Reciprocal approximation theory with table compensation
Albert A. Liddicoat, Michael J. Flynn · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
Schwarz demonstrates the reuse of a multiplier partial product array (PPA) to approximate higher-order functions such as the reciprocal, division, and square root. This work presents techniques to decrease the worst case error for the reciprocal approximation computed on a fixed height PPA. In addition, a compensation table is proposed that when combined with the reciprocal approximation produces a fixed precision result. The design space for a 12-bit reciprocal is then studied and the area- time tradeoff for three design points is presented. Increasing the reciprocal approximation computation decreases the area needed to implement the function while increasing the overall latency. Finally, the applicability of the proposed technique to the bipartite ROM reciprocal table is discussed. The proposed technique allows hardware reconfigurability. Programmable inputs for the PPA allow the hardware unit to be reconfigured to compute various higher-order function approximations.