Density results on floating-point invertible numbers

✍ Scribed by G Hanrot; J Rivat; G Tenenbaum; P Zimmermann

• Book ID: 104325431
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 118 KB
• Volume: 291
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(02)00222-0

✦ Synopsis

Let F k denote the k-bit mantissa oating-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 1 2 -3 2 log 4 3 ≈ 0:06847689 as k → ∞. We investigate a similar question for the inverse square root.