On Reducing Overhead in Loops

In this paper we discuss several techniques for reducing the overhead in Fortran-like DO loops. In particular, we describe two topics: 1. Simplifying loop bounds. 2. Removing a ne IF-statements from loops. The objective is to isolate the part of the iteration space of the original loop in which the bounds take simpler forms, or in which the condition is satis ed. The main technical tool for determining this subspace is Fourier-Motzkin elimination. We show an easy way to generate code for scanning the di erent parts of an iteration space that have been isolated in this way. We present our techniques as a number of elementary transformation steps. SInce these steps only partition the iteration space, the steps can always legally be employed. The full e ect of these steps is obtained by iterating them until no more changes occur. The result will be a loop structure in which all bounds are simple a ne expressions and from which all IF-statements with a ne conditions have been eliminated.