Single Assignment C: efficient support for high-level array operations in a functional setting

Abstract

This paper presents a novel approach for integrating arrays with access time ${\cal O}$(1) into functional languages. It introduces n-dimensional arrays combined with a type system that supports hierarchies of array types with varying shape information as well as a shape-invariant form of array comprehension called WITH-loop. Together, these constructs allow for a programming style similar to that of array programming languages such as APL. We use Single Assignment C (SAC), a functional C-variant aimed at numerical applications that is based on the proposed design, to demonstrate that programs written in that style can be compiled to code whose runtime performance is competitive with that of hand-optimized Fortran programs. However, essential prerequisites for such performance figures are a shape inference system integrated in the type system as well as several high-level optimizations. Most notably of these is With Loop Folding, an optimization technique for eliminating intermediate arrays.