Mersenne Digest V1 #553

1999-05-08 Thread Mersenne Digest


Mersenne Digest Saturday, May 8 1999 Volume 01 : Number 553




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Date: Wed, 05 May 1999 23:47:19 -0500
From: Ken Kriesel [EMAIL PROTECTED]
Subject: Mersenne: volunteers  nominees for the QA effort

Here is the list to date of volunteers.  If I missed anyone, or understated
or overstated your areas of involvement, please reply offline to me,
and I'll update the other participants in a single summary message.



George Woltman [EMAIL PROTECTED] is in it by default, as 
a code developer and tester (presumably on Win95 and NT)
Any additions George?

George nominated (drafted?) the next two:

Richard McDonald [EMAIL PROTECTED]
PPC-based MAC client software (MacGIMPS) developer

"Ernst W. Mayer" [EMAIL PROTECTED]
DEC Alpha  SGI client software (lucas_mayer) developer


In somewhat random order are those who volunteered themselves:

Guillermo Ballester Valor [EMAIL PROTECTED]
linux win95
pentium166mmx
QAtest
Basic, Fortran, assembler (for I86X), C and C++


"Brian J Beesley" [EMAIL PROTECTED]
Run QA tests - on Intel Pentium II under Windows 95  NT WS 4.0
 - on Alpha 21164 under Red Hat Linux 5.1
 - maybe on Intel Pentium II under Linux, later
Help design QA tests
Help keep testing databases  provide statistics. Can provide 
filestore to assist with this.
Will assist in any coding which may be necessary
I'm less happy about reviewing code, but I'll give it a bash if necessary


Shane Sanford [EMAIL PROTECTED]
QAtest  C/C++ code
MS Visual C/C++ 4.0,5.0,  6.0; P2 450 196 meg ram
access to Win95a/Win95b/Win98/NT 4.0


Ken Kriesel [EMAIL PROTECTED]
NT4 and win95 now, linux eventually
assorted systems including 486-66, pentium, dual-pentium, dual-pentiumpro,
pentiumII-400
QAtest
generating full LLtests under prime95 v14.4, v16.3, v18.1, and others.

Nick Craig-Wood [EMAIL PROTECTED]
http://www.axis.demon.co.uk/
suggests his ARMprime program as another means of independent-architecture
and program test results

"Jean-Yves Canart" [EMAIL PROTECTED]
QAtest
PentiumII-266 with unspecified OS


So to reach the QAtesters, use this list:
[EMAIL PROTECTED],[EMAIL PROTECTED],[EMAIL PROTECTED],BJ.Beesley
@ulst.ac.uk,[EMAIL PROTECTED],[EMAIL PROTECTED]

And for the code reviewers or developers:
[EMAIL PROTECTED],[EMAIL PROTECTED],[EMAIL PROTECTED],rmc
[EMAIL PROTECTED],[EMAIL PROTECTED]



Ken
Ken Kriesel
(resident of Madison WI, last year's #1 city and this year's #7)

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Date: Thu, 6 May 1999 01:11:25 -0700 
From: Paul Leyland [EMAIL PROTECTED]
Subject: RE: Mersenne: ECM question

 At Paul Zimmerman's ECM page,
http://www.loria.fr/~zimmerma/records/ecmnet.html
 the optimal B1 value listed for finding 50-digit factors is 
 4300, but 
 George's ECM factoring page uses 4400 for the same 
 purpose. Is one of 
 them wrong, or is there a reason for the difference?

No, neither is "wrong", for at least two reasons.

First, ECM is a probabalistic algorithm.  Each run chooses a random elliptic
curve and has a certain chance to find a factor of a particular size.   When
enough curves have been run, there is particular probability of finding a
factor of that size, assuming that one exists.  If one choose 50% as the
desired probability, the number of curves required will obviously be fewer
than if one chooses 60%, say.  A similar choice can be made for trading off
B1 value against probability, as long as the trade isn't pushed too far.

Another reason is that the B1 value is only one quantity of importance.
Even if the probability mentioned above is fixed, the optimal number of
curves depends on the value of B2.  Different implementations of ECM (or
even different runs of the same implementation) are free to choose different
values of B2 for a given B1.


A non-reason, but still of interest, is that the maximum in the probability
agains B1 curve is really rather flat, and it doesn't matter too much if
parameters are chosen which are not strictly optimum.


Paul

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Date: Thu, 6 May 1999 14:13:35 +
From: "Steinar H . Gunderson" [EMAIL PROTECTED]
Subject: Mersenne: Re: Mersenne Digest V1 #552 (IA-64)

On Wed, May 05, 1999 at 05:54:50PM -0700, Mersenne Digest wrote:
From the IA-64 register set figure in the advert, one weakness appears to me
to be the sheer amount of silicon: Intel is going from just 8 FP registers
in all the Pentium incarnations to a whopping 128, each still having the
x86's full 80 bits, in the IA-64 There are also 128 65-bit general purpose
(64-bit integer plus carry bit) registers.

I've heard the main problem is getting efficient code out of it. Merced (IA-64)
is 

Re: Mersenne: Any statistics majors out there?

1999-05-08 Thread Chris Nash


 though.  So outside about 14 sigmas you should be able to say the
 probability is below 10e-40. The problem is that if there are small
 deviations from "Gaussian-ness" way out on the wings of your distribution,
 the REAL probability of a certain result is not well approximated by the
 Error Function result.

This is a real good point - if we are assuming a Gaussian distribution, then
we are assuming the best case. The worst case is given by Tchebycheff's
theorem, which states that, given a probability distribution where only the
mean and standard deviation is known, then the probability that an
observation will fall more than x standard deviations from the mean is
bounded above *only* by 1/x^2. (It's a tight bound for one value of x, but
with a very unlikely distribution). In other words, if you have no
guarantees about the distribution, "counting sigmas" is going to give you a
false sense of security, and if the distribution is even slightly deviant
from Gaussian, then the result can be very wrong indeed.

However we do have a little comfort. George's function - maximum convolution
error from a single iteration - does have some distribution. It "appears"
bell-shaped, and looks like a normal distribution, the samples George has
made are also reasonably-sized. Not only that, each observation is actually
the maximum of the deviations from integer over many channels in the FFT -
in other words, the observations are already coming from a "smoothed"
distribution. I'm sure the distribution of a maximum of several observations
is something which there is a statistical test for. (The resulting
distribution may not be normal, but may have an analogous test).

Thanks too Todd for backing up the heuristic calculation of "14 sigmas" that
I got the hard way :)

Chris



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Re: Mersenne: Any statistics majors out there?

1999-05-08 Thread Jud McCranie

At 12:00 PM 5/8/99 -0400, Chris Nash wrote:

This is a real good point - if we are assuming a Gaussian distribution, then
we are assuming the best case. The worst case is given by Tchebycheff's
theorem, which states that, given a probability distribution where only the
mean and standard deviation is known, then the probability that an
observation will fall more than x standard deviations from the mean is
bounded above *only* by 1/x^2. 

Yes, but that is a really bad worst case.  Pathological even.  Looking at the
graphs of the two data sets, you can tell that it is reasonably well behaved.


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Re: Mersenne: Any statistics majors out there?

1999-05-08 Thread Jud McCranie

At 06:17 PM 5/8/99 -0500, Ken Kriesel wrote:
Aren't gaussians symmetric about the mean value?  What George plotted is not.


Yes, but isn't too far off.  But it does drop off quite a bit faster onthe
left.  That is why I think it may be better to chop the data at the mean, throw
away that under the mean, reflect the other data with respect to the mean, and
calculate the standard deviation from that "massaged" data.  Then a Normal
distribution should approximate it pretty well.


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