"A parallel-processing-oriented method for the representation of multi-digit floating-point numbers"
Isupov K.S. and Maltsev A.N.

The extended precision of calculations is required in solving many scientific and engineering problems. The solution time is a critical parameter to accomplish and, therefore, new methods should be developed for fast high-precision arithmetic. In this paper a new modular-positional format for the representation of floating-point multi-digit numbers is proposed. The main concept of this format is to represent and ensure the digit-parallel processing of floating-point mantissas in residue number systems. The method of interval-positional characteristics is used to increase the speed of complex non-modular operations. Several algorithms for performing arithmetic operations and rounding in the new modular-positional floating-point format are considered. The results of studies of their vectorization efficiency and performance compared to some analogs (MPFR - Multiple Precision Floating-Point Reliable library, NTL - Number Theory Library, and Wolfram Mathematica) are discussed.

Keywords: residue number system, high-precision computations, modular-position floating-point format, multi-digit numbers, arithmetic operations, high performance.

  • Isupov K.S. – Vyatka State University, Faculty of Automation and Computing Machines; ulitsa Moskovskaya 36, Kirov, 610000, Russia; Ph.D., Assistant, e-mail: isupov.k@gmail.com
  • Maltsev A.N. – Vyatka State University, Faculty of Automation and Computing Machines; ulitsa Moskovskaya 36, Kirov, 610000, Russia; Postgraduate Student, e-mail: maltsev_a@list.ru