performance problem in python 2.2

[Paul Rubin]

Jeff Davis <jdavis at empires.org> writes:
> >  $p = 2**64;
> >  $c = $ARGV[0];
> >  $n = exp(-($c*$c) / (2*$p));
> >  print 1-$n, "\n";
> > 
> I learned to never underestimate the usefulness of mathematics in 
> programming. Lucky for me, I had a teacher to ask and he gave me a lot of 
> good info as well. After giving me some advice (including CS related tips 
> that mostly boiled down to "Use assembly, or maybe C if you can about 
> getting an answer"), he pointed me to Sterling's Theorem, which seems 
> similar to what you did. 

Stirling's approximation is pretty complicated to prove.  The formula
I gave for hash collisions is a lot simpler and you should be able to
discover it with basic calculus.  I'll leave the details as an
exercise for you ;-).