Re: Pari Slowdown?

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Sun, Jun 28, 2009 at 09:16:30PM +0200, Bill Allombert wrote:
> On Sun, Jun 28, 2009 at 01:02:57AM +0100, Jason Moxham wrote:
> > Hi
> > 
> > Doing some very rough benchmarks of Pari on 64bit linux with GMP
> > pari-2.4.2-alpha
> > ? gettime() ; isprime(2^127-1,2);gettime()
> > %3 = 4
> > ? gettime() ; isprime(2^521-1,2);gettime()
> > %4 = 332
> > ? gettime() ; isprime(2^607-1,2);gettime()
> > %5 = 857
> > ? gettime() ; isprime(2^1279-1,2);gettime()
> > %6 = 9845
> > 
> > pari-svn
> > ? gettime() ; isprime(2^127-1,2) ; gettime()
> > %1 = 8
> > ? gettime() ; isprime(2^521-1,2) ; gettime()
> > %2 = 420
> > ? gettime() ; isprime(2^607-1,2) ; gettime()
> > %3 = 1108
> > ? gettime() ; isprime(2^1279-1,2) ; gettime()
> > %4 = 12885
> > 
> > 
> > This is all on the same machine with gcc-4.2.2,MPIR-1.2.1, nehalem 2.6Ghz
> > 
> > I tried make tune , but it didn't make any significant difference.
> 
> Thanks, this is a slowdown caused by this change:
> 
>   BA 35- direct implementation of ZX_mul, ZX_sqr using Kronecker's trick + mul
> 
> We really need to tune ZX_mul and ZX_sqr.

However, there might be a problem with GMP itself (or the GMP kernel):

for(i=1,20,a=random(2^(100000+10000*i));gettime();for(j=1,1000,a^2);print(i,":",gettime()))
1:745
2:849
3:925
4:1028
5:1156
6:1248
7:1372
8:1485
9:1569
10:1740
11:1825
12:1945
13:1408
14:1409
15:1624
16:1625
17:1629
18:1624
19:1969
20:1965

entry 12 is much slower than entry 13.

(This interfers with my attempts at tuning ZX_sqr).

Cheers,
Bill.