[Rd] all zeroes in Mersenne Twister state may remain undetected

From: Petr Savicky <savicky_at_cs.cas.cz>
Date: Mon, 15 Oct 2007 12:49:22 +0200

The function runif(n) contains a protection against a corrupted .Random.seed. Besides other things, it tests whether at least one of the numbers .Random.seed[3:626] is not zero. If all(.Random.seed[3:626]==0), then the internal Mersenne Twister state is regenerated using current time, since a zero state is a fixed point of the recurrence and, hence, produces a constant sequence.

However, the condition any(.Random.seed[3:626]!=0) does not imply that the internal Mersenne Twister state is indeed not zero, since only the most significant bit of .Random.seed[3] belongs to the internal state. Hence, the number of bits in the state of Mersenne Twister is 624*32 - 31 = 19937, which explains the period 2^19937-1.

For example, if .Random.seed[3] == 1, we always have the condition   any(.Random.seed[3:626]!=0)
satisfied, but the internal state may still be effectively zero. An example of such a situation is
.Random.seed[3:626] <- as.integer(0)
.Random.seed[3] <- as.integer(1)

  x <- runif(10000)
  all(x==x[1]) # TRUE
  length(unique(x)) # 1
  all(.Random.seed[3:626]==0) # TRUE
Here, the internal state was effectively zero, but this fact was not detected, since some (unimportant) bits of .Random.seed[3] were not zero.

On the contrary, if also .Random.seed[3]==0, then the internal state is regenerated and the output of runif() becomes non constant:   RNGkind("default")
.Random.seed[3:626] <- as.integer(0)

  x <- runif(10000)
  all(x==x[1]) # FALSE
  length(unique(x)) # 10000
  all(.Random.seed[3:626]==0) # FALSE

The following patch to FixupSeeds corrects the detection of zero state:

Petr Savicky.

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