# [Haskell-cafe] Parallel Karatsuba - A Weird speed up value greater than 4 on an Intel Quadcore CPU!

Eugene Kirpichov ekirpichov at gmail.com
Sat Dec 24 17:04:45 CET 2011

```Well, assume that cache is x times faster than main memory and that the hot working set size is y, and cache size of one core is z, and that the algorithm is really bound by memory access. Then some simple math should give the answer :) I can't do it myself now as I don't have a pen and paper at the moment.

24.12.2011, в 19:58, Burak Ekici <ekcburak at hotmail.com> написал(а):

>
> However, the question is what are the approximate limits
> of this super-linear speedup? I mean, is it acceptable, if
> parallelization happens even 100 time faster?
>
> How can I calculate the limits of this speedup via the
> cache size of my processor?
>
> Cheers,
> Burak.
>
> From: ekirpichov at gmail.com
> Subject: Re: [Haskell-cafe] Parallel Karatsuba - A Weird speed up value greater than 4 on an Intel Quadcore CPU!
> Date: Sat, 24 Dec 2011 19:53:26 +0400
> To: ekcburak at hotmail.com
>
> Superlinear speedup can occur due to the increased cache size.
>
>
>
> 24.12.2011, в 19:49, Burak Ekici <ekcburak at hotmail.com> написал(а):
>
> Dear List,
>
> I am trying to parallelize Karatsuba multiplication with Haskell's
> second generation strategies. Although, I am running the code on an
> Intel quad-core  CPU, I abnormally have a speedup much greater
> than 4, around 10, which means a weird parallelization or something
> occurs.
>
> I would be appreciated, if anyone make some comments on the issue
> explaining the possible reasons why this weird incident occurs?
>
> Here is the basic parallel portion of the code:
>
> karatsuba :: Int -> [Bool] -> [Bool] -> [Bool]
> karatsuba _ [] _ = []
> karatsuba _ _ [] = []
> karatsuba currentDepth xs ys
>  | (l < 32 || currentDepth >= limit) = mul xs ys
>  | otherwise = (x `add` (replicate l False ++ (z `add` (replicate l False ++ y)))) `Main.using` strategy
>   where
>    l = (min (length xs) (length ys)) `div` 2
>    (xs0, xs1) = splitAt l xs
>    (ys0, ys1) = splitAt l ys
>    x  = (normalize (karatsuba (currentDepth+1) xs0 ys0))
>    y  = (normalize (karatsuba (currentDepth+1) xs1 ys1))
>    z  = ((karatsuba (currentDepth+1) (add xs0 xs1) (add ys0 ys1)) `sub` (normalize (karatsuba (currentDepth+1) xs0 ys0)) `sub` (normalize (karatsuba (currentDepth+1) xs1 ys1)))
>    strategy res = do (Main.rpar) (x)
>                      (Main.rpar) (y)
>                      (Main.rpar) (z)
>                      Main.rdeepseq res
>
> Many thanks in advance and kind regards.
>
> Saluti,
> Burak.
>
>
>
>
> _______________________________________________