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

Burak Ekici ekcburak at hotmail.com
Sat Dec 24 16:58:54 CET 2011

First of all, thanks a lot for your quick answer!
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?


CC: haskell-cafe at haskell.org
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 

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  
   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.


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