Performance evaluation of tiling for the register level

Tiling is a well-known loop transformation, which is basically used to expose coarse-grain parallelism and to exploit data reuse at the cache level. However, it can also be used to exploit data reuse at the register level and to improve programs's ILP. Previous work on tiling and also commercial compilers are able to perform tiling for the register level in more than one dimension when the iteration space is rectangular. Non-rectangular iteration spaces are commonly found in linear algebra algorithms or can arise as a result of applying previous transformations such as loop skewing. In this paper we evaluate the technique presented in Jimenez et al. (1996) which is able to perform tiling for the register level in more than one dimension in both rectangular and non-rectangular iteration spaces. We use typical linear algebra algorithms having non-rectangular iteration spaces as benchmarks and compare our proposal against commercial preprocessors able to perform optimizing code transformations such as inner unrolling, outer unrolling and software pipelining. We will also present quantitative data showing the benefits of tiling only for the register level, tiling only for the cache level and tiling for both levels simultaneously. Results measured on a ALPHA 21164 processor show that tiling for both cache and register levels improves upon commercial compilers and preprocessors by factors in the range of 1.3 to 6.3.