R devel - Aug 2008 - [R] RNG Cycle and Duplication (PR#12537)

Shengqiao Li wrote:
> Hello all,
>
> I am generating large samples of random numbers. The RNG help page 
> says: "All the supplied uniform generators return 32-bit integer 
> values that are converted to doubles, so they take at most 2^32 
> distinct values and long runs will return duplicated values." But I 
> find that the cycles are not the same as the 32-bit integer.
>
> My test indicated that the cycles for Knuth's methods were 2^30 while 
> Wichmann-Hill's cycle was larger than 2^32! No numbers were duplicated 
> in 10M numbers generated by runif using Wichmann-Hill. The other three 
> methods had cycle length of 2^32.
>
> So, anybody can explain this? And any improvement to the 
> implementation can be made to increase the cycle length like the 
> Wichmann-Hill method?
>
What test? These are not simple linear congruential generators. Just 
because you get the same value twice, it doesn't mean that the sequence 
is repeating. Perhaps you should read the entire help page rather than 
just the note.

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