FPGA-Specific Arithmetic Optimizations of Short-Latency Adders

Integer addition is a pervasive operation in FPGA designs. The need for fast wide adders grows with the demand for large precisions as, for example, required for the implementation of IEEE-754 quadruple precision and elliptic-curve cryptography. The FPGA realization of fast and compact binary adders relies on hardware carry chains. These provide a natural implementation environment for the ripple-carry addition (RCA) scheme. As its latency grows linearly with operand width, wide additions call for acceleration, which is quite reasonably achieved by addition schemes built from parallel RCA blocks. This study presents FPGA-specific arithmetic optimizations for the mapping of carry-select and carry-increment adders targeting the hardware carry chains of modern FPGAs. Different trade-offs between latency and area are explored. The proposed architectures can be successfully used in the context of latency-critical systems or as attractive alternatives to deeply pipelined RCA schemes.