Jason Anderson and Qiang Wang,
University of Toronto and Xilinx, Inc.
January, 2011
We consider architecture and synthesis techniques for FPGA logic elements (function generators) and show that the LUT-based logic elements in modern commercial FPGAs are over-engineered. Circuits mapped into traditional LUT-based logic elements have speeds that can be achieved by alternative logic elements that consume considerably less silicon area. We introduce the concept of a trimming input to a logic function, which is an input to a K-variable function about which Shannon decomposition produces a co-factor having fewer than K-1 variables. We show that trimming inputs occur frequently in circuits and we propose low-cost asymmetric FPGA logic element architectures that leverage the trimming input concept, as well as some other properties of a circuit's AND-inverter graph (AIG) functional representation. We describe synthesis techniques for the proposed architectures that combine a standard cut-based FPGA technology mapping algorithm with two straightforward procedures: 1) Shannon decomposition, and 2) finding non-inverting paths in the circuit's AIG. The proposed architectures exhibit improved logic density versus traditional LUT-based architectures with minimal impact on circuit speed.