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Journal Articles Theoretical Computer Science Year : 2003

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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Other [cs.OH]

Dates and versions

inria-00099510 , version 1 (26-09-2006)

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Guillaume Hanrot, Joel Rivat, Gérald Tenenbaum, Paul Zimmermann. Density results on floating-point invertible numbers. Theoretical Computer Science, 2003, 291 (2), pp.135-141. ⟨10.1016/S0304-3975(02)00222-0⟩. ⟨inria-00099510⟩
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