A uniform way of reasoning about array-based computation in radar: Algebraically connecting the hardware/software boundary

Embedded software processing requirements will exceed 1 trillion operations per second in the 2005-2010 time frame. Consequently, efficient use of processors and memory, at all levels, is essential. In many defense environments, e.g., radar, as well as medical and other real-time embedded systems, operations are primarily array-based. Although languages support high level, monolithic, array based computation through classes, functions, templates (C++), and grammars (Fortran 95, ZPL), limited optimizations occur to eliminate array valued temporaries, which for embedded real time systems, is enormous. Without an underlying theory of arrays, e.g., an algebra and index calculus, it is difficult, if not impossible to provide such optimizations. This paper presents a Mathematics of Arrays and Psi Calculus. Together they are used to reason about array based computation in radar; the algorithm, decomposition, mapping to processors and memory, performance.