High Precision, High Performance FPGA Adders

FPGAs are now being commonly used in the datacenter as smart Network Interface Cards (NICs), with cryptography as one of the strategic application areas. Public key cryptography algorithms in particular require arithmetic with thousands of bits of precision. Even an operation as simple as addition can be difficult for the FPGA when dealing with large integers, because of the high resource count and high latency needed to achieve usable performance levels with known methods. This paper examines the architecture and implementation of high-performance integer adders on FPGAs for widths ranging from 1024 to 8192 bits, in both single-instance and many-core chip-filling configurations. For chip-filling designs the routing impact of these wide busses are assessed, as they often have an impact outside the immediate locality of the structures. The architectures presented in this work show 1 to 2 orders magnitude reduction in the area-latency product over commonly used approaches. Routing congestion is managed, with near 100% logic efficiency (packing) for the adder function. Performance for these largely automatically placed designs are approximately the same as for carefully floor-planned non-arithmetic applications. In one example design, we show a 2048 bit adder in 5021 ALMs, with a latency of 6 clock cycles, at 628 MHz in a Stratix 10 E-2 device.