Bit-level arithmetic optimization for carry-save additions

Addresses the bit-level optimization of carry-save adder (CSA) arrays when the operands are of unequal wordlength (such as in some datapaths in digital signal processing circuits). We first show that by relaxing the carry-save representation to allow for more than two signals per bit position, we gain flexibility in the bit-level implementation of CSA arrays that can be exploited to achieve a more efficient design. We then propose algorithms to optimize a single adder array at the bit-level. In addition, we proposed a heuristic to optimize a series of adder arrays that might occur in a datapath. We have applied our algorithms to the optimization of high-speed digital FIR filters and have achieved 15% to 30% savings (weighted cost) in the overall filter implementation array in comparison to the standard carry-save implementation.