Proceedings ArticleDOI
A feasibility analysis of binary fixed-slash and floating-slash number systems
David W. Matula,Peter Kornerup +1 more
- pp 29-38
TLDR
Design and analysis of finite precision rational number systems based on fixed-slash and floating-Slash representation is pursued, and the concept of adaptive variable precision in the rounding is developed.Abstract:
Design and analysis of finite precision rational number systems based on fixed-slash and floating-slash representation is pursued. Natural formats for binary fixed-slash and binary floating-slash number representation in computer words are described. Compatibility with standard integer representation is obtained. Redundancy in the' representation is shown to be minimal. Arithmetic register requirements are considered. Worst case and average case rounding errors are determined, and the concept of adaptive variable precision in the rounding is developed.read more
Citations
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Journal ArticleDOI
Finite Precision Rational Arithmetic: Slash Number Systems
TL;DR: Multitiered precision hierarchies of both the fixed-Slash and floating-slash type are described and analyzed with regards to their support of both exact rational and approximate real computation.
Book ChapterDOI
Foundations of Finite Precision Rational Arithmetic
David W. Matula,Peter Kornerup +1 more
TL;DR: The overall goal is to better understand the inherent mathematical properties of finite precision arithmetic and to provide a most natural and convenient computation system for approximating real arithmetic on a Computer.
Book ChapterDOI
Arithmetic in Basic Algebraic Domains
TL;DR: This chapter is devoted to the arithmetic Operations, essentially addition, multiplication, exponentiation, division, gcd calculation and evaluation, on the basic algebraic domains.
BookDOI
Fundamentals of numerical computation (computer-oriented numerical analysis)
TL;DR: On Methods for the Construction of the Boundaries of Sets of Solutions for Differential Equations or Finite-Dimensional Approximations with Input Sets.
An approximate rational arithmetic system with intrinsic recovery of simple fractions during expression evaluation
David W. Matula,Peter Kornerup +1 more
TL;DR: Closed approximate rational arithmetic systems are described and their number theoretic foundations are surveyed in this paper, where the arithmetic implicitly contain an adaptive single-to-double precision natural rounding behavior that acts to recover true simple fractional results.
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