r"""
Bitsets
A Python interface to the fast bitsets in Sage. Bitsets are fast
binary sets that store elements by toggling bits in an array of
numbers. A bitset can store values between `0` and ``capacity - 1``,
inclusive (where ``capacity`` is finite, but arbitrary). The storage cost is
linear in ``capacity``.
.. warning::
This class is most likely to be useful as a way to store Cython
bitsets in Python data structures, acting on them using the Cython
inline functions. If you want to use these classes for a Python
set type, the Python ``set`` or ``frozenset`` data types may be
faster.
"""
include "bitset.pxi"
cdef class FrozenBitset:
r"""
A frozen bitset class which leverages inline Cython functions for
creating and manipulating bitsets.
A bitset can be thought of in two ways. First, as a set of elements
from the universe of the `n` natural numbers `0, 1, \dots, n-1` (where
the capacity `n` can be specified), with typical set operations such as
intersection, union, symmetric difference, etc. Secondly, a bitset can
be thought of as a binary vector with typical binary operations such as
``and``, ``or``, ``xor``, etc. This class supports both interfaces.
The interface in this class mirrors the interface in the ``frozenset``
data type of Python. See the Python documentation on `set types
<http://docs.python.org/library/stdtypes.html#set-types-set-frozenset>`_
for more details on Python's ``set`` and ``frozenset`` classes.
.. warning::
This class is most likely to be useful as a way to store
Cython bitsets in Python data structures, acting on them using
the Cython inline functions. If you want to use this class
for a Python set type, the Python ``frozenset`` data type may
be faster.
INPUT:
- ``iter`` -- initialization parameter (default: ``None``). Valid input
are:
- :class:`Bitset` and :class:`FrozenBitset` -- If this is a
:class:`Bitset` or :class:`FrozenBitset`, then it is copied.
- ``None`` -- If ``None``, then the bitset is set to the empty set.
- string -- If a nonempty string, then the bitset is initialized by
including an element if the index of the string is ``1``. If the
string is empty, then raise a ``ValueError``.
- iterable -- If an iterable, then it is assumed to contain a list of
nonnegative integers and those integers are placed in the set.
- ``capacity`` -- (default: ``None``) The maximum capacity of the bitset.
If this is not specified, then it is automatically calculated from the
passed iterable. It must be at least one.
OUTPUT:
- None.
The string representation of a :class:`FrozenBitset` ``FB`` can be
understood as follows. Let `B = b_0 b_1 b_2 \cdots b_k` be the string
representation of the bitset ``FB``, where each `b_i \in \{0, 1\}`. We
read the `b_i` from left to right. If `b_i = 1`, then the nonnegative
integer `i` is in the bitset ``FB``. Similarly, if `b_i = 0`, then `i`
is not in ``FB``. In other words, ``FB`` is a subset of
`\{0, 1, 2, \dots, k\}` and the membership in ``FB`` of each `i` is
determined by the binary value `b_i`.
.. seealso::
- :class:`Bitset`
- Python's `set types <http://docs.python.org/library/stdtypes.html#set-types-set-frozenset>`_
EXAMPLES:
The default bitset, which has capacity 1::
sage: FrozenBitset()
0
sage: FrozenBitset(None)
0
Trying to create an empty bitset fails::
sage: FrozenBitset([])
Traceback (most recent call last):
...
ValueError: Bitsets must not be empty
sage: FrozenBitset(list())
Traceback (most recent call last):
...
ValueError: Bitsets must not be empty
sage: FrozenBitset(())
Traceback (most recent call last):
...
ValueError: Bitsets must not be empty
sage: FrozenBitset(tuple())
Traceback (most recent call last):
...
ValueError: Bitsets must not be empty
sage: FrozenBitset("")
Traceback (most recent call last):
...
ValueError: Bitsets must not be empty
We can create the all-zero bitset as follows::
sage: FrozenBitset(capacity=10)
0000000000
sage: FrozenBitset([], capacity=10)
0000000000
We can initialize a :class:`FrozenBitset` with a :class:`Bitset` or
another :class:`FrozenBitset`, and compare them for equality. As they
are logically the same bitset, the equality test should return ``True``.
Furthermore, each bitset is a subset of the other. ::
sage: def bitcmp(a, b, c): # custom function for comparing bitsets
....: print(a == b == c)
....: print(a <= b, b <= c, a <= c)
....: print(a >= b, b >= c, a >= c)
....: print(a != b, b != c, a != c)
sage: a = Bitset("1010110"); b = FrozenBitset(a); c = FrozenBitset(b)
sage: a; b; c
1010110
1010110
1010110
sage: a < b, b < c, a < c
(False, False, False)
sage: a > b, b > c, a > c
(False, False, False)
sage: bitcmp(a, b, c)
True
(True, True, True)
(True, True, True)
(False, False, False)
Try a random bitset::
sage: a = Bitset(randint(0, 1) for n in range(1, randint(1, 10^4)))
sage: b = FrozenBitset(a); c = FrozenBitset(b)
sage: bitcmp(a, b, c)
True
(True, True, True)
(True, True, True)
(False, False, False)
A bitset with a hard-coded bitstring::
sage: FrozenBitset('101')
101
For a string, only those positions with ``1`` would be initialized to ``1``
in the corresponding position in the bitset. All other characters in the
string, including ``0``, are set to ``0`` in the resulting bitset. ::
sage: FrozenBitset('a')
0
sage: FrozenBitset('abc')
000
sage: FrozenBitset('abc1')
0001
sage: FrozenBitset('0abc1')
00001
sage: FrozenBitset('0abc10')
000010
sage: FrozenBitset('0a*c10')
000010
Represent the first 10 primes as a bitset. The primes are stored as a
list and as a tuple. We then recover the primes from its bitset
representation, and query the bitset for its length (how many elements
it contains) and whether an element is in the bitset. Note that the
length of a bitset is different from its capacity. The length counts
the number of elements currently in the bitset, while the capacity
is the number of elements that the bitset can hold. ::
sage: p = primes_first_n(10); p
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
sage: tuple(p)
(2, 3, 5, 7, 11, 13, 17, 19, 23, 29)
sage: F = FrozenBitset(p); F; FrozenBitset(tuple(p))
001101010001010001010001000001
001101010001010001010001000001
Recover the primes from the bitset::
sage: for b in F:
....: print b,
2 3 5 7 11 13 17 19 23 29
sage: list(F)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
Query the bitset::
sage: len(F)
10
sage: len(list(F))
10
sage: F.capacity()
30
sage: s = str(F); len(s)
30
sage: 2 in F
True
sage: 1 in F
False
A random iterable, with all duplicate elements removed::
sage: L = [randint(0, 100) for n in range(1, randint(1, 10^4))]
sage: FrozenBitset(L) == FrozenBitset(list(set(L)))
True
sage: FrozenBitset(tuple(L)) == FrozenBitset(tuple(set(L)))
True
TESTS:
Loading and dumping objects::
sage: a = FrozenBitset('1101')
sage: loads(dumps(a)) == a
True
sage: a = FrozenBitset('1101' * 64)
sage: loads(dumps(a)) == a
True
If ``iter`` is a nonempty string and ``capacity`` is specified, then
``capacity`` must match the number of elements in ``iter``::
sage: FrozenBitset("110110", capacity=3)
Traceback (most recent call last):
...
ValueError: bitset capacity does not match passed string
sage: FrozenBitset("110110", capacity=100)
Traceback (most recent call last):
...
ValueError: bitset capacity does not match passed string
The parameter ``capacity`` must be positive::
sage: FrozenBitset("110110", capacity=0)
Traceback (most recent call last):
...
ValueError: bitset capacity must be greater than 0
sage: FrozenBitset("110110", capacity=-2)
Traceback (most recent call last):
...
OverflowError: can't convert negative value to unsigned long
"""
def __cinit__(self, iter=None, capacity=None):
"""
Allocate the bitset.
See the class documentation of :class:`FrozenBitset` for details
on the parameters.
EXAMPLES::
sage: FrozenBitset('1101')
1101
sage: FrozenBitset('1101' * 32)
11011101110111011101110111011101110111011101110111011101110111011101110111011101110111011101110111011101110111011101110111011101
"""
if capacity is None:
bitset_init(self._bitset, 1)
else:
bitset_init(self._bitset, capacity)
def __dealloc__(self):
"""
Deallocate the C bitset data structure.
EXAMPLES::
sage: a = FrozenBitset('11010')
sage: del a
sage: b = FrozenBitset('11010' * 64)
sage: del b
"""
bitset_free(self._bitset)
def __init__(self, iter=None, capacity=None):
"""
Initialize a bitset.
See the class documentation of ``FrozenBitset`` for details on the
parameters.
EXAMPLES::
sage: FrozenBitset(capacity=3)
000
sage: FrozenBitset('11011')
11011
sage: FrozenBitset('110' * 32)
110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110
sage: FrozenBitset([0,3,2])
1011
sage: FrozenBitset(set([0,3,2]))
1011
sage: FrozenBitset(FrozenBitset('11011'))
11011
sage: FrozenBitset([0,3,2], capacity=10)
1011000000
sage: FrozenBitset([i for i in range(100) if i % 2 == 0])
101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
TESTS:
The capacity must be at least one::
sage: FrozenBitset()
0
If capacity is specified, it must match up with the
initialization items::
sage: FrozenBitset('10', capacity=3)
Traceback (most recent call last):
...
ValueError: bitset capacity does not match passed string
sage: FrozenBitset([0,3,2], capacity=2)
Traceback (most recent call last):
...
ValueError: bitset capacity does not allow storing the passed iterable
sage: FrozenBitset(FrozenBitset('1101'), capacity=2)
Traceback (most recent call last):
...
ValueError: bitset capacity does not match passed bitset
sage: FrozenBitset(FrozenBitset('1101'), capacity=5)
Traceback (most recent call last):
...
ValueError: bitset capacity does not match passed bitset
"""
cdef unsigned long n
cdef FrozenBitset b
if iter is not None and not isinstance(iter, (str, tuple, list, FrozenBitset, Bitset)):
iter = list(iter)
if iter is None:
bitset_clear(self._bitset)
elif isinstance(iter, (FrozenBitset, Bitset)):
b = iter
if capacity is None:
bitset_realloc(self._bitset, b._bitset.size)
elif self._bitset.size != b._bitset.size:
raise ValueError("bitset capacity does not match passed bitset")
bitset_copy(self._bitset, b._bitset)
elif isinstance(iter, str):
if len(iter) == 0:
raise ValueError("Bitsets must not be empty")
if capacity is None:
bitset_realloc(self._bitset, len(iter))
elif self._bitset.size != len(iter):
raise ValueError("bitset capacity does not match passed string")
bitset_from_str(self._bitset, iter)
else:
iter = list(iter)
if len(iter) > 0:
need_capacity = max(iter) + 1
else:
need_capacity = 0
if capacity is None:
if need_capacity == 0:
raise ValueError("Bitsets must not be empty")
bitset_realloc(self._bitset, need_capacity)
elif self._bitset.size < need_capacity:
raise ValueError("bitset capacity does not allow storing the passed iterable")
bitset_clear(self._bitset)
for n in iter:
bitset_add(self._bitset, n)
cdef FrozenBitset _new(self, long int capacity):
r"""
Return an object of the same type as ``self``, initialized with a
bitset of capacity ``capacity``.
"""
cdef FrozenBitset b
b = FrozenBitset.__new__(FrozenBitset, None, capacity)
return b
def __getstate__(self):
"""
Return the current state of the object as a string.
EXAMPLES::
sage: FrozenBitset('1101').__getstate__()
'1101'
sage: FrozenBitset('110'*32).__getstate__()
'110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110'
"""
return str(self)
def __setstate__(self, state):
"""
Set the state of the object from the string state.
EXAMPLES::
sage: a = FrozenBitset()
sage: a.__setstate__('1101')
sage: a
1101
sage: a.__setstate__('110'*32)
sage: a
110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110
"""
bitset_realloc(self._bitset, len(state))
bitset_from_str(self._bitset, state)
def __iter__(self):
"""
Return an iterator over ``self``.
EXAMPLES::
sage: list(FrozenBitset('11011'))
[0, 1, 3, 4]
sage: list(FrozenBitset('00001' * 20))
[4, 9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59, 64, 69, 74, 79, 84, 89, 94, 99]
sage: set(FrozenBitset('11011'))
set([0, 1, 3, 4])
"""
return iter(bitset_list(self._bitset))
cpdef FrozenBitset _larger_capacity_(self, long capacity):
"""
Return a copy of ``self`` where the bitset has the maximum of the
current capacity and the capacity passed. If no resizing is needed,
return ``self``.
This function is mainly used to satisfy the assumption of the
underlying bitset functions that all bitsets are of the same
capacity.
INPUT:
- ``capacity`` -- the underlying bitset of the returned bitset
will have this capacity if it is bigger than the current
capacity.
EXAMPLES::
sage: a = FrozenBitset('11010')
sage: a.capacity()
5
sage: a._larger_capacity_(4) is a
True
sage: a._larger_capacity_(5) is a
True
sage: b = a._larger_capacity_(6)
sage: b
110100
sage: b is a
False
sage: b.capacity()
6
sage: c = a._larger_capacity_(98)
sage: c
11010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
sage: c.capacity()
98
"""
cdef FrozenBitset temp
if self._bitset.size >= capacity:
return self
else:
temp = self._new(self._bitset.size)
bitset_copy(temp._bitset, self._bitset)
bitset_realloc(temp._bitset, capacity)
return temp
cpdef long capacity(self):
"""
Return the size of the underlying bitset.
The maximum value that can be stored in the current underlying
bitset is ``self.capacity() - 1``.
EXAMPLES::
sage: FrozenBitset('11000').capacity()
5
sage: FrozenBitset('110' * 32).capacity()
96
sage: FrozenBitset(range(20), capacity=450).capacity()
450
"""
return self._bitset.size
def __hash__(self):
"""
Return a hash value for a bitset.
EXAMPLES::
sage: hash(FrozenBitset(capacity=5))
0
sage: hash(FrozenBitset('10110'))
13
sage: hash(FrozenBitset('10110' + '0' * 120, capacity=125))
13
"""
cdef long hash
hash = bitset_hash(self._bitset)
if hash == -1:
return 0
else:
return hash
cpdef bint isempty(self):
"""
Test if the bitset is empty.
INPUT:
- None.
OUTPUT:
- ``True`` if the bitset is empty; ``False`` otherwise.
EXAMPLES::
sage: FrozenBitset().isempty()
True
sage: FrozenBitset([1]).isempty()
False
sage: FrozenBitset([], capacity=110).isempty()
True
sage: FrozenBitset(range(99)).isempty()
False
"""
return bitset_isempty(self._bitset)
def __richcmp__(FrozenBitset self, FrozenBitset other not None, int op):
"""
Implement comparisons, using the Cython richcmp convention.
Comparison is done by inclusion. That is, a set ``A`` is less than
another set ``B``, written ``A < B``, if ``A`` is a subset of ``B``.
EXAMPLES::
sage: FrozenBitset('11') < FrozenBitset('101')
False
sage: FrozenBitset('11') <= FrozenBitset('110')
True
sage: FrozenBitset('11') != FrozenBitset('10')
True
sage: FrozenBitset('11') == FrozenBitset('10')
False
sage: FrozenBitset('11') == FrozenBitset('110')
True
sage: FrozenBitset('11') > FrozenBitset('10')
True
sage: FrozenBitset('11') >= FrozenBitset('10')
True
sage: FrozenBitset('11') < FrozenBitset('110' * 32)
True
TESTS:
When performing comparison, ``other`` cannot be ``None``. ::
sage: F = FrozenBitset('11')
sage: F < None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: F <= None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: F > None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: F >= None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: F == None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: F != None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None < F
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None <= F
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None > F
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None >= F
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None == F
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None != F
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
"""
cdef FrozenBitset left, right
if self._bitset.size == other._bitset.size:
left = self
right = other
elif self._bitset.size < other._bitset.size:
left = self._larger_capacity_(other._bitset.size)
right = other
else:
left = self
right = other._larger_capacity_(self._bitset.size)
if op == 2:
return bitset_eq(left._bitset, right._bitset)
elif op == 3:
return not bitset_eq(left._bitset, right._bitset)
elif op == 0:
return bitset_issubset(left._bitset, right._bitset) and not bitset_eq(left._bitset, right._bitset)
elif op == 1:
return bitset_issubset(left._bitset, right._bitset)
elif op == 4:
return bitset_issuperset(left._bitset, right._bitset) and not bitset_eq(left._bitset, right._bitset)
elif op == 5:
return bitset_issuperset(left._bitset, right._bitset)
cpdef bint issubset(self, FrozenBitset other) except -1:
"""
Test to see if ``self`` is a subset of ``other``.
EXAMPLES::
sage: FrozenBitset('11').issubset(FrozenBitset('01'))
False
sage: FrozenBitset('01').issubset(FrozenBitset('11'))
True
sage: FrozenBitset('01').issubset(FrozenBitset('01' * 45))
True
TESTS::
sage: FrozenBitset('11').issubset(None)
Traceback (most recent call last):
...
ValueError: other cannot be None
"""
if other is None:
raise ValueError("other cannot be None")
cdef FrozenBitset left, right
if self._bitset.size == other._bitset.size:
left = self
right = other
elif self._bitset.size < other._bitset.size:
left = self._larger_capacity_(other._bitset.size)
right = other
else:
left = self
right = other._larger_capacity_(self._bitset.size)
return bitset_issubset(left._bitset, right._bitset)
cpdef bint issuperset(self, FrozenBitset other) except -1:
"""
Test to see if ``self`` is a superset of ``other``.
EXAMPLES::
sage: FrozenBitset('11').issuperset(FrozenBitset('01'))
True
sage: FrozenBitset('01').issuperset(FrozenBitset('11'))
False
sage: FrozenBitset('01').issuperset(FrozenBitset('10' * 45))
False
TESTS::
sage: FrozenBitset('11').issuperset(None)
Traceback (most recent call last):
...
ValueError: other cannot be None
"""
if other is None:
raise ValueError("other cannot be None")
cdef FrozenBitset left, right
if self._bitset.size == other._bitset.size:
left = self
right = other
elif self._bitset.size < other._bitset.size:
left = self._larger_capacity_(other._bitset.size)
right = other
else:
left = self
right = other._larger_capacity_(self._bitset.size)
return bitset_issuperset(left._bitset, right._bitset)
cpdef bint isdisjoint(self, FrozenBitset other) except -1:
"""
Test to see if ``self`` is disjoint from ``other``.
EXAMPLES::
sage: FrozenBitset('11').isdisjoint(FrozenBitset('01'))
False
sage: FrozenBitset('01').isdisjoint(FrozenBitset('001'))
True
sage: FrozenBitset('00101').isdisjoint(FrozenBitset('110' * 35))
False
TESTS::
sage: FrozenBitset('11').isdisjoint(None)
Traceback (most recent call last):
...
ValueError: other cannot be None
"""
cdef bint retval
if other is None:
raise ValueError("other cannot be None")
cdef FrozenBitset smaller, larger
cdef bitset_t temp
if self._bitset.size == other._bitset.size:
bitset_init(temp, self._bitset.size)
bitset_intersection(temp, self._bitset, other._bitset)
retval = bitset_isempty(temp)
bitset_free(temp)
return retval
elif self._bitset.size < other._bitset.size:
smaller = self
larger = other
else:
smaller = other
larger = self
bitset_init(temp, smaller._bitset.size)
bitset_copy(temp, smaller._bitset)
bitset_realloc(temp, larger._bitset.size)
bitset_intersection(temp, temp, larger._bitset)
retval = bitset_isempty(temp)
bitset_free(temp)
return retval
def __contains__(self, unsigned long n):
"""
Test to see if ``n`` is in ``self``.
EXAMPLES::
sage: 0 in FrozenBitset([0,1])
True
sage: 0 in FrozenBitset([1,2])
False
sage: 10 in FrozenBitset([0,1])
False
sage: 121 in FrozenBitset('110' * 50)
True
sage: 122 in FrozenBitset('110' * 50)
False
TESTS::
sage: None in FrozenBitset([0,1])
Traceback (most recent call last):
...
TypeError: an integer is required
"""
if n < self._bitset.size:
return bitset_in(self._bitset, n)
else:
return False
def __len__(self):
"""
Return the number of elements in the bitset (which may be
different from the capacity of the bitset).
EXAMPLES::
sage: len(FrozenBitset([0,1], capacity=10))
2
sage: len(FrozenBitset(range(98)))
98
"""
return bitset_len(self._bitset)
def __str__(self):
"""
Return a string representing the bitset as a binary vector.
EXAMPLES::
sage: a = FrozenBitset('10110')
sage: str(a)
'10110'
sage: str(FrozenBitset('110' * 32))
'110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110'
"""
return bitset_string(self._bitset)
def __repr__(self):
"""
Return a string representing the bitset as a binary vector.
EXAMPLES::
sage: a = FrozenBitset('10110')
sage: repr(a)
'10110'
sage: repr(FrozenBitset('110' * 32))
'110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110'
"""
return self.__str__()
cpdef _union(self, FrozenBitset other):
"""
Return the union of ``self`` and ``other``.
In order to get a Cython "union" function, we have to use the
underscore since "union" is a C keyword.
EXAMPLES::
sage: FrozenBitset('10101')._union(FrozenBitset('11100'))
11101
sage: FrozenBitset('10101' * 10)._union(FrozenBitset('01010' * 10))
11111111111111111111111111111111111111111111111111
TESTS::
sage: set(FrozenBitset('10101' * 10)._union(FrozenBitset('01010' * 10))) == set(FrozenBitset('10101' * 10)).union(FrozenBitset('01010' * 10))
True
sage: set(FrozenBitset('10101')._union(FrozenBitset('01010' * 20))) == set(FrozenBitset('10101')).union(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20)._union(FrozenBitset('01010'))) == set(FrozenBitset('10101' * 20)).union(FrozenBitset('01010'))
True
sage: FrozenBitset('10101' * 10)._union(None)
Traceback (most recent call last):
...
ValueError: other cannot be None
"""
if other is None:
raise ValueError("other cannot be None")
cdef FrozenBitset temp, smaller, larger
if self._bitset.size <= other._bitset.size:
smaller = self
larger = other
else:
smaller = other
larger = self
temp = self._new(smaller._bitset.size)
bitset_copy(temp._bitset, smaller._bitset)
bitset_realloc(temp._bitset, larger._bitset.size)
bitset_union(temp._bitset, temp._bitset, larger._bitset)
return temp
def union(self, FrozenBitset other):
"""
Return the union of ``self`` and ``other``.
EXAMPLES::
sage: FrozenBitset('10101').union(FrozenBitset('11100'))
11101
sage: FrozenBitset('10101' * 10).union(FrozenBitset('01010' * 10))
11111111111111111111111111111111111111111111111111
TESTS::
sage: set(FrozenBitset('10101' * 10).union(FrozenBitset('01010' * 10))) == set(FrozenBitset('10101' * 10)).union(FrozenBitset('01010' * 10))
True
sage: set(FrozenBitset('10101').union(FrozenBitset('01010' * 20))) == set(FrozenBitset('10101')).union(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20).union(FrozenBitset('01010'))) == set(FrozenBitset('10101' * 20)).union(FrozenBitset('01010'))
True
sage: FrozenBitset('10101' * 10).union(None)
Traceback (most recent call last):
...
ValueError: other cannot be None
"""
return self._union(other)
def __or__(self, FrozenBitset other not None):
"""
Return the union of ``self`` and ``other``.
EXAMPLES::
sage: FrozenBitset('10101') | FrozenBitset('11100')
11101
sage: FrozenBitset('10101' * 10) | FrozenBitset('01010' * 10)
11111111111111111111111111111111111111111111111111
TESTS::
sage: set(FrozenBitset('10101' * 10) | FrozenBitset('01010' * 10)) == set(FrozenBitset('10101' * 10)) | set(FrozenBitset('01010' * 10))
True
sage: set(FrozenBitset('10101') | FrozenBitset('01010' * 20)) == set(FrozenBitset('10101')) | set(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20) | FrozenBitset('01010')) == set(FrozenBitset('10101' * 20)) | set(FrozenBitset('01010'))
True
sage: FrozenBitset('10101') | None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None | FrozenBitset('10101')
Traceback (most recent call last):
...
AttributeError: 'NoneType' object has no attribute '_union'
"""
return self._union(other)
cpdef intersection(self, FrozenBitset other):
"""
Return the intersection of ``self`` and ``other``.
EXAMPLES::
sage: FrozenBitset('10101').intersection(FrozenBitset('11100'))
10100
sage: FrozenBitset('11111' * 10).intersection(FrozenBitset('010101' * 10))
010101010101010101010101010101010101010101010101010000000000
TESTS::
sage: set(FrozenBitset('11111' * 10).intersection(FrozenBitset('010101' * 10))) == set(FrozenBitset('11111' * 10)).intersection(FrozenBitset('010101' * 10))
True
sage: set(FrozenBitset('1' * 5).intersection(FrozenBitset('01010' * 20))) == set(FrozenBitset('1' * 5)).intersection(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20).intersection(FrozenBitset('1' * 5))) == set(FrozenBitset('10101' * 20)).intersection(FrozenBitset('1' * 5))
True
sage: FrozenBitset("101011").intersection(None)
Traceback (most recent call last):
...
ValueError: other cannot be None
"""
if other is None:
raise ValueError("other cannot be None")
cdef FrozenBitset temp, smaller, larger
if self._bitset.size <= other._bitset.size:
smaller = self
larger = other
else:
smaller = other
larger = self
temp = self._new(smaller._bitset.size)
bitset_copy(temp._bitset, smaller._bitset)
bitset_realloc(temp._bitset, larger._bitset.size)
bitset_intersection(temp._bitset, temp._bitset, larger._bitset)
return temp
def __and__(self, FrozenBitset other not None):
"""
Return the intersection of ``self`` and ``other``.
EXAMPLES::
sage: FrozenBitset('10101') & FrozenBitset('11100')
10100
sage: FrozenBitset('11111' * 10) & FrozenBitset('010101' * 10)
010101010101010101010101010101010101010101010101010000000000
TESTS::
sage: set(FrozenBitset('11111' * 10) & FrozenBitset('010101' * 10)) == set(FrozenBitset('11111' * 10)) & set(FrozenBitset('010101' * 10))
True
sage: set(FrozenBitset('1' * 5) & FrozenBitset('01010' * 20)) == set(FrozenBitset('1' * 5)) & set(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20) & FrozenBitset('1' * 5)) == set(FrozenBitset('10101' * 20)) & set(FrozenBitset('1' * 5))
True
sage: FrozenBitset("101011") & None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None & FrozenBitset("101011")
Traceback (most recent call last):
...
AttributeError: 'NoneType' object has no attribute 'intersection'
"""
return self.intersection(other)
cpdef difference(self, FrozenBitset other):
"""
Return the difference of ``self`` and ``other``.
EXAMPLES::
sage: FrozenBitset('10101').difference(FrozenBitset('11100'))
00001
sage: FrozenBitset('11111' * 10).difference(FrozenBitset('010101' * 10))
101010101010101010101010101010101010101010101010100000000000
TESTS::
sage: set(FrozenBitset('11111' * 10).difference(FrozenBitset('010101' * 10))) == set(FrozenBitset('11111' * 10)).difference(FrozenBitset('010101' * 10))
True
sage: set(FrozenBitset('1' * 5).difference(FrozenBitset('01010' * 20))) == set(FrozenBitset('1' * 5)).difference(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20).difference(FrozenBitset('1' * 5))) == set(FrozenBitset('10101' * 20)).difference(FrozenBitset('1' * 5))
True
sage: FrozenBitset('10101').difference(None)
Traceback (most recent call last):
...
ValueError: other cannot be None
"""
if other is None:
raise ValueError("other cannot be None")
cdef FrozenBitset temp = self._new(self._bitset.size)
bitset_copy(temp._bitset, self._bitset)
if temp._bitset.size == other._bitset.size:
bitset_difference(temp._bitset, temp._bitset, other._bitset)
elif temp._bitset.size < other._bitset.size:
bitset_realloc(temp._bitset, other._bitset.size)
bitset_difference(temp._bitset, temp._bitset, other._bitset)
else:
bitset_difference(temp._bitset, temp._bitset, other._larger_capacity_(temp._bitset.size)._bitset)
return temp
def __sub__(self, FrozenBitset other not None):
"""
Return the difference of ``self`` and ``other``.
EXAMPLES::
sage: FrozenBitset('10101') - FrozenBitset('11100')
00001
sage: FrozenBitset('11111' * 10)-FrozenBitset('010101' * 10)
101010101010101010101010101010101010101010101010100000000000
TESTS::
sage: set(FrozenBitset('11111' * 10)-FrozenBitset('010101' * 10)) == set(FrozenBitset('11111' * 10))-set(FrozenBitset('010101' * 10))
True
sage: set(FrozenBitset('1' * 5)-FrozenBitset('01010' * 20)) == set(FrozenBitset('1' * 5))-set(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20)-FrozenBitset('1' * 5)) == set(FrozenBitset('10101' * 20))-set(FrozenBitset('1' * 5))
True
sage: FrozenBitset('10101') - None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None - FrozenBitset('10101')
Traceback (most recent call last):
...
AttributeError: 'NoneType' object has no attribute 'difference'
"""
return self.difference(other)
cpdef symmetric_difference(self, FrozenBitset other):
"""
Return the symmetric difference of ``self`` and ``other``.
EXAMPLES::
sage: FrozenBitset('10101').symmetric_difference(FrozenBitset('11100'))
01001
sage: FrozenBitset('11111' * 10).symmetric_difference(FrozenBitset('010101' * 10))
101010101010101010101010101010101010101010101010100101010101
TESTS::
sage: set(FrozenBitset('11111' * 10).symmetric_difference(FrozenBitset('010101' * 10))) == set(FrozenBitset('11111' * 10)).symmetric_difference(FrozenBitset('010101' * 10))
True
sage: set(FrozenBitset('1' * 5).symmetric_difference(FrozenBitset('01010' * 20))) == set(FrozenBitset('1' * 5)).symmetric_difference(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20).symmetric_difference(FrozenBitset('1' * 5))) == set(FrozenBitset('10101' * 20)).symmetric_difference(FrozenBitset('1' * 5))
True
sage: FrozenBitset('11111' * 10).symmetric_difference(None)
Traceback (most recent call last):
...
ValueError: other cannot be None
"""
if other is None:
raise ValueError("other cannot be None")
cdef FrozenBitset temp, smaller, larger
if self._bitset.size <= other._bitset.size:
smaller = self
larger = other
else:
smaller = other
larger = self
temp = self._new(smaller._bitset.size)
bitset_copy(temp._bitset, smaller._bitset)
bitset_realloc(temp._bitset, larger._bitset.size)
bitset_symmetric_difference(temp._bitset, temp._bitset, larger._bitset)
return temp
def __xor__(self, FrozenBitset other not None):
"""
Return the symmetric difference of ``self`` and ``other``.
Note that because of the Sage preprocessor, in Sage, ``^^`` is the
exclusive or, rather than ``^``.
EXAMPLES::
sage: FrozenBitset('10101') ^^ FrozenBitset('11100')
01001
sage: FrozenBitset('11111' * 10) ^^ FrozenBitset('010101' * 10)
101010101010101010101010101010101010101010101010100101010101
TESTS::
sage: set(FrozenBitset('11111' * 10) ^^ FrozenBitset('010101' * 10)) == set(FrozenBitset('11111' * 10)) ^^ set(FrozenBitset('010101' * 10))
True
sage: set(FrozenBitset('1' * 5) ^^ FrozenBitset('01010' * 20)) == set(FrozenBitset('1' * 5)) ^^ set(FrozenBitset('01010' * 20))
True
sage: set(FrozenBitset('10101' * 20) ^^ FrozenBitset('1' * 5)) == set(FrozenBitset('10101' * 20)) ^^ set(FrozenBitset('1' * 5))
True
sage: FrozenBitset('11111' * 10) ^^ None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None ^^ FrozenBitset('11111' * 10)
Traceback (most recent call last):
...
AttributeError: 'NoneType' object has no attribute 'symmetric_difference'
"""
return self.symmetric_difference(other)
cpdef complement(self):
"""
Return the complement of self.
EXAMPLES::
sage: ~FrozenBitset('10101')
01010
sage: ~FrozenBitset('11111'*10)
00000000000000000000000000000000000000000000000000
sage: x = FrozenBitset('10'*40)
sage: x == ~x
False
sage: x == ~~x
True
sage: x|(~x) == FrozenBitset('11'*40)
True
sage: ~x == FrozenBitset('01'*40)
True
"""
cdef FrozenBitset temp = self._new(self._bitset.size)
bitset_complement(temp._bitset, self._bitset)
return temp
def __invert__(self):
"""
Return the complement of self.
EXAMPLES::
sage: ~FrozenBitset('10101')
01010
sage: ~FrozenBitset('11111'*10)
00000000000000000000000000000000000000000000000000
sage: x = FrozenBitset('10'*40)
sage: x == ~x
False
sage: x == ~~x
True
sage: x|(~x) == FrozenBitset('11'*40)
True
sage: ~x == FrozenBitset('01'*40)
True
"""
return self.complement()
cpdef __copy__(self):
"""
Return ``self`` (since ``self`` is immutable).
EXAMPLES::
sage: a = FrozenBitset('10101')
sage: from copy import copy
sage: b = copy(a)
sage: b is a
True
sage: c = FrozenBitset('1010' * 32)
sage: d = copy(c)
sage: d is c
True
"""
return self
cdef class Bitset(FrozenBitset):
r"""
A bitset class which leverages inline Cython functions for creating
and manipulating bitsets. See the class documentation of
:class:`FrozenBitset` for details on the parameters of the constructor
and how to interpret the string representation of a :class:`Bitset`.
A bitset can be thought of in two ways. First, as a set of elements
from the universe of the `n` natural numbers `0, 1, \dots, n-1` (where
the capacity `n` can be specified), with typical set operations such as
intersection, union, symmetric difference, etc. Secondly, a bitset can
be thought of as a binary vector with typical binary operations such as
``and``, ``or``, ``xor``, etc. This class supports both interfaces.
The interface in this class mirrors the interface in the ``set``
data type of Python.
.. warning::
This class is most likely to be useful as a way to store
Cython bitsets in Python data structures, acting on them using
the Cython inline functions. If you want to use this class
for a Python set type, the Python ``set`` data type may be
faster.
.. seealso::
- :class:`FrozenBitset`
- Python's `set types <http://docs.python.org/library/stdtypes.html#set-types-set-frozenset>`_
EXAMPLES::
sage: a = Bitset('1101')
sage: loads(dumps(a)) == a
True
sage: a = Bitset('1101' * 32)
sage: loads(dumps(a)) == a
True
"""
cpdef __copy__(self):
"""
Return a copy of ``self``.
EXAMPLES::
sage: a = Bitset('10101')
sage: from copy import copy
sage: b = copy(a)
sage: b is a
False
sage: b == a
True
sage: c = Bitset('1010' * 32)
sage: d = copy(c)
sage: d is c
False
sage: d == c
True
"""
cdef FrozenBitset temp = self._new(self._bitset.size)
bitset_copy(temp._bitset, self._bitset)
return temp
def __hash__(self):
"""
Raise an error, since mutable ``Bitset``s are not hashable.
EXAMPLE::
sage: hash(Bitset('110'))
Traceback (most recent call last):
...
TypeError: Bitset objects are unhashable; use FrozenBitset
"""
raise TypeError("Bitset objects are unhashable; use FrozenBitset")
def __richcmp__(FrozenBitset self, FrozenBitset other not None, int op):
"""
Implement comparisons, using the Cython richcmp convention.
Comparison is done by inclusion. That is, a set ``A`` is less than
another set ``B``, written ``A < B``, if ``A`` is a subset of ``B``.
EXAMPLES::
sage: Bitset('11') < Bitset('101')
False
sage: Bitset('11') <= Bitset('110')
True
sage: Bitset('11') != Bitset('10')
True
sage: Bitset('11') == Bitset('10')
False
sage: Bitset('11') == Bitset('110')
True
sage: Bitset('11') > Bitset('10')
True
sage: Bitset('11') >= Bitset('10')
True
sage: FrozenBitset('11') < FrozenBitset('110' * 32)
True
TESTS:
During comparison, ``other`` cannot be ``None``. ::
sage: Bitset('11') < None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: Bitset('11') <= None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: Bitset('11') > None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: Bitset('11') >= None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: Bitset('11') == None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: Bitset('11') != None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None < Bitset('11')
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None <= Bitset('11')
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None > Bitset('11')
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None >= Bitset('11')
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None == Bitset('11')
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
sage: None != Bitset('11')
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
"""
cdef FrozenBitset left, right
if self._bitset.size == other._bitset.size:
left = self
right = other
elif self._bitset.size < other._bitset.size:
left = self._larger_capacity_(other._bitset.size)
right = other
else:
left = self
right = other._larger_capacity_(self._bitset.size)
if op == 2:
return bitset_eq(left._bitset, right._bitset)
elif op == 3:
return not bitset_eq(left._bitset, right._bitset)
elif op == 0:
return bitset_issubset(left._bitset, right._bitset) and not bitset_eq(left._bitset, right._bitset)
elif op == 1:
return bitset_issubset(left._bitset, right._bitset)
elif op == 4:
return bitset_issuperset(left._bitset, right._bitset) and not bitset_eq(left._bitset, right._bitset)
elif op == 5:
return bitset_issuperset(left._bitset, right._bitset)
cdef FrozenBitset _new(self, long int capacity):
"""
Return an object of the same type as ``self``, initialized with a
bitset of capacity ``capacity``.
"""
cdef Bitset b
b = Bitset.__new__(Bitset, None, capacity)
return b
cpdef update(self, FrozenBitset other):
"""
Update the bitset to include items in ``other``.
EXAMPLES::
sage: a = Bitset('110')
sage: a.update(Bitset('0101'))
sage: a
1101
sage: a_set = set(a)
sage: a.update(Bitset('00011' * 25))
sage: a
11011000110001100011000110001100011000110001100011000110001100011000110001100011000110001100011000110001100011000110001100011
sage: a_set.update(Bitset('00011' * 25))
sage: set(a) == a_set
True
TESTS:
During update, ``other`` cannot be ``None``. ::
sage: a = Bitset('1101')
sage: a.update(None)
Traceback (most recent call last):
...
TypeError: other cannot be None
"""
if other is None:
raise TypeError("other cannot be None")
cdef bitset_t temp
if self._bitset.size == other._bitset.size:
bitset_union(self._bitset, self._bitset, other._bitset)
elif self._bitset.size < other._bitset.size:
bitset_realloc(self._bitset, other._bitset.size)
bitset_union(self._bitset, self._bitset, other._bitset)
else:
bitset_init(temp, other._bitset.size)
bitset_copy(temp, other._bitset)
bitset_realloc(temp, self._bitset.size)
bitset_union(self._bitset, self._bitset, temp)
bitset_free(temp)
def __ior__(self, FrozenBitset other not None):
"""
Update the bitset to include items in ``other``.
EXAMPLES::
sage: a = Bitset('110')
sage: a |= Bitset('0101')
sage: a
1101
sage: a_set = set(a)
sage: a |= Bitset('00011' * 25)
sage: a
11011000110001100011000110001100011000110001100011000110001100011000110001100011000110001100011000110001100011000110001100011
sage: a_set |= set(Bitset('00011' * 25))
sage: set(a) == a_set
True
TESTS::
sage: a = Bitset('110')
sage: a |= None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
"""
self.update(other)
return self
cpdef intersection_update(self, FrozenBitset other):
"""
Update the bitset to the intersection of ``self`` and ``other``.
EXAMPLES::
sage: a = Bitset('110')
sage: a.intersection_update(Bitset('0101'))
sage: a
0100
sage: a_set = set(a)
sage: a.intersection_update(Bitset('0110' * 25))
sage: a
0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
sage: a_set.intersection_update(Bitset('0110' * 25))
sage: set(a) == a_set
True
TESTS::
sage: Bitset('110').intersection_update(None)
Traceback (most recent call last):
...
TypeError: other cannot be None
"""
if other is None:
raise TypeError("other cannot be None")
cdef bitset_t temp
if self._bitset.size == other._bitset.size:
bitset_intersection(self._bitset, self._bitset, other._bitset)
elif self._bitset.size < other._bitset.size:
bitset_realloc(self._bitset, other._bitset.size)
bitset_intersection(self._bitset, self._bitset, other._bitset)
else:
bitset_init(temp, other._bitset.size)
bitset_copy(temp, other._bitset)
bitset_realloc(temp, self._bitset.size)
bitset_intersection(self._bitset, self._bitset, temp)
bitset_free(temp)
def __iand__(self, FrozenBitset other not None):
"""
Update the bitset to the intersection of ``self`` and ``other``.
EXAMPLES::
sage: a = Bitset('110')
sage: a &= Bitset('0101')
sage: a
0100
sage: a_set = set(a)
sage: a &= Bitset('0110' * 25)
sage: a
0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
sage: a_set &= set(Bitset('0110' * 25))
sage: a_set == set(a)
True
TESTS::
sage: a = Bitset('110')
sage: a &= None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
"""
self.intersection_update(other)
return self
cpdef difference_update(self, FrozenBitset other):
"""
Update the bitset to the difference of ``self`` and ``other``.
EXAMPLES::
sage: a = Bitset('110')
sage: a.difference_update(Bitset('0101'))
sage: a
1000
sage: a_set = set(a)
sage: a.difference_update(FrozenBitset('010101' * 10)); a
100000000000000000000000000000000000000000000000000000000000
sage: a_set.difference_update(FrozenBitset('010101' * 10))
sage: a_set == set(a)
True
sage: a.difference_update(FrozenBitset('110'))
sage: a_set.difference_update(FrozenBitset('110'))
sage: a_set == set(a)
True
sage: a.difference_update(FrozenBitset('01010' * 20)); a
0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
sage: a_set.difference_update(FrozenBitset('01010' * 20))
sage: a_set == set(a)
True
sage: b = Bitset('10101' * 20)
sage: b_set = set(b)
sage: b.difference_update(FrozenBitset('1' * 5)); b
0000010101101011010110101101011010110101101011010110101101011010110101101011010110101101011010110101
sage: b_set.difference_update(FrozenBitset('1' * 5))
sage: b_set == set(b)
True
TESTS::
sage: Bitset('110').difference_update(None)
Traceback (most recent call last):
...
TypeError: other cannot be None
"""
if other is None:
raise TypeError("other cannot be None")
cdef bitset_t temp
if self._bitset.size == other._bitset.size:
bitset_difference(self._bitset, self._bitset, other._bitset)
elif self._bitset.size < other._bitset.size:
bitset_realloc(self._bitset, other._bitset.size)
bitset_difference(self._bitset, self._bitset, other._bitset)
else:
bitset_init(temp, other._bitset.size)
bitset_copy(temp, other._bitset)
bitset_realloc(temp, self._bitset.size)
bitset_difference(self._bitset, self._bitset, temp)
bitset_free(temp)
def __isub__(self, FrozenBitset other not None):
"""
Update the bitset to the difference of ``self`` and ``other``.
EXAMPLES::
sage: a = Bitset('110')
sage: a -= Bitset('0101')
sage: a
1000
sage: a_set = set(a)
sage: a -= FrozenBitset('010101' * 10); a
100000000000000000000000000000000000000000000000000000000000
sage: a_set -= set(FrozenBitset('010101' * 10))
sage: a_set == set(a)
True
sage: a = Bitset('110')
sage: a_set = set(a)
sage: a -= FrozenBitset('01010' * 20); a
1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
sage: a_set -= set(FrozenBitset('01010' * 20))
sage: a_set == set(a)
True
sage: b = FrozenBitset('10101' * 20)
sage: b_set = set(b)
sage: b -= FrozenBitset('1' * 5); b
0000010101101011010110101101011010110101101011010110101101011010110101101011010110101101011010110101
sage: b_set -= FrozenBitset('1' * 5)
sage: b_set == set(b)
True
TESTS::
sage: a = Bitset('110')
sage: a -= None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
"""
self.difference_update(other)
return self
cpdef symmetric_difference_update(self, FrozenBitset other):
"""
Update the bitset to the symmetric difference of ``self`` and
``other``.
EXAMPLES::
sage: a = Bitset('110')
sage: a.symmetric_difference_update(Bitset('0101'))
sage: a
1001
sage: a_set = set(a)
sage: a.symmetric_difference_update(FrozenBitset('010101' * 10)); a
110001010101010101010101010101010101010101010101010101010101
sage: a_set.symmetric_difference_update(FrozenBitset('010101' * 10))
sage: a_set == set(a)
True
sage: a.symmetric_difference_update(FrozenBitset('01010' * 20)); a
1001011111000001111100000111110000011111000001111100000111110101001010010100101001010010100101001010
sage: a_set.symmetric_difference_update(FrozenBitset('01010' * 20))
sage: a_set == set(a)
True
sage: b = Bitset('10101' * 20)
sage: b_set = set(b)
sage: b.symmetric_difference_update( FrozenBitset('1' * 5)); b
0101010101101011010110101101011010110101101011010110101101011010110101101011010110101101011010110101
sage: b_set.symmetric_difference_update( FrozenBitset('1' * 5))
sage: b_set == set(b)
True
TESTS::
sage: Bitset('110').symmetric_difference_update(None)
Traceback (most recent call last):
...
TypeError: other cannot be None
"""
if other is None:
raise TypeError("other cannot be None")
cdef bitset_t temp
if self._bitset.size == other._bitset.size:
bitset_symmetric_difference(self._bitset, self._bitset, other._bitset)
elif self._bitset.size < other._bitset.size:
bitset_realloc(self._bitset, other._bitset.size)
bitset_symmetric_difference(self._bitset, self._bitset, other._bitset)
else:
bitset_init(temp, other._bitset.size)
bitset_copy(temp, other._bitset)
bitset_realloc(temp, self._bitset.size)
bitset_symmetric_difference(self._bitset, self._bitset, temp)
bitset_free(temp)
def __ixor__(self, FrozenBitset other not None):
"""
Update the bitset to the symmetric difference of ``self`` and
``other``.
EXAMPLES::
sage: a = Bitset('110')
sage: a ^^=Bitset('0101')
sage: a
1001
sage: a_set = set(a)
sage: a ^^= FrozenBitset('010101' * 10); a
110001010101010101010101010101010101010101010101010101010101
sage: a_set ^^= set(FrozenBitset('010101' * 10))
sage: a_set == set(a)
True
sage: a ^^= FrozenBitset('01010' * 20); a
1001011111000001111100000111110000011111000001111100000111110101001010010100101001010010100101001010
sage: a_set ^^= set(FrozenBitset('01010' * 20))
sage: a_set == set(a)
True
sage: b = Bitset('10101' * 20)
sage: b_set = set(b)
sage: b ^^= FrozenBitset('1' * 5); b
0101010101101011010110101101011010110101101011010110101101011010110101101011010110101101011010110101
sage: b_set ^^= set(FrozenBitset('1' * 5))
sage: b_set == set(b)
True
TESTS::
sage: a = Bitset('110')
sage: a ^^= None
Traceback (most recent call last):
...
TypeError: Argument 'other' has incorrect type (expected sage.misc.bitset.FrozenBitset, got NoneType)
"""
self.symmetric_difference_update(other)
return self
cpdef add(self, unsigned long n):
"""
Update the bitset by adding ``n``.
EXAMPLES::
sage: a = Bitset('110')
sage: a.add(5)
sage: a
110001
sage: a.add(100)
sage: sorted(list(a))
[0, 1, 5, 100]
sage: a.capacity()
101
TESTS:
The input ``n`` must be an integer. ::
sage: Bitset('110').add(None)
Traceback (most recent call last):
...
TypeError: an integer is required
"""
if n >= self._bitset.size:
bitset_realloc(self._bitset, n + 1)
bitset_add(self._bitset, n)
cpdef remove(self, unsigned long n):
"""
Update the bitset by removing ``n``. Raises ``KeyError`` if ``n`` is
not contained in the bitset.
EXAMPLES::
sage: a = Bitset('110')
sage: a.remove(1)
sage: a
100
sage: a.remove(2)
Traceback (most recent call last):
...
KeyError: 2L
sage: a.remove(4)
Traceback (most recent call last):
...
KeyError: 4L
sage: a
100
sage: a = Bitset('000001' * 15); sorted(list(a))
[5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89]
sage: a.remove(83); sorted(list(a))
[5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 89]
TESTS:
The input ``n`` must be an integer. ::
sage: Bitset('110').remove(None)
Traceback (most recent call last):
...
TypeError: an integer is required
"""
if n >= self._bitset.size:
raise KeyError(n)
else:
bitset_remove(self._bitset, n)
cpdef discard(self, unsigned long n):
"""
Update the bitset by removing ``n``.
EXAMPLES::
sage: a = Bitset('110')
sage: a.discard(1)
sage: a
100
sage: a.discard(2)
sage: a.discard(4)
sage: a
100
sage: a = Bitset('000001' * 15); sorted(list(a))
[5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 83, 89]
sage: a.discard(83); sorted(list(a))
[5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 89]
sage: a.discard(82); sorted(list(a))
[5, 11, 17, 23, 29, 35, 41, 47, 53, 59, 65, 71, 77, 89]
TESTS:
The input ``n`` must be an integer. ::
sage: Bitset('110').discard(None)
Traceback (most recent call last):
...
TypeError: an integer is required
"""
if n < self._bitset.size:
bitset_discard(self._bitset, n)
cpdef pop(self):
"""
Remove and return an arbitrary element from the set. Raises
``KeyError`` if the set is empty.
EXAMPLES::
sage: a = Bitset('011')
sage: a.pop()
1
sage: a
001
sage: a.pop()
2
sage: a
000
sage: a.pop()
Traceback (most recent call last):
...
KeyError: 'pop from an empty set'
sage: a = Bitset('0001'*32)
sage: a.pop()
3
sage: [a.pop() for _ in range(20)]
[7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59, 63, 67, 71, 75, 79, 83]
"""
return bitset_pop(self._bitset)
cpdef clear(self):
"""
Removes all elements from the bitset.
EXAMPLES::
sage: a = Bitset('011')
sage: a.clear()
sage: a
000
sage: a = Bitset('011' * 32)
sage: a.clear()
sage: set(a)
set([])
"""
bitset_clear(self._bitset)
def test_bitset(py_a, py_b, long n):
"""
Test the Cython bitset functions so we can have some relevant doctests.
TESTS::
sage: from sage.misc.bitset import test_bitset
sage: test_bitset('00101', '01110', 4)
a 00101
list a [2, 4]
a.size 5
len(a) 2
a.limbs 1
b 01110
a.in(n) True
a.not_in(n) False
a.add(n) 00101
a.discard(n) 00100
a.set_to(n) 00101
a.flip(n) 00100
a.set_first_n(n) 11110
a.first_in_complement() 4
a.isempty() False
a.eq(b) False
a.cmp(b) 1
a.lex_cmp(b) -1
a.issubset(b) False
a.issuperset(b) False
a.copy() 00101
r.clear() 00000
complement a 11010
a intersect b 00100
a union b 01111
a minus b 00001
a symmetric_difference b 01011
a.rshift(n) 10000
a.lshift(n) 00000
a.first() 2
a.next(n) 4
a.first_diff(b) 1
a.next_diff(b, n) 4
a.hamming_weight() 2
a.map(m) 10100
a == loads(dumps(a)) True
reallocating a 00101
to size 4 0010
to size 8 00100000
to original size 00100
::
sage: test_bitset('11101', '11001', 2)
a 11101
list a [0, 1, 2, 4]
a.size 5
len(a) 4
a.limbs 1
b 11001
a.in(n) True
a.not_in(n) False
a.add(n) 11101
a.discard(n) 11001
a.set_to(n) 11101
a.flip(n) 11001
a.set_first_n(n) 11000
a.first_in_complement() 2
a.isempty() False
a.eq(b) False
a.cmp(b) 1
a.lex_cmp(b) 1
a.issubset(b) False
a.issuperset(b) True
a.copy() 11101
r.clear() 00000
complement a 00010
a intersect b 11001
a union b 11101
a minus b 00100
a symmetric_difference b 00100
a.rshift(n) 10100
a.lshift(n) 00111
a.first() 0
a.next(n) 2
a.first_diff(b) 2
a.next_diff(b, n) 2
a.hamming_weight() 4
a.map(m) 10111
a == loads(dumps(a)) True
reallocating a 11101
to size 2 11
to size 4 1100
to original size 11000
Test a corner-case: a bitset that is a multiple of words::
sage: test_bitset('00'*64, '01'*64, 127)
a 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
list a []
a.size 128
len(a) 0
a.limbs ...
b 01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
a.in(n) False
a.not_in(n) True
a.add(n) 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
a.discard(n) 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
a.set_to(n) 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
a.flip(n) 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
a.set_first_n(n) 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110
a.first_in_complement() 127
a.isempty() True
a.eq(b) False
a.cmp(b) -1
a.lex_cmp(b) -1
a.issubset(b) True
a.issuperset(b) False
a.copy() 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
r.clear() 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
complement a 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
a intersect b 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
a union b 01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
a minus b 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
a symmetric_difference b 01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101
a.rshift(n) 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
a.lshift(n) 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
a.first() -1
a.next(n) -1
a.first_diff(b) 1
a.next_diff(b, n) 127
a.hamming_weight() 0
a.map(m) 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
a == loads(dumps(a)) True
rshifts add True
lshifts add True
intersection commutes True
union commutes True
not not = id True
flipped bit 127
add bit 127
discard bit 127
lshift add unset ok True
rshift set unset ok True
reallocating a 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
to size 127 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
to size 254 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
to original size 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Large enough to span multiple limbs. We don't explicitly check the number of limbs below because it will be different in the 32 bit versus 64 bit cases::
sage: test_bitset('111001'*25, RealField(151)(pi).str(2)[2:], 69)
a 111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001
list a [0, 1, 2, 5, 6, 7, 8, 11, 12, 13, 14, 17, 18, 19, 20, 23, 24, 25, 26, 29, 30, 31, 32, 35, 36, 37, 38, 41, 42, 43, 44, 47, 48, 49, 50, 53, 54, 55, 56, 59, 60, 61, 62, 65, 66, 67, 68, 71, 72, 73, 74, 77, 78, 79, 80, 83, 84, 85, 86, 89, 90, 91, 92, 95, 96, 97, 98, 101, 102, 103, 104, 107, 108, 109, 110, 113, 114, 115, 116, 119, 120, 121, 122, 125, 126, 127, 128, 131, 132, 133, 134, 137, 138, 139, 140, 143, 144, 145, 146, 149]
a.size 150
len(a) 100
a.limbs ...
b 000100100001111110110101010001000100001011010001100001000110100110001001100011001100010100010111000000011011100000111001101000100101001000000100100111
a.in(n) False
a.not_in(n) True
a.add(n) 111001111001111001111001111001111001111001111001111001111001111001111101111001111001111001111001111001111001111001111001111001111001111001111001111001
a.discard(n) 111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001
a.set_to(n) 111001111001111001111001111001111001111001111001111001111001111001111101111001111001111001111001111001111001111001111001111001111001111001111001111001
a.flip(n) 111001111001111001111001111001111001111001111001111001111001111001111101111001111001111001111001111001111001111001111001111001111001111001111001111001
a.set_first_n(n) 111111111111111111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000
a.first_in_complement() 69
a.isempty() False
a.eq(b) False
a.cmp(b) -1
a.lex_cmp(b) 1
a.issubset(b) False
a.issuperset(b) False
a.copy() 111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001
r.clear() 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
complement a 000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110000110
a intersect b 000000100001111000110001010001000000001001010001100001000000100000001001100001001000010000010001000000011001100000111001101000100001001000000000100001
a union b 111101111001111111111101111001111101111011111001111001111111111111111001111011111101111101111111111001111011111001111001111001111101111001111101111111
a minus b 111001011000000001001000101000111001110000101000011000111001011001110000011000110001101001101000111001100000011001000000010001011000110001111001011000
a symmetric_difference b 111101011000000111001100101000111101110010101000011000111111011111110000011010110101101101101110111001100010011001000000010001011100110001111101011110
a.rshift(n) 001111001111001111001111001111001111001111001111001111001111001111001111001111001000000000000000000000000000000000000000000000000000000000000000000000
a.lshift(n) 000000000000000000000000000000000000000000000000000000000000000000000111001111001111001111001111001111001111001111001111001111001111001111001111001111
a.first() 0
a.next(n) 71
a.first_diff(b) 0
a.next_diff(b, n) 73
a.hamming_weight() 100
a.map(m) 100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111100111
a == loads(dumps(a)) True
rshifts add True
lshifts add True
intersection commutes True
union commutes True
not not = id True
flipped bit 69
add bit 69
discard bit 69
lshift add unset ok True
rshift set unset ok True
reallocating a 111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001111001
to size 69 111001111001111001111001111001111001111001111001111001111001111001111
to size 138 111001111001111001111001111001111001111001111001111001111001111001111000000000000000000000000000000000000000000000000000000000000000000000
to original size 111001111001111001111001111001111001111001111001111001111001111001111000000000000000000000000000000000000000000000000000000000000000000000000000000000
"""
cdef bint bit = True
cdef bitset_t a, b, r
bitset_from_str(a, py_a)
bitset_from_str(b, py_b)
if a.size != b.size:
raise ValueError("inputs must have same size")
print "a", bitset_string(a)
print "list a", bitset_list(a)
print "a.size", a.size
print "len(a)", bitset_len(a)
print "a.limbs", a.limbs
print "b", bitset_string(b)
print "a.in(n) ", bitset_in(a, n)
print "a.not_in(n) ", bitset_not_in(a, n)
bitset_add(a, n)
print "a.add(n) ", bitset_string(a)
bitset_from_str(a, py_a)
bitset_discard(a, n)
print "a.discard(n) ", bitset_string(a)
bitset_from_str(a, py_a)
bitset_set_to(a, n, bit)
print "a.set_to(n) ", bitset_string(a)
bitset_from_str(a, py_a)
bitset_flip(a, n)
print "a.flip(n) ", bitset_string(a)
bitset_set_first_n(a, n)
print "a.set_first_n(n) ", bitset_string(a)
print "a.first_in_complement() ", bitset_first_in_complement(a)
bitset_from_str(a, py_a)
bitset_from_str(b, py_b)
print "a.isempty() ", bitset_isempty(a)
print "a.eq(b) ", bitset_eq(a, b)
print "a.cmp(b) ", bitset_cmp(a, b)
print "a.lex_cmp(b)", bitset_lex_cmp(a, b)
print "a.issubset(b)", bitset_issubset(a, b)
print "a.issuperset(b)", bitset_issuperset(a, b)
bitset_from_str(a, py_a)
bitset_from_str(b, py_b)
bitset_init(r, a.size)
bitset_copy(r, a)
print "a.copy() ", bitset_string(r)
bitset_clear(r)
print "r.clear() ", bitset_string(r)
bitset_complement(r, a)
print "complement a ", bitset_string(r)
bitset_intersection(r, a, b)
print "a intersect b ", bitset_string(r)
bitset_union(r, a, b)
print "a union b ", bitset_string(r)
bitset_difference(r, a, b)
print "a minus b ", bitset_string(r)
bitset_symmetric_difference(r, a, b)
print "a symmetric_difference b ", bitset_string(r)
bitset_rshift(r, a, n)
print "a.rshift(n) ", bitset_string(r)
bitset_lshift(r, a, n)
print "a.lshift(n) ", bitset_string(r)
print "a.first() ", bitset_first(a)
print "a.next(n) ", bitset_next(a, n)
print "a.first_diff(b) ", bitset_first_diff(a, b)
print "a.next_diff(b, n) ", bitset_next_diff(a, b, n)
print "a.hamming_weight() ", bitset_hamming_weight(a)
morphism = {}
for i in xrange(a.size):
morphism[i] = a.size - i - 1
bitset_map(r, a, morphism)
print "a.map(m) ", bitset_string(r)
data = bitset_pickle(a)
bitset_unpickle(r, data)
print "a == loads(dumps(a)) ", bitset_eq(r, a)
cdef bitset_t s
bitset_init(s, a.size)
if a.size > 100:
bitset_rshift(r, b, 3)
bitset_rshift(r, r, 77)
bitset_rshift(s, b, 80)
print "rshifts add ", bitset_eq(s, r)
bitset_lshift(r, b, 69)
bitset_lshift(r, r, 6)
bitset_lshift(s, b, 75)
print "lshifts add ", bitset_eq(s, r)
bitset_intersection(r, a, b)
bitset_intersection(s, b, a)
print "intersection commutes", bitset_eq(s, r)
bitset_union(r, a, b)
bitset_union(s, b, a)
print "union commutes ", bitset_eq(s, r)
bitset_complement(r, b)
bitset_complement(s, r)
print "not not = id", bitset_eq(s, b)
bitset_copy(r, b)
bitset_flip(r, n)
print "flipped bit ", bitset_first_diff(b, r)
bitset_clear(r)
bitset_add(r, n)
print "add bit ", bitset_first(r)
bitset_clear(r)
bitset_complement(r, r)
bitset_discard(r, n)
bitset_complement(r, r)
print "discard bit ", bitset_first(r)
bitset_clear(r)
bitset_add(r, 10)
bitset_lshift(r, r, 68)
bitset_flip(r, 78)
print "lshift add unset ok", bitset_isempty(r)
bitset_clear(r)
bitset_add(r, 19)
bitset_rshift(r, r, 8)
bitset_discard(r, 11)
print "rshift set unset ok", bitset_isempty(r)
print "reallocating a ", bitset_string(a)
bitset_realloc(a, n)
print "to size %d " % n, bitset_string(a)
bitset_realloc(a, 2 * n)
print "to size %d " % (2 * n), bitset_string(a)
bitset_realloc(a, b.size)
print "to original size ", bitset_string(a)
bitset_free(a)
bitset_free(b)
bitset_free(r)
bitset_free(s)
def test_bitset_set_first_n(py_a, long n):
"""
Test the bitset function set_first_n.
TESTS::
sage: from sage.misc.bitset import test_bitset_set_first_n
sage: test_bitset_set_first_n('00'*64, 128)
a.set_first_n(n) 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
"""
cdef bint bit = True
cdef bitset_t a
bitset_from_str(a, py_a)
bitset_set_first_n(a, n)
print "a.set_first_n(n) ", bitset_string(a)
bitset_free(a)
def test_bitset_remove(py_a, long n):
"""
Test the bitset_remove function.
TESTS::
sage: from sage.misc.bitset import test_bitset_remove
sage: test_bitset_remove('01', 0)
Traceback (most recent call last):
...
KeyError: 0L
sage: test_bitset_remove('01', 1)
a 01
a.size 2
a.limbs 1
n 1
a.remove(n) 00
"""
cdef bitset_t a
bitset_from_str(a, py_a)
print "a", bitset_string(a)
print "a.size", a.size
print "a.limbs", a.limbs
print "n", n
bitset_remove(a, n)
print "a.remove(n) ", bitset_string(a)
bitset_free(a)
def test_bitset_pop(py_a):
"""
Tests for the bitset_pop function.
TESTS::
sage: from sage.misc.bitset import test_bitset_pop
sage: test_bitset_pop('0101')
a.pop() 1
new set: 0001
sage: test_bitset_pop('0000')
Traceback (most recent call last):
...
KeyError: 'pop from an empty set'
"""
cdef bitset_t a
bitset_from_str(a, py_a)
i = bitset_pop(a)
print "a.pop() ", i
print "new set: ", bitset_string(a)
bitset_free(a)
def test_bitset_unpickle(data):
"""
This (artificially) tests pickling of bitsets across systems.
INPUT:
- ``data`` -- A tuple of data as would be produced by the internal, Cython-only, method ``bitset_pickle``.
OUTPUT:
A list form of the bitset corresponding to the pickled data.
EXAMPLES:
We compare 64-bit and 32-bit encoding. Both should unpickle on any system::
sage: from sage.misc.bitset import test_bitset_unpickle
sage: test_bitset_unpickle((0, 100, 2, 8, (33, 6001)))
[0, 5, 64, 68, 69, 70, 72, 73, 74, 76]
sage: test_bitset_unpickle((0, 100, 4, 4, (33, 0, 6001, 0)))
[0, 5, 64, 68, 69, 70, 72, 73, 74, 76]
"""
cdef bitset_t bs
bitset_init(bs, 1)
bitset_unpickle(bs, data)
L = bitset_list(bs)
bitset_free(bs)
return L
