bitarray: efficient arrays of booleans

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 a contiguous block of memory. The user can select between two representations: little-endian and big-endian. All 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.

Key features

> - 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. > > - Fast methods for encoding and decoding variable bit length prefix > codes > > - Bitwise operations: &, class="title-ref">|, ^, > &=, class="title-ref">|=, ^=, > ~ > > - Sequential search > > - Packing and unpacking to other binary data formats, e.g. class="title-ref">numpy.ndarray. > > - Pickling and unpickling of bitarray objects. > > - Bitarray objects support the buffer protocol > > - frozenbitarray objects which are > hashable > > - Extensive test suite with about 300 unittests > > - On 32-bit systems, a bitarray object may contain up to 2 Gbits. > > - a separate utility module `bitarray.util`:
> - conversion to hexadecimal string > - serialization > - pretty printing > - conversion to integers > - creating Huffman codes > - various count functions > - other helpful functions

Installation

Bitarray can be installed from source:

> $ tar xzf bitarray-1.8.3.tar.gz $ cd bitarray-1.8.3 $ python setup.py > install

On Unix systems, the latter command may have to be executed with root privileges. You can also pip install bitarray. Please note that you need a working C compiler to run the python setup.py install command. If you rather want to use precompiled binaries, you can:

• pip install bitarray-hardbyte (this PyPI package contains Python wheels for Linux, MaxOSX and Windows and all common Python versions)
• conda install bitarray (both the default Anaconda repository as well as conda-forge support bitarray)
• download Windows wheels from [Chris Gohlke]()

Once you have installed the package, you may want to test it:

> $ python -c 'import bitarray; bitarray.test()' bitarray is installed > in: /Users/ilan/bitarray/bitarray bitarray version: 1.8.3 sys.version: > 2.7.15 (default, Mar 5 2020, 14:58:04) [GCC Clang 9.0.1] sys.prefix: > /Users/ilan/Mini3/envs/py27 pointer size: 64 bit > ......................................................................... > ......................................................................... > ........................................ > ----------------------------------------------------------------------Ran > 291 tests in 0.638s > > OK

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

Using the module

As mentioned above, bitarray objects behave very much like lists, so there is not too much to learn. The biggest difference from list objects (except that bitarray are obviously homogeneous) 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('1001 011') # from a string > (whitespace is ignored) 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) 4 >>> 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 are two obvious choices for this mapping: little-endian and big-endian. When creating a new bitarray object, the endianness can always be specified explicitly:

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

Here, the low-bit comes first because little-endian means that increasing numeric significance corresponds to an increasing address (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.frombytes(b'A') > >>> a bitarray('01000001') >>> a[6] = 1 > >>> a.tobytes() b'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 tobytes, frombytes, tofile and fromfile methods, the endianness matters:

> >>> a = bitarray(endian='little') >>> > a.frombytes(b'x01') >>> a bitarray('10000000') >>> b > = bitarray(endian='big') >>> b.frombytes(b'x80') >>> > b bitarray('10000000') >>> a == b True >>> > a.tobytes() == b.tobytes() False

The endianness can not be changed once an object is created. However, you can create a new bitarray with different endianness:

> >>> a = bitarray('111000', endian='little') >>> b = > bitarray(a, endian='big') >>> b bitarray('111000') > >>> a == b 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 tobytes, frombytes, tofile and fromfile methods, the bit endianness will have no effect on any computation, and one can safely ignore setting the endianness, and other details of this section.

Buffer protocol

Python 2.7 provides memoryview objects, which allow Python code to access the internal data of an object that supports the buffer protocol without copying. Bitarray objects support this protocol, with the memory being interpreted as simple bytes.

> >>> a = bitarray('01000001 01000010 01000011', endian='big') > >>> v = memoryview(a) >>> len(v) 3 >>> > v[-1] 67 >>> v[:2].tobytes() b'AB' >>> > v.readonly # changing a bitarray's memory is also possible False > >>> v[1] = 111 >>> a > bitarray('010000010110111101000011')

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, in fact any immutable 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.

When the codes are large, and you have many decode calls, most time will be spent creating the (same) internal decode tree objects. In this case, it will be much faster to create a decodetree object (which is initialized with a prefix code dictionary), and can be passed to bitarray's .decode() and .iterdecode() methods, instead of passing the prefix code dictionary to those methods itself.

The above dictionary d can be efficiently constructed using the function bitarray.util.huffman_code(). I also wrote [Huffman coding in Python using bitarray]() for more background information.

Reference

The bitarray object:

bitarray(initializer=0, /, endian='big') -> bitarray

Return a new bitarray object whose items are bits initialized from the optional initial object, and endianness. The initializer may be of the following types:

`int`: Create a bitarray of given integer length. The initial values are arbitrary. If you want all values to be set, use the .setall() method.

`str`: Create bitarray from a string of 0 and 1.

list, tuple, `iterable`: Create bitarray from a sequence, each element in the sequence is converted to a bit using its truth value.

`bitarray`: Create bitarray from another bitarray. This is done by copying the buffer 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 the strings 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, tobytes, frombytes.

A bitarray object supports the following methods:

all() -> bool

Return True when all bits in the array are True.

any() -> bool

Return True when any bit in the array is True.

append(item, /)

Append the truth value bool(item) to the end of the bitarray.

buffer_info() -> tuple

Return a tuple (address, size, endianness, unused, allocated) giving the memory address of the bitarray's buffer, the buffer size (in bytes), the bit endianness as a string, the number of unused bits within the last byte, and the allocated memory for the buffer (in bytes).

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.

clear()

Remove all items from the bitarray.

copy() -> bitarray

Return a copy of the bitarray.

count(value=True, start=0, stop=<end of array>, /) -> int

Count the number of occurrences of bool(value) in the bitarray.

decode(code, /) -> list

Given a prefix code (a dict mapping symbols to bitarrays, or decodetree object), decode the content of the bitarray and return it as a list of symbols.

encode(code, iterable, /)

Given a prefix code (a dict mapping symbols to bitarrays), iterate over the iterable object with symbols, and extend the bitarray with the corresponding bitarray for each symbol.

endian() -> str

Return the bit endianness of the bitarray as a string (little or big).

extend(iterable, /)

Extend bitarray by appending the truth value of each element given by iterable. If a string is provided, each 0 and 1 are appended as bits (whitespace is ignored).

fill() -> int

Add zeros to the end of the bitarray, such that the length of the bitarray will be a multiple of 8, and return the number of bits added (0..7).

frombytes(bytes, /)

Extend bitarray with raw bytes. That is, each append byte will add eight bits to the bitarray.

fromfile(f, n=-1, /)

Extend bitarray with up to n bytes read from the file object f. When n is omitted or negative, reads all data until EOF. When n is provided and positive but exceeds the data available, EOFError is raised (but the available data is still read and appended.

index(value, start=0, stop=<end of array>, /) -> int

Return index of the first occurrence of bool(value) in the bitarray. Raises ValueError if the value is not present.

insert(index, value, /)

Insert bool(value) into the bitarray before index.

invert(index=<all bits>, /)

Invert all bits in the array (in-place). When the optional index is given, only invert the single bit at index.

iterdecode(code, /) -> iterator

Given a prefix code (a dict mapping symbols to bitarrays, or decodetree object), decode the content of the bitarray and return an iterator over the symbols.

itersearch(bitarray, /) -> iterator

Searches for the given a bitarray in self, and return an iterator over the start positions where bitarray matches self.

length() -> int

Return the length - a.length() is the same as len(a). Deprecated since 1.5.1, use len().

pack(bytes, /)

Extend the bitarray from bytes, where each byte corresponds to a single bit. The byte b'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 memory view.

pop(index=-1, /) -> item

Return the i-th (default last) element and delete it from the bitarray. Raises IndexError if bitarray is empty or index is out of range.

remove(value, /)

Remove the first occurrence of bool(value) in the bitarray. Raises ValueError if item is not present.

reverse()

Reverse the order of bits in the array (in-place).

search(bitarray, limit=<none>, /) -> list

Searches for the given bitarray in self, and return the list of start positions. The optional argument limits the number of search results to the integer specified. By default, all search results are returned.

setall(value, /)

Set all bits in the bitarray to bool(value).

sort(reverse=False)

Sort the bits in the array (in-place).

to01() -> str

Return a string containing '0's and '1's, representing the bits in the bitarray object.

tobytes() -> bytes

Return the byte representation of the bitarray. When the length of the bitarray is not a multiple of 8, the few remaining bits (1..7) are considered to be 0.

tofile(f, /)

Write the byte representation of the bitarray 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(as_ints=False, /) -> list

Return a list with the items (False or True) in the bitarray. The optional parameter, changes the items in the list to integers (0 or 1). Note that the list object being created will require 32 or 64 times more memory (depending on the machine architecture) than the bitarray object, which may cause a memory error if the bitarray is very large.

unpack(zero=b'x00', one=b'xff') -> bytes

Return bytes containing one character for each bit in the bitarray, using the specified mapping.

The frozenbitarray object:

This object is very similar to the bitarray object. The difference is that this a frozenbitarray is immutable, and hashable:

> >>> from bitarray import frozenbitarray >>> a = > frozenbitarray('1100011') >>> a[3] = 1 Traceback (most > recent call last): File "<stdin>", line 1, in <module> > File "bitarray/__init__.py", line 40, in __delitem__ raise > TypeError("'frozenbitarray' is immutable") TypeError: 'frozenbitarray' > is immutable >>> {a: 'some value'} > {frozenbitarray('1100011'): 'some value'}

frozenbitarray(initializer=0, /, endian='big') -> frozenbitarray

Return a frozenbitarray object, which is initialized the same way a bitarray object is initialized. A frozenbitarray is immutable and hashable. Its contents cannot be altered after it is created; however, it can be used as a dictionary key.

The decodetree object:

This (immutable and unhashable) object stores a binary tree initialized from a prefix code dictionary. It's sole purpose is to be passed to bitarray's .decode() and .iterdecode() methods, instead of passing the prefix code dictionary to those methods directly:

> >>> from bitarray import bitarray, decodetree >>> t > = decodetree({'a': bitarray('0'), 'b': bitarray('1')}) >>> a > = bitarray('0110') >>> a.decode(t) ['a', 'b', 'b', 'a'] > >>> ''.join(a.iterdecode(t)) 'abba'

decodetree(code, /) -> decodetree

Given a prefix code (a dict mapping symbols to bitarrays), create a binary tree object to be passed to .decode() or .iterdecode().

Functions defined in the bitarray module:

bits2bytes(n, /) -> int

Return the number of bytes necessary to store n bits.

get_default_endian() -> string

Return the default endianness for new bitarray objects being created. Under normal circumstances, the return value is big.

test(verbosity=1, repeat=1) -> TextTestResult

Run self-test, and return unittest.runner.TextTestResult object.

Functions defined in bitarray.util module:

zeros(length, /, endian=None) -> bitarray

Create a bitarray of length, with all values 0, and optional endianness, which may be 'big', 'little'.

urandom(length, /, endian=None) -> bitarray

Return a bitarray of length random bits (uses os.urandom).

pprint(bitarray, /, stream=None, group=8, indent=4, width=80)

Prints the formatted representation of object on stream, followed by a newline. If stream is None, sys.stdout is used. By default, elements are grouped in bytes (8 elements), and 8 bytes (64 elements) per line. Non-bitarray objects are printed by the standard library function pprint.pprint().

make_endian(bitarray, endian, /) -> bitarray

When the endianness of the given bitarray is different from endian, return a new bitarray, with endianness endian and the same elements as the original bitarray. Otherwise (endianness is already endian) the original bitarray is returned unchanged.

rindex(bitarray, value=True, /) -> int

Return the rightmost index of bool(value) in bitarray. Raises ValueError if the value is not present.

strip(bitarray, mode='right', /) -> bitarray

Strip zeros from left, right or both ends. Allowed values for mode are the strings: left, right, both

count_n(a, n, /) -> int

Return the smallest index i for which a[:i].count() == n. Raises ValueError, when n exceeds total count (a.count()).

parity(a, /) -> bool

Return the parity of bitarray a. This is equivalent to bool(a.count() % 2) (but more efficient).

count_and(a, b, /) -> int

Return (a & b).count() in a memory efficient manner, as no intermediate bitarray object gets created.

count_or(a, b, /) -> int

Return (a | b).count() in a memory efficient manner, as no intermediate bitarray object gets created.

count_xor(a, b, /) -> int

Return (a ^ b).count() in a memory efficient manner, as no intermediate bitarray object gets created.

subset(a, b, /) -> bool

Return True if bitarray a is a subset of bitarray b (False otherwise). subset(a, b) is equivalent to (a & b).count() == a.count() but is more efficient since we can stop as soon as one mismatch is found, and no intermediate bitarray object gets created.

ba2hex(bitarray, /) -> hexstr

Return a string containing the hexadecimal representation of the bitarray (which has to be multiple of 4 in length).

hex2ba(hexstr, /, endian=None) -> bitarray

Bitarray of hexadecimal representation. hexstr may contain any number (including odd numbers) of hex digits (upper or lower case).

ba2int(bitarray, /, signed=False) -> int

Convert the given bitarray into an integer. The bit-endianness of the bitarray is respected. signed indicates whether two's complement is used to represent the integer.

int2ba(int, /, length=None, endian=None, signed=False) -> bitarray

Convert the given integer to a bitarray (with given endianness, and no leading (big-endian) / trailing (little-endian) zeros), unless the length of the bitarray is provided. An OverflowError is raised if the integer is not representable with the given number of bits. signed determines whether two's complement is used to represent the integer, and requires length to be provided. If signed is False and a negative integer is given, an OverflowError is raised.

serialize(bitarray, /) -> bytes

Return a serialized representation of the bitarray, which may be passed to deserialize(). It efficiently represents the bitarray object (including its endianness) and is guaranteed not to change in future releases.

deserialize(bytes, /) -> bitarray

Return a bitarray given the bytes representation returned by serialize().

huffman_code(dict, /, endian=None) -> dict

Given a frequency map, a dictionary mapping symbols to their frequency, calculate the Huffman code, i.e. a dict mapping those symbols to bitarrays (with given endianness). Note that the symbols may be any hashable object (including None).

Change log

2021-04-XX 1.8.3:

> - documentation and tests

1.8.2 (2021-03-31):

> - fix crash caused by unsupported types in binary operations, #116 > - speedup initializing or extending a bitarray from another with > different bit endianness > - add formatting options to class="title-ref">bitarray.util.pprint() > - add documentation on [bitarray > representations](examples/represent.md) > - add and improve tests (all 291 tests run in less than half a > second on a modern machine)

1.8.1 (2021-03-25):

> - moved implementation of and class="title-ref">hex2ba() and class="title-ref">ba2hex() to C-level > - add bitarray.util.parity()

1.8.0 (2021-03-21):

> - add bitarray.util.serialize() and > bitarray.util.deserialize() > - allow whitespace (ignore space and class="title-ref">nrtv) in input strings, e.g. class="title-ref">bitarray('01 11') or class="title-ref">a += '10 00' > - add bitarray.util.pprint() > - When initializing a bitarray from another with different bit > endianness, e.g. a = bitarray('110', > 'little') and b = bitarray(a, > 'big'), the buffer used to be simply copied, with > consequence that a == b would > result in False. This is fixed now, > that is a == b will always evaluate > to True. > - add example showing how to [jsonize > bitarrays](examples/extend_json.py) > - add tests

1.7.1 (2021-03-12):

> - fix issue #114, raise TypeError when incorrect index is used > during assignment, e.g. a[1.5] = > 1 > - raise TypeError (not IndexError) when assigning slice to incorrect > type, e.g. a[1:4] = 1.2 > - improve some docstrings and tests

1.7.0 (2021-02-27):

> - add bitarray.util.urandom() > - raise TypeError when trying to extend bitarrays from bytes on > Python 3, ie. bitarray(b'011') and > .extend(b'110'). (Deprecated since > 1.4.1)

1.6.3 (2021-01-20):

> - add missing .h files to sdist tarball, #113

1.6.2 (2021-01-20):

> - use Py_SET_TYPE() and class="title-ref">Py_SET_SIZE() for Python 3.10, #109 > - add official Python 3.10 support > - fix slice assignment to same object, e.g. class="title-ref">a[2::] = a or class="title-ref">a[::-1] = a, #112 > - add bitarray.h, #110

1.6.1 (2020-11-05):

> - use PyType_Ready for all types: bitarray, bitarrayiterator, > decodeiterator, decodetree, searchiterator

1.6.0 (2020-10-17):

> - add decodetree object, for speeding > up consecutive calls to .decode() > and .iterdecode(), in particular > when dealing with large prefix codes, see #103 > - add optional parameter to .tolist() > which changes the items in the returned list to integers (0 or 1), > as opposed to Booleans > - remove deprecated bitdiff(), which > has been deprecated since version 1.2.0, use class="title-ref">bitarray.util.count_xor() instead > - drop Python 2.6 support > - update license file, #104

1.5.3 (2020-08-24):

> - add optional index parameter to class="title-ref">.index() to invert single bit > - fix sys.getsizeof(bitarray) by > adding .__sizeof__(), see issue > #100

1.5.2 (2020-08-16):

> - add PyType_Ready usage, issue #66 > - speedup search() for bitarrays with length 1 in sparse bitarrays, > see issue #67 > - add tests

1.5.1 (2020-08-10):

> - support signed integers in class="title-ref">util.ba2int() and class="title-ref">util.int2ba(), see issue #85 > - deprecate .length() in favor of > len()

1.5.0 (2020-08-05):

> - Use Py_ssize_t for bitarray > index. This means that on 32bit systems, the maximum number of > elements in a bitarray is 2 GBits. We used to have a special 64bit > index type for all architectures, but this prevented us from using > Python's sequence, mapping and number methods, and made those > method lookups slow. > - speedup slice operations when step size = 1 (if alignment allows > copying whole bytes) > - Require equal endianness for operations: class="title-ref">&, |, > ^, class="title-ref">&=, |=, > ^=. This should have always been > the case but was overlooked in the past. > - raise TypeError when trying to create bitarray from boolean > - This will be last release to still support Python 2.6 (which was > retired in 2013). We do NOT plan to stop support for Python 2.7 > anytime soon.

Please find the complete change log [here]().