7.3.3 Loop Peeling

In cases where an array is used to simulate a cylindrical coordinate system, where the left edge of the array must be adjacent to its right edge, a "wraparound variable" is often used, as follows:

jm1 = n;
   for ( j=0; j<n; j++ ) {
   b[j] = (a[j] + a[jm1]) / 2;
   jm1 = j;
 }

In the first iteration, jm1 is n . In all iterations except for j=0 , the value of jm1 is j-1 . Thus, jm1 is an induction variable for the loop after the first iteration.

By peeling off the first iteration of the loop, the jm1 induction variable can be exploited, as follows:

if (n >= 1) {
   b[0] = (a[0] + a[n]) / 2;
   for ( j = 1; j<n; j++ ) {
     b[j] = (a[j] + a[j-1]) / 2;
       }
   }

KAP may peel off several iterations in cases where multiple wraparound variables exist.