[Haskell-cafe] Splittable random numbers

[Luke Palmer]

On Thu, Nov 11, 2010 at 3:13 AM, Richard Senington <sc06r2s at leeds.ac.uk> wrote:
> I got hold of, and looked through the paper suggested in the root of this
> thread “Pseudo random trees in Monte-Carlo", and based upon this
> I have thrown together a version of the binary tree based random number
> generator suggested.
>
> I would like to point out that I do not know very much about random number
> generators, the underlying mathematics or any subsequent papers on this
> subject, this is just a very naive implementation based upon this one paper.
>
> As a question, the following code actually generates a stream of numbers
> that is more random than I was expecting, if anyone can explain why I would
> be very interested.

What do you mean more random than you were expecting?  Shouldn't they
be "maximally random"?

BTW, nice module.  Do you want to hackage it up?  If not, I will.

> import System.Random
>
> data LehmerTree = LehmerTree {nextInt :: Int,
>                               leftBranch :: LehmerTree,
>                               rightBranch :: LehmerTree}
>
> instance Show LehmerTree where
>   show g = "LehmerTree, current root = "++(show $ nextInt g)
>
> mkLehmerTree :: Int->Int->Int->Int->Int->Int->LehmerTree
> mkLehmerTree aL aR cL cR m x0 = innerMkTree x0
>   where
>     mkLeft x = (aL * x + cL) `mod` m
>     mkRight x = (aR * x + cR) `mod` m
>     innerMkTree x = let l = innerMkTree (mkLeft x)
>                         r = innerMkTree (mkRight x)
>                     in LehmerTree x l r
>
> mkLehmerTreeFromRandom :: IO LehmerTree
> mkLehmerTreeFromRandom = do gen<-getStdGen
>                             let a:b:c:d:e:f:_ = randoms gen
>                             return $ mkLehmerTree a b c d e f

This can be pure:

mkLehmerTreeFromRandom :: (RandomGen g) => g -> LehmerTree

> instance RandomGen LehmerTree where
>   next g = (fromIntegral.nextInt $ g, leftBranch g)
>   split g = (leftBranch g, rightBranch g)
>   genRange _ = (0, 2147483562) -- duplicate of stdRange
>
>
>
> test :: IO()
> test = do gen<-mkLehmerTreeFromRandom
>           print gen
>           let (g1,g2) = split gen
>           let p = take 10 $ randoms gen :: [Int]
>           let p' = take 10 $ randoms g1 :: [Int]
>           -- let p'' = take 10 $ randoms g2 :: [Float]
>           print p
>           print p'
>           -- print p''
>
>
>
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