Re: [OctDev] random numbers for distributed computations

[Paul Kienzle]

On Apr 11, 2005, at 6:42 AM, Michael Creel wrote:

> On Monday 11 April 2005 11:57, Francesco Potorti` wrote:
> > > I have a question about this. If a RNG has a period of X, that means 
> > > that
> > > there are X unique values that are generated, and then the sequence
> > > repeats.
> >
> > No, it means that the sequence repeats after X values are produced.  
> > The
> > period length says nothing about the space of values.  However, for 
> > good
> > general purpose generators, the size of the space of values is much
> > smaller than the period.
>
> OK, you're saying that a generator with period 5 could produce values 
> like
> 1 2 2 1 2 *** 1 2 2 1 2 *** 1 2 2 1 2
> so the set of unique values is smaller than the period, correct?
>
> This may be, but for the moment my main question is whether the set of 
> unique
> values that is generated depends upon the initial seed, or whether 
> it's just
> the starting point in the sequence that depends on the initial seed. 
> Could
> the unique values be 3 and 4, say, or will they always be 1 and 2?

You are correct that the generator is entirely deterministic and the 
numbers
will occur in the same order.  As David says elsewhere, however, if the
sequence is very long and you start each processor at a different part 
of
the sequence then you should be okay (e.g., by including processor # in 
the
seed value).

A better approach is to use independent sequences on each processor, 
which
you can do by choosing different constants in your random number 
generator.
There is some concern that any RNG which is simple enough that you can 
do
this will not have good statistical properties.

You could try the parallel Mersenne Twister program (available from the
main Mersenne Twister site):

    http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html

or the SPRNG scalable parallel random number generator:

    http://sprng.cs.fsu.edu/

I haven't tried either of these.

Hope that helps,

        - Paul



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