Mersenne Digest Tuesday, 19 January 1999 Volume 01 : Number 498
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From: Leu Enterprises Unlimited <[EMAIL PROTECTED]>
Date: Sat, 16 Jan 1999 23:52:26 -0800 (PST)
Subject: Re: Mersenne: mprime for QA or performance?
> From [EMAIL PROTECTED] Fri Jan 15 19:39:41 1999
> Hi,
Greetings! My sincerest thanks for clarifying this issue.
I have some comments and questions.
> I'd be surprised if burning in had an effect on iteration times.
I'm keeping an open mind here. Now that I know that mprime is
capable of accurately measuring this, and I suspect what the difference
is (see below), I'm going to do a quick observation on 6 CPU's which
I've just gotten in.
I too would be surprised - but the potential benefit is too great
to leave without some investigation.
> More likely, 100 iterations is not enough to get a truly accurate
> timing.
I haven't noticed much, if any variation, in reported times whether
it be with 100 samples, or 1000. Granted, I haven't done an in-depth
analysis of this; I've just noticed that the variation seems
minimal over a number of 100-unit samples across many time intervals.
> I don't know about Linux, but it has been noted before prime95
> iteration times can vary a few percent from day to day.
Indeed. I've come to the conclusion that what I'm seeing is clock
oscillator drift. This could explain what I've seen, if the CPU
wasn't warm enough to begin with. And it's consistent with the
above reports - assuming there are no background activity going on.
> mprime is great for QA. It generates heat (by FPU use) and tons of
> memory accesses. If there are any hardware problems there, they are likely
> to show up in an extended torture test.
Though my comments were more focused on the timing issue, on this I
heartily agree! It has been my experience as well.
Actually, I don't think people appreciate mprime enough. As I stated earlier,
using it has identified that a key point of failure on overclocking is
the FPU - and not the L2 cache (as many have thought).
Regarding heat - hmm. Here, you have to be careful. Generally this is
true. While mprime does take second place to memtest86, this is due
to the fact that mprime requires an O.S. (and hence you have other
distractions going on - like interrupts, etc.).
I've measured the difference in temp. to be around 2 C (this does depend
on your fansink, though).
But, there is one reported exception - win98. It's been reported (and
I haven't verified), that prime95 generates significantly less heat when
it's run on win98 than with other O.S.'s.
I have no idea why, and can only speculate.
> >and/or performance measurements,
>
> I'd guess its as good as but no better than any of hundreds
> of publicly available benchmarks.
A fair statement, as performance and the application should be considered
together.
What I was wondering specifically is how one can determine the Mflops
rating of a given system via mprime? I know how to measure it with various
benchmarks, and was curious how mprime could be used.
Pardon me if this is a FAQ; I haven't seen this described anywhere.
If someone could either point me to a reference, or give an explanation,
I would be greatly appreciative. Thanks in advance!
Best regards,
-dwight-
===============================================================
To learn how to build your own supercomputer,
for under $10,000, go to www.supercomputer.org
===============================================================
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From: [EMAIL PROTECTED]
Date: Sun, 17 Jan 1999 16:10:47 +0100 (MET)
Subject: Re: Mersenne: Basic question: Working modulo 2^n-1
Hi,
In solidarity with all the thousands of people looking for the same Mersenne numbers,
I had a look at my Masters, where I was developing Mersenne like tests. I see that for
instance for numbers J(m,n) = 2^m * 3^n - 1 ( I call them Jacobi nunmbers, since proofs
use Jacobi reciprocity), there are criteria simple as Mersenne. Here is one of them:
Let (m,n) denote the pair of remainders ( m mod 3, n mod 6). For (m,n) \in
\{ (0,1), (1,5), (2,3), (0,5), (1,3), (2,1) \} the Lucas sequence L(5,7) is such that
the zeroes of the generating polynomial x^2 - 5 * x + 7 generate
F^2_{J(m,n)}* / F*_{J(m,n)}, i.e. they have order J(m,n)+1, is J(m,n) is prime.
One has thus the following test:
1. Let r_0 = u_{2^m}, and q_0 = u_{2^{m-1}} mod J(m.n)
(the L(5,7) u sequence), easy with the Lucas doubling theorem.
2. Let f_3(u_n) = u_n*( (P-4Q)u_n^2 + 3Q^n) ( = u_{3n} ) be the trippling rule for
the Lucas sequence L(P,Q) and
r_{s+1} = f_3(r_s), q_{s+1} = f_3(q_s} mod J(m,n).
D(m,n) is prime iff r_n = 0 and q_t \neq 0 \forall t <= n.
Another way to put it is:
v_{2^{m-2}3^n} \neq 0 and v_{2^{m-1}3^{n-1} \neq 0 but
v_{2^{m-1}3^n} = 0.
There are many similar exact tests that can be derived and they may offer
highly larger chances for finding the first Megaprime. The computational
effort migth maybe double or tripple, arithmetic mod 2^m.3^n-1 is easier
than general but harder than mod Mersenne primes, etc.
This is just to ask whether you think that the GIMPS community might be
interested in more details along these lines ?
Sincerely
Preda Mihailescu
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From: [EMAIL PROTECTED]
Date: Sun, 17 Jan 1999 16:19:25 +0100 (MET)
Subject: Re: Mersenne: Basic question: Working modulo 2^n-1
PS. I forgot vor the v_n approach, the
doubling formula, as used in Mersenne is
v_{2n} = v^2_n - 2 Q^n
and the trippling formula is
v_{3n} = v_n(v^2_n - 3 Q^n ).
Like in the Mersenne Sequences, since only comparison to 0 is required,
one could factor out the Q^n ...
Preda
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From: "John R Pierce" <[EMAIL PROTECTED]>
Date: Sun, 17 Jan 1999 10:08:50 -0800
Subject: Re: Mersenne: mprime for QA or performance?
> > I don't know about Linux, but it has been noted before prime95
> > iteration times can vary a few percent from day to day.
>
> Indeed. I've come to the conclusion that what I'm seeing is clock
> oscillator drift. This could explain what I've seen, if the CPU
> wasn't warm enough to begin with. And it's consistent with the
> above reports - assuming there are no background activity going on.
IMHO, unlikely. The CPU clock is the same clock being used to measure the
time via the pentium's RDTSC instruction. Speed up or slow down the CPU
clock, it would still take the same number of clocks.
Far more likely is minor variations in page table hits and cache misses due
to distribution of the prime95 pages in ram.
- -jrp
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From: Henk Stokhorst <[EMAIL PROTECTED]>
Date: Mon, 18 Jan 1999 23:00:03 +0100
Subject: Mersenne: no more exponents
L.S.,
>Getting exponents from server
>Error 7: Server has run out of exponents to assign
What? is n in 2^n -1 finite?
YotN,
Henk Stokhorst
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End of Mersenne Digest V1 #498
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