(j3.2006) (SC22WG5.4110) [ukfortran] Standard intrinsics and coarrays

[Bill Long]

Aleksandar Donev wrote:
> Malcolm Cohen wrote:
> 
>> In a "shared" generator there is a single seed and a single sequence.  
>> Images take values from that single sequence.
> Presumably if two calls to RANDOM_NUMBER are unordered, what order they 
> take from the sequence is undefined. These kinds of things would need to 
> be spelled out explicitly.

Unordered references would be the normal case. As Van correctly pointed 
out, this mode of operation is essentially useless in many (most?) cases.

On the other hand, one might argue that the SOLE purpose of the 
random_number routine is high performance on a benchmark, and as a 
result they tend to be very simplistic linear congruential generators. 
For some purpose the quality of the default sequence is OK.


> 
>> In a "separate" generator, each image has a seed and a sequence.  Each 
>> image takes values from its own sequence.
> Are the generators the same on each image (i.e., same sequence for the 
> same seed)? Also needs to be spelled out explicitly.
> 

You would want separated sequences on each image.  If the generator has 
more than one seed, you can choose one seed value to be the same on 
every image and another one that is unique on each image. At least some 
classes of such generators assure independent sequences on each image in 
this case.

However, since we say such things (number of seeds, sequence 
characteristics) are processor dependent already, you can't really write 
portable code that depends on these details. Unless you use a separate, 
known library routine.


>> Perhaps we should require that it should be one or the other.
> If we do the choice is obvious: separate generators on each image.
> 

Certainly the cleanest choice. At least in that case it could be used 
for at least some applications.


> Isn't there some room in-between. One can have separate streams but that 
> get initialized during a call to RANDOM_SEED together so that they are 
> independent on each image. Perhap's we should allow for such cases? For 
> example, the SPRNG library (http://sprng.cs.fsu.edu/sprng.html) has a 
> Modified Lagged Fibonacci Generator generator that:
> 
> "The seed used during initialization for this generator does not move 
> one to a different point in the sequence. Rather, it returns a different 
> sequence. The seeding algorithms ensures that if the same seed is used 
> for all the streams, then the streams obtained are independent. If a 
> user initializes different streams with different seeds, then it is 
> possible that the same sequence may be assigned to two different streams 
> and hence we may no longer have independent streams. Thus it is 
> important to use the same seed while initializing all the streams with 
> this generator."


My current favorite is the Mersenne Twister generator (with 4 seed 
values).  It has a very long period, and contiguous blocks of values can 
be used as the coordinates in a multi-dimensional space without nasty 
planing (critical for some Monte Carlo uses). There are other 
non-planing generators, such as ones based on Halton sequences, but the 
Mersenne Twister is faster.  According to Wikipedia, it is the standard 
generator for Maple, Matlab, R, Ruby, and Python. Notably, all cases 
where performance is not the typical focus.


Cheers,
Bill



> 
> Aleks
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-- 
Bill Long                                   longb at cray.com
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