II. Notes on Data Structuring * - Cornell University

130 c.A.R. HOARE
end
end primefinder
begin next. w" -- next. w + 1 ;
if next. w > W then exit primefinder
end;
next. b: = min (sieve [next. w]);
primes [next. w]: v {next. b );
,
n" = next,
while n. w ~< W do
begin sieve [n. w]: - {n. b );
end
n.b: = n.b + next.b;
n.w: = n.w + next.w;
if n.b >~ wordlength then
beginn.w'= n.w +l;
n. b: = n. b - wordlength
end
One feature of this program is that it uses an environment enquiry word-
length to achieve the full efficiency of which a machine is capable, and yet
does so in a completely machine-independent fashion. The program will not
only work, but work with high efficiency, on machines with widely varying
word lengths.
But the most interesting feature about the program is the way in which
it is related to the previous version. From an abstract point of view it
expresses an identical algorithm; all that has changed is the manner in which
the data has been represented on the computer. The original design acted as
a framework or pattern, on which the more intricate coding of the second
version was structured. By carrying out the design in two stages, we simplify
the task of ensuring that each part of the finalprogram works successfully
in conjunction with the other parts.
Exercise
Rewrite the program using sets representing only the odd numbers. (Hint:
rewrite the more abstract program first.)
8. THE SEQUENCE
The previous chapters have dealt with the topic of elementary data structures,
which are of great importance in practical programming, and present very