On Mon, 2021-11-22 at 13:03 -0500, Arthur O'Dwyer via Std-Proposals
wrote:
> Correct. I think you misunderstood the point of my message. I'm not
> saying that "specifying a number of bits to take from random_device,
> and then 'key-stretching' those into a larger seed value suitable
> for MT19937," a.k.a. "under-seeding MT19937," is a good operation nor
> that any working programmer should ever want to do it. I'm just
> saying that if you wanted to do it, then you could easily do it via
> an intermediate PRNG that takes a seed of the proper size.

What you call "underseeding" and key-stretching is the default way of
working. What you call "fully seeding" with 624 integers is a new and
unexplored land. There is a reason for that. Let's look at the original
implementation from 2002. There are two initialization functions, one
that accepts a 32-bit integer, and another that accepts a sequence of
arbitrary length. Not 624, but arbitrary, can be less can be more. That
function does not copy directly the seeding sequence, instead it does a
lot of bit manipulation. That is because there are some initial states
that are unwanted. From what I read, states with lot of consecutive
zeroes are unwanted initial states. No matter what size is the seed,
the initialization routines avoid some states. Thus the total number of
initial states is not (2^32)^624 but is something less. Therefore, not
any PRNG can be used to do the "stretching". The standard C++ MT19937
has this protection in the constructor that that takes seed sequence,
and that should remain there.