----- Original Message ----- From: "Brian J. Beesley" <[EMAIL PROTECTED]> To: "Richard Woods" <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]> Sent: Saturday, July 13, 2002 10:15 PM Subject: Re: Mersenne: Re: P-1 limits
> On Saturday 13 July 2002 10:04, Richard Woods wrote: > > V22 non-P4 FFTs are 384K in length for exponents 6545000 through > > 7779000, then 448K for exponents 7779000-9071000. The two exponents you > > list are on opposite sides of that division, so the higher exponent will > > require substantially longer for each FFT operation. That cost > > difference affects the outcome of the algorithm that selects P-1 limits. > > Shouldn't make much difference - P-1 computation rate is directly linked to > LL testing computation rate, since the same crossover points are used and the > main cost of both is FFT multiplication. I agree. I did wonder about the following (from the guess_pminus1_bounds function in file commonc.c):- /* Pass 2 FFT multiplications seem to be at least 20% slower than */ /* the squarings in pass 1. This is probably due to several factors. */ /* These include: better L2 cache usage and no calls to the faster */ /* gwsquare routine. */ pass2_squarings *= 1.2; However, the adjustment is linear, so should have no effect upon the relative costs across the FFT boundary. > I think the most likely cause is that the P-1 limits depend on the relative > speed of P-1/LL computation speed and trial factoring speed. If > RollingAverage was slightly different, the relative computation rate might be > "guessed" to be different enough for the P-1 limits to vary slightly. I don't understand this. Why should the relative speeds of P-1/LL vs TF vary? And what difference would it make if they did? The depth - hence the cost - of TF is fixed (at 63 bits for these exponents). The only trade-off is between the cost of the P-1 vs the expected cost of the LL computation. > Regards > Brian Beesley Daran G. _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
