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.
- 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
- 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 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
Donald E. Knuth, The Art of Computer Programming, Vol. 2, Addison-Wesley, Menlo Park, Calif., 1969.
U. W. Kulisch & W. L. Miranker, Computer Arithmetic in Theory and Practice, Academic Press, New York, 1981.
L. B. Rall, Accurate Arithmetic for Scientific Computation, Proceedings of the 1982 Army Numerical Analysis and Computer Conference, 1982.
J. H. Wilkenson, Rounding Errors in Algebraic Processes, Prentice-Hall, Englewood Cliffs, N. J., 1963.