Performance-improved computation of very large word-length LNS addition/subtraction using signed-digit arithmetic

Pipelined computation of very large word-length LNS addition/subtraction requires a significant amount of hardware and long pipeline latency. We propose a base-e exponential algorithm to simplify the exponential computation and to replace half of the pipeline stages by multiplication-and-accumulate operations. By using this approach, the circuit cost of the previously proposed 64 bit pipelined LNS addition/subtraction unit can be reduced by more than fifty percent. We also developed signed-digit (SD) algorithms to further enhance the performance of the LNS computation. From our analysis, the throughput of the 64 bit LNS unit can be increased by a factor of 4.62, and the pipeline latency can be reduced by a factor of seven. Furthermore, this SD approach can still save more than 50% of the table size and 27.6% of the circuit of the previously proposed LNS unit. The proposed approaches and algorithms have been verified by comprehensive simulations on the designed 32 bit SD hardware-reduced LNS unit. We have concluded that the proposed approaches can significantly improve the performance of very large word-length LNS addition/subtraction computation.