bitarray: efficient arrays of booleans
======================================

This library 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 functionality is implemented in C.
Methods for accessing the machine representation are provided, including the
ability to import and export buffers.  This allows creating bitarrays that
are mapped to other objects, including memory-mapped files.


Key features
------------

* The bit-endianness can be specified for each bitarray object, see below.
* Sequence methods: slicing (including slice assignment and deletion),
  operations ``+``, ``*``, ``+=``, ``*=``, the ``in`` operator, ``len()``
* Bitwise operations: ``~``, ``&``, ``|``, ``^``, ``<<``, ``>>`` (as well as
  their in-place versions ``&=``, ``|=``, ``^=``, ``<<=``, ``>>=``).
* Fast methods for encoding and decoding variable bit length prefix codes.
* Bitarray objects support the buffer protocol (both importing and
  exporting buffers).
* Packing and unpacking to other binary data formats, e.g. ``numpy.ndarray``.
* Pickling and unpickling of bitarray objects.
* Immutable ``frozenbitarray`` objects which are hashable
* Sequential search
* Type hinting
* Extensive test suite with over 500 unittests
* Utility module ``bitarray.util``:

  * conversion to and from hexadecimal strings
  * generating random bitarrays
  * pretty printing
  * conversion to and from integers
  * creating Huffman codes
  * compression of sparse bitarrays
  * (de-) serialization
  * various count functions
  * other helpful functions


Installation
------------

Python wheels are are available on PyPI for all mayor platforms and Python
versions.  Which means you can simply:

.. code-block:: shell-session

    $ pip install bitarray

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

.. code-block:: shell-session

    $ python -c 'import bitarray; bitarray.test()'
    bitarray is installed in: /Users/ilan/bitarray/bitarray
    bitarray version: 3.6.1
    sys.version: 3.13.5 (main, Jun 16 2025) [Clang 18.1.8]
    sys.prefix: /Users/ilan/miniforge
    pointer size: 64 bit
    sizeof(size_t): 8
    sizeof(bitarrayobject): 80
    HAVE_BUILTIN_BSWAP64: 1
    default bit-endianness: big
    machine byte-order: little
    DEBUG: 0
    .........................................................................
    .........................................................................
    ................................................................
    ----------------------------------------------------------------------
    Ran 591 tests in 0.163s

    OK

The ``test()`` function is part of the API.  It will return
a ``unittest.runner.TextTestResult`` object, such that one can verify that
all tests ran successfully by:

.. code-block:: python

    import bitarray
    assert bitarray.test().wasSuccessful()


Usage
-----

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:

.. code-block:: python

    >>> from bitarray import bitarray
    >>> a = bitarray()         # create empty bitarray
    >>> a.append(1)
    >>> a.extend([1, 0])
    >>> a
    bitarray('110')
    >>> x = bitarray(2 ** 20)  # bitarray of length 1048576 (initialized to 0)
    >>> len(x)
    1048576
    >>> bitarray('1001 011')   # initialize from string (whitespace is ignored)
    bitarray('1001011')
    >>> lst = [1, 0, False, True, True]
    >>> a = bitarray(lst)      # initialize from iterable
    >>> a
    bitarray('10011')
    >>> a[2]    # indexing a single item will always return an integer
    0
    >>> a[2:4]  # whereas indexing a slice will always return a bitarray
    bitarray('01')
    >>> a[2:3]  # even when the slice length is just one
    bitarray('0')
    >>> a.count(1)
    3
    >>> a.remove(0)            # removes first occurrence of 0
    >>> a
    bitarray('1011')

Like lists, bitarray objects support slice assignment and deletion:

.. code-block:: python

    >>> a = bitarray(50)
    >>> a.setall(0)            # set all elements in a to 0
    >>> a[11:37:3] = 9 * bitarray('1')
    >>> 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:

.. code-block:: python

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

This is easier and faster than:

.. code-block:: python

    >>> 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.  Another example of assigning slices to Booleans,
is setting ranges:

.. code-block:: python

    >>> a = bitarray(30)
    >>> a[:] = 0         # set all elements to 0 - equivalent to a.setall(0)
    >>> a[10:25] = 1     # set elements in range(10, 25) to 1
    >>> a
    bitarray('000000000011111111111111100000')

As of bitarray version 2.8, indices may also be lists of arbitrary
indices (like in NumPy), or bitarrays that are treated as masks,
see `Bitarray indexing <https://github.com/ilanschnell/bitarray/blob/master/doc/indexing.rst>`__.


Bitwise operators
-----------------

Bitarray objects support the bitwise operators ``~``, ``&``, ``|``, ``^``,
``<<``, ``>>`` (as well as their in-place versions ``&=``, ``|=``, ``^=``,
``<<=``, ``>>=``).  The behavior is very much what one would expect:

.. code-block:: python

    >>> a = bitarray('101110001')
    >>> ~a  # invert
    bitarray('010001110')
    >>> b = bitarray('111001011')
    >>> a ^ b  # bitwise XOR
    bitarray('010111010')
    >>> a &= b  # inplace AND
    >>> a
    bitarray('101000001')
    >>> a <<= 2  # in-place left-shift by 2
    >>> a
    bitarray('100000100')
    >>> b >> 1  # return b right-shifted by 1
    bitarray('011100101')

The C language does not specify the behavior of negative shifts and
of left shifts larger or equal than the width of the promoted left operand.
The exact behavior is compiler/machine specific.
This Python bitarray library specifies the behavior as follows:

* the length of the bitarray is never changed by any shift operation
* blanks are filled by 0
* negative shifts raise ``ValueError``
* shifts larger or equal to the length of the bitarray result in
  bitarrays with all values 0

It is worth noting that (regardless of bit-endianness) the bitarray left
shift (``<<``) always shifts towards lower indices, and the right
shift (``>>``) always shifts towards higher indices.


Bit-endianness
--------------

Unless explicitly converting to machine representation, i.e. initializing
the buffer directly, using ``.tobytes()``, ``.frombytes()``, ``.tofile()``
or ``.fromfile()``, as well as using ``memoryview()``, the bit-endianness
will have no effect on any computation, and one can skip this section.

Since bitarrays allows addressing 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 dealing with the machine representation of bitarray objects, it is
recommended to always explicitly specify the endianness.

By default, bitarrays use big-endian representation:

.. code-block:: python

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

Big-endian means that the most-significant bit comes first.
Here, ``a[0]`` is the lowest address (index) and most significant bit,
and ``a[7]`` is the highest address and least significant bit.

When creating a new bitarray object, the endianness can always be
specified explicitly:

.. code-block:: python

    >>> a = bitarray(b'A', endian='little')
    >>> a
    bitarray('10000010')
    >>> a.endian
    'little'

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

The bit-endianness is a property of the bitarray object.
The endianness cannot be changed once a bitarray object has been created.
When comparing bitarray objects, the endianness (and hence the machine
representation) is irrelevant; what matters is the mapping from indices
to bits:

.. code-block:: python

    >>> bitarray('11001', endian='big') == bitarray('11001', endian='little')
    True
    >>> a = bitarray(b'\x01', endian='little')
    >>> b = bitarray(b'\x80', endian='big')
    >>> a == b
    True
    >>> a.tobytes() == b.tobytes()
    False

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, it is not possible to perform bitwise operators on bitarrays
with different endianness.

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

.. code-block:: python

    >>> a = bitarray('111000', endian='little')
    >>> b = bitarray(a, endian='big')
    >>> b
    bitarray('111000')
    >>> a == b
    True


Buffer protocol
---------------

Bitarray objects support the buffer protocol.  They can both export their
own buffer, as well as import another object's buffer.  To learn more about
this topic, please read `buffer protocol <https://github.com/ilanschnell/bitarray/blob/master/doc/buffer.rst>`__.  There is also an example that shows how
to memory-map a file to a bitarray: `mmapped-file.py <https://github.com/ilanschnell/bitarray/blob/master/examples/mmapped-file.py>`__


Variable bit length prefix codes
--------------------------------

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

.. code-block:: python

    >>> 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 an iterable of the symbols:

.. code-block:: python

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

Symbols are not limited to being characters.
The above dictionary ``d`` can be efficiently constructed using the function
``bitarray.util.huffman_code()``.  I also wrote `Huffman coding in Python
using bitarray <http://ilan.schnell-web.net/prog/huffman/>`__ for more
background information.

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 can be
passed to bitarray's ``.decode()`` method, instead of passing the prefix
code dictionary to those methods itself:

.. code-block:: python

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

The sole purpose of the immutable ``decodetree`` object is to be passed
to bitarray's ``.decode()`` method.


Frozenbitarrays
---------------

A ``frozenbitarray`` object is very similar to the bitarray object.
The difference is that this a ``frozenbitarray`` is immutable, and hashable,
and can therefore be used as a dictionary key:

.. code-block:: python

    >>> from bitarray import frozenbitarray
    >>> key = frozenbitarray('1100011')
    >>> {key: 'some value'}
    {frozenbitarray('1100011'): 'some value'}
    >>> key[3] = 1
    Traceback (most recent call last):
        ...
    TypeError: frozenbitarray is immutable


Reference
=========

bitarray version: 3.6.1 -- `change log <https://github.com/ilanschnell/bitarray/blob/master/doc/changelog.rst>`__

In the following, ``item`` and ``value`` are usually a single bit -
an integer 0 or 1.

Also, ``sub_bitarray`` refers to either a bitarray, or an ``item``.


The bitarray object:
--------------------

``bitarray(initializer=0, /, endian='big', buffer=None)`` -> bitarray
   Return a new bitarray object whose items are bits initialized from
   the optional initializer, and bit-endianness.
   The initializer may be one of the following types:
   a.) ``int`` bitarray, initialized to zeros, of given length
   b.) ``bytes`` or ``bytearray`` to initialize buffer directly
   c.) ``str`` of 0s and 1s, ignoring whitespace and "_"
   d.) iterable of integers 0 or 1.

   Optional keyword arguments:

   ``endian``: Specifies the bit-endianness of the created bitarray object.
   Allowed values are ``big`` and ``little`` (the default is ``big``).
   The bit-endianness effects the buffer representation of the bitarray.

   ``buffer``: Any object which exposes a buffer.  When provided, ``initializer``
   cannot be present (or has to be ``None``).  The imported buffer may be
   read-only or writable, depending on the object type.

   New in version 2.3: optional ``buffer`` argument

   New in version 3.4: allow initializer ``bytes`` or ``bytearray`` to set buffer directly


bitarray methods:
-----------------

``all()`` -> bool
   Return True when all bits in bitarray are True.
   Note that ``a.all()`` is faster than ``all(a)``.


``any()`` -> bool
   Return True when any bit in bitarray is True.
   Note that ``a.any()`` is faster than ``any(a)``.


``append(item, /)``
   Append ``item`` to the end of the bitarray.


``buffer_info()`` -> tuple
   Return a tuple containing:

   0. memory address of buffer
   1. buffer size (in bytes)
   2. bit-endianness as a Unicode string
   3. number of pad bits
   4. allocated memory for the buffer (in bytes)
   5. memory is read-only
   6. buffer is imported
   7. number of buffer exports


``bytereverse(start=0, stop=<end of buffer>, /)``
   For each byte in byte-range(start, stop) reverse bits in-place.
   The start and stop indices are given in terms of bytes (not bits).
   Also note that this method only changes the buffer; it does not change the
   bit-endianness of the bitarray object.  Pad bits are left unchanged such
   that two consecutive calls will always leave the bitarray unchanged.

   New in version 2.2.5: optional start and stop arguments


``clear()``
   Remove all items from the bitarray.

   New in version 1.4


``copy()`` -> bitarray
   Return a copy of the bitarray.


``count(value=1, start=0, stop=<end>, step=1, /)`` -> int
   Number of occurrences of ``value`` bitarray within ``[start:stop:step]``.
   Optional arguments ``start``, ``stop`` and ``step`` are interpreted in
   slice notation, meaning ``a.count(value, start, stop, step)`` equals
   ``a[start:stop:step].count(value)``.
   The ``value`` may also be a sub-bitarray.  In this case non-overlapping
   occurrences are counted within ``[start:stop]`` (``step`` must be 1).

   New in version 1.1.0: optional start and stop arguments

   New in version 2.3.7: optional step argument

   New in version 2.9: add non-overlapping sub-bitarray count


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

   See also: `Bitarray 3 transition <https://github.com/ilanschnell/bitarray/blob/master/doc/bitarray3.rst>`__

   New in version 3.0: returns iterator (equivalent to past ``.iterdecode()``)


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


``extend(iterable, /)``
   Append items from to the end of the bitarray.
   If ``iterable`` is a Unicode string, each ``0`` and ``1`` are appended as
   bits (ignoring whitespace and underscore).

   New in version 3.4: allow ``bytes`` object


``fill()`` -> int
   Add zeros to the end of the bitarray, such that the length will be
   a multiple of 8, and return the number of bits added [0..7].


``find(sub_bitarray, start=0, stop=<end>, /, right=False)`` -> int
   Return lowest (or rightmost when ``right=True``) index where sub_bitarray
   is found, such that sub_bitarray is contained within ``[start:stop]``.
   Return -1 when sub_bitarray is not found.

   New in version 2.1

   New in version 2.9: add optional keyword argument ``right``


``frombytes(bytes, /)``
   Extend bitarray with raw bytes from a bytes-like object.
   Each added byte will add eight bits to the bitarray.

   New in version 2.5.0: allow bytes-like argument


``fromfile(f, n=-1, /)``
   Extend bitarray with up to ``n`` bytes read from file object ``f`` (or any
   other binary stream what supports a ``.read()`` method, e.g. ``io.BytesIO``).
   Each read byte will add eight bits to the bitarray.  When ``n`` is omitted
   or negative, reads and extends all data until EOF.
   When ``n`` is non-negative but exceeds the available data, ``EOFError`` is
   raised.  However, the available data is still read and extended.


``index(sub_bitarray, start=0, stop=<end>, /, right=False)`` -> int
   Return lowest (or rightmost when ``right=True``) index where sub_bitarray
   is found, such that sub_bitarray is contained within ``[start:stop]``.
   Raises ``ValueError`` when the sub_bitarray is not present.

   New in version 2.9: add optional keyword argument ``right``


``insert(index, value, /)``
   Insert ``value`` into bitarray before ``index``.


``invert(index=<all bits>, /)``
   Invert all bits in bitarray (in-place).
   When the optional ``index`` is given, only invert the single bit at index.

   New in version 1.5.3: optional index argument


``pack(bytes, /)``
   Extend bitarray from a bytes-like object, where each byte corresponds
   to a single bit.  The byte ``b'\x00'`` maps to bit 0 and all other bytes
   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.

   New in version 2.5.0: allow bytes-like argument


``pop(index=-1, /)`` -> item
   Remove and return item at ``index`` (default last).
   Raises ``IndexError`` if index is out of range.


``remove(value, /)``
   Remove the first occurrence of ``value``.
   Raises ``ValueError`` if value is not present.


``reverse()``
   Reverse all bits in bitarray (in-place).


``search(sub_bitarray, start=0, stop=<end>, /, right=False)`` -> iterator
   Return iterator over indices where sub_bitarray is found, such that
   sub_bitarray is contained within ``[start:stop]``.
   The indices are iterated in ascending order (from lowest to highest),
   unless ``right=True``, which will iterate in descending order (starting with
   rightmost match).

   See also: `Bitarray 3 transition <https://github.com/ilanschnell/bitarray/blob/master/doc/bitarray3.rst>`__

   New in version 2.9: optional start and stop arguments - add optional keyword argument ``right``

   New in version 3.0: returns iterator (equivalent to past ``.itersearch()``)


``setall(value, /)``
   Set all elements in bitarray to ``value``.
   Note that ``a.setall(value)`` is equivalent to ``a[:] = value``.


``sort(reverse=False)``
   Sort all bits in bitarray (in-place).


``to01(group=0, sep=' ')`` -> str
   Return bitarray as Unicode string of '0's and '1's.
   The bits are grouped into ``group`` bits (default is no grouping).
   When grouped, the string ``sep`` is inserted between groups
   of ``group`` characters, default is a space.

   New in version 3.3: optional ``group`` and ``sep`` arguments


``tobytes()`` -> bytes
   Return the bitarray buffer in bytes (pad bits are set to zero).


``tofile(f, /)``
   Write byte representation of bitarray to file object f.


``tolist()`` -> list
   Return bitarray as list of integers.
   ``a.tolist()`` equals ``list(a)``.

   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'\x01')`` -> bytes
   Return bytes that contain one byte for each bit in the bitarray,
   using specified mapping.


bitarray data descriptors:
--------------------------

Data descriptors were added in version 2.6.

``endian`` -> str
   bit-endianness as Unicode string

   New in version 3.4: replaces former ``.endian()`` method


``nbytes`` -> int
   buffer size in bytes


``padbits`` -> int
   number of pad bits


``readonly`` -> bool
   bool indicating whether buffer is read-only


Other objects:
--------------

``frozenbitarray(initializer=0, /, endian='big', buffer=None)`` -> frozenbitarray
   Return a ``frozenbitarray`` object.  Initialized the same way a ``bitarray``
   object is initialized.  A ``frozenbitarray`` is immutable and hashable,
   and may therefore be used as a dictionary key.

   New in version 1.1


``decodetree(code, /)`` -> decodetree
   Given a prefix code (a dict mapping symbols to bitarrays),
   create a binary tree object to be passed to ``.decode()``.

   New in version 1.6


Functions defined in the `bitarray` module:
-------------------------------------------

``bits2bytes(n, /)`` -> int
   Return the number of bytes necessary to store n bits.


``get_default_endian()`` -> str
   Return the default bit-endianness for new bitarray objects being created.
   Unless ``_set_default_endian('little')`` was called, the default
   bit-endianness is ``big``.

   New in version 1.3


``test(verbosity=1)`` -> TextTestResult
   Run self-test, and return unittest.runner.TextTestResult object.


Functions defined in `bitarray.util` module:
--------------------------------------------

This sub-module was added in version 1.2.

``any_and(a, b, /)`` -> bool
   Efficient implementation of ``any(a & b)``.

   New in version 2.7


``ba2base(n, bitarray, /, group=0, sep=' ')`` -> str
   Return a string containing the base ``n`` ASCII representation of
   the bitarray.  Allowed values for ``n`` are 2, 4, 8, 16, 32 and 64.
   The bitarray has to be multiple of length 1, 2, 3, 4, 5 or 6 respectively.
   For ``n=32`` the RFC 4648 Base32 alphabet is used, and for ``n=64`` the
   standard base 64 alphabet is used.
   When grouped, the string ``sep`` is inserted between groups
   of ``group`` characters, default is a space.

   See also: `Bitarray representations <https://github.com/ilanschnell/bitarray/blob/master/doc/represent.rst>`__

   New in version 1.9

   New in version 3.3: optional ``group`` and ``sep`` arguments


``ba2hex(bitarray, /, group=0, sep=' ')`` -> hexstr
   Return a string containing the hexadecimal representation of
   the bitarray (which has to be multiple of 4 in length).
   When grouped, the string ``sep`` is inserted between groups
   of ``group`` characters, default is a space.

   New in version 3.3: optional ``group`` and ``sep`` arguments


``ba2int(bitarray, /, signed=False)`` -> int
   Convert the given bitarray to an integer.
   The bit-endianness of the bitarray is respected.
   ``signed`` indicates whether two's complement is used to represent the integer.


``base2ba(n, asciistr, /, endian=None)`` -> bitarray
   Bitarray of base ``n`` ASCII representation.
   Allowed values for ``n`` are 2, 4, 8, 16, 32 and 64.
   For ``n=32`` the RFC 4648 Base32 alphabet is used, and for ``n=64`` the
   standard base 64 alphabet is used.  Whitespace is ignored.

   See also: `Bitarray representations <https://github.com/ilanschnell/bitarray/blob/master/doc/represent.rst>`__

   New in version 1.9

   New in version 3.3: ignore whitespace


``byteswap(a, /, n=<buffer size>)``
   Reverse every ``n`` consecutive bytes of ``a`` in-place.
   By default, all bytes are reversed.  Note that ``n`` is not limited to 2, 4
   or 8, but can be any positive integer.
   Also, ``a`` may be any object that exposes a writable buffer.
   Nothing about this function is specific to bitarray objects.

   New in version 3.4


``canonical_decode(bitarray, count, symbol, /)`` -> iterator
   Decode bitarray using canonical Huffman decoding tables
   where ``count`` is a sequence containing the number of symbols of each length
   and ``symbol`` is a sequence of symbols in canonical order.

   See also: `Canonical Huffman Coding <https://github.com/ilanschnell/bitarray/blob/master/doc/canonical.rst>`__

   New in version 2.5


``canonical_huffman(dict, /)`` -> tuple
   Given a frequency map, a dictionary mapping symbols to their frequency,
   calculate the canonical Huffman code.  Returns a tuple containing:

   0. the canonical Huffman code as a dict mapping symbols to bitarrays
   1. a list containing the number of symbols of each code length
   2. a list of symbols in canonical order

   Note: the two lists may be used as input for ``canonical_decode()``.

   See also: `Canonical Huffman Coding <https://github.com/ilanschnell/bitarray/blob/master/doc/canonical.rst>`__

   New in version 2.5


``correspond_all(a, b, /)`` -> tuple
   Return tuple with counts of: ~a & ~b, ~a & b, a & ~b, a & b

   New in version 3.4


``count_and(a, b, /)`` -> int
   Return ``(a & b).count()`` in a memory efficient manner,
   as no intermediate bitarray object gets created.


``count_n(a, n, value=1, /)`` -> int
   Return lowest index ``i`` for which ``a[:i].count(value) == n``.
   Raises ``ValueError`` when ``n`` exceeds total count (``a.count(value)``).

   New in version 2.3.6: optional value argument


``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.

   This is also known as the Hamming distance.


``deserialize(bytes, /)`` -> bitarray
   Return a bitarray given a bytes-like representation such as returned
   by ``serialize()``.

   See also: `Bitarray representations <https://github.com/ilanschnell/bitarray/blob/master/doc/represent.rst>`__

   New in version 1.8

   New in version 2.5.0: allow bytes-like argument


``hex2ba(hexstr, /, endian=None)`` -> bitarray
   Bitarray of hexadecimal representation.  hexstr may contain any number
   (including odd numbers) of hex digits (upper or lower case).
   Whitespace is ignored.

   New in version 3.3: ignore whitespace


``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 bit-endianness).  Note that the symbols are not limited
   to being strings.  Symbols may be any hashable object.


``int2ba(int, /, length=None, endian=None, signed=False)`` -> bitarray
   Convert the given integer to a bitarray (with given bit-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.


``intervals(bitarray, /)`` -> iterator
   Compute all uninterrupted intervals of 1s and 0s, and return an
   iterator over tuples ``(value, start, stop)``.  The intervals are guaranteed
   to be in order, and their size is always non-zero (``stop - start > 0``).

   New in version 2.7


``ones(n, /, endian=None)`` -> bitarray
   Create a bitarray of length ``n``, with all values ``1``, and optional
   bit-endianness (``little`` or ``big``).

   New in version 2.9


``parity(a, /)`` -> int
   Return parity of bitarray ``a``.
   ``parity(a)`` is equivalent to ``a.count() % 2`` but more efficient.

   New in version 1.9


``pprint(bitarray, /, stream=None, group=8, indent=4, width=80)``
   Prints the formatted representation of object on ``stream`` (which defaults
   to ``sys.stdout``).  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()``.

   New in version 1.8


``random_k(n, /, k, endian=None)`` -> bitarray
   Return (pseudo-) random bitarray of length ``n`` with ``k`` elements
   set to one.  Mathematically equivalent to setting (in a bitarray of
   length ``n``) all bits at indices ``random.sample(range(n), k)`` to one.
   The random bitarrays are reproducible when giving Python's ``random.seed()``
   with a specific seed value.

   This function requires Python 3.9 or higher, as it depends on the standard
   library function ``random.randbytes()``.  Raises ``NotImplementedError``
   when Python version is too low.

   New in version 3.6


``random_p(n, /, p=0.5, endian=None)`` -> bitarray
   Return (pseudo-) random bitarray of length ``n``, where each bit has
   probability ``p`` of being one (independent of any other bits).  Mathematically
   equivalent to ``bitarray((random() < p for _ in range(n)), endian)``, but much
   faster for large ``n``.  The random bitarrays are reproducible when giving
   Python's ``random.seed()`` with a specific seed value.

   This function requires Python 3.12 or higher, as it depends on the standard
   library function ``random.binomialvariate()``.  Raises ``NotImplementedError``
   when Python version is too low.

   See also: `Random Bitarrays <https://github.com/ilanschnell/bitarray/blob/master/doc/random_p.rst>`__

   New in version 3.5


``sc_decode(stream)`` -> bitarray
   Decompress binary stream (an integer iterator, or bytes-like object) of a
   sparse compressed (``sc``) bitarray, and return the decoded  bitarray.
   This function consumes only one bitarray and leaves the remaining stream
   untouched.  Use ``sc_encode()`` for compressing (encoding).

   See also: `Compression of sparse bitarrays <https://github.com/ilanschnell/bitarray/blob/master/doc/sparse_compression.rst>`__

   New in version 2.7


``sc_encode(bitarray, /)`` -> bytes
   Compress a sparse bitarray and return its binary representation.
   This representation is useful for efficiently storing sparse bitarrays.
   Use ``sc_decode()`` for decompressing (decoding).

   See also: `Compression of sparse bitarrays <https://github.com/ilanschnell/bitarray/blob/master/doc/sparse_compression.rst>`__

   New in version 2.7


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

   See also: `Bitarray representations <https://github.com/ilanschnell/bitarray/blob/master/doc/represent.rst>`__

   New in version 1.8


``strip(bitarray, /, mode='right')`` -> bitarray
   Return a new bitarray with zeros stripped from left, right or both ends.
   Allowed values for mode are the strings: ``left``, ``right``, ``both``


``subset(a, b, /)`` -> bool
   Return ``True`` if bitarray ``a`` is a subset of bitarray ``b``.
   ``subset(a, b)`` is equivalent to ``a | b == b`` (and equally ``a & b == a``) but
   more efficient as no intermediate bitarray object is created and the buffer
   iteration is stopped as soon as one mismatch is found.


``sum_indices(a, /)`` -> int
   Return sum of indices of all active bits in bitarray ``a``.
   Equivalent to ``sum(i for i, v in enumerate(a) if v)``.

   New in version 3.6


``urandom(n, /, endian=None)`` -> bitarray
   Return random bitarray of length ``n`` (uses ``os.urandom()``).

   New in version 1.7


``vl_decode(stream, /, endian=None)`` -> bitarray
   Decode binary stream (an integer iterator, or bytes-like object), and
   return the decoded bitarray.  This function consumes only one bitarray and
   leaves the remaining stream untouched.  Use ``vl_encode()`` for encoding.

   See also: `Variable length bitarray format <https://github.com/ilanschnell/bitarray/blob/master/doc/variable_length.rst>`__

   New in version 2.2


``vl_encode(bitarray, /)`` -> bytes
   Return variable length binary representation of bitarray.
   This representation is useful for efficiently storing small bitarray
   in a binary stream.  Use ``vl_decode()`` for decoding.

   See also: `Variable length bitarray format <https://github.com/ilanschnell/bitarray/blob/master/doc/variable_length.rst>`__

   New in version 2.2


``xor_indices(a, /)`` -> int
   Return xor reduced indices of all active bits in bitarray ``a``.
   This is essentially equivalent to
   ``reduce(operator.xor, (i for i, v in enumerate(a) if v))``.

   New in version 3.2


``zeros(n, /, endian=None)`` -> bitarray
   Create a bitarray of length ``n``, with all values ``0``, and optional
   bit-endianness (``little`` or ``big``).