[Rd] [R] RNG Cycle and Duplication (PR#12540)

[Prof Brian Ripley]

Remember Wichmann-Hill is a composite generator.  Its composition does 
take more than 2^32 distinct values.

You still haven't identifed a problem here.  The note is to warn that 
runif() does repeat within a cycle, because people wrote code assuming 
otherwise.  It would be a poor use of runif() to rely on the low-order 
bits, and that's standard advice in the field.

For a large sample of uniforms use something like the normal inversion 
does, e.g. 2^(-30) * (runif(N, 0, 2^30) %% 2^30 + runif(N))

Please do leave R-bugs out of this: we already have 4 entries as a result 
of your misunderstandings and false claims.

On Thu, 14 Aug 2008, shli at stat.wvu.edu wrote:

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> I didn't describe the problem clearly. It's about the number of distinct=20
> values. So just ignore cycle issue.
>
> My tests were:
>
> RNGkind(kind=3D"Knuth-TAOCP");
> sum(duplicated(runif(1e7))); #return 46552
>
> RNGkind(kind=3D"Knuth-TAOCP-2002");
> sum(duplicated(runif(1e7))); #return 46415
>
> #These collision frequency suggested there were 2^30 distinct values by=20
> birthday problem.
>
>
> RNGkind(kind=3D"Marsaglia-Multicarry");
> sum(duplicated(runif(1e7))); #return 11682
>
> RNGkind(kind=3D"Super-Duper");
> sum(duplicated(runif(1e7))); #return 11542
>
> RNGkind(kind=3D"Mersenne-Twister");
> sum(duplicated(runif(1e7))); #return 11656
>
> #These indicated there were 2^32 distinct values, which agrees with the=20
> help info.
>
> RNGkind(kind=3D"Wichmann-Hill");
> sum(duplicated(runif(1e7))); #return 0
>
> #So for this method, there should be more than 2^32 distinct values.
>
> You may not get the exact numbers, but they should be close. So how to=20
> explain above problem?
>
> I need generate a large sample without any ties, it seems to me=20
> "Wichmann-Hill" is only choice right now.
>
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
> Shengqiao Li
>
> The Department of Statistics
> PO Box 6330
> West Virginia University
> Morgantown, WV 26506-6330
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=
> =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D
>
> On Thu, 14 Aug 2008, Peter Dalgaard wrote:
>
>> Shengqiao Li wrote:
>>> Hello all,
>>> =20
>>> I am generating large samples of random numbers. The RNG help page says:=
> =20
>>> "All the supplied uniform generators return 32-bit integer values that a=
> re=20
>>> converted to doubles, so they take at most 2^32 distinct values and long=
> =20
>>> runs will return duplicated values." But I find that the cycles are not =
> the=20
>>> same as the 32-bit integer.
>>> =20
>>> My test indicated that the cycles for Knuth's methods were 2^30 while=20
>>> Wichmann-Hill's cycle was larger than 2^32! No numbers were duplicated i=
> n=20
>>> 10M numbers generated by runif using Wichmann-Hill. The other three meth=
> ods=20
>>> had cycle length of 2^32.
>>> =20
>>> So, anybody can explain this? And any improvement to the implementation =
> can=20
>>> be made to increase the cycle length like the Wichmann-Hill method?
>>> =20
>> What test? These are not simple linear congruential generators. Just beca=
> use=20
>> you get the same value twice, it doesn't mean that the sequence is repeat=
> ing.=20
>> Perhaps you should read the entire help page rather than just the note.
>>
>> --=20
>>  O__  ---- Peter Dalgaard             =D8ster Farimagsgade 5, Entr.B
>> c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
>> (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
>> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907
>>
>>
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>
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>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595