SETS(2) SETS(2)
NAME
Sets - sets of non-negative integers
SYNOPSIS
include "sets.m";
OR include "sets32.m";
sets := load Sets Sets->PATH;
A, B: import Sets;
Sets: adt {
init: fn();
set: fn(): Set;
str2set: fn(str: string): Set;
bytes2set: fn(d: array of byte): Set;
Set: adt {
# opaque data
X: fn(s1: self Set, op: int, s2: Set): Set;
add: fn(s: self Set, n: int): Set;
addlist: fn(s: self Set, ns: list of int): Set;
del: fn(s: self Set, n: int): Set;
invert: fn(s: self Set): Set;
eq: fn(s1: self Set, s2: Set): int;
holds: fn(s: self Set, n: int): int;
isempty: fn(s: self Set): int;
msb: fn(s: self Set): int;
limit: fn(s: self Set): int;
str: fn(s: self Set): string;
bytes: fn(s: self Set, n: int): array of byte;
};
};
DESCRIPTION
The Sets module provides routines for manipulating sets of
small non-negative integers. There are currently two imple-
mentations available: the implementation declared in
sets32.m stores sets of numbers from 0 to 31 inclusive; the
implementation in sets.m stores arbitrary sets of non-
negative integers. The description given is for the more
general implementation; behaviour of the other is undefined
if an integer higher than 31 is used.
Init must be called first, to allow Sets to initialise its
internal state. Set returns a new set, containing nothing.
Str2set converts a string to a new set; the string should
have been created with Set.str(). Bytes2set converts an
array of bytes, d, as returned by Set.bytes(), to a new set.
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SETS(2) SETS(2)
Note that all set operations are copy operations; none
change an existing set.
s1.X(op, s2)
Returns a new set, the result of combining s1 and
s2 according to boolean operator op. Op can be any
bitwise boolean combination of the two constants A
and B, defined in the module. Notionally, each set
is an infinitely long string of bits, each bit
representing a non-negative integer: zero if the
integer is present, and one if absent. For each
corresponding bit in s1 and s2, X sets a corre-
sponding bit in the returned set according to the
calculation s1 op s2.
s.add(n) Returns the set s with n added.
s.addlist(ns)
Addlist is the same as calling add on each member
of the list ns, but somewhat more efficient.
s.del(n) Returns s with n removed.
s.invert()
Invert returns a set holding all non-negative
integers other than those already in s. Hence
set().invert() holds all non-negative integers.
s1.eq(s2) Returns non-zero if s1 is identical to s2.
s.holds(n)
Returns non-zero if s holds n as a member.
s.isempty()
Returns non-zero if s holds no members.
s.msb() Returns the "most significant bit": the membership
status of all members that have not been explic-
itly set. For example, set().msb() is 0;
set().invert().msb() is 1.
s.limit() If s.msb() is zero, s.limit() returns one more
than the largest member contained in s, otherwise
it returns one more than the largest member not
contained in s. Thus set().limit() yields 0, and
set().invert().del(5).limit() yields 6.
s.str() Returns a string corresponding to s. The format is
hexdigits:msb, where hexdigits give the least sig-
nificant members of the set, most significant on
the left, in hexadecimal format; msb gives the
padding bit that fills the rest of the set. Note
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SETS(2) SETS(2)
that this format is compatible between the two
implementations.
s.bytes(n)
Returns a packed byte representaton of s . The
array is held in little-endian order, with the
topmost bit of the top byte holding the msb of the
set. The array returned will contain at least n
bytes.
EXAMPLES
Given two sets, s1 and s2, s1.X(A&B, s2) gives their inter-
section; s1.X(A|B, s2) their union; s1.X(A&~B, s2) gives the
set of all members of s1 that aren't in s2; s1.X(~(A|B), s2)
gives the set of all integers in neither s1 nor s2.
sys->print("%s\n", set().addlist(1::2::5::nil)
.invert().X(A|B, set().add(2)).str());
produces the string ``dd:1'', corresponding to the set of
all non-negative integers except 1 and 5.
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