Mersenne: Re: Roundoff errors

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Daran wrote:

>Twice, in the past three days I've had the message:
>"Possible roundoff error (0.4xxxxxxx), backtracking to
>last save file.", while performing P-1 stage one on
>M13194707 and M12898349 respectively.

George Woltman replied:

>The M12898349 error may be OK as it may have been very
>close to the limit of the 640K FFT (I don't recall the
>22.3 crossover points).

According the the GIMPS status page, the 640K crossover
point for the more-accurate x86 client (i.e. the non-
SSE2 code) is 12.83M, which is already less than the
smaller of Daran's exponents - the SSE2 crossovers
(irrespective of the precise code version) are going
to be smaller still. Thus, neither of these exponents
should be yielding close-to-crossover roundoff errors,
since both should be running in the lower part of the
768K-FFT-length exponent range.

>
>Errors during P-1 are not particularly critical.

Except that P-1 stage 1 (unless I'm mistaken about
Prime95's particular implementation thereof) uses the
same FFT-based squaring code that the LL test does. If
there's a hardware problem or (say) a device driver that
is corrupting data, it would seem to be just as likely
to do so in either the p-1 step or the LL test. Still,
it seems curious that Daran mentions seeing the roundoff
warnings in p-1 stage 1, and not in the subsequent LL
tests of these exponents. George, is error checking done
more frequently in p-1 than in LL? Daran, were you doing
p-1 ONLY on these exponents, or were these the first
Prime95 runs you did on some new machines? (In which case
the code perhaps hadn't gotten to the LL stage yet.)

-Ernst