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. OnExpand
978-0-521-19469-3-Modern Computer Arithmetic
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, for teaching and research institutions in France or abroad. Expand
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. Expand
Level-index arithmetic operations
In a recent paper the authors described a system for the internal representation of numbers in a computer, based on repeated exponentiations. The main objective in introducing this system is toExpand
Floating Point Verification in HOL Light: The Exponential Function
This work presents a machine-checked verification of an algorithm for computing the exponential function in IEEE-754 standard binary floating point arithmetic, and confirms (indeed strengthen) the main result of a previously published error analysis. Expand
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
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. Expand
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 positiveExpand
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
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


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. Expand
A New Approach to Error Arithmetic
By modification of the standard definition of relative error, a form of error arithmetic is developed that is well suited to floating-point computations. Rules are given for conversion from intervalExpand
Algorithm 524: MP, A Fortran Multiple-Precision Arithmetic Package [A1]
  • R. Brent
  • Mathematics, Computer Science
  • TOMS
  • 1978
A collection of ANSI Standard Fortran subroutines for performing multiple-precision floatingpoint arithmetic and evaluating elementary and special functions is given. The subroutines are machineExpand
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. Expand
Foundations of Finite Precision Rational Arithmetic
Finite precision fraction number systems are characterized and their number theoretic foundations are developed. Closed approximate rational arithmetic in these systems is obtained by the naturalExpand
Underflow and the Denormalized Numbers
Although there have been misconceptions about it, gradual underflow fits naturally into the proposed standard and leads to simple, general statements about the arithmetic.
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. Expand
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 theExpand
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,Expand
Journal of the AssociaUon for CompuUng Maclunery
  • Journal of the AssociaUon for CompuUng Maclunery
  • 1984