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Mathematics of Computation

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A complete axiomatization of computer arithmetic


Author: Richard Mansfield
Journal: Math. Comp. 42 (1984), 623-635
MSC: Primary 65G99; Secondary 03B70, 03C70, 68Q40
DOI: https://doi.org/10.1090/S0025-5718-1984-0736458-7
MathSciNet review: 736458
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Abstract: We define an axiom system for rounded arithmetic to be complete if we can recover from any model of the axioms the exact algebra from whence it came. A complete set of axioms is given for rounded addition and multiplication.


References [Enhancements On Off] (What's this?)

  • [1] Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR 633878
  • [2] Ulrich W. Kulisch and Willard L. Miranker, Computer arithmetic in theory and practice, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. Computer Science and Applied Mathematics. MR 606741
  • [3] L. B. Rall, Accurate Arithmetic for Scientific Computation, Proceedings of the 1982 Army Numerical Analysis and Computer Conference, 1982.
  • [4] J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1984-0736458-7
Article copyright: © Copyright 1984 American Mathematical Society