A Design Method for Programmable Two-Variable Discrete Function Generators Using Spline and Bilinear Interpolations

This paper presents a design method for programmable two-variable discrete (real-valued) function generators based on a piecewise polynomial approximation. To approximate a given discrete function by polynomials efficiently, we propose a hybrid approximation method using both spline and bilinear interpolations. The proposed method can significantly reduce memory size needed to implement a two-variable discrete function by accepting a small approximation error, and thus it can be used to explore design space taking into account a trade-off between memory size and approximation error. Experimental results show that the proposed design method reduces 75% of memory size without losing circuit speed by accepting only 1% error, and the circuits designed by the proposed method achieve about 650 times greater throughput than their software programs. We can automatically synthesize such compact and fast function generators using the proposed design method.