[Haskell-cafe] Bug in random shuffle algorithm

Viktor Dukhovni ietf-dane at dukhovni.org
Tue May 9 05:46:52 UTC 2017

```> On May 8, 2017, at 12:02 PM, David Turner <dct25-561bs at mythic-beasts.com> wrote:
>
> But this doesn't yield a uniformly-chosen random permutation of its input, because at the i'th step the first `i` elements are not fixed as they are in the other algorithms on that page.

Channeling Samuel Dukhovni, who provided a patch for the same bug in
older versions of Postfix a few years back, his suggested patch is:

shuffle :: RandomGen g => [a] -> Rand g [a]
shuffle xs = do
let l = length xs
-     rands <- take l `fmap` getRandomRs (0, l-1)
+     rands <- forM [0..(l-1)] (\i -> getRandomR (i, l-1))
let ar = runSTArray \$ do
ar <- thawSTArray \$ listArray (0, l-1) xs
forM_ (zip [0..(l-1)] rands) \$ \(i, j) -> do
writeSTArray ar j vi
writeSTArray ar i vj
return ar
return (elems ar)

Perhaps someone can forward this along to the package maintainer.

Also as an optimization, the `rands` list should be made one element
shorter, and likewise the `zip [0..(l-1)]` should become `zip [0..(l-2)]`.
The reason is of course that by the time we only have one final element
left there's nothing left to permute.

--
Viktor.

P.S.  The corresponding new Postfix code can be found at

https://github.com/vdukhovni/postfix/blob/master/postfix/src/dns/dns_rr.c#L305

/*
* Shuffle resource records. Every element has an equal chance of landing
* in slot 0.  After that every remaining element has an equal chance of
* landing in slot 1, ...  This is exactly n! states for n! permutations.
*/
for (i = 0; i < len - 1; i++) {
r = i + (myrand() % (len - i));         /* Victor&Son */
rr = rr_array[i];
rr_array[i] = rr_array[r];
rr_array[r] = rr;
}

```