On Jan 30, 1:57 pm, "James J. Weinkam" <j...@[EMAIL PROTECTED]
> wrote:
> Charles Brenner wrote:
> > On Jan 27, 1:33 pm, "Curtis A. Jones" <curtis_jo...@[EMAIL PROTECTED]
> wrote:
> >> Charles,
> >> Simply constructing an integer from the system clock to use as the
> >> seed {quadRL} for the random number generator may give a less than
> >> ideal sequence.
>
> >> James J. Weinkam discusses this in this comp.lang.apl group under
> >> "Random Number Generation in IP Sharp APL" (29 Jun 2006
1917)http://groups.google.com/group/comp.lang.apl/browse_frm/thread/33c60d...
>
> >> Among the consequences of a poor choice of seed:
> >> "Moreover choosing a seed which is nor relatively prime to the
modulus
> >> causes the generator to produce a subsequence which is not of maximum
> >> length."
>
> >> One recommendation he makes:
> >> "...saving the value of the seed at the end or each run and using
that
> >> value to seed the generator at the start of the next run."
>
> > Yes, I thought of that but would rather not decide on all the
> > housekeeping issues.
>
> >> I imagine you know this and have a function that selects only "valid
> >> values for {quadRL}" from the clock. Would you share it?
>
> > That's quite easy. The random number generation algorithm is
> > multiply by 5*7
> > reduce modulo (2*31)-1.
> > This algorithm generates every possible value before it repeats (I
> > checked the cycle length, which didn't take very long. In formal
> > language, the modulus is a prime and 5*7 is a primitive root, meaning
> > a number whose powers include every modulus class except 0. The fact
> > is that every prime does have primitive roots, so once you realize
> > that (2*31)-1 is a prime it follows that unless the implementor
> > blundered remarkably, the chosen multiplier must be a primitive root
> > and the generated numbers must be the full cycle. There was really no
> > need to check.)
>
> > That is, all numbers
> > 0 < n < 2*31
> > are in the cycle, so start with any one of them. For example
>
> > 1. Hash the system clock or whatever to a number. To ensure a valid
> > and efficient []RL
> > 2. Reduce that number modulus (2*31)-2
> > 3. Add 1.
>
> > Charles
>
> You are missing the point.
>
> It is true in the present instance that any non zero value less than
> 2*31 is a valid seed;
less than (2*31)-1
> but if you simply choose a new seed at random
> there is a risk that you will simply be generating the same stream of
> random numbers you used in a previous experiment shifted by a bit.
That an inevitable consequence of using a deterministic random number
generator, i.e. one for which the sequence depends only on the
starting point.
> This can lead to undesirable correlation between runs which can
invalidate
> subsequent statistical analysis.
That would be true if one used a method of choosing a restart point
for the random seed which is limited to a relative (relative to
2*31-1) handful of possible values. If the restart method truly chose
at random -- equal probability -- among all possible seed values, then
it would have no more tendency toward serial correlation than would
saving []RL. If you disbelieve this, that would explain the sense in
which you think I missed "the" point.
I think hashing []TS is good enough -- as opposed to the method of
counting loop iterations in a fixed short time which I remarked
earlier turned out to be even worse than I expected.
> Saving {quad}RL at the end of a run and restoring it at the beginning of
> the next is hardly a major housekeeping issue.
Given the nature of my application the mechanism would be tedious
enough that I prefer not to bother. I don't force my decision on
anyone else.
Charles
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