Isaac Dupree:
We could try to find out how large Integers get, in practice, in existing Haskell code (this may be difficult to find out).
Daniel Fischer wrote:
Just as a data-point, my code rarely exceeds 128 bits (at least, beyond that performance isn't so important anymore).
And Daniel, who is part of the Project Euler team, uses large integers far more than most people. As another data point, Python has also re-invented the GMP wheel, likely for the same licensing reasons. They have been using a simple implementation of Karatsuba multiplication for years. I have never heard of anyone complaining about it. Furthermore, they currently use naive multiplication and don't even bother with Karatsuba for less than about 2000 bits on most recent platforms. Regards, Yitz