Post-mapping Topology Rewriting for FPGA Area Minimization

Abstract

Circuit designers require Computer-Aided Design (CAD) tools when compiling designs into Field Programmable Gate Arrays (FPGAs) in order to achieve high quality results due to the complexity of the compilation tasks involved. Technology mapping is one critical step in the FPGA CAD flow. The final mapping result has significant impact on the subsequent steps of clustering, placement and routing, for the objectives of delay, area and power dissipation. While depth-optimal FPGA technology mapping can be solved in polynomial time, area minimization has proven to be NP-hard.

Most modern state-of-the-art FPGA technology mappers are structural in nature; they are based on cut enumeration and use various heuristics to yield depth and area minimized solutions. However, the results produced by structural technology mappers rely strongly on the structure of the input netlists. Hence, it is common to apply additional heuristics after technology mapping to further optimize area and reduce the amount of structural bias while not harming depth. Recently, SAT-based Boolean matching has been used for post-mapping area minimization. However, SAT-based matching is computationally complex and too time consuming in practice.

This thesis proposes an alternative Boolean matching approach based on NPN equivalence. Using a library of pre-computed topologies, the matching problem becomes as simple as performing NPN encoding followed by a hash lookup which is very efficient. In conjunction with Ashenhurst decomposition, the NPN-based Boolean matching is allowed to handle up to 10-input Boolean functions. When applied to a large set of designs, the proposed algorithm yields, on average, more than 3% reduction in circuit area without harming circuit depth. The priori generation of a library of topologies can be difficult; the potential difficulty in generating a library of topologies represents one limitation of the proposed algorithm.