Roger Hui wrote:
> The limit is 5.

Roger, you're absolutely correct.  This example is one where a 53-bit
mantissa gives 100, while a 64-bit mantissa gives 5. It is due to
Jean-Michel Muller.

I took the particular formulation from William Kahan's paper (discussion
starts at page 14)

<http://www.cs.berkeley.edu/~wkahan/Mindless.pdf>

Kahan is well worth reading on floating-point issues.  His polemical style
is either amusing or annoying, depending on your taste.  However, he is
not a crank: he was the prime architect of the IEEE floating-point
standard, and in 1989 received the Turing Award for his work in numerical
analysis.

Best wishes,

John



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