Imagine I want to sample [0,2), then I can use the following table: [0,0,0,1,1,0,1,1]. This has cycle length 8. Much longer cycles can be obtained, it just requires the state of the prng to be larger than range being sampled.
It is not, at least not the way you (and me) are interpreting it. A RNG's period is bounded by the number of states it has, internally[1]:
The period is bounded by the number of the states
If a PRNG's internal state contains n bits, its period can be no longer than 2 ^ n results, and may be much shorter.
Our state in the Doom generator is the variable rndindex (or prndindex; we have two generators here); rndindex holds an index in [0, 256) (it is 8 bits), hence we have at most that many states (2 ^ 8, or 256). (I'm assuming the table does not repeat itself, as that would be silly, so in this case, the period is exactly 256 outputs long.)
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Is that true?
Imagine I want to sample [0,2), then I can use the following table: [0,0,0,1,1,0,1,1]. This has cycle length 8. Much longer cycles can be obtained, it just requires the state of the prng to be larger than range being sampled.
It is not, at least not the way you (and me) are interpreting it. A RNG's period is bounded by the number of states it has, internally[1]:
Our state in the Doom generator is the variable rndindex (or prndindex; we have two generators here); rndindex holds an index in [0, 256) (it is 8 bits), hence we have at most that many states (2 ^ 8, or 256). (I'm assuming the table does not repeat itself, as that would be silly, so in this case, the period is exactly 256 outputs long.)
[1]: https://en.wikipedia.org/wiki/Pseudorandom_number_generator#...
Thanks for pointing this out. I have confused the size of output with the size of state.