Nathan Russell wrote:
> For those who don't know, due to CPU design reasons
> that I don't claim to understand, factoring to 65 bits
> takes easily four or five times as long as factoring
> to 64 bits. In version 19, it was set to take place
> for exponents 13.38M and up. I believe PrimeNet will
> reach this point in a few months.
The reason is quite simple: Prime95 can do speedy
factoring up to 64 bits by using the 64-bit mantissa of
an x86 register float to store the trial factor (and
various intermediate quantities modulo the trial factor)
and doing integer multiply (which is normally quite slow
on x86) by way of the FPU, which can pipeline the MULs.
As soon as the trial factor size exceeds this 64-bit
natural wordsize, one must go to a double-word
representation, hence the factor-of-four-or-so slowdown.
I'm in agreement with Brian Beesley on this issue:
especially now that there's the capability to do P-1, I
think sieving to > 64 bits will prove to be a waste of
time, since we should be able to find nearly all the
factors > 64 bits that sieving would turn up more
cheaply using P-1.
That assumes that our priority is maximizing GIMPS
throughput, rather than being able to say with certainty
that such-and-such a number has no factors less than,
e.g., sixty-eight bits.
George, when do you expect sufficient data to be able
to quantify the relative effectiveness of sieving vs.
P-1 for these larger factor size ranges?
-Ernst
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