On the Possibility of Implementing High-Precision Calculations in Residue Numeral System

This article proposes a method for accelerating high-precision calculations by parallelizing arithmetic operations of addition, subtraction and multiplication. The proposed approach allows us to apply the advantages of the residue numeral system: absence of carry-overs when adding, subtracting, multiplying and reducing high-precision calculations with numbers of high digit capacity to parallel and independent execution of arithmetic operations with numbers of low digit capacity across many modules. Due to the complexity of performing non-modular operations such as: inverse transformation into a positional numeral system, number comparisons, sign identification and number rank calculation in a residue numeral system, the effect of acceleration of high-precision calculations is possible when solving some computational problems with a small number of non-modular operations, for example: determination of the scalar product of vectors, discrete Fourier transformation, iterative solution of systems of linear equations by the methods of Jacoby, Gaussa-Zeidel, etc. Implementation of the proposed method are demonstrated by the example of finding the scalar product of vectors.

@article{A2019,
  title     = {On the Possibility of Implementing High-Precision Calculations in Residue Numeral System},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {10},
  number    = {11},
  year      = {2019},
  publisher = {The Science and Information Organization},
  author    = {Otsokov Sh A and Magomedov Sh.G},
  doi       = {10.14569/IJACSA.2019.0101102},
  url       = {https://doi.org/10.14569/IJACSA.2019.0101102}
}