Here's my version... maybe not as elegant as some, but it seems to
work. For base 2 (or 2^k), it's probably possible to make this even
more efficient by just walking along the integer as stored in memory,
but that difference probably won't show up until at least tens of
thousands of digits.
Uwe
ilogb :: Integer -> Integer -> Integer
ilogb b n | n < 0 = ilogb b (- n)
| n < b = 0
| otherwise = (up 1) - 1
where up a = if n < (b ^ a)
then bin (quot a 2) a
else up (2*a)
bin lo hi = if (hi - lo) <= 1
then hi
else let av = quot (lo + hi) 2
in if n < (b ^ av)
then bin lo av
else bin av hi
numDigits n = 1 + ilogb 10 n
[fire up ghci, load, etc]
*Main> numDigits (10^1500 - 1)
1500
*Main> numDigits (10^1500)
1501
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