Efficient FPGA implementation of digit parallel online arithmetic operators

Online arithmetic has been widely studied for ASIC implementation. Online components were originally designed to perform computations in digit serial with most significant digit (MSD) first, resulting in the ability to chain arithmetic operators together for low latency. More recently, research has shown that digit parallel online operators can fail more gracefully when operating beyond the deterministic clocking region in comparison to operators with conventional arithmetic. Unfortunately, the utilization of online arithmetic operators in the past has required a large area overhead for FPGA implementation. In this paper, we propose novel approaches to implement the key primitives of online arithmetic, adders and multipliers, efficiently on modern Xilinx FPGAs with 6-input LUTs and carry resources. We demonstrate experimentally that in comparison to a direct RTL synthesis, the proposed architectures achieve slice savings of over 67% and 69%, and speed-ups of over 1.2x and 1.5x for adders and multipliers, respectively. As a result, the area overheads of using online adders and multipliers in place of traditional arithmetic primitives is reduced from 8.41 x and 8.11 x to 1.88x and 1.84x respectively. Finally, because an online multiplier generates MSDs first, we also demonstrate the method to create an online multiplier with a reduced precision output that is smaller than a traditional multiplier producing the same result. We show that this can lead to silicon area savings of up to 56%.