Enabling unimodular transformations

Abstract

The development of a unimodular transformation theory and associated algorithms has renewed interest in Fortran do loops that are not perfectly (or tightly) nested. In this paper we summarize a number of techniques that convert imperfectly nested loops into perfectly nested loops. We examined over 25,000 lines of scientific Fortran kernels and benchmarks. Statistics are reported on how often imperfect loops occur and how effective two transformations (scalar forward substitution and loop distribution) are at converting imperfectly nested loops into perfectly nested loops. Further, we describe a compiler that integrates scalar forward substitution, loop distribution, and unimodular transformations while maintaining the basic philosophy of unimodular transformation theory. While our data indicate that imperfectly nested loops still present a problem, the compiler we describe is no more limited by perfectly nested loops than other restructuring compilers available today.