Compiler transformations can significantly improve data locality for many scientific programs. In this paper, we show iterative solvers for partial differential equations (PDEs) in three dimensions require new compiler optimizations not needed for 2D codes, since reuse along the third dimension cannot fit in cachefor larger problem sizes. Tiling is a program transformation compilers can apply to capture this reuse, but successful application of tiling requires selection of non-conflicting tiles and/or padding array dimensions to eliminate conflicts. We present new algorithms and cost models for selecting tiling shapes and array pads. We explain why tiling is rarely needed for 2D PDE solvers, but can be helpful for 3D stencil codes. Experimental results show tiling 3D codes can reduce miss rates and achieve performance improvements of 17-121% for key scientific kernels, including a 27% average improvement for the key computational loop nest in the SPEC/NAS benchmark MGRID.

Compiler transformations can significantly improve data locality of scientific programs. In this paper, we examine the impact of multi-level caches on data locality optimizations. We find nearly all the benefits can be achieved by simply targeting the L1 (primary) cache. Most locality transformations are unaffected because they improve reuse for all levels of the cache; however, some optimizations can be enhanced. Inter-variable padding can take advantage of modular arithmetic to eliminate conflict misses and preserve group reuse on multiple cache levels. Loop fusion can balance increasing group reuse for the L2 (secondary) cache at the expense of losing group reuse at the smaller L1 cache. Tiling for the L1 cache also exploits locality available in the L2 cache. Experiments show enhanced algorithms are able to reduce cache misses, but performance improvements are rarely significant. Our results indicate existing compiler optimizations are usually sufficient to achieve good performance...

Many cache misses in scientific programs are due to conflicts caused by limited set associativity. Two data-layout transformations, inter- and intra-variable padding, can eliminate many conflict misses at compile time. We present GroupPad, an inter-variable padding heuristic to preserve group reuse in stencil computations frequently found in scientific computations. We show padding can also improve performance in parallel programs. Our optimizations have been implemented and tested on a collection of kernels and programs for different cache and data sizes. Preliminary results demonstrate GroupPad is able to consistently preserve group reuse among the programs evaluated, though execution time improvements are small for actual problem and cache sizes tested. Padding improves performance of parallel versions of programs approximately the same magnitude as sequential versions of the same program. 1 Introduction Effectively exploiting caches is widely regarded as the key to achieving good...

Many cache misses in scientific programs are due to conflicts caused by limited set associativity. We examine two compile-time data-layout transformations for eliminating conflict misses, concentrating on misses occuring on every loop iteration. Inter-variable padding adjusts variable base addresses, while intra-variable padding modifies array dimension sizes. Two levels of precision are evaluated. PADLITE only uses array and column dimension sizes, relying on assumptions about common array reference patterns. PAD analyzes programs, detecting conflict misses by linearizing array references and calculating conflict distances between uniformly-generated references. The Euclidean algorithm for computing the gcd of two numbers is used to predict conflicts between different array columns for linear algebra codes. Experiments on a range of programs indicate PADLITE can eliminate conflicts for benchmarks, but PAD is more effective over a range of cache and problem sizes. Padding reduces cache miss rates by 16% on average for a 16K direct-mapped cache. Execution times are reduced by 6% on average, with some SPEC95 programs improving up to 15%.