Re^13: How likely is rand() to repeat?

[JavaFan]

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.

[BrowserUk]

Okay. When reason fails, how's about a little empirical evidence?

#! perl -slw
use strict;
use Math::Random::MT qw[ rand srand ];

$|++;
my @c = ( 'A'..'Z', 'a'..'z', 0..9 );

for my $run  ( 1 .. 1e6 ) {
    my %seen; keys %seen = 1e6;
    printf "\rrun: $run";
    for my $id ( 1 .. 1e6 ) {
        srand( $run + $id );
        my $ID = join '', map $c[ int rand( 62 ) ], 1 .. 25;
        warn "Dup $ID at $run/$id" if exists $seen{ $ID };
        undef $seen{ $ID };
    }
}

__END__

C:\test>"IDrand(62)x25.pl"
run: 254

That console log is a snapshot. After generating 254 sets of 1 million 25-char keys, with each key being generated at a new seed position, NO DUPS SEEN!

How long will it need to run before you are convinced that the OP is safe to use this?

[JavaFan]

How long will it need to run before you are convinced that the OP is safe to use this?

Did I ever claim otherwise?

All I've been claiming is that if you're seeding a deterministic random number generator with k bits, you will not be getting more than 2^k sequences, and that I've seen no evidence whatsoever that you can pull more out of thin air.

After generating 254 sets of 1 million 25-char keys, with each key being generated at a new seed position, NO DUPS SEEN!

254 sets of 1 million keys? Call me confused, but:

for my $run  ( 1 .. 1e6 ) {
    ...
    for my $id ( 1 .. 1e6 ) {
        srand ( $run + $id );
        ...
    }
}

Aren't you generating a million sets of a million keys each? But with only 2 million different keys, as $run + $id ranges from 2 .. 2e6.

But never mind that. I've never questioned that picking a different seed is very likely to give you a different key. My claim is, that if you have only 2³² different seeds you will not get more than 2³² keys this way. You exercise showed that if you pick a million different seeds, you get a million different keys. And you repeated that experiment a million times, each time removing a single seed from the set of a million, and adding another one.

[BrowserUk]

More to your satisfaction?

#! perl -slw
use strict;
use Math::Random::MT qw[ rand srand ];

$|++;
my @c = ( 'A'..'Z', 'a'..'z', 0..9 );

for my $run  ( 1 .. 1e6 ) {
    my %seen; keys %seen = 1e6;
    printf "\rrun: $run";
    for my $id ( 1 .. 1e5 ) {
        srand( $run * $id );
        for( 1 .. 10 ) {
            my $ID = join '', map $c[ int rand( 62 ) ], 1 .. 25;
            warn "Dup $ID at $run/$id" if exists $seen{ $ID };
            undef $seen{ $ID };
        }
    }
}

__END__
C:\test>"IDrand(62)x25.pl"
run: 54