A floating-point technique for extending the available precision
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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.
KeywordsMathematical Method Basic Algorithm Number System Double Precision Floating Point
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- Babuška, I.: Numerical stability in mathematical analysis. IFIP congr. 68, Invited papers, 1–13 (1968).Google Scholar
- Grau, A. A.: On a floating-point number representation for use with algorithmic languages. Comm. ACM5, 160–161 (1962).Google Scholar
- Kahan, W.: Further remarks on reducing truncation errors. Comm. ACM8, 40 (1965).Google Scholar
- Knuth, D. E.:The art of computer programming, vol. 2. Addison Wesley (1969).Google Scholar
- Møller, O.: Quasi double-precision in floating-point addition. BIT5, 37–50 (1965).Google Scholar
- Naur, P. (ed.): Revised report on the algorithmic language, ALGOL 60 (1962).Google Scholar
- Veltkamp, G. W.: Private communications (see also RC Informatie Nr. 21 & 22, Technological University, Eindhoven). (1968).Google Scholar
- Wilkinson, J. H.: Rounding errors in algebraic processes. Her Majesty's Stationary Office (1963).Google Scholar