Re: Way for computing random primes in standard C.

In article <1141107962.224007.23810@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mensanator@xxxxxxx <mensanator@xxxxxxx> wrote:

When it's stated that
"...the Mersenne Twister as the core generator.
It produces 53-bit precision floats and has a period of 2**19937-1."

Doesn't it mean that there are 2**19937-1 states and if one were
to actually call it 2**19937 times, then one would be right back
where one started regardless of what number srand() was called with?

Not necessarily.

I was not implying that srand(1) and srand(2) have adjacent states.
But doesn't periodic mean that at whatever state # srand(1) starts in,
it must eventually reach the same state that srand(2) starts in?

Not necessarily.

It would be possible to the initial seed to affect parameters
in the PRNG, such that srand(1) and srand(2) each had the same
period, but that the cyles for the two were not the same.


Getting further OT:

It appears to me that the traditional Unix drand48() might be
an instance of this. According to the man page:

The initializer function srand48 sets the high-order 32 bits of Xi
to the 32 bits contained in its argument. The low-order 16 bits of
Xi are set to the arbitrary value 330E16.

and

The value returned by any of the functions drand48, erand48,
lrand48, nrand48, mrand48, or jrand48 is computed by first
generating the next 48-bit Xi in the sequence. Then the
appropriate number of bits, according to the type of data item to
be returned, are copied from the high-order (leftmost) bits of Xi
and transformed into the returned value.


If we put these together, we would see that srand(1) and srand(2)
would have the same cycles -only- if it happened the the linear
congruential generator applied to 0x1330E16 happened to result
in 0x2330E16 at some point. Further analysis would be needed to
see whether that ever happened -- the default multiplier and
constant for drand48() and kin are both even, so it is not
the usual case that "every possible n-bit value will be generated,
eventually".
--
All is vanity. -- Ecclesiastes
.