# Implementaion of random.shuffle

shabda raaj shabda.raaj at gmail.com
Tue Jul 17 10:35:15 CEST 2007

```Ah, thanks I get it now!

--Shabda

On Jul 17, 7:52 am, Steven D'Aprano
<ste... at REMOVE.THIS.cybersource.com.au> wrote:
> On Mon, 16 Jul 2007 14:45:48 +0000,shabdaraaj wrote:
> > On Jul 16, 5:53 pm, Steve Holden <st... at holdenweb.com> wrote:
> >>shabdaraaj wrote:
> >> > I was going through the docs for module-random
> >> > <http://docs.python.org/lib/module-random.html>  And I came through
> >> > this,
>
> >> > * shuffle*(        x[, random])
>
> >> >     Shuffle the sequence x in place. The optional argument random is
> >> >     a 0-argument function returning a random float in [0.0, 1.0); by
> >> >     default, this is the function random().
>
> >> >     Note that for even rather small |len(x)|, the total number of
> >> >     permutations of x is larger than the period of most random number
> >> >     generators; this implies that most permutations of a long
> >> >     sequence can never be generated.
>
> [snip]
>
> > Oh, I wasn't aware that I could see the source of all python modules. I
> > guess, then the implementation is correct(its just the knuth shuffle,
> > moving downward), its just the doc which is in error. Might be we should
> > log a doc bug for this?
>
> No, it is not a doc error, you are confused.
>
> Suppose you have a random number generator that has the tiny period of
> 120. (Obviously that's a really lousy RNG, but it will do for an
> example.) That means it can only produce 120 different results (the
> current number, plus the state the generator it is in) before repeating.
>
> Note that the period is not the same as the spread of values returned,
> the two are independent, although naturally the period must be at least
> equal to the number of unique values returned.
>
> If you have a list of just six items, there are 6! = 720 possible
> permutations of the list, so AT BEST the random number generator can
> produce 120/720 or 17% of the permutations.
>
> That's an example of the pigeonhole principle, one of the most simple yet
> powerful mathematical principles around. If you've got more items than
> pigeonholes to put them in, either some will double up or some will miss
> out.
>
> In the case of CPython, the current implementation uses the Mersenne
> Twister, which has a huge period of 2**19937. However, 2081! is larger
> than that number, which means that at best a list of 2081 items or longer
> can't be perfectly shuffled (not every permutation can be selected by the
> algorithm).
>
> --
> Steven.

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