Quote Originally Posted by bonis62 View Post
you says
When the denominator goes to zero, the run-time (and memory) blows up to infinity - in other words, the algorithm fails.

i reply
use NaN and Float


sorry, i am not a native speaker, might, indeed, surely i expressed myself badly
I understand you're not a native speaker.

Either you're being sarcastic, or you're completely missing the point...
That complexity is just part of the analysis of the algorithm.
It has nothing to do with 0 or NaN or anything hardware...

Basically I'm saying that (now, I'm just making these numbers up):

at 10,000,000 digits, it needs 100MB and 1 second
at 100,000,000 digits, it needs 2GB and 20 seconds
at 1 billion digits, it needs 50GB and 10 minutes
at 10 billion digits, it needs 5TB and 10 hours
at 100 billion digits, it needs 1000TB and 10 years
at 1 trillion digits, it needs infinite memory, and infinite time.

That's what I mean by blows up.

Basically, you get to the point where you have so many operations that no matter what you do, 53 bits of precision isn't enough, because roundoff error alone takes up 53 bits of precision.