Density results on floating-point invertible numbers
Résumé
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.