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So in short my question would be this:

How one should test a short period PRNG?

Emphasis being on short period, like from 2^8 up to at most 2^32. These small generators may have more compact and faster code, small state, might making them suitable for certain procedural generation tasks. The importance is that their generated sequence should be "reasonably random". In this case it may even be viable to test every seed one plans to use, so technically just the output stream itself may be sufficient.

I am aware of other similar questions like this, but they rather target long period, probably even cryptographically secure PRNGs.

So far I see that for example the Overlapping permutations test from the Diehard harness may work, but others seem to rather target long periods.

I tried to do X:Y plots to see correlations such as here, this seems to work and visually provide a good feedback, but I would like to see more if possible (if needed?).

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Jubatian
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  • 2^32 is [long enough](http://stackoverflow.com/a/17055537/2417578) to satisfy all of the dieharder tests. I'm not sure how far you could reduce that before it started causing failures, though. Certainly not 2^8! – sh1 Jul 08 '13 at 12:08

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