On 20 Apr 00, at 15:07, [EMAIL PROTECTED] wrote:
> Come to think of it, factoring would be an excellent
> application for a 21264 without an L2 cache, but I don't
> know if they come that way (except perhaps in a
> massively parallel setting, where the problem of
> maintaining cache coherency in a multilevel cache
> hierarchy often is nearly intractable).
Either the L2 cache is on the chip, a la Celeron/PIIIE, or it's on a
board - either a cartridge slot, a la PII, or on the mainboard, a la
Pentium Classic. If the L2 cache is off chip, then clearly systems
not containing L2 cache can be manufactured. If it's on chip,
presumably you can still turn it off - though you're going to be
stuck with the manufacturing cost.
BTW the linux SMP kernel seems to do a pretty good job of managing
"n" processors with individual caches, by weighting the process
queues in a manner which allows for the cost of resuming a process on
a different processor, thereby losing the cache contents.
> Then again, if
> one turned a MP machine to factoring, GIMPS might soon
> run out of factoring assignments,
Who said we could ever run out? There's certainly an infinite supply
of wholly untouched Mersenne numbers out there - whether or not the
number of Mersenne primes is finite!
Since "advanced" factoring techniques like P-1 and ECM have greater
memory demands than trial factoring (in fact, stage 2 of P-1 seems to
stress the memory subsystem even more than LL testing the same
exponent), this type of work would surely also be appropriate to
large cache systems.
BTW I'm wondering whether the introduction of P-1 means that the
trial factoring depth should be _reduced_. The last bit in depth
costs half the total time involved in trial factoring yet gains only
a small percentage of extra factors, and some of these would in any
case be found by P-1.
I suppose it's probably better to leave things as they are, at any
rate until P-1 following completion of trial factoring becomes
"compulsory".
As an alternative to the last bit depth of trial factoring, we could
also consider implementing Pollard's rho method. This would seem to
be reasonably efficient at finding factors round about that size and
yet does not have the heavy memory overheads associated with P-1.
Regards
Brian Beesley
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