Functional multiple-output decomposition with application to technology mapping for lookup table-based FPGAs

Functional decomposition is an important technique for technology mapping to look up table-based FPGA architectures. We present the theory of and a novel approach to functional disjoint decomposition of multiple-output functions, in which common subfunctions are extracted during technology mapping. While a Boolean function usually has a very large number of subfunctions, we show that not all of them are useful for multiple-output decomposition. We use a partition of the set of bound set vertices as the basis to compute preferable decomposition functions, which are sufficient for an optimal multiple-output decomposition. We propose several new algorithms that deal with central issues of functional multiple-output decomposition. First, an efficient algorithm to solve the variable partitioning problem is described. Second, we show how to implicitly compute all preferable functions of a single-output function and how to identify all common preferable functions of a multiple-output function. Due to implicit computation in the crucial steps, the algorithm is very efficient. Experimental results show significant reductions in area.