(j3.2006) Rationale for RANDOM_INIT?

[Steven G. Kargl]

On Wed, Jan 10, 2018 at 07:13:48PM -0500, Steve Lionel wrote:
> On 1/10/2018 4:06 PM, Steven G. Kargl wrote:
> > Now, suppose that the executable instantiates two images, and for
> > this discussion call them image0 and image1.
> >
> > 2) IMAGE_DISTINCT=.true. means *distinct* seeds are used to seed
> >     the PRNG in image0 and image1.  This suggests that there is an
> >     implied assumption that the *distinct* seeds will lead to
> >     *distinct* sequences of RN.  Is this the intent of the Standard?
> >     If yes, then the Standard should remove the assumption and state
> >     the expected behavior.
> >
> >     Compilers likely use a PRNG with some long period.  The seed
> >     initializes the PRNG by essentially pointing to a particular
> >     member in the sequence of all RN.  It is then possible that
> >     *distinct* seeds lead to a sequence for image0 of [A B C D E ...]
> >     and for image1 of [C D E ...].  That is, the two sequences have
> >     a significant overlap.  Here, a question of how much overlap
> >     should be permissable arises.
> >
> >     So, what does *distinct* mean?
> >
> > 3) Given the requirement of *distinct* seeds, this eliminates a class
> >     of PRNG that can use a single seed to select a particular member in
> >     the sequence of all RN, and then use a transform to select independent
> >     subsequences.  For example, internally, xform(0) would cause image0
> >     to select subsequence 0 and xform(1) causes image1 to select
> >     the subsequence 1.  A description of this class of generator can
> >     be found at http://vigna.di.unimi.it/ftp/papers/xorshift.pdf.
> >
> > It seems to me that the Standard should not require *distinct* seeds
> > when IMAGE_DISTINCT=.true., but rather require independent sequences.
> > The level of independence can be some statistical metric.
> The design of RANDOM_NUMBER and, in particular, RANDOM_SEED, has the 
> explicit assumption that a given seed will generate a given sequence. 
> There is no opportunity here for a RNG that can generate distinct 
> sequences from a given seed. Users who want such behavior would need to 
> look at supplying their own RNG.

I think we are talking passed each other here as I have a
proof-of-concept patch for gfortran that uses a PRNG
with a single seed that generates different non-overlapping
sequences for the different images via an xform() function
(the cited paper calls it a jump function).  From a user's
prespective, she has no way of knowing whether a single
seed was used to initialize the PRNG in each image or
*distinct* seeds were used.  That's an implementation detail,
and the Fortran Standard normally avoids implementation
details.  The only thing that the user cares about is what
does RANDOM_NUMBER return after a call to RANDOM_INIT with
IMAGE_DISTINCT=.true. (and whether the sequences satisfy the
properties of a uniform distribution on [0,1)).  If the intent
of the Standard is that each image has access to different
sequence of random number, then that's what the Standard 
ought to state.  Implementation details should be removed.

-- 
Steve