Numerical function generators using bilinear interpolation

Abstract

Two-variable numerical functions are widely used in various applications, such as computer graphics and digital signal processing. Fast and compact hardware implementations are required. This paper introduces the bilinear interpolation method to produce fast and compact numerical function generators (NFGs) for two-variable functions. This paper also introduces a design method for symmetric two-variable functions. This method can reduce the memory size needed for symmetric functions by nearly half with small speed penalty. Experimental results show that the bilinear interpolation method can significantly reduce the memory size needed for two-variable functions, and the speed of NFGs based on the bilinear method is comarable to that of NFGs based on the tangent plane approximation. For a complicated function, our NFG is faster and more compact than a circuit designed using a one-variable NFG.