On Sun, Nov 6, 2011 at 9:10 PM, Bin Jin <
bjin1990@gmail.com> wrote:
> 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