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 implementations 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.

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 corresponding 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 explicitly 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 significant 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 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 intersection; 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());