Seed limits in R

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Consensus on set.seed in R is that that it effectively generates a long sequence of pseudo-random numbers, pre-determined by the seed. Then the first call you make to this sequence (with the first non-deterministic function you use) takes the first batch from that sequence, the second call takes the next batch, so forth.

I am wondering what the limits to this are. Specifically, what happens when you get to the end of that long sequence? Let's say, after setting a seed, you then sample from the first 100 integers repeatedly. Would there come a point where you start generating the same samples (in the same order) as you were seeing at the beginning? How long would this take? (Does it depend on the seed?) If not, how would reaching the 'end' of the sequence and presumably circling back to the beginning manifest?

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1 Answers

The ?RNGkind help page in R gives more details on the default random number generator, the "Mersenne Twister" algorithm:

"Mersenne-Twister": From Matsumoto and Nishimura (1998); code updated in 2002. A twisted GFSR with period 2^19937 - 1 and equidistribution in 623 consecutive dimensions (over the whole period). The ‘seed’ is a 624-dimensional set of 32-bit integers plus a current position in that set.

As stated there, the "period" (the length of time it takes to get back to the beginning and start repeating values is 2^19937-1, or approximately 10^(19937/log2(10)) = 10^6001.

  • If the size of your "batches" happened to line up exactly with the period, then you would indeed start getting the same batches again.
  • I'm not sure how many pseudorandom samples R uses to pick a sample of size 1 from a set. Ideally it would be only 1 (so your "batch size" would be 1), but it might be more depending on the generality/complexity of the sampling algorithm.
  • I know that runif() translates more or less directly from the PRNG, so a sequence of runif() calls would indeed repeat exactly.
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