[R] RNG Cycle and Duplication

Duncan Murdoch murdoch at stats.uwo.ca
Thu Aug 14 23:04:14 CEST 2008

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.

This is no bug.  Cycle length and the set of possible values are 
different concepts. 

And please don't cross-post.

Duncan Murdoch
> 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?
> ========================================
> Shengqiao Li
> Research Associate
> The Department of Statistics
> West Virginia University
> Morgantown, WV 26506-6330
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