[Haskell-cafe] Infelicity in StdGen?

[Krzysztof Skrzętnicki]

I think the confusion may be come from the understanding of "distinct". The
documentation is right that the generators are not equal which is easily
checked e.g. using their Show instance. They *will* produce different
random numbers. The user of the library might OTOH assume that "distinct"
mean "producing uncorrelated output". This is harder and may simply not
hold, especially that it doesn't mention sequentially increasing integers
or any other kinds of sequences.

The property you seem to be looking for is "have vastly different output
for similar numbers". Sounds a lot like a hash function to me.

> import Data.Hashable -- hashable
> import System.Random -- random
> hGen :: (Hashable a) => a -> StdGen
> hGen = mkStdGen . hash

GHCi:
> mkStdGen <$> [1..10]
[2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 1,10 1,11 1]
> hGen <$> [1..10]
[2113803271 1,707778093 1,377439146 1,354368904 1,1689773631 1,1515981814
1,1419492475 1,1232077631 1,2037530173 1,1078099554 1]

You can also ask System.Random for a required set of random numbers for use
as seeds.

> map mkStdGen <$> replicateM 10 randomIO
[817657009 1,491059977 1,1962205061 1,375413047 1,626395891 1,1694342924
1,1145131839 1,441215930 1,1278080790 1,1524285256 1]

Finally, StdGen provides 'split' since it implements RandomGen typeclass.
Using Data.List.unfoldr:

> take 10 $ unfoldr (Just . split) (mkStdGen 1)
[3 40692,80029 2147442707,1054756830 2147402015,545291968
2147361323,879767459 2147320631,1464499717 2147279939,2107652444
2147239247,1777851630 2147198555,1414574869 2147157863,1574498162
2147117171]

The question is what really are your needs here. Different applications
will require different properties. I hope the above will give some hints.

On Fri, Jan 3, 2014 at 5:28 PM, Rob Arthan <rda at lemma-one.com> wrote:

> Either I am misunderstanding something or there is an infelicity
> in the implementation of StdGen. The documentation on mkStdGen says
> that distinct arguments should be likely to produce distinct generators.
> This made me think that I would get a reasonable pseudo-random function
> to simulate n rolls of a die by using n to seed the random
> number generator:
>
> import System.Random
> roll :: Int -> String
> roll n = take n . randomRs ('1', '6') . mkStdGen $ n
>
> However, this produces a string beginning with a '6' for 0 <= n <= 53667.
> In fact the dependency of the first value on the seed seems to be far from
> random:
>
> map (\l -> (head l, length l)) . group . map (fst . randomR (1, 6) .
> mkStdGen) $ [0..25*53668+6]
>
> returns:
>
>
> [(6,53668),(5,53668),(4,53668),(3,53669),(2,53668),(1,53668),(6,53669),(5,53668),(4,53668),(3,53669),(2,53668),(1,53668),(6,53668),(5,53669),(4,53668),(3,53668),(2,53669),(1,53668),(6,53668),(5,53669),(4,53668),(3,53668),(2,53669),(1,53668),(6,53668)]
>
> The behaviour seems to be related to the length of the range.
> You get similar behaviour for ranges of length 2, 3, 6 and 9 for example,
> but not for 4, 5, 7 or 8.
>
> If it is relevant, I am using ghc version 7.6.3.
>
> Regards,
>
> Rob.
>
>
>
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