)
['H', 'e', 'l', 'l', 'o']
>>> ''.join(a.decode(d))
'Hello'

Since symbols are not limited to being characters, it is necessary to return them as elements of a list, rather than simply returning the joined string.

## Reference

The bitarray class:

bitarray([initial][endian=string])

Return a new bitarray object whose items are bits initialized from the optional initial, and endianness. If no object is provided, the bitarray is initialized to have length zero. The initial object may be of the following types:

int, long
Create bitarray of length given by the integer. The initial values in the array are random, because only the memory allocated.
string
Create bitarray from a string of '0's and '1's.
list, tuple, iterable
Create bitarray from a sequence, each element in the sequence is converted to a bit using truth value value.
bitarray
Create bitarray from another bitarray. This is done by copying the memory holding the bitarray data, and is hence very fast.

The optional keyword arguments 'endian' specifies the bit endianness of the created bitarray object. Allowed values are 'big' and 'little' (default is 'big').

Note that setting the bit endianness only has an effect when accessing the machine representation of the bitarray, i.e. when using the methods: tofile, fromfile, tostring, fromstring.

A bitarray object supports the following methods:

all()
Returns True when all bits in the array are True.
any()
Returns True when any bit in the array is True.
append(x)
Append the value bool(x) to the end of the bitarray.
buffer_info()
Return a tuple (address, size, endianness, unused, allocated) giving the current memory address, the size (in bytes) used to hold the bitarray's contents, the bit endianness as a string, the number of unused bits (e.g. a bitarray of length 11 will have a buffer size of 2 bytes and 5 unused bits), and the size (in bytes) of the allocated memory.
bytereverse()
For all bytes representing the bitarray, reverse the bit order (in-place). Note: This method changes the actual machine values representing the bitarray; it does not change the endianness of the bitarray object.
copy()
Return a copy of the bitarray.
count([x])
Return number of occurrences of x in the bitarray. x defaults to True.
decode(code)
Given a prefix code (a dict mapping symbols to bitarrays), decode the content of the bitarray and return the list of symbols.
encode(code, iterable)
Given a prefix code (a dict mapping symbols to bitarrays), iterates over iterable object with symbols, and extends the bitarray with the corresponding bitarray for each symbols.
endian()
Return the bit endianness as a string (either 'little' or 'big').
extend(object)
Append bits to the end of the bitarray. The objects which can be passed to this method are the same iterable objects which can given to a bitarray object upon initialization.
fill()
Returns the number of bits added (0..7) at the end of the array. When the length of the bitarray is not a multiple of 8, increase the length slightly such that the new length is a multiple of 8, and set the few new bits to False.
fromfile(f [, n])
Read n bytes from the file object f and append them to the bitarray interpreted as machine values. When n is omitted, as many bytes are read until EOF is reached.
fromstring(string)
Append from a string, interpreting the string as machine values.
index(x)
Return index of the first occurrence of x in the bitarray. It is an error when x does not occur in the bitarray
insert(i, x)
Insert a new item x into the bitarray before position i.
invert(x)
Invert all bits in the array (in-place), i.e. convert each 1-bit into a 0-bit and vice versa.
length()
Return the length, i.e. number of bits stored in the bitarray. This method is preferred over __len__, [used when typing len(a)], since __len__ will fail for a bitarray object with 2^31 or more elements on a 32bit machine, whereas this method will return the correct value, on 32bit and 64bit machines.
pack(string)
Extend the bitarray from a string, where each characters corresponds to a single bit. The character 'x00' maps to bit 0 and all other characters map to bit 1. This method, as well as the unpack method, are meant for efficient transfer of data between bitarray objects to other python objects (for example NumPy's ndarray object) which have a different view of memory.
pop([i])
Return the i-th element and delete it from the bitarray. i defaults to -1.
remove(x)
Remove the first occurrence of x in the bitarray.
reverse()
Reverse the order of bits in the array (in-place).
search(x[, limit])
Given a bitarray x (or an object which can be converted to a bitarray), returns the start positions of x matching self as a list. The optional argument limits the number of search results to the integer specified. By default, all search results are returned.
setall(x)
Set all bits in the bitarray to bool(x).
sort(reverse=False)
Sort the bits in the array (in-place).
to01()
Return a string containing '0's and '1's, representing the bits in the bitarray object. Note: To extend a bitarray from a string containing '0's and '1's, use the extend method.
tofile(f)
Write all bits (as machine values) to the file object f. When the length of the bitarray is not a multiple of 8, the remaining bits (1..7) are set to 0.
tolist()
Return an ordinary list with the items in the bitarray. Note: To extend a bitarray with elements from a list, use the extend method.
tostring()
Return the string representing (machine values) of the bitarray. When the length of the bitarray is not a multiple of 8, the few remaining bits (1..7) are set to 0.
unpack(zero='\x00', one='\xff')
Return a string containing one character for each bit in the bitarray, using the specified mapping. Note that unpack('0', '1') has the same effect as to01(). See also the pack method.

Functions defined in the module:

test(verbosity=1)
Run self-test.
bits2bytes(n)
Return the number of bytes necessary to store n bits.