Improving the Parallelism and Balance of RNS with Low-Cost and 2 k+ 1 Modules

Abstract

In this paper, extending the set of low-cost modules with modules of 2 k+ 1 form, which are considered next in the complexity of implementation after modules of 2 k- 1 proposed to consider. An experiment was carried out on the construction of various RNSs for the ranges from 16 to 64 bits and the number of modules from 3 to 8. The results of the experiment showed a significant increase in parallelism and improvement in the balance of RNS with modules of the 2 k, 2 k- 1 and 2 k+ 1 forms, compared to using only modules of the 2 k and 2 k- 1 forms. In the discussion of the experiment, we raised the questions of more effective measurement of the balance of the RNS, as well as the problem of using the diminished-1 encoding. This problem is a subject to a thorough study both at the theoretical level, for example, using a unit-gate model, and practical tests on modern FPGA and ASIC microelectronic devices.