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