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Density results on floating-point invertible numbers. (English) Zbl 1064.68003

Summary: Let \(F_{k}\) denote the \(k\)-bit mantissa floating-point (FP) numbers. We prove a conjecture of Muller according to which the proportion of numbers in \(F_{k}\) with no FP-reciprocal (for rounding to the nearest element) approaches \(\frac12-\frac32\log\frac43\approx0.06847689\) as \(k\rightarrow \infty\). We investigate a similar question for the inverse square root.

MSC:

68M07 Mathematical problems of computer architecture
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