Salamin-Brent algorithm

Net researching algorithms for calculating pi, I found the wikipedia
page of that title and learned of the Salamin-Brent algorithm (I'm new
to this particular mathematical esoterica). Therein it states that
the algorithm is O(N log(N) log(log(N))) (i.e., time to calculate N
digits of pi is proportional to N log(N) log(log(N))). My question
is, is the log base the number system base, e.g., the time to
calculate the binary expression of pi is O(N log2(N) log2(log2(N))),
whereas the time to compute the hexadecimal expression is O(N log16(N)
log16(log16(N))), etc. (neglecting any benefits the binary calculation
might gain from taking place on a binary digital computer)?

Oh, and while I have someone's attention, what is done about the
"floating point epsilon" problem, i.e., when the precision of the
calculation reaches the point where it would exceed the representable
precision of the implemented floating point standard? Is it as simple
as just adequately scaling all the numbers involved? Or is there more
to it than that?

Thanks!

DG

.

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