A Case Study : E ects of With - Loop - Folding onthe NAS Benchmark MG

Sac is a functional C variant with eecient support for high-level array operations. This paper investigates the applicability of a Sac speciic optimization technique called with-loop-folding to real world applications. As an example program which originates from the Numerical Aerodynamic Simulation (NAS) Program developed at NASA Ames Research Center, the so-called NAS benchmark MG is chosen. It comprises a kernel from the NAS Program which implements 3-dimensional multigrid relaxation. Several run-time measurements exploit two diierent beneets of with-loop-folding: First, an overall speed-up of about 20% can be observed. Second, a comparison between the run-times of a hand-optimized specii-cation and of Apl-like speciications yields identical run-times, although a naive compilation that does not apply with-loop-folding leads to slowdowns of more than an order of magnitude. Furthermore, With-loop-folding makes a slight variation of the algorithm feasible which substantially simpliies the program speciication and requires less memory during execution. Finally, the optimized run-times are compared against run-times gained from the original Fortran program, which shows that for diierent problem sizes, the code generated from the Sac program does not only reach the execution times of the code generated from the Fortran program but even outperforms them by about 10%.