The Symmetric Level-Index System

  title={The Symmetric Level-Index System},
  author={C. W. Clenshaw and Peter R. Turner},
  journal={Ima Journal of Numerical Analysis},
On presente un systeme arithmetique de representation des nombres qui supprime virtuellement les phenomenes de defaut de capacite. On utilise une fonction exponentielle generalisee pour la representation des grands nombres (et des petits nombres par reciprocite) avec une precision uniforme 
Root squaring using level-index arithmetic
The practical benefits of the symmetric level-index system for representing numbers are displayed, using the root-squaring method of Graeffe as a vehicle, to ease the monitoring of precision while avoiding the problems associated with overflow and underflow. Expand
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Hyperoperations in exponential fields.
New sequences of hyperoperations \cite{BE15,HI26,ACK28,GO47,TAR69} are presented together with their local algebraic properties. The commutative hyperoperations reported by Bennet \cite{BE15} areExpand
A Hybrid Number Representation Scheme Based on Symmetric Level-Index Arithmetic
A hybrid SLI-FLP number system, together with some recent improvements of SLI arithmetic can result in a sound implementation of over/underflow free computer arithmetic. Expand
Taylor approximation for symmetric level-index arithmetic processing
Symmetric level-index arithmetic was introduced to overcome the problems of overflow and underflow in the floating-point system. The purpose of this paper is to improve the algorithm performance ofExpand
Complex SLI arithmetic: Representation, algorithms and analysis
  • P. Turner
  • Computer Science
  • Proceedings of IEEE 11th Symposium on Computer Arithmetic
  • 1993
The extension of the SLI (symmetric level index) system to complex numbers and arithmetic is discussed and the modulus-argument form, and the arithmetic algorithms prove to be very slightly more complicated than for real SLI arithmetic. Expand
The Symmetric Level Index System with an Application to Chaos
In this paper we present a brief summary of the Symmetric Level Index, SLI, system of number representation and computer arithmetic with only enough detail to allow the reader to understand theExpand
Closure and precision in level-index arithmetic
First it is proved that two recently introduced systems of computer arithmetic, the level-index (li) and symmetric level-index (sli) systems are closed under the four basic arithmetic operations,Expand
Error-Bounding in Level-Index Computer Arithmetic | NIST
This paper proposes the use of level-index (LI) and symmetric level-index (SLI) computer arithmetic for practical computation with error bounds. Comparisons are made with oating-point and severalExpand
A software implementation of SLI arithmetic
  • P. Turner
  • Computer Science
  • Proceedings of 9th Symposium on Computer Arithmetic
  • 1989
The computational experiments reported show the great simplicity of program structure which this robust arithmetic permits and the ease of performing extended computational operations, such as scalar products and evaluation of polynomials, is evident from the package. Expand