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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
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, Addison-Wesley, Menlo Park, Calif., 1969. MR 633878 (83i:68003)
  • [2] U. W. Kulisch & W. L. Miranker, Computer Arithmetic in Theory and Practice, Academic Press, New York, 1981. MR 606741 (83b:65046)
  • [3] L. B. Rall, Accurate Arithmetic for Scientific Computation, Proceedings of the 1982 Army Numerical Analysis and Computer Conference, 1982.
  • [4] J. H. Wilkenson, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, N. J., 1963. MR 0161456 (28:4661)

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Article copyright: © Copyright 1984 American Mathematical Society

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