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On Local Roundoff Errors in Floating-Point Arithmetic
Journal of the ACM, 1973A bound on the relative error in floating-point addition using a single-precision accumulator with guard digits is derived. It is shown that even with a single guard digit, the accuracy can be almost as good as that using a double-precision accumulator.
Toyohisa Kaneko, Bede Liu
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Floating point arithmetic and digital filters
IEEE Transactions on Signal Processing, 1992The roundoff noise properties of floating point digital filters are examined. To make the analysis tractable, a high level model to deal with the errors in the inner product operation is developed. This model establishes a broad connection between coefficient sensitivity and roundoff noise.
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Formalization and implementation of floating-point arithmetics
Computing, 1975The paper is intended to show that floating-point arithmetic can be implemented in a way which leads to reasonable mathematical structures as described in chapters 5 and 6. It turns out for instance that all the rules of the minus-operator of the real numbers can be saved and that with respect to ≦ and ≧ inequalities can be manipulated as if they were ...
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Required scientific floating point arithmetic
1978 IEEE 4th Symposium onomputer Arithmetic (ARITH), 1978Previous papers in computer arithmetic have shown that correct rounded floating point with good arithmetic properties can be attained using guard digits and careful algorithms on the floating point fractions. This paper combines that body of knowledge with proposed exponent forms that are closed with respect to inversion and detection and recovery of ...
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Is Floating-Point. Arithmetic Still Adequate?
1988For complicated numerical problems, the error analysis has to be performed by the computer. Several methods for automated error analysis are known. Floating-point arithmetic has to be augmented and programming languages for scientific computation have to be provided (PASCAL-SC and FORTRAN-SC) for that purpose.
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Accurate and Reliable Computing in Floating-Point Arithmetic
2010Methods will be discussed on how to compute accurate and reliable results in pure floating-point arithmetic. In particular, verification methods with INTLAB and error-free transformations will be presented in some detail.
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Rational Arithmetic in Floating-Point.
1986Abstract : Calculating M/N := A/B + or - C/D in lowest terms, given the integers A, B, C and D, is a task in Elementary schools; and it is an easy exercise in Computer Programming too provided the given integers must be less than half as wide as the widest integers that can be handled conveniently by the computer's hardware or by its programming ...
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What Every Computer Scientist Should Know About Floating-Point Arithmetic
ACM Computing Surveys, 1991David M. Goldberg
exaly