A parallel-processing-oriented method for the representation of multi-digit floating-point numbers

Authors

  • K.S. Isupov Vyatka State University
  • A.N. Maltsev Vyatka State University

Keywords:

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

Abstract

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 mdash; Multiple Precision Floating-Point Reliable library, NTL mdash; Number Theory Library, and Wolfram Mathematica) are discussed.

Author Biographies

K.S. Isupov

A.N. Maltsev

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Published

2014-11-13

How to Cite

Исупов К.С., Мальцев А.Н. A Parallel-Processing-Oriented Method for the Representation of Multi-Digit Floating-Point Numbers // Numerical methods and programming. 2014. 15. 631-643

Issue

Section

Section 1. Numerical methods and applications