Scientific programs often include multiple loops over the same data; interleaving parts of different loops may greatly improve performance. We exploit this in a compiler for Titanium, a dialect of Java. Our compiler combines reordering optimizations such as loop fusion and tiling with storage optimizations such as array contraction (eliminating or reducing the size of temporary arrays). The programmers we have in mind are willing to spend some time tuning their code and their compiler parameters. Given that, and the difficulty in statically selecting parameters such as tile sizes, it makes sense to provide automatic parameter searching alongside the compiler. Our strategy is to optimize aggressively but to expose the compiler’s decisions to external control. We double or triple the performance of Gauss-Seidel relaxation and multi-grid (versus an optimizing compiler without tiling and array contraction), and we argue that ours is the best compiler for that kind of program.

Titanium is a language and system for high-performance parallel scientific computing. Titanium uses Java as its base, thereby leveraging the advantages of that language and allowing us to focus attention on parallel computing issues. The main additions to Java are immutable classes, multidimensional arrays, an explicitly parallel SPMD model of computation with a global address space, and zone-based memory management. We discuss these features and our design approach, and report progress on the development of Titanium, including our current driving application: a three-dimensional adaptive mesh refinement parallel Poisson solver. © 1998 John Wiley & Sons, Ltd.