Beyond Floating Point

  title={Beyond Floating Point},
  author={C. W. Clenshaw and Frank W. J. Olver},
  journal={J. ACM},
Un systeme numerique est propose pour l'arithmetique d'ordinateur basee sur des fonctions exponentielles iterees. L'avantage principal est d'extirper le sous-passement et le depassement de capacite, mais il y a quelques autres avantages et ceux-ci sont decrits et discutes 
Une méthodologie du calcul hardware des fonctions élémentaires
On presente en detail la notion de «base discrete» qui permet d'elaborer des algorithmes de calcul des fonctions mathematiques usuelles se pretant particulierement bien a une realisation câblee. On
978-0-521-19469-3-Modern Computer Arithmetic
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Basic Linear Algebra Operations in SLI Arithmetic
The main purpose of this paper is to present parallel SLI algorithms for arithmetic and basic linear algebra operations.
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.
Implementation and analysis of extended SLI operations
  • P. Turner
  • Computer Science
    [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic
  • 1991
The implementation details suggest that any time-penalty associated with the use of SLI arithmetic can be kept to a very small factor on highly parallel computers, perhaps on the order of just two or three for typical scientific computing programs.
Universal coding of the reals: alternatives to IEEE floating point
We propose a modular framework for representing the real numbers that generalizes ieee, posits, and related floating-point number systems, and which has its roots in universal codes for the positive
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} are
An underflow-induced graphics failure solved by SLI arithmetic
  • D. Lozier
  • Computer Science
    Proceedings of IEEE 11th Symposium on Computer Arithmetic
  • 1993
Support is provided for considering symmetric level-index arithmetic, a new form of computer arithmetic which is immune to underflow and overflow, and which arose as an asymptotic solution to a model problem in turbulent combustion.
Number Theories
We will see that key concepts of number theory can be defined for arbitrary operations. We give a generalized distributivity for hyperoperations (usual arithmetic operations and operations going
A Bibliography of Publications on Floating-Point Arithmetic
This is a bibliography of material on floating-point arithmetic that I came up with while doing research on a floating-point package of my own. I don’t claim it to be anywhere near complete. The


Extended-Range Arithmetic and Normalized Legendre Polynomials
An algorithm is presented for the computation of normalrzed Legendre polynomials whereby a separate storage location is allocated to the exponent of a floatmg-pomt number.
Algorithm 524: MP, A Fortran Multiple-Precision Arithmetic Package [A1]
A collection of ANSI Standard Fortran subroutines for performing multiple-precision floatingpoint arithmetic and evaluating elementary and special functions is given. The subroutines are machine
Algorithm 567: Extended-Range Arithmetic and Normalized Legendre Polynomials [A1], [C1]
The desire to produce a robust F O R T R A N subroutine to compute these polynomials st imulated the development of the extended-range software package and may prove to be useful for many other computations.
Foundations of Finite Precision Rational Arithmetic
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.
Impact of the proposed IEEE floating point standard on numerical software
The proposed IEEE Floating Point Standard appears to be the answer to long-standing pleas for sensible floating-point arithmetic systems, but the committee drafting the standard has not settled some of the details, but it has agreed that the standard is intended to encourage high-quality numerical programming.
An Unrestricted Algorithm for the Exponential Function
An algorithm is presented for the computation of the exponential function of real argument. There are no restrictions on the range of the argument or on the precision that may be demanded in the
Reelle analytische Lösungen der Gleichung ... und verwandter Funktionalgleichungen.
DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen,
Further Developments of Rp and Ap Error Analysis
A New Approach to Error Arithmetic
  • F. Olver
  • Mathematics, Computer Science
  • 1978
By modification of the standard definition of relative error, a form of error arithmetic is developed that is well suited to floating-point computations and illustrated applications include accumulation of products, quotients, sums and inner products, and the evaluation of polynomials.