Richard Senington sc06r2s at leeds.ac.uk
Thu Nov 11 05:13:00 EST 2010

```I got hold of, and looked through the paper suggested in the root of
this thread "Pseudo random trees in Monte-Carlo
<http://portal.acm.org/citation.cfm?id=1746034>", 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.

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

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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