Investigation of the Rank of Numbers Represented in the Residue Number System

The rank of a number in a residue number system allows for improving the efficiency of non-modular operations and determining values out of range. The paper proposes an approach that allows to find the rank from multiples of the bases of rank numbers. Proof of the correctness of the method is given. It also finds the required accuracy for the transition to the approximate computation of the rank of a number. Simulations of the considered methods in the RTL and physical synthesis environment have shown a twofold reduction in the hardware area with comparable running time for the computed ranks. An approach for determining the sign of a number in a residue number system based on the rank of a number is also proposed.