Using of Redundant Signed-Digit Numeral System for Accelerating and Improving the Accuracy of Computer Floating-Point Calculations

The article proposes a method for software implementation of floating-point computations on a graphics processing unit (GPU) with an increased accuracy, which eliminates sharp increase in rounding errors when performing arithmetic operations of addition, subtraction or multiplication with numbers that are significantly different from each other in magnitude. The method is based on the representation of floating-point numbers in the form of decimal fractions that have uniform distribution within a range and the use of redundant signed-digit numeral system to speed up calculations. The results of computational experiments for evaluating the effectiveness of the proposed approach are presented. The effect of accelerating computations is obtained for the problems of calculating the sum of an array of numbers and determining the dot product of vectors. The proposed approach is also applicable to the discrete Fourier transform.

@article{A2020,
  title     = {Using of Redundant Signed-Digit Numeral System for Accelerating and Improving the Accuracy of Computer Floating-Point Calculations},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {11},
  number    = {9},
  year      = {2020},
  publisher = {The Science and Information Organization},
  author    = {Otsokov Sh. A and Magomedov Sh.G},
  doi       = {10.14569/IJACSA.2020.0110942},
  url       = {https://doi.org/10.14569/IJACSA.2020.0110942}
}