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.
-
class
sage.data_structures.bitset.
Bitset
¶ Bases:
sage.data_structures.bitset.FrozenBitset
A bitset class which leverages inline Cython functions for creating and manipulating bitsets. See the class documentation of
FrozenBitset
for details on the parameters of the constructor and how to interpret the string representation of aBitset
.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.See also
FrozenBitset
- Python’s set types
EXAMPLES:
sage: a = Bitset('1101') sage: loads(dumps(a)) == a True sage: a = Bitset('1101' * 32) sage: loads(dumps(a)) == a True
-
add
(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
-
clear
()¶ 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()
-
difference_update
(other)¶ Update the bitset to the difference of
self
andother
.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
-
discard
(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
-
intersection_update
(other)¶ Update the bitset to the intersection of
self
andother
.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
-
pop
()¶ 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]
-
remove
(n)¶ Update the bitset by removing
n
. RaisesKeyError
ifn
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
-
symmetric_difference_update
(other)¶ Update the bitset to the symmetric difference of
self
andother
.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
-
update
(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 beNone
.sage: a = Bitset('1101') sage: a.update(None) Traceback (most recent call last): ... TypeError: other cannot be None
-
class
sage.data_structures.bitset.
FrozenBitset
¶ Bases:
object
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 for more details on Python’sset
andfrozenset
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:Bitset
andFrozenBitset
– If this is aBitset
orFrozenBitset
, then it is copied.None
– IfNone
, 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 aValueError
. - 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
FrozenBitset
FB
can be understood as follows. Let \(B = b_0 b_1 b_2 \cdots b_k\) be the string representation of the bitsetFB
, 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 bitsetFB
. Similarly, if \(b_i = 0\), then \(i\) is not inFB
. In other words,FB
is a subset of \(\{0, 1, 2, \dots, k\}\) and the membership inFB
of each \(i\) is determined by the binary value \(b_i\).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
FrozenBitset
with aBitset
or anotherFrozenBitset
, and compare them for equality. As they are logically the same bitset, the equality test should returnTrue
. 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 to1
in the corresponding position in the bitset. All other characters in the string, including0
, are set to0
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 ... 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 andcapacity
is specified, thencapacity
must match the number of elements initer
: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 mp_bitcnt_t
-
capacity
()¶ 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
-
complement
()¶ 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
-
difference
(other)¶ Return the difference of
self
andother
.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
-
intersection
(other)¶ Return the intersection of
self
andother
.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
-
isdisjoint
(other)¶ Test to see if
self
is disjoint fromother
.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
-
isempty
()¶ 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
-
issubset
(other)¶ Test to see if
self
is a subset ofother
.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
-
issuperset
(other)¶ Test to see if
self
is a superset ofother
.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
-
symmetric_difference
(other)¶ Return the symmetric difference of
self
andother
.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
-
union
(other)¶ Return the union of
self
andother
.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
-
sage.data_structures.bitset.
test_bitset
(py_a, py_b, n)¶ Test the Cython bitset functions so we can have some relevant doctests.
TESTS:
sage: from sage.data_structures.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
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sage.data_structures.bitset.
test_bitset_pop
(py_a)¶ Tests for the bitset_pop function.
TESTS:
sage: from sage.data_structures.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'
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sage.data_structures.bitset.
test_bitset_remove
(py_a, n)¶ Test the bitset_remove function.
TESTS:
sage: from sage.data_structures.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
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sage.data_structures.bitset.
test_bitset_set_first_n
(py_a, n)¶ Test the bitset function set_first_n.
TESTS:
sage: from sage.data_structures.bitset import test_bitset_set_first_n sage: test_bitset_set_first_n('00'*64, 128) a.set_first_n(n) 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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sage.data_structures.bitset.
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, methodbitset_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.data_structures.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]