A practical functional program for the CRAY X-MP

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Abstract
One can have all the advantages of functional programming – correctness, clarity, simplicity, and flexibility – without any sacrifice in performance, even for a scientifically significant computation on a supercomputer. Therefore, why use Fortran? We demonstrate parity – equality of speed and storage use – between a program generated automatically from a functional specification and a program written by hand in the procedural style. To our knowledge, this demonstration of parity is the first for a program that solves a scientifically significant problem – quasi-linear hyperbolic partial differential equations – on a scientifically interesting supercomputer – the CRAY X-MP. We use pure Lisp, including higher-order functions, to express the functional specification for the PDE solver. We designed this specification for maximal clarity and flexibility, rather than for efficiency. Nevertheless, we obtain a highly efficient program to solve the PDEs: automated program transformations put back the missing efficiency as they produce an executable Fortran program from the specification. The generated Fortran program vectorizes on the CRAY X-MP and runs about 4% faster than a handwritten Fortran program for the same problem. We describe the problem and the specification, and some of the problem-domain-specific and hardware-specific transformations that we use to obtain the high-efficiency program.

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