Density results on floating-point invertible numbers (original) (raw)

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Article Dans Une Revue Theoretical Computer Science Année : 2003

Guillaume Hanrot (1) , Joel Rivat (2) , Gérald Tenenbaum (2) , Paul Zimmermann (1)

1 SPACES - Solving problems through algebraic computation and efficient software
2 ST-CROLLES - STMicroelectronics [Crolles]

Guillaume Hanrot

SPACES - Solving problems through algebraic computation and efficient software

Joel Rivat

ST-CROLLES - STMicroelectronics [Crolles]

Gérald Tenenbaum

ST-CROLLES - STMicroelectronics [Crolles]

CV

Paul Zimmermann

SPACES - Solving problems through algebraic computation and efficient software

CV

Résumé

Let FkF_kFk denote the kkk-bit mantissa floating-point (FP) numbers. We prove a conjecture of J.-M. Muller according to which the proportion of numbers in FkF_kFk with no FP-reciprocal (for rounding to the nearest element) approaches frac12−frac32logfrac43approx0.06847689\frac{1}{2}-\frac{3}{2}\log\frac43\approx 0.068476\ 89frac12−frac32logfrac43approx0.06847689 as ktoinftyk\to\inftyktoinfty. We investigate a similar question for the inverse square root.

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https://inria.hal.science/inria-00099510

Soumis le : mardi 26 septembre 2006-09:37:58

Dernière modification le : mardi 4 novembre 2025-12:04:19

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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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