On the Space-Time Mapping of While-Loops

A WHILE-loop can be viewed as a FOR-loop with a dynamic upper bound. The computational model of convex polytopes is useful for the automatic parallelization of FOR-loops. We investigate its potential for the parallelization of WHILE-loops. 1. WHILE-loops as FOR-loops We denote a FOR-loop as follows: FOR index := lower bound TO upper bound DO body The step size (also called stride) of a FOR-loop is +1. (A FOR-loop with a diierent stride can easily be transformed to one with stride +1.) If the upper bound of the FOR-loop is smaller than the lower bound, the loop deenes the empty statement. A WHILE-loop is commonly denoted as follows: WHILE condition DO body One can view a WHILE-loop as a generalized FOR-loop, with a conditional upper bound that is reevaluated after every iteration: FOR new index := 0 TO (IF condition THEN new index ELSE new index?1) DO body Here, new index is a new index variable. The upper bound of the loop is incremented at each iteration. When the condition is found to be violated, the upper bound is reduced to cause termination. We shall use the following syntax for a WHILE-loop written as a FOR-loop: FOR new index := 0 WHILE condition DO body Hereby, the new index works as a counter for the number of executed iterations of the WHILE-loop. As in FOR-loops, its increment is not explicitly speciied in the body.