Abstract
A technique is described for expressing multilength floating-point arithmetic in terms of singlelength floating point arithmetic, i.e. the arithmetic for an available (say: single or double precision) floating-point number system. The basic algorithms are exact addition and multiplication of two singlelength floating-point numbers, delivering the result as a doublelength floating-point number. A straight-forward application of the technique yields a set of algorithms for doublelength arithmetic which are given as ALGOL 60 procedures.
Similar content being viewed by others
References
Babuška, I.: Numerical stability in mathematical analysis. IFIP congr. 68, Invited papers, 1–13 (1968).
Grau, A. A.: On a floating-point number representation for use with algorithmic languages. Comm. ACM5, 160–161 (1962).
Kahan, W.: Further remarks on reducing truncation errors. Comm. ACM8, 40 (1965).
Knuth, D. E.:The art of computer programming, vol. 2. Addison Wesley (1969).
Møller, O.: Quasi double-precision in floating-point addition. BIT5, 37–50 (1965).
Naur, P. (ed.): Revised report on the algorithmic language, ALGOL 60 (1962).
Veltkamp, G. W.: Private communications (see also RC Informatie Nr. 21 & 22, Technological University, Eindhoven). (1968).
Wilkinson, J. H.: Rounding errors in algebraic processes. Her Majesty's Stationary Office (1963).
Author information
Authors and Affiliations
Additional information
Report MR 118/70, Computation Department, Mathematical Centre, Amsterdam. Part of this research was done while the author was visiting Bell Telephone Laboratories, Murray Hill, New Jersey.
Rights and permissions
About this article
Cite this article
Dekker, T.J. A floating-point technique for extending the available precision. Numer. Math. 18, 224–242 (1971). https://doi.org/10.1007/BF01397083
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01397083