A floating-point technique for extending the available precision

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.

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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.

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Dekker, T.J. A floating-point technique for extending the available precision. Numer. Math. 18, 224–242 (1971). https://doi.org/10.1007/BF01397083

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Keywords

  • Mathematical Method
  • Basic Algorithm
  • Number System
  • Double Precision
  • Floating Point