Re: Pari Slowdown?

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

On Thu, Jul 09, 2009 at 04:20:17PM +0100, Jason Moxham wrote:
>> 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.
>
> Depending on cpu and limb size your at about the FFT range , which is 
> well known for timings that don't smoothly increase.

Sure, but this is a case of sharply decreasing :)

Cheers,
Bill.