Density results on floating-point invertible numbers

Abstract : Let $F_k$ denote the $k$-bit mantissa floating-point (FP) numbers. We prove a conjecture of J.-M. Muller according to which the proportion of numbers in $F_k$ with no FP-reciprocal (for rounding to the nearest element) approaches $\frac{1}{2}-\frac{3}{2}\log\frac43\approx 0.068476\ 89$ as $k\to\infty$. We investigate a similar question for the inverse square root.
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https://hal.inria.fr/inria-00099510
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Submitted on : Tuesday, September 26, 2006 - 9:37:58 AM
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Guillaume Hanrot, Joel Rivat, Gérald Tenenbaum, Paul Zimmermann. Density results on floating-point invertible numbers. Theoretical Computer Science, Elsevier, 2003, 291 (2), pp.135-141. ⟨inria-00099510⟩

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