Algorithms and Data Structures

N.Wirth. Algorithms and Data Structures. Oberon version 23
data structures. However, it should be possible to indicate the desirability of packing at least in those cases
in which more than one component would fit into a single word, i.e., when a gain of storage economy by a
factor of 2 and more could be achieved. We propose the convention to indicate the desirability of packing
by prefixing the symbol ARRAY (or RECORD) in the declaration by the symbol PACKED.
1.6.2 Representation of Records
Records are mapped onto a computer store by simply juxtaposing their components. The address of a
component (field) r i relative to the origin address of the record r is called the field's offset k i . It is computed
as
k i = s 1 + s 2 + ... + s i-1 k 0 = 0
where s j is the size (in words) of the j-th component. We now realize that the fact that all components of an
array are of equal type has the welcome consequence that k i = i × s. The generality of the record
structure does unfortunately not allow such a simple, linear function for offset address computation, and it is
therefore the very reason for the requirement that record components be selectable only by fixed
identifiers. This restriction has the desirable benefit that the respective offsets are known at compile time.
The resulting greater efficiency of record field access is well-known.
The technique of packing may be beneficial, if several record components can be fitted into a single
storage word (see Fig. 1.7). Since offsets are computable by the compiler, the offset of a field packed
within a word may also be determined by the compiler. This means that on many computers packing of
records causes a deterioration in access efficiency considerably smaller than that caused by the packing of
arrays.
s 1
s 2 s 3
s 4
padded
s 5
s 6 s 7 s 8
Fig. 1.7. Representation of a packed record
1.6.3 Representation of Sets
A set s is conveniently represented in a computer store by its characteristic function C(s). This is an
array of logical values whose ith component has the meaning "i is present in s". As an example, the set of
small integers s = {2, 3, 5, 7, 11, 13} is represented by the sequence of bits, by a bitstring:
C(s) = (… 0010100010101100)
The representation of sets by their characteristic function has the advantage that the operations of
computing the union, intersection, and difference of two sets may be implemented as elementary logical
operations. The following equivalences, which hold for all elements i of the base type of the sets x and y,
relate logical operations with operations on sets:
i IN (x+y) = (i IN x) OR (i IN y)
i IN (x*y) = (i IN x) & (i IN y)
i IN (x-y) = (i IN x) & ~(i IN y)