Research of effective methods of conversion from positional notation to RNS on FPGA

In this article we propose the implementation of different RNS moduli sets on FPGA. We also reviewed methods for calculation of remainder of division by modules of special form. In addition, the application of logical sharing schemes with effective distributing of FPGA resources is presented in the paper. We modified the algorithm of residue calculation by using distributed arithmetic's methods and shared resources of FPGA. Proposed algorithm allows to improve scheme performance by 14% while hardware costs were increased only by 1%. The simulation of described algorithms of residues finding is performed by FPGA Xilinx Spartan-6 SP605.