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

Authors

  • K.S. Isupov
  • A.N. Maltsev

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.

New computational technologies

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Published

2014-11-13

Issue

Vol. 15 (2014): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biographies

K.S. Isupov

Vyatka State University,
Faculty of Automation and Computer Engineering
• Assistant

A.N. Maltsev

Vyatka State University,
Faculty of Automation and Computer Engineering
• PhD Student

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