RE: Celestial bodies (was RE: Mersenne: Re: Is 128 bit instruction code needed ?)

1998-11-06 Thread Aaron Blosser

 magically,
 the "universe cycle" theories have an unfortunate side effect of
 causing a
 reversal of entropy.

 Such a side effect is unfortunate? Entropy is not an immutable physical
 law, but a statistical property of closed physical systems.

I'd call the universe a closed system.  It'd take some pretty interesting
evidence to convince me otherwise :-)  "Unfortunate side effect" in that it
goes against known facts.

 A cyclic
 universe has infinitely many predecessors, hence is not a closed system.

But even a cyclic universe would consist of the same bits of matter that our
current universe contains...matter is neither created nor destroyed.  There
is no input nor output to the system, so it is, in fact, closed.  The
question of where matter came from in the first place is another matter
altogether. ;-)

 I'll lay you ten to one odds that within 200 years, this civilization (if
 it hasn't blown itself to kingdom come) has access to one or more of: FTL
 travel, multiple universes, a method of obtaining an unending  supply of
 fresh energy.

Or a way to calculate giga-digit mersenne primes in a millisecond (OMPR =
Obligatory Mersenne Prime Reference)

 Note already that recent observations about quantum mechanics hint at the
 existence of multiple universes, and new up and coming quantum gravity
 hypotheses produce causally-isolated topologically connected spaces (i.e.
 parallel universes able to access one another in principle) when a
 superposition of states of spatial topology reaches a certain threshold of
 energy difference between pairs of orthogonal superposed states.

I look at quantum physics as nothing more than a clever way to model
observed behaviour which we can't understand by any other means.  To say
that an electron can travel from one orbit to another without traversing the
distance between is nothing more than fantasy, yet quantum physics would
have us believe that it happens.  Sure it violates all known laws of
physics, a supporter might say, but the theory gives us working results!
Well, sure, the theories do have practical end results, but pre-Copernican
societies could do amazing predictions of astronomical events, despite their
belief in geo-centrism.  Hmmm...  It's just that, the more they tried to
predict, the more their model failed.  Quantum physics in it's current form
is a lovely model that has some real results, but I don't think it's a model
that will hold up over time as it receives more scrutiny.




Re: Mersenne: 128 floatingpoint operations

1998-11-06 Thread Foghorn Leghorn

The library gmp (GNU multi-precision) uses this algorithm
although it is much slower than FFT-like methods.
Maybe because it only involves integers,
and there is no danger at all of rounding errors.
I once wrote a gmp-based program to perform LL tests:
for low exponents it worked fine but for the prime 65537
it already took much longer that mprime.

Could you tell me how to find this gmp library? I searched gnu.org site 
for it, but I couldn't find anything.

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