in reply to Re^9: How likely is rand() to repeat?
in thread How likely is rand() to repeat?

But that's not 8-bits.

By that assessment, then neither is MT19973 a "32-bit PRNG", so basing probabilities relating to its use upon 2^32-bits are wrong also.

As I've shown with my 8 bit toy rand, you can get more than 8-bits of entropy out of a "headline" 8-bit RCPRNG.

Equally, the win32 built-in which is described as a 2^15 bit generator, cannot be assessed entirely by formulae using 2^15 either, because it has a period of close to 2^31.

There are 2^32 seeds. Each of them starts a different sequence.

Are you sure about that?

Sure it isn't a single, 4e6001 value non-repeating sequence, and all the seeding does it start you at a different place within it.

Ie. think of the sequence folding back on itself in a circle. The seeding picks a starting point on that circle and then the generator runs around the circle until it finally reaches back to it starting point when it then repeats.

Of course, there is no way to prove that for the MT.

I read this as "the more he generates, the more it takes for a duplication to happen". That seems quite counter intuitive to me, and I'm not sure if that's what you mean.

Come on. The OP needs 25 rands for each string. If he only picks one set of 25 from each seeded starting position, and there are 2^32 such positions, then he can pick at most 2^32.

But, we know there are 6.45e44 possible strings. So he'd only have obtained 0.00000000000000000000000000000000066% of the possibilities. However, if he grabs 50 values from each start position and builds 2 strings with them, he now has twice as many strings.

And if he builds 10 strings from each starting point, he has ten times as many strings, but that's still a vanishingly small proportion of the total possibilities: 0.0000000000000000000000000000000066%.

So no, I didn't mean what you said. I am saying that you are only limited to 2**32 strings if you only generate 1 string from each seed position.

But that you can generate 10 (or 100 or 1000) strings from each starting position, thereby producing 10 (or 100 or 1000) * 2^32 strings, and the odds of having produced a duplicate are still "vanishingly small". Slightly higher than if you only pick 1 at each position, but even 10 (or 100 or 1000) times the infinitesimal, is still infinitesimal.

Minute; way less than micro nano pico femto atto zepto yoctoscopic.

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

The start of some sanity?

Replies are listed 'Best First'.
Re^11: How likely is rand() to repeat?
by JavaFan (Canon) on Mar 09, 2012 at 17:37 UTC
    By that assessment, then neither is MT19973 a "32-bit PRNG", so basing probabilities relating to its use upon 32-bits are wrong also
    MT19973 generates 32 bit numbers. It will not generate more than 232 different numbers. It takes 32 bits as a seed. It uses just short of 20k bits to keep state. I don't know what the term "k-bit PRNG" exactly means, which why I tried avoiding that term and keep using seed and state sizes.
    There are 232 seeds. Each of them starts a different sequence.
    Are you sure about that?

    Sure it isn't a single, 4e6001 value non-repeating sequence, and all the seeding does it start you at a different place within it.

    Fine, whatever. Doesn't make a iota difference to the argument. But if you want to split hairs, be my guest. So you have 232 different starting points in the sequence.
[reply]
      MT19973 generates 32 bit numbers. It will not generate more than 232 different numbers. It takes 32 bits as a seed.

      If the important bit is that it produces 32-bit numbers and is seeded by a 32-bit number -- though from memory, the underlying C implementation can be seeded with 640 32-bit numbers, as can Math::Random::MT::Auto I believe; but let's skip that detail -- why do you think it is named MT19937?

      But if you want to split hairs, be my guest.

      You started it. I was responding to you.

      And it does make a difference.

      With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.

      The start of some sanity?
[reply]
        why do you think it is named MT19937?
        Lemme guess, because they followed the example of drand48, and put the number of number of bits that's needed for the state in the name? Or perhaps because it's related to the length of the period? Not quite sure which point you're trying to make. I never claimed it was a "32-bit PRNG", but I guess you seem to think it is. After all, a few posts ago, you write By that assessment, then neither is MT19973 a "32-bit PRNG", which makes me think that's a classification that's important to you.
        And it does make a difference.
        Well, that's fine. It doesn't make a difference to me, and if all you can say about the difference that it exists, I cannot imagine it's an important difference.
[reply]
[d/l]

In Section Seekers of Perl Wisdom