Hardware Support for Multivariable Floating Point Function Generation

Abstract

A method suited for hardware implementation as sists in evaluating a multivariable, floating-point function F(X,Y,...Z) defined on an N-dimensional rectangular grid. A preprocessing stage analyzes the function's breakpoints for each dimension. It determines a subinterval range that includes the breakpoint range for that dimension and subdivides the subinterval range into equal-sized subintervals in a procedure that enables easy identification of the breakpoint interval containing a subinterval. The method's run-time stage processes the N com ponents of the input argument in parallel to iden tify the N-dimensional rectangular cell containing the input argument. At run time, two additions and a multiplication convert each component of the input argument to an index identifying the sub intervat containing it. Then two table lookups iden tify the breakpoint interval containing the sub interval. An implementation of a two-variable function generator that uses bilinear interpolation is sketched to illustrate application of the cell-iden tification method.