Mersenne Digest Sunday, August 15 1999 Volume 01 : Number 614
----------------------------------------------------------------------
Date: Thu, 12 Aug 1999 21:25:59 -0400 (EDT)
From: Jason Stratos Papadopoulos <[EMAIL PROTECTED]>
Subject: Mersenne: UltraSPARC-optimized Pepin test available
Hey everybody. Now that our Fermat testing is starting to wind down
I've decided to make available the source I've written for it.
www.glue.umd.edu/~jasonp/f24v131.zip
The code there is heavily optimized for the UltraSPARC processor,
and includes gobs and gobs of sparc assembly language. Squaring
times are as follows:
ultra-1 ultra-1 ultra-2i
number bits 143MHz 167MHz 300MHz
F22 4.2M .229 .196 .167
F23 8.4M .465 .404 .322
F24 16.8M 1.08 .885 .700
F25 33.6M 1.58
The GIMPS speed page places the Ultra-2i times in the neighborhood
of a PII-300 (a Pepin test takes about the same time as an LL test
of similar size, maybe a little less).
So, a few questions:
How do these times compare with MacLucasUnix on an Ultra, or with
Prime95 for the really big sizes?
How fast does the program run on a really big Ultra, i.e. a 440MHz
server with piles of RAM and a 4MB cache?
Are there enough Ultras out there to justify making a fast LL test out
of this code? I'd be willing to try, but only if there's sufficient
interest; the code won't run on normal sparcs, my time is very
limited I don't want to expend a considerable amount of
energy on something no one will use. Would anyone like to help?
jasonp
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------------------------------
Date: Fri, 13 Aug 1999 11:37:06 +1000
From: Simon Burge <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Testing times
Bill Rea wrote:
> Is this about right for this type of system?
>
> Details:-
>
> Ultra-5 270Mhz CPU, 128Mb RAM
> Solaris 7
> gcc version 2.8.1
For a comparison, I've got some Ultra2s with 2x 200MHz CPUs under Solaris 2.5.1.
One is double-checking some numbers in the 4.6M range (with a 256k FFT)
and is getting approx 0.4s per iteration, and another is checking a number in
the 2.4M range (128k FFT) and is getting 0.22s per iteration. MacLucasUNIX
was compiled with egcs 1.1.2 with
-mcpu=ultrasparc -O6 -funroll-loops -funroll-all-loops
for options.
For 7902277 I'd guess an FFT size of 512k, so you should be getting
roughly double the iteration time divided by 270/200 for CPU speeed -
roughly 0.6s per iteration at a guess. What compiler options were you
using for gcc? I can send you my ultrasparc binary if you want to test
that.
0.4 * 2 * (270/200)
> Also, I've tested MacLucasUNIX with the Sun CC compiler using the
> -fast option and it's about a third faster than when compiled with gcc,
> but there are warnings like:-
>
> The -fast option is unsuitable for programs that require strict
> conformance to the IEEE 754 Standard.
>
> Should I be using this option?
Good question - sounds scary. Unless you get some informed opinion, I'd
be staying clear of that...
Simon.
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------------------------------
Date: Thu, 12 Aug 1999 22:05:20 -0400
From: George Woltman <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Cleared exponents
Hi,
At 06:07 PM 8/11/99 +0200, Guillermo Ballester Valor wrote:
>There are two databases in GIMPS/Primenet project. The master is the
>GIMPS one and includes all information about the search, and therefore
>includes the basic information from Primenet data. There is a lot of
>data in Primenet and the synchronization is performed every few months.
Correct.
>It seems the last synchronization was on Aug-9, and my exponents
>finished before that day disappeared from my personal account report as
>I supposed correct. But in the cleared exponents report there are a lot
>of results sent to Primenet before Aug-9. My results are not in this
>list, so... Why other results from other accounts remain in it?
The synchronization scheme is not particularly robust. There are
three possible causes for an exponent to remain on the cleared
exponents report.
1) It was a double-check and did not match the original test.
2) It was a bad v17 result. Thus it did not get entered in the
master database and was not cleared in the synchronization.
3) The result never made it to the master database. This is
pretty rare and I round these up every once in a while and
have Scott do some research to get the data added to the master
database.
You'll note that a few thousand "small" exponents between 5,000,000
and 8,000,000 were just made available. These are mostly exponents
that were tested by v17 the first time and need retesting. I've asked
Scott to make available some smaller exponents for necessary triple
checks too.
These occasional synchronizations allow me to run some scripts and
find any exponents that have "fallen through the cracks".
Regards,
George
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------------------------------
Date: Thu, 12 Aug 1999 23:00:29 -0400 (EDT)
From: Lucas Wiman <[EMAIL PROTECTED]>
Subject: Mersenne: Probabilities of P-1
A week ago, George asked about probability in P-1 factoring. I haven't
seen a single response, though I would guess that he has received many
private emails. Could this please be included on the list? I am interested
in this, as (I'm guessing) many others are.
> Extra credit: Can someone tell me the probability that P-1 factoring
> will find an n-bit factor?
Shouldn't the probability of it finding a n-bit factor be immaterial,
as the fact that it finds a factor is all that matters. The whole
n-bit concept should only matter if we speak of trial factoring.
> This is but one piece of the puzzle in
> determining the best trial factoring limits and P-1 bounds. To compute
> this probability the k in the 2kp+1 factor must be "smooth", that is
> all factors must be less than bound #1 except for one factor that
> must be less than bound #2. I'm sure I have the info around here somewhere,
> but everyone might be interested in the math behind deriving trial factoring
> limits and P-1 bounds.
The k must be smooth to B1, yes, but a more rigorous requirement is there
also. What if k=2^70? Smooth to any B1, but this number would not be found
by P-1 factoring. I'm guessing that numbers that are smooth with high
exponents is low, so it should be about the same.
Here's what I was able to come up with while doing repetitive jobs at work:
A number p^x (p prime) is said to be "enough for" n if p^(x+1) does not
divide n.
Let f(p,a,b)="the sum from v=a to v=b of 1/p^v"
(note for those of you who don't know, f(p,0,b)=(1-(1/p)^n)/(1-1/p))
The probability that p^x is not enough for n is
p(p,x,n)=1-f(p,1,x)+f(p,x+1,[log_p(n)])
Thus the probability that value of Q=2^x_1*3^x_2...B1^x_(pi(B1)) will
be enough for n, for all p_i<B1 is
1-(prod(p(p_i,x_i,n), i=1, i=B1))
(I think this should be about 1-exp(-gamma)/log(B1)).
This should make the probability that P-1 will find a d bit factor
~(1-exp(-gamma)/log(B1))*.81*(1/d-1/(d+1))
- -Lucas
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------------------------------
Date: Thu, 12 Aug 1999 23:24:50 -0500
From: Herb Savage <[EMAIL PROTECTED]>
Subject: Re: Mersenne: athlon interation speeds
Paul Missman wrote:
> Interesting.
>
> My 400 MHz Celeron, working on 7450277 is getting
> 0.203 per iteration.
This is too fast for a 400 MHz Celeron. My best guess is ifyou look at the
speed being using by Prime95 for the calculation
of the iteration speed (under options) you will see that Prime95 is
using about 500 MHz for the calculation. You probably had your
computer overclocked the 1st time Prime95 was run.
A 550 MHz Celeron (my son's computer) does .183 seconds per
iteration on that same number.
Regards,
Herb Savage
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------------------------------
Date: Thu, 12 Aug 1999 23:41:05 -0700
From: "Scott Kurowski" <[EMAIL PROTECTED]>
Subject: Mersenne: RE: Mersenne Digest V1 #613
A digest reply:
> questions, but I really try to get to all the FAQs/digests/ReadMes
> before I post, and I'm still not satisfied with the answers...
You can always ask us directly at <[EMAIL PROTECTED]>.
> Should I contact PrimeNet from time to time to assure it (her? ;)
> that I'm still whith the GIMPS?
Yes. At least every 59 days, but monthly is better. More often doesn't hurt -
in fact it gives your account report the most accurate snapshot of your
progress.
However, after 60 days without communication with your program PrimeNet will
automatically expire your exponent assignments and give them to someone else.
The Vacation feature in Prime95 and the assignment extension form on the manual
testing page can reserve longer timeouts, if necessary.
> If I should contact PrimeNet, how should I do it?
Just connect to the Internet. The program knows when it needs to contact
PrimeNet and will do so automatically, even in mid-test. The "Send new
completion dates..." feature forces the program to update the server between
automatic updates. In most cases, the default 'start & forget' behavior of the
program works best.
> It seems the last synchronization was on Aug-9, and my exponents
> finished before that day disappeared from my personal account report as
> I supposed correct. But in the cleared exponents report there are a lot
> of results sent to Primenet before Aug-9. My results are not in this
> list, so... Why other results from other accounts remain in it?.
Exponents left on the Cleared Exponents list after a merge were either received
since George Woltman last retrieved PrimeNet's results logs for the GIMPS
'database' file update, or are invalid. Most are either removed in a subsequent
merge or requeued for assignment.
Back to v19 work...
Regards,
scott
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------------------------------
Date: Fri, 13 Aug 1999 22:59:58 +1000
From: Simon Burge <[EMAIL PROTECTED]>
Subject: Re: Mersenne: UltraSPARC-optimized Pepin test available
Jason Stratos Papadopoulos wrote:
> Hey everybody. Now that our Fermat testing is starting to wind down
> I've decided to make available the source I've written for it.
Cool!
> www.glue.umd.edu/~jasonp/f24v131.zip
>
> The code there is heavily optimized for the UltraSPARC processor,
> and includes gobs and gobs of sparc assembly language. Squaring
> times are as follows:
>
> ultra-1 ultra-1 ultra-2i
> number bits 143MHz 167MHz 300MHz
>
> F22 4.2M .229 .196 .167
> F23 8.4M .465 .404 .322
> F24 16.8M 1.08 .885 .700
> F25 33.6M 1.58
>
> The GIMPS speed page places the Ultra-2i times in the neighborhood
> of a PII-300 (a Pepin test takes about the same time as an LL test
> of similar size, maybe a little less).
>
> So, a few questions:
>
> How do these times compare with MacLucasUnix on an Ultra, or with
> Prime95 for the really big sizes?
Today I posted some times - I was getting approx 0.4s per iteration for
a 256K element FFT (testing in the 4.6M range) and 0.22s for a 128K FFT
on a 200MHz Ultra.
> How fast does the program run on a really big Ultra, i.e. a 440MHz
> server with piles of RAM and a 4MB cache?
I've only got up-to-200MHz Ultras :-(
> Are there enough Ultras out there to justify making a fast LL test out
> of this code? I'd be willing to try, but only if there's sufficient
> interest; the code won't run on normal sparcs, my time is very
> limited I don't want to expend a considerable amount of
> energy on something no one will use. Would anyone like to help?
I'd be interested in helping - I think I can see the gist of what
you are doing at first glance. A whiles back I wrote a very simple
implementation of the LL test using FFTW, so I should be able to use
that as a framework. It's at
ftp://melanoma.cs.rmit.edu.au/pub/simonb/fftwll.tar.gz
if anyone's interested...
While on the subject of FFTW, I tried to use a multithreaded FFTW but
came up with the wrong results (M1279 wasn't prime :-( ). The aim of
the exercise was a fast double-checker - imagine throwing a 64 CPU Sparc
E10000 at a double checking exercise next time we want to double check
a number quickly! Has anyone used FFTW's threads?
Simon.
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------------------------------
Date: Fri, 13 Aug 1999 18:54:08 -0400 (EDT)
From: Jason Stratos Papadopoulos <[EMAIL PROTECTED]>
Subject: Mersenne: Re: UltraSPARC-optimized Pepin test available
Sorry; it's come to my attention that I made a slight omission in
the source for my Fermat code.
If compiling in gcc or egcs, be sure to append -fno-inline-functions
to the compile line in f24main.c
jasonp
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------------------------------
Date: Sat, 14 Aug 1999 15:26:20 -0500
From: Ken Kriesel <[EMAIL PROTECTED]>
Subject: Mersenne: Prime95 V19 QA testers
Did I miss anyone who wishes to participate in the Quality
Assurance testing of Prime95 V19?
To reach the QAtesters group for prime95 v19, use this list
(in alphabetical order by last name):
Brian Beesley <[EMAIL PROTECTED]>,
"Jean-Yves Canart" <[EMAIL PROTECTED]>,
Marc Getty <[EMAIL PROTECTED]>,
Alex Healy <[EMAIL PROTECTED]>,
Ken Kriesel <[EMAIL PROTECTED]>,
Shane Sanford <[EMAIL PROTECTED]>,
Gordon Spence <[EMAIL PROTECTED]>,
"Joth Tupper" <[EMAIL PROTECTED]>,
Guillermo Ballester Valor <[EMAIL PROTECTED]>,
"Willmore, David" <[EMAIL PROTECTED]>,
George Woltman <[EMAIL PROTECTED]>
Ken
Ken Kriesel, PE <[EMAIL PROTECTED]>
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------------------------------
Date: Sat, 14 Aug 1999 15:40:36 -0700
From: Will Edgington <[EMAIL PROTECTED]>
Subject: Mersenne: Up to date benchmarks sites?
The benchmarks site linked from www.mersenne.org:
http://www2.tripnet.se/~nlg/mersenne/benchmk.htm
... has not been updated in over a year. Is there an up to date one?
Further, the link there to another site for non Intel/Cyrix/Mac/AMD
systems at:
http://www.via.nl/users/mccidd/html/mersenne/benchmark.html
... is timing out in the nameserver. Anyone know the status of it?
Please reply to me privately; I'll reply to the list when I have
solid info.
While I'm here, I now have more room at my ISP, so I'll be adding more
files there as I have time. I've just put mersdata.zip there again
for those of you that have asked for that data but couldn't unpack
mersdata.tgz for whatever reason.
Will
http://www.garlic.com/~wedgingt/mersdata.zip
mersdata.tgz
mersdata.tar.gz
mersenne.html
README.html
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------------------------------
Date: Sun, 15 Aug 1999 13:13:14 +0200
From: "Steinar H. Gunderson" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Chirpy chirpy chirpy! (Heh, full message this time)
On Sat, Aug 07, 1999 at 11:59:17AM -0400, [EMAIL PROTECTED] wrote:
>The chirping also changes speed with the level of CPU usage I put
>on my computer, and it _seems_ to be one chirp per iteration.
Could it be that GIMPS initializes the FPU (ie. does FINIT) every iteration?
Just a thought :-)
/* Steinar */
- --
Homepage: http://members.xoom.com/sneeze/
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------------------------------
End of Mersenne Digest V1 #614
******************************
