$title fast shifting of set elements (SET9,SEQ=448)

$onText

The execution time depends on the size of the reference set i and
the position of the dynamic set elements in the reference set. The
old implementation has an execution time that is proportional to the
size of the reference set. The new coding depends on the position of
the element in the reference set. At the expense of memory, we could
make the time proportional to the number of elements in the dynamic
set only.
   k(i) = k(i-1)        candidate for fast execution but only inside a loop
   k(i) = k(i-1) + no   the +no makes it slow

Contributor: Alex

$offText

set i reference set / 1*1000000 /, k(i), m(i) / 1,10000,50000/;

parameter s, rep execution counts;

loop(m,
   k(i) = no; k(m) = yes; s = timeExec;
   repeat
      k(i) = k(i-1) until (timeExec-s) > 0.5 ;
   rep(m,'fast') = sum(k, k.val)-m.val; display k;
   k(i) = no; k(m) = yes; s = timeExec;
   repeat
      k(i) = k(i-1) + no until (timeExec-s) > 0.5 ;
   rep(m,'slow') = sum(k, k.val)-m.val; display k );

rep(m,'ratio') = rep(m,'fast')/rep(m,'slow');

display rep;

* We cannot do this test, because of old machines with timing/memory issues
* abort$sum(m, rep(m,'ratio') < 50) 'something looks funny';
abort$(smax(m, rep(m,'ratio')) < 50) 'something looks funny';

$exit

----     28 PARAMETER rep  execution counts

             fast        slow       ratio

1       10115.000       3.000    3371.667
10000    4366.000       3.000    1455.333
50000     830.000       3.000     276.667