Table-Lookup/Interpolation Function Generation for Fixed-Point Digital Computations

Abstract

For very fast function generation with small fixed-point digital computers, the n-bit argument word x is split into an N-bit word representing the breakpoint abscissa Xi for table-lookup by indirect addressing, and an n-N bit word representing the interpolation difference X-Xi. The complete procedure takes only about 50 machine cycles (50 μs) for equal breakpoint intervals, and about 70 machine cycles for variable breakpoint density. A sine-cosine generator for digital or hybrid-computer simulation is exhibited as an example.