Proposal: Array.prototype.shuffle (Fisher-Yates)
J Decker
d3ck0r at gmail.com
Mon Apr 30 05:50:11 UTC 2018
>
>
> >
> > While a good shuffle should be able to start from the initial state and
> > generate a good shuffled result, it is slightly better to progressively
> > shuffle the previous result array into new positions than to start from
> an
> > initial state and compute a 1-off.
>
> Evidence? (BTW, the Fisher-Yates shuffle is theoretically as biased as
> the RNG that powers it.)
>
>
Specifically re-1-off vs progressive shuffling? Not on-hand; it was an
evaluation I did 10 years ago; and while the difference wasn't that much,
it was notable. the rate for any single ball to be in a specific position
took longer (by iteration count) when resetting the array to shuffle to
initial conditions (1-N)
Fisher-Yates. is biased by the usage of the number generator; not just the
generator.
I've been considering how to graphically/visually demonstrate it; but I'v
failed so far.
for a list of 10 numbers; and a 'perfect' RNG.
For the last number, it's 90% guaranteed to evaluate it's shuffle twice.
(10% it won't move) It has a 10% chance to be in the last position, but
only a 1.1% chance to be in the second to last position. (1/10 * 1/9 =
1/90 = 0.011...) so it will NOT be the last position 90% but it will NOT be
the second to last 98.9% of the time. For an ideal shuffle, every original
position will end up in every other position 10% of the time.
> >
> > On Sun, Apr 29, 2018 at 3:27 PM, Isiah Meadows <isiahmeadows at gmail.com>
> > wrote:
> >>
> >> BTW, I added this to my list of various proposed array additions (as a
> >> weak one) [1].
> >>
> >> I did do a little reading up and found that in general, there's a
> >> major glitch that makes shuffling very hard to get right (issues even
> >> Underscore's `_.shuffle` doesn't address), specifically that of the
> >> size of the random number generator vs how many permutations it can
> >> hit. Specifically, if you want any properly unbiased shuffles covering
> >> all permutations of arrays larger than 34 entries (and that's not a
> >> lot), you can't use any major engines' `Math.random` (which typically
> >> have a max seed+period of 128 bits). You have to roll your own
> >> implementation, and you need at least something like xorshift1024* [2]
> >> (1024-bit max seed/period size) for up to 170 entries, MT19937
> >> [3]/WELL19937 [4] (seed/period up to 2^19937-1) for up to 2080
> >> entries, or MT44497/WELL44497 for up to 4199 entries. Keep in mind the
> >> minimum seed/period size in bits grows roughly `ceil(log2(fact(N)))`
> >> where `N` is the length of the array [5], and the only way you can
> >> guarantee you can even generate all possible permutations of all
> >> arrays (ignoring potential bias) is through a true hardware generator
> >> (with its potentially infinite number of possibilities). Also, another
> >> concern is that the loop's bottleneck is specifically the random
> >> number generation, so you can't get too slow without resulting in a
> >> *very* slow shuffle.
> >>
> >> If you want anything minimally biased and much larger than that,
> >> you'll need a cryptographically secure pseudorandom number generator
> >> just to cover the possible states. (This is about where the
> >> intersection meets between basic statistics and cryptography, since
> >> cipher blocks are frequently that long.) But I'm leaving that as out
> >> of scope of that proposal.
> >>
> >> [1]:
> >> https://github.com/isiahmeadows/array-additions-
> proposal#arrayprototypeshuffle
> >> [2]: https://en.wikipedia.org/wiki/Xorshift#xorshift*
> >> [3]: https://en.wikipedia.org/wiki/Mersenne_Twister
> >> [4]: https://en.wikipedia.org/wiki/Well_equidistributed_long-
> period_linear
> >> [5]:
> >> http://www.wolframalpha.com/input/?i=plot+ceiling(log2(x!)
> )+where+0+%3C+x+%3C+10000
> >>
> >> -----
> >>
> >> Isiah Meadows
> >> me at isiahmeadows.com
> >>
> >> Looking for web consulting? Or a new website?
> >> Send me an email and we can get started.
> >> www.isiahmeadows.com
> >>
> >>
> >> On Sun, Apr 29, 2018 at 4:01 PM, Alexander Lichter <es at lichter.io>
> wrote:
> >> > On 29.04.2018 18:34, Naveen Chawla wrote:
> >> >>
> >> >> I don't think there's such a thing as "real random" in digital algos,
> >> >> just
> >> >> "pseudo random".
> >> >
> >> > You are right. I meant 'unbiased' pseudo randomness here.
> >> >
> >> >> Apart from card games, what's the use case?
> >> >
> >> > There are a lot of potential use cases. The best that comes into my
> mind
> >> > is
> >> > sampling test data.
> >> >
> >> >
> >> > On 29.04.2018 19:01, Isiah Meadows wrote:
> >> >>
> >> >> I think this would be better suited for a library function rather
> than
> >> >> a
> >> >> language feature. I could see this also being useful also for
> >> >> randomized displays, but that's about it. And I'm not sure what an
> >> >> engine could provide here that a library couldn't - you can't really
> >> >> get much faster than what's in the language (minus bounds checking,
> >> >> but the likely frequent cache misses will eclipse that greatly), and
> >> >> it's not unlocking any real new possibilities.
> >> >
> >> > As Tab Atkins Jr. already pointed out it's not about performance
> >> > benefits.
> >> > It's about how error-prone custom shuffle implementations are/can be.
> >> >
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>
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