Approximate rational arithmetic systems: Analysis of recovery of simple fractions during expression evaluation
Closed approximate rational arithmetic systems are described and their number theoretic foundations are surveyed. The arithmetic is shown to implicitly contain an adaptive single-to-double precision natural rounding behavior that acts to recover true simple fractional results. The probability of such recovery is investigated and shown to be quite favorable.
Key WordsRational arithmetic gcd-algorithm continued fractions fixed- and floating-slash number systems adaptive variable precision recovery of exactness symbolic/numberic interface
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