set representation question

[Hal Daume III]

this is somewhat off topic, but i'll add "does anyone have a haskell 
implementation of..." to the beginning to make it more on topic :).  
anyway there are a lot of smart people here...

i'm looking for a representation for a set of natural numbers.  right now, 
my representation is sorted array, which works well.  *all* i care about 
is being able to quickly calculate the size of the intersection of two 
sets.  these sets are, in general, very sparse, which means that the 
intersections tend to be small.

for example, i might have two sets reprsented by the arrays:

 {0,1,10,346,398,1039,3289,3853,9811,89231,50913}
 {0,3,98,183,398,1038,5319,7642,9811,13893,93123}

and all i need to be able to do is respond with "3" very very quickly.  
using sorted arrays, this takes O(n+m) time (where n and m are the sizes 
of the arrays).

i'm willing to pay some up front cost for creating a data structure that 
could do this more quickly (i.e., in logarithmic time).

is such a thing possible?  "does anyone have a haskell implementation of" 
such a thing?  :P

thanks!

 - hal

-- 
 Hal Daume III                                   | hdaume at isi.edu
 "Arrest this man, he talks in maths."           | www.isi.edu/~hdaume