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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A complete axiomatization of computer arithmetic
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by Richard Mansfield PDF
Math. Comp. 42 (1984), 623-635 Request permission

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
  • Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
  • Ulrich W. Kulisch and Willard L. Miranker, Computer arithmetic in theory and practice, Computer Science and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 606741
  • L. B. Rall, Accurate Arithmetic for Scientific Computation, Proceedings of the 1982 Army Numerical Analysis and Computer Conference, 1982.
  • J. H. Wilkinson, Rounding errors in algebraic processes, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0161456
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • 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