Fast modulo 2n-1 and 2n+1 adder using carry-chain on FPGA

Modular addition is a widely used operation in Residue Number System applications. Specific sets of moduli allow fast RNS operations such as binary conversions and multiplications. Most of them use modulo 2(n) - 1 and 2(n) + 1 additions. This paper presents four fast and small architectures for these specific moduli targeting modern FPGAs with fast carry chains. The use of this arithmetic dedicated feature allows fast and small modular adders. Our modulo 2(n) - 1 adders have a single zero representation. Our modulo 2(n) + 1 adders are designed for binary and diminished-one representation with and without zero value management.