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

16 May 2014

      I had some fears, that there will be answers like this ;)

The problem with improving the generation itself is, that I don't
understand the faster implementations that I found (namely the
implementation of `Data.Numbers.Primes` in the `primes`-package and some
other Wheel-Sieves).

And for the Project-Euler-Problems I only use code that I have created
myself or at least I have a small idea how it works if it is from a package…

2014-05-16 18:33 GMT+02:00 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 
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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