[Haskell-beginners] parallelizing a function for generating prime numbers

[Benjamin Edwards]

Given the linear dependencies in prime number generation, shy of using a
probabilistic sieving method, I'm not sure that it's possible to hope for
any kind of parallel number generation. All you are going to do is for
yourself to eat the cost of synchronisation for no gain.

Ben

On Fri May 16 2014 at 16:53:38, Norbert Melzer <timmelzer at gmail.com> wrote:

> Hi there!
>
> I am trying to enhence the speed of my Project Euler solutions…
>
> My original function is this:
>
> ```haskell
> problem10' ::  Integer
> problem10' = sum $ takeWhile (<=2000000) primes
>   where
>     primes                  = filter isPrime possiblePrimes
>     isPrime n               = n == head (primeFactors n)
>     possiblePrimes          = (2:3:concat [ [6*pp-1, 6*pp+1] | pp <- [1..]
> ])
>     primeFactors m          = pf 2 m
>     pf n m | n*n > m        = [m]
>            | n*n       == m  = [n,n]
>            | m `mod` n == 0  = n:pf n (m `div` n)
>            | otherwise      = pf (n+1) m
> ```
>
> Even if the generation of primes is relatively slow and could be much
> better, I want to focus on parallelization, so I tried the following:
>
> ```haskell
> parFilter :: (a -> Bool) -> [a] -> [a]
> parFilter _ [] = []
> parFilter f (x:xs) =
>   let px = f x
>       pxs = parFilter f xs
>   in par px $ par pxs $ case px of True -> x : pxs
>                                    False -> pxs
>
> problem10' ::  Integer
> problem10' = sum $ takeWhile (<=2000000) primes
>   where
>     primes                  = parFilter isPrime possiblePrimes
>     isPrime n               = n == head (primeFactors n)
>     possiblePrimes          = (2:3:concat [ [6*pp-1, 6*pp+1] | pp <- [1..]
> ])
>     primeFactors m          = pf 2 m
>     pf n m | n*n > m        = [m]
>            | n*n       == m  = [n,n]
>            | m `mod` n == 0  = n:pf n (m `div` n)
>            | otherwise      = pf (n+1) m
> ```
>
> This approach was about half as slow as the first solution (~15 seconds
> old, ~30 the new one!).
>
> Trying to use `Control.Parallel.Strategies.evalList` for `possiblePrimes`
> resulted in a huge waste of memory, since it forced to generate an endless
> list, and does not stop…
>
> Trying the same for `primeFactors` did not gain any speed, but was not
> much slower at least, but I did not expect much, since I look at its head
> only…
>
> Only thing I could imagine to parallelize any further would be the
> takeWhile, but then I don't get how I should do it…
>
> Any ideas how to do it?
>
> TIA
> Norbert
>
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