Re: Re: APRCL e(t) table

[m-m <numerics@free.fr>]

tom@womack.net wrote:
> 
> On Feb 3, 2009, Bill.Allombert@math.u-bordeaux1.fr wrote: 
>>On Mon, Feb 02, 2009 at 04:32:27PM +0000, tom@womack.net wrote:
>>> I am very impressed with the speed of the pari APRCL implementation -
>>> it beats by a long way the best public ECPP implementations, and looks
> 
>> Really ? I find that rather unexpected and vaguely alarming. 
> 
> I've tested against Morain's ecpp-6.4.5 and got other people to test
> against primo on Windows;
> 

Contrary to what suggests the previous line, Primo was also written by
someone and it also works
on Linux with Wine (just it requires 32-bit Intel like processors).

Moreover, not only I find it surprising that APRCL "beats ECPP by a long
way" but, in any case,
ECPP and APRCL are not comparable. ECPP produces a primality certificate and
it makes a big
difference. ECPP replaces a difficult question ("Is this number prime?") by
an easier one ("Is this
certificate valid?") whereas APRCL... in fact, assuming the probability of 
bug and of hardware 
failure is not 0, APRCL answers no question.



> On the same hardware, I find that ecpp for 10^500+961 takes 428.2 seconds
> and 
> isprime(10^500+961,2) under pari takes 93.8.  For 10^800+1537 the timings
> are 1537
> seconds for ECPP and 508.3 for pari.
> 

With Primo, on a PC with a AMD Athlon 3000+ processor,
the certification of 10^500 + 961 takes 59.6 seconds (checking the
certificate takes 6.1 s),
the certification of 10^800 + 1537 takes 396 s (checking the certificate
takes 25.6 s).

mm

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