Re: Ada.Numerics.Float_Random.Generator question

[Robert Eachus <rieachus@comcast.net>]

On Saturday, October 1, 2016 at 11:50:04 AM UTC-4, Dmitry A. Kazakov wrote:
> On 2016-10-01 16:23, Robert Eachus wrote:
> 
> > But there is infinite state, and infinite state. An infinite state
> > that is a simple counter of the number of values returned is probably
> > acceptable, a generator that requires storing the whole sequence is not.
> 
> There is no difference both are infinite. Single infinite counter is 
> capable to store whole sequence and conversely.

My point was that a state which slowly grows toward infinity (the counter) can easily be stored.  Any state that requires infinite storage or grows non-polynomially is right out.  States which grow by some polynomial in the counter?  Depends. 

On the issue of multiple seeds, Pi times an integer is also trancendental, but the values would be correlated between sequences.  Multiplying Pi by a rational number is better, but I think natural logs of primes would work.  Of course, now we have the problem of converting the seed selected by the programmer, or the clock, or whatever, into unique prime seeds.