Speedup Studies of Leading Iteration Model for Non-DO Loops in Comparison with Sequential Iteration Model

In this paper, we present an approximate formula for calculating the speedup of a concurrent non-DO loop. The execution pattern of a concurrent non-DO loop is analyzed. As a result, the optimal concurrent step for a non-DO loop is presented and proved. With the analysis of the speedup of a concurrent non-DO loop, a simple and useful approximate formula is deduced, which is just the mathematical limit of speedup when the number of iterations is approaching infinity.