Why isn't rand() random??

[joex444]

<?php
function randkeys($i) {
  $select = 'abcdefghijklmnopqrstuvwxyz';
  for($k=0;$k<$i;$k++) {
    $key .= $select{rand(0,25)};
  }
  return $key;
}
$test = randkeys(8);
$i=0;
while(randkeys(8)!=$test) {
  $i++;
}
echo 'Odds of duplicates: 1 in '.$i;
?>

OK, so is there some major defect in my reasoning that would make this thing return the same odds each time? I keep getting 1:4095 for an 8 letter string. That's not very random. Other sizes help, like 7 puts it at 16383, IIRC.

Anyways, I know the counter can go really high, because if you don't let them be the same size, it quickly gets into the millions...

[NogDog]

If you are using a PHP version older than 4.2.0, you need to seed the random number generator via srand(), such as srand(time()); (just seed it once in your script, not repeatedly within your loop).

[bradgrafelman]

Actually, I'm using PHP 4.4.2 and getting the same results. Must be something in the logic... though I can't see it.

EDIT: The problem is indeed the [man]rand/man function, but look at it's definition:

... returns a pseudo-random integer between 0 and RAND_MAX ...

The solution? Use [man]mt_rand/man which is actually 4 times faster and it's actually random - I lowered your script down to randkeys(3) and got largely variable results.

[Weedpacket]

rand() uses whichever RNG is supplied in whichever C library was used to compile the executable. And some of them are pretty crappy (I guess they're just not intended for serious random number generation, just "good enough" for occasional purposes). As bradgrafelman notes, mt_rand() is much better, though not for the reason he gives: the Mersenne Twister is just as pseudorandom as whatever algorithm (probably linear-congruential) that your rand() is using.

In fact, I'm guessing that you're testing this on a Windows machine. The standard rand() function there is particularly crappy. Not only does it only produce a sixteen-bit number, but it only uses the previous (sixteen-bit) value to determine the next value. Which means that it can't ever produce a sequence longer than 2^{15=32768=8*(4095+1)} terms before it starts repeating itself.

The careful reader would have wondered why "15" and not "16" there. Joy of joys, Windows uses a signed sixteen-bit integer, and then ignores the sign bit for RNG purposes.

The Mersenne Twister retains a lot more than sixteen bits of history, and under typical conditions has a period of 2^19937-1; so it should take somewhat longer to start repeating. (It's also platform-independent, which it doesn't hurt to have.)