Accelerating Computations on FPGA Carry Chains by Operand Compaction

This work describes the carry-compact addition (CCA), a novel addition scheme that allows the acceleration of carry-chain computations on contemporary FPGA devices. While based on concepts known from the carry-look ahead addition and from parallel prefix adders, their adaptation by the CCA takes the context of an FPGA as implementation environment into account. These typically provide carry-chain structures to accelerate the simple ripple-carry addition (RCA). Rather than contrasting this scheme with the hierarchical addition approaches favored in hard-core VLSI designs, the CCA combines the benefits of both and uses hierarchical structures to shorten the critical path, which is still left on a core carry chain. In contrast to previous studies examining the asymptotically superior parallel prefix adders on FPGAs, the CCA is shown to outperform the standard RCA already for operand widths starting at 50~bits. Wider adders such as used in extended-precision floating-point units and in cryptographic applications even benefit from increasing speedups. The concrete mapping of the CCA as achieved for current Xilinx and Altera architectures is described and shown to be very favorable so as to yield a high speedup for a very modest investment of additional LUT resources.