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AD…tMtZMIII9wI9vULH1DH1ҹ҉!HIº1뀃HMHu HcyIHLX(fDH&H_H5H8xE1E1H+t Imu3fHCLD$HP0ImLD$uIELD$LP0LD$I.uIFLD$LP0LD$MtI,$uID$LD$LP0LD$MtI(u I@LP0E1H:_H5H8#xH+uE1E1HCHP0MuDE1vIHtHH{HHt]H(LaH@P0UH+tE1+H+qE1xI;|Ir>|IeL[IwfBf2f"ffATIUHHHH5^H9t ztH^HLH]A\鍓DHLH]A\ATIUHHHH5]H9t ZztH]HLH]A\-DHLH]A\QATIUHHHH5T]H9t ytH7]HLH]A\͒DHLH]A\ATUHHxvHtEIHt HHpHHtH(uH@P0HL]A\I,$u ID$LP0E1HL]A\UH HHHHHdH%(HD$1IH$wA1EtH4$1HhtHT$dH+%(uH]tff.fATIUHH8HH5\dH%(HD$(1H9t xI|$H5.\Hl$Ld$H9t rxtfHT$H5RH*vHEHH|$L9tHtH/uHWHD$R0HD$HT$(dH+%(uzH8]A\CsHD$HtHLHHtH(nH@P0b1fHD$(dH+%(uH8LH]A\s@SHtHtHX(H[ff.@UHH HV HvdH%(HD$1D$vH$HtHH5FDD U GBD JAB<hEDG T CAH D FAE RDA0\izBAD G@  AABE j\XX H O<j(PjZFAD \ ABF <|(kFDD C DBI [ DBG NDBDk~MAD l DBD NDBDP GDB k ؀> E[ H E C L<BBB B(A0A8G 8 8D0A(B BBBA dEJ0~ AB 4<FAF U HBD oAE4BHD _ ABH \AE| (FBE D(G@ (A BBBD c (A BBBF o (C BBBH o (A BBBJ Z(C BBB8e@tBIB A(D0GP 0A(A BBBA ЋUHBBB B(A0F8G` 8A0A(B BBBF HDYBBE B(A0D8Dp< 8A0A(B BBBF LԐaBBE B(A0C8D\ 8D0A(B BBBA (^EDD G AAA  (,HY G L(<FBB B(D0C8J 8A0A(B BBBJ xܚ8BBD  BBC o BBE 4؛>FDD0 DBJ t CBG qE[ J AA 8 some kind of bitset Internal function used to form a bitset when unpickling. It is designed to be 'safe' with any data but may give strange results if given something else than what x.__reduce__() generated.immbitset() -> empty immutable bitset immbitset(bitset) -> immutable bitset with bitset's bits immbitset(iterable) -> immutable bitset with iterable's bits (int items) immbitset(integer) -> immutable bitset with integer's bits (binary 2-complement) Return an immutable bitset. It will be complemented if the argument is a complemented bitset or a negative integer. If the argument is an immutable bitset, the result is the same object. immbitrange([start,] stop[, step]) -> immutable bitset Return an immutable bitset containing an arithmetic progression of integers. immbitrange(i, j) equals immbitset([i, i+1, i+2, ..., j-1]). Start defaults to 0. If step is given, it specifies a positive increment. For example, immbitrange(3) equals immbitset([0, 1, 2]).immbit(bit) -> immutable bitset Return an immutable bitset containing the single bit specified. The bit must be an integer in the range of an int.S.tac(e) -> bool Test and Clear. If e is in S, remove e from S and return True, else return False.S.tas(e) -> bool Test and Set. If e is in S return True, else add e to S and return False.S.remove(e) Remove e from S, or raise ValueError if e was not in S.S.pop() -> object Remove and return some object from S, or raise ValueError if S was empty.S.discard(e) Remove e from S; no effect if e was not in S.S.clear() Remove all elements from S, and compact its storage.S.append(e) Add e to S, or raise ValueError if e was already in S.S.add(e) Add e to S; no effect if e was already in S.x.obj_at(address) Return the object in x that is at a specified address, if any, otherwise raise ValueErrorImmBitSet() -> empty immutable bitset ImmBitSet(bitset) -> immutable bitset with bitset's bits ImmBitSet(iterable) -> immutable bitset with iterable's bits (int items) ImmBitSet(integer) -> immutable bitset with integer's bits (binary 2-complement) The result can only be non-complemented; TypeError is raised otherwise. (The function immbitset() can be used to create both complemented and non-complemented bitsets.) An immutable bitset provides the operations common for all bitsets as described for the BitSet base class. It also defines the following: hash(x) -> int Return a hash value based on the bit numbers of the elements. MutNodeSet([iterable]) Return a new mutable nodeset with elements from iterable. A mutable nodeset inherits the operations defined for NodeSet. It also supports the following methods: add, append, clear, discard, pop, remove, tac, tas. ImmNodeSet([iterable]) Return a new immutable nodeset with elements from iterable. An immutable nodeset inherits the operations defined for NodeSet. It also supports the following operation: hash(x) -> int Return a hash value based on the addresses of the elements.S.is_immutable == True True since S is immutable.The class BitSet is the base class for all bitset classes. A bitset is a set of 'bits'. Bits are integers, in a range that is typically [-2**31 .. 2**31-1] or the range of the builtin Python int type. The implementation of bitsets is such that it handles dense sets the most efficiently while sparse sets are handled reasonably well. Bitsets can be either mutable or immutable. Mutable bitsets have various operations to add and remove bits in-place. Immutable bitsets have hashing so they can be used as keys in dicts. Both kinds of bitsets have several operations in common. Sometimes an operand can be either a bitset or a 'convertible', which means it is one of the following kinds. iterable An iterable argument is convertible to a bitset if each object yielded is an integer in the range of an int. int A positive argument, x, of one of these types will be converted to a bitset with the same bits as the binary representation of x. A negative argument will be converted to a complemented bitset, equivalent to the following expression: ~immbitset(~x) This corresponds to the bits in the 2-complement binary representation of x, except that the result conceptually has all negative bits set. The difference shows (only) when shifting a complemented bitset. The following operations are common for mutable and immutable bitsets. ------------------------------------------ Standard binary operations. In the usual case the left argument is some kind of bitset, and the right argument is a bitset or a 'convertible' as defined above. The return value is then an immutable bitset. x & y -> Intersection: the set of bits that are in both x and y. x | y -> Union: the set of bits that are in either x or y. x ^ y -> Symmetric difference: the set of bits that are in exactly one of x and y. x - y -> Difference: the set of bits that are in x but not in y. If the right argument is a bitset but not the left argument, the result will be an immutable bitset if only the left argument is a convertible that does not define the same operation; otherwise the result is what is returned by the operation of the left argument or a TypeError will be raised. The following table gives the result for the different kinds of arguments. Left argument Right argument Result - - - - - - - - - - - - - - - - - - - - - - - - - - - - - bitset bitset immutable bitset bitset convertible immutable bitset bitset other TypeError defining the same op bitset handled by left argument convertible bitset immutable bitset other bitset TypeError ------------------------------------------ In-place binary operations. The left argument must be a bitset. If it is mutable, it is updated in place and returned. If it is immutable, the result is a new immutable bitset. The right argument is a bitset or a convertible. x &= y -> Intersection x |= y -> Union x ^= y -> Symmetric difference x -= y -> Difference ------------------------------------------ Complement operation. ~x -> immutable bitset Return the complement of x. This is a bitset that, conceptually, contains all bits in the universe except the ones in x. [ Subtle If x is not already complemented, ~x will return a special complemented kind of set. This can be used like other bitsets except for two operations that are not supported: it is not possible to iterate over, or take the length of a complemented bitset. If x is a complemented bitset, ~x returns a non-complemented bitset. Mutable bitsets may become complemented in-place if given a complemented argument to a suitable in-place operation. This is represented by a flag. Immutable complemented bitsets are represented by a special type, but this is to be considered an implementation detail, it could as well be using a flag. ] ------------------------------------------ Shift operation. x << y -> immutable bitset Return the set of bits of x, with the integer y added to each one. Raise OverflowError if some bit would exceed the range of an int. [ Subtle For non-complemented x and positive y, the result is what one would expect if x was a number in binary representation. But when x is complemented, the result will equal ~((~x) << y) which is different from what one would expect from binary number shifting, since 1's are shifted in from the right. The operation allows both positive or negative y values, unlike the shift for integer objects. For negative y's, the operation will shift bits to the right but not quite in the same way as a binary integer right-shift operation would do it, because the low bits will not disappear but be shifted towards negative bits. ] ------------------------------------------ Inclusion test. The left argument is an integer in the range of an int. The right argument is a bitset. x in y -> bool True if x is an element of y, False otherwise. ------------------------------------------ Relational operations. These return a boolean value. The left argument is a bitset. The right argument is a bitset. If the right argument is another type, TypeError will be raised. (This restriction may be reconsidered in the future.) x == y -> Equal: x and y contain the same bits. x != y -> Not equal: x and y do not contain the same bits. x <= y -> Subset, non-strict: all bits in x are also in y. x < y -> Subset, strict: all bits in x are also in y, and y contains some bits not in x. x >= y -> Superset, non-strict: all bits in y are also in x. x > y -> Superset, strict: all bits in y are also in x, and x contains some bit not in y. ------------------------------------------ Iteration. iter(x) -> iterator The iterator yields the bits of x. Raises TypeError if x is complemented. [The order is implementation dependent.] ------------------------------------------ Length. len(x) -> int Return the number of bits in x. Raises TypeError if x is complemented. ------------------------------------------ Truth-value testing. bool(x) -> bool Return True if x is not empty, False otherwise. ------------------------------------------ Conversions. int(x) -> int Return an integer having the same binary representation as the bits of x, or raise an exception if the bitset can not be represented in the choosen type. When no exception is raised, the bitset x can be exactly recreated and the following invariants will hold. immbitset(int(x)) == x The exception OverflowError will be raised if it is found that x can not be represented. Note that for a sparse bitset with high bit numbers, int(x) may create a very big object since it allocates storage for all the low bits up to the highest bit number set, unlike bitsets that use a sparse representation. Creating such big objects may run out of storage which may raise a MemoryError or cause some other malfunction depending on the system. ------------------------------------------ Mutable copy S.mutcopy() -> mutable bitset Return a mutable copy of S. S.is_immutable == False False since S is not immmutable.S.tac(e) -> bool Test and Clear. If e is in S, remove e from S and return True, else return False.S.tas(e) -> bool Test and Set. If e is in S return True, else add e to S and return False.S.mutcopy() -> mutable bitset Return a mutable copy of S. S.remove(e) Remove e from S, or raise ValueError if e was not in S.S.pop([index]) -> int Remove and return a bit, or raise ValueError if there is no bit to pop. The index must be -1 (default) to pop the highest bit or 0 to pop the lowest bit; otherwise IndexError will be raised.S.discard(e) Remove e from S; no effect if e was not in S.S.clear() Remove all elements from S, and compact its storage.S.append(e) Add e to S, or raise ValueError if e was already in S.S.add(e) Add e to S; no effect if e was already in S The class NodeSet is the base class for ImmNodeSet and MutNodeSet. A nodeset is a set of objects with equality based on heap address. The following operations are defined for both mutable and immutable nodesets. ------------------------------------------ Binary operations. The following operations all return an immutable nodeset. The left argument must be a nodeset. The right argument can be any iterable object. x & y -> Intersection: the set of objects that are in both x and y. x | y -> Union: the set of objects that are in either x or y. x ^ y -> Symmetric difference: the set of objects that are in exactly one of x and y. x - y -> Difference: the set of objects that are in x but not in y. ------------------------------------------ In-place binary operations. The left argument can be mutable or immutable. If it is mutable, it is updated in place and returned. If it is immutable, the result is a new immutable nodeset. The right argument can be any iterable object. x &= y -> Intersection x |= y -> Union x ^= y -> Symmetric difference x -= y -> Difference ------------------------------------------ Inclusion test. The left argument can be any object. The right argument is a nodeset. x in y -> bool True if x is an element of y, False otherwise. ------------------------------------------ Relational operations. These return a boolean value. The left argument is a nodeset. The right argument is a nodeset. If the right argument is another type, TypeError will be raised. (This may be relaxed in future.) x == y -> Equal: x and y contain the same elements. x != y -> Not equal: x and y do not contain the same elements. x <= y -> Subset, non-strict: all elements in x are also in y. x < y -> Subset, strict: all elements in x are also in y, and y contains some element not in x. x >= y -> Superset, non-strict: all elements in y are also in x. x > y -> Superset, strict: all elements in y are also in x, and x contains some element not in y. ------------------------------------------ Iteration. iter(x) -> iterator The iterator yields the elements of x. [The order is implementation dependent.] ------------------------------------------ Length. len(x) -> int Return the number of elements in x. ------------------------------------------ Truth-value testing. bool(x) -> bool Return True if x is not empty, False otherwise. CplBitSet(x:ImmBitSet) -> complemented immutable bitset. If the argument is an instance of ImmBitSet, this is the same as ~x, otherwise TypeError is raised. A complemented immutable bitset provides the same operations as non-complemented immutable bitsets, except for len() and iter(). MutBitSet() -> new empty mutable bitset MutBitSet(bitset) -> new mutable bitset with bitset's bits MutBitSet(iterable) -> new mutable bitset with iterable's bits (int items) MutBitSet(integer) -> new mutable bitset with integer's bits (binary 2-complement) A mutable bitset has operations common for all bitsets as described for the BitSet base class. It also defines the following methods: add, append, clear, discard, pop, remove, tac, tas This module implements two specialized kinds of sets, 'bitsets' and 'nodesets'. Bitsets are sets of 'bits' -- here meaning integers in a particular range -- and designed to be efficient with dense as well as sparse distributions. Nodesets are sets of 'nodes', i.e. objects with equality based on their address; this makes inclusion test work with any combination of objects independently from how equality or hashing has been defined for the objects involved. Summary of module content. Classes BitSet Abstract bitset base class. CplBitSet Complemented immutable bitset. ImmBitSet Immutable bitset, non-complemented. MutBitSet Mutable bitset, complemented or not. NodeSet Abstract nodeset base class. ImmNodeSet Immutable nodeset. MutNodeSet Mutable nodeset. Functions immbit Immutable bitset singleton constructor. immbitrange Immutable bitset range constructor. immbitset Immutable bitset constructor. 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