Hi, everyone
I'm recently trying to implement the Montgomery reduction algorithm[1] in Haskell, the code can be found on
my Github page[2]. After doing some benchmark testing I found that the library works rather slow. With the
help of `trace` function from Debug.Trace, I found that GHC is not magical enough to memorize values with
the same type(well, it's actually dynamically generated number parameterized type).
I used binary representation to handle all positive numbers in type system.
> data One = One
> data D0 a = D0 a
> data D1 a = D1 a
> class PostiveN a where
> p2num :: (Num b, Bits b) => a -> b
> instance PostiveN One ...
> instance PostiveN a => PostiveN (D0 a) ...
> instance PostiveN a => PostiveN (D1 a) ...
Here is a function that will be called everytime by `(*)` in `Num` typeclass
> montgKeys :: (PostiveN p, Integral a, Bits a) => p -> a
as you can imagine, I always pass (undefined :: p) as parameter to `montgKeys`, so if it's handled
well, it should be memorized for future usage. But tracing shows that both `p2num` and `montgKeys`
are evaluated every time being called.
So my question is, how to force GHC memorizing this kind of functions?
[1]: http://en.wikipedia.org/wiki/Montgomery_reduction
[2]: https://github.com/bjin/montg-reduce
Regards,
Bin