Re: How likely is rand() to repeat?

[aaron_baugher]

I'm following this discussion with interest, though I don't completely understand it. But it reminds me that on the old Commodore 64, we got random values by reading a value from an 8-bit register on the sound chip after putting it into 'noise' mode. My understanding was that this was truly random, and although there were only 256 values, people recorded tens of thousands without a pattern ever repeating.

So I'm wondering: Why don't we have something like that in systems today? That function could probably be added to a BIOS chip today for less than a penny. I suppose that reading voltage fluctuations or keyboard timings is another way to bring in outside randomness, but reading a value from a register sure was a simple way to do it.

[BrowserUk]

The trouble with hardware generators is that, as there is no record of their output, you will never detect if the have gone wrong. For example, it is possible for pink noise generators to devolve into harmonic resonance -- through partial hardware failure or externally source interference -- which could combine with particular sampling rates to generate short repeating sequences.

The problem was first recognised by Von Neumann:

Von Neumann judged hardware random number generators unsuitable, for, if they did not record the output generated, they could not later be tested for errors. If they did record their output, they would exhaust the limited computer memories available then, and so the computer's ability to read and write numbers. If the numbers were written to cards, they would take very much longer to write and read. On the ENIAC computer he was using, the "middle square" method generated numbers at a rate some hundred times faster than reading numbers in from punched cards.

Of course, he was working with valves (vacuum tubes), coils etc. It is probably far less likely for modern electronics to be susceptible to such interference or failure, but the underlying problem of being unable to detect failure remains.

The repeatability of PRNGs has the distinct advantage that you can subject them to a battery of repeatable tests before using them.