... assuming that mpfr is using the exact value of the double precision ...

It is - unless there's a bug at work.

which makes d = 58

Here's a couple of values that, according to mpfr, require 60 decimal digits:

1 / 526
1.90114068441064637711435114653113487293012440204620361328125e-3

1 / 535
1.86915887850467297461032334382480257772840559482574462890625e-3
[download]

Might be time I stopped fiddling and started thinking. (Have you got a spare one of those in-skull emulators that you could send over ?)

Update: Fiddling is much easier, especially on a Sat'dy night. I've found numerous doubles that apparently require 122 decimal digits for exact representation, but haven't found any that require more than 122. For example:

25 / (8360484 ** 15)
3.66833261843476555514935702258199343058161821865425601769198458144384
+41059633175331427349000780680559003454762069283595612e-103
[download]

Cheers,
Rob

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