Re: Comparaison between PARI MPQS, PPMPQS and PPSIGS

[Igor Schein <igor@txc.com>]

On Wed, Nov 27, 2002 at 05:26:39PM +0100, Bill Allombert wrote:
> Hello developers,
> 
> I have factored 
> 117433370311644622074182931512170893877890957626285922622753078073774028918529
> (78 digits)
> 
> on a 1GHz PIV
> with PARI (2.2.5), and then I try PPMPQS (2.8) and PPSIGS (1.1) from 
> http://www.asahi-net.or.jp/~KC2H-MSM/cn/
> 
> here the running time:
> PARI   : 3h 9 min
> PPMPQS : 1h 58 min
> PPSIGS : 1h 46 min
> 
> Karim's FAQ states 
> 
> > PARI's MPQS is about as fast as PPMPQS-2.7 in the 60 digits range, and much
> > slower afterwards, e.g already 3 times slower for 70 digits. We have not
> > tested mpqs4linux.

Well, here's a problem with PARI's MPQS on Linux which I noticed some
time ago. If you run N consecutive factorizations with PPxxxx on the
same number, the timing results will be consistent.  Not so the case
for PARI.  Here's the timings for several consecutive MPQS
factorizations of C78 above on an otherwise empty machine: 

MPQS: passing the 5.0% checkpoint, time = 214100 ms
MPQS: passing the 5.0% checkpoint, time = 246240 ms
MPQS: passing the 5.0% checkpoint, time = 245310 ms
MPQS: passing the 5.0% checkpoint, time = 315090 ms
MPQS: passing the 5.0% checkpoint, time = 308890 ms
MPQS: passing the 5.0% checkpoint, time = 309300 ms
MPQS: passing the 5.0% checkpoint, time = 247500 ms
MPQS: passing the 5.0% checkpoint, time = 207190 ms
MPQS: passing the 5.0% checkpoint, time = 257400 ms
MPQS: passing the 5.0% checkpoint, time = 233020 ms
MPQS: passing the 5.0% checkpoint, time = 185880 ms
MPQS: passing the 5.0% checkpoint, time = 228530 ms
MPQS: passing the 5.0% checkpoint, time = 242010 ms
MPQS: passing the 5.0% checkpoint, time = 282820 ms
MPQS: passing the 5.0% checkpoint, time = 270460 ms
MPQS: passing the 5.0% checkpoint, time = 338840 ms
MPQS: passing the 5.0% checkpoint, time = 301620 ms
MPQS: passing the 5.0% checkpoint, time = 237830 ms

The speed is constant within each session, it's just that some
sessions are faster, some sessions are slower for no apparent reason.  

Based on above, it's really hard to compare speed for this size
integer on Linux.  However, I was able to obtain more consistent
results for C60=nextprime(10^60)*precprime(10^60) - PPSIGS is almost
twice faster than PARI on a 512MB full speed L2 cache Linux machine. 

Igor