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Abstract: If the non-zero finite floating-point numbers are interpreted as pointintervals, then the effect of rounding can be interpreted as computing one ofthe bounds of the result according to interval arithmetic. We give an intervalinterpretation for the signed zeros and infinities, so that the undefinedoperations 0*inf, inf - inf, inf-inf, and 0-0 become defined.In this way no operation remains that gives rise to an error condition.Mathematically questionable features of the floating-point standard becomewell-defined sets of reals. Interval semantics provides a basis for theverification of numerical algorithms. We derive the results of the newlydefined operations and consider the implications for hardware implementation.



Author: W.W. Edmonson, M.H. van Emden

Source: https://arxiv.org/







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