THE AUTOMATED TRANSFORMATION OF ABSTRACT SPECIFICATIONS OF NUMERICAL ALGORITHMS INTO EFFICIENT ARRAY PROCESSOR IMPLEMENTATIONS

We present a set of program transformations which are applied automati cally to convert abstract functional specifications of numerical algor ithms into efficient implementations tailored to the AMT DAP array pro cessor. The transformations are based upon a formal algebra of a funct ional array form, which provides a functional model of the array opera tions supported by the DAP programming language, The transformations a re shown to be complete. We present specifications and derivations of two example algorithms: an algorithm for computing eigensystems and an algorithm for solving systems of linear equations. For the former, we compare the execution performance of the implementation derived by tr ansformation with the performance of an independent, manually construc ted implementation; the efficiency of the derived implementation match es that of the manually constructed implementation.