On Tuesday 17 January 2006 21:30, Tim Sloane wrote: > > > > Probably that your machine gets overheated. Check the temperature of > > your processor
Reproducible errors, very unlikely to be a hardware problem. > > Actually, I believe this type of error comes from the Fast Fourier > Transform (FFT) length not being big enough. In Prime95, it occasionally > checks the round-off error from doing the FFT required for the > multiplication of large numbers during the Lucas-Lehmer test. If it's > rounding off more than 0.4from the resultant numbers, it switches to a > longer FFT length > which is more > precise, but takes longer to test. About right. The problem is that the round-off error is distributed approximately normally; very occasionally there is a rogue set of data - resulting from correct operation of the correct algorithm - which results in an unusually large round-off error. Towards the top of the range of exponents for any particular FFT run length there is always a small risk of an excess round-off error. If we're lucky then we catch it & generate the output seen. If we're unlucky then we might miss it. > > So the error is a most likely due the algorithm, not your hardware. If it > was a hardware problem, it is likely that the error would not be > reproducible, which it was. Not the algorithm's fault - but the way in which we implement it. We could be ultracautious and use a larger FFT run length, or even just turn on round-off error checking every iteration, but there would _still_ be a finite chance something would get missed, and the whole project would run significantly slower. Double-checking with a different offset makes the data input to the FFT different at every iteration, so a double-checked residue match is reliable. A missed excess round-off error on either run - should be very rare - will cause a mismatched residue and result in an additional run being necessary. Regards Brian Beesley p.s. isn't this in the FAQ? _______________________________________________ Prime mailing list [email protected] http://hogranch.com/mailman/listinfo/prime
