Improving Scalability with Loop Transformations and

Application codes reliably achieve performance far less than the advertised capabilities of existing architectures, and this problem is worsening with increasingly-parallel machines. For large-scale numerical applications, stencil operations are often impose the greater part of the computational cost, and the primary sources of ineeciency are the costs of message passing and poor cache utilization. This paper proposes and demonstrates optimizations for stencil and stencil-like computations for both serial and parallel environments that ameliorate these sources of ineeciency. Achieving scalability, we believe, requires both algorithm design and compile-time support. The optimizations we present are automatable because our stencil-like computations are implemented at a high level of abstraction using object-oriented parallel array class libraries. These optimizations, which are beyond the capabilities of today compilers, may be performed automatically by a preprocessor such as the one we are currently developing.