mersenneforum.org roundoff = 0.224. Normal? Yes. [solved]
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 2016-02-04, 14:18 #1 Fred     "Ron" Jan 2016 Fitchburg, MA 6116 Posts roundoff = 0.224. Normal? Yes. [solved] New to the project and have been trying to do as much reading as possible to learn more with out having to post every 2 seconds, but I was wondering if someone could weigh in on the following. Code: Iteration: 59080000 / 76088891 [77.64%], roundoff: 0.224, ms/iter: 7.160, ETA: 33:49:49 So this is saying there was a rounding error? I read (I think) somewhere that as long as the roundoff doesn't get above .5, then it's ok? Is this an indication of a hardware issue? Or is it normal to not get through an LL test of this size with no roundoff errors? Thanks.
2016-02-04, 14:58   #2
ET_
Banned

"Luigi"
Aug 2002
Team Italia

52·193 Posts

Quote:
 Originally Posted by Fred New to the project and have been trying to do as much reading as possible to learn more with out having to post every 2 seconds, but I was wondering if someone could weigh in on the following. Code: Iteration: 59080000 / 76088891 [77.64%], roundoff: 0.224, ms/iter: 7.160, ETA: 33:49:49 So this is saying there was a rounding error? I read (I think) somewhere that as long as the roundoff doesn't get above .5, then it's ok? Is this an indication of a hardware issue? Or is it normal to not get through an LL test of this size with no roundoff errors? Thanks.
You are mostly correct with your deductions

The roundoff happens because double-precision numbers are used in place of integers to either speed up or optimize the algorithm: as long as it is kept below a defined threshold, it's not obnoxious and does not indicate a hardware malfunction.

Happy crunching!

Last fiddled with by ET_ on 2016-02-04 at 14:59

2016-02-04, 22:07   #3
Serpentine Vermin Jar

Jul 2014

63618 Posts

Quote:
 Originally Posted by Fred New to the project and have been trying to do as much reading as possible to learn more with out having to post every 2 seconds, but I was wondering if someone could weigh in on the following. Code: Iteration: 59080000 / 76088891 [77.64%], roundoff: 0.224, ms/iter: 7.160, ETA: 33:49:49 So this is saying there was a rounding error? I read (I think) somewhere that as long as the roundoff doesn't get above .5, then it's ok? Is this an indication of a hardware issue? Or is it normal to not get through an LL test of this size with no roundoff errors? Thanks.
Roundoff errors above 0.4 are more interesting and will trigger the code to retry from the last save file to see if it's repeatable. If so, Prime95 starts from that last save file again using a "safer" method.

If those > 0.4 occur frequently it could be a case of the FFT size being too small for that exponent, but it could indicate hardware problems too.

For 0.224 I wouldn't worry too much.

 2016-02-05, 00:01 #4 VBCurtis     "Curtis" Feb 2005 Riverside, CA 4,943 Posts To add a little bit to their quality answers: If roundoff error were exactly 0.5, we wouldn't know if the number was meant to be rounded down or rounded up- so the result of the floating-point calculation, when converted back to integer, would be wrong 50% of the time (since the algo would, in a sense, guess which way to round). If roundoff error exceeds 0.4, say, 0.4125, there's a chance it's really a roundoff error of 0.5875 from the adjacent integer. The difference between 0.4 and 0.6 is large enough that roundoff errors below 0.4 are ignored and considered accurate when rounded, but 0.4 to 0.5 causes the program to redo the calculation with a more accurate floating-point algorithm to decrease the error inherent to these calculations. Short version: a result of 34563456.5 is unclear from the FPU algo, because we don't know which way to round back to integer-land. A result of 34563456.46 is clear, but slightly dangerous because the real value might be 34453457 but the FPU had roundoff error of 0.54; so, that calc is redone with a more accurate but slower method. Results like 34563456.22 are clear, and not in danger of being accidentally rounded wrong.

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