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 method known as a wraparound variable is often used:
JM1 = N DO 10 J = 1,N B(J) = (A(J) + A(JM1)) /2 JM1 = J 10 CONTINUE
In the first iteration, JM1 is N .
In all iterations except for J=1 , 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 recognized, as follows:
JM1 = N IF (N .GE. 1) THEN RR1 = A(1) + A(N) JM1 = 1 II1 = N - 1 B(1) = RR1 / 2 DO 3 J=2,N B(J) = (A(J) + A(J-1)) / 2 3 CONTINUE IF (II1 .GT. 0) JM1 = II1 + 1 ENDIF
KAP may peel off several iterations in cases where multiple wraparound variables exist.