Mersenne: Re: Mersenne Digest V1 #551

1999-05-05 Thread Steinar H . Gunderson

On Mon, May 03, 1999 at 11:22:02AM -0700, Mersenne Digest wrote:
Also, I'm wondering if any pattern begins to occur in the N=N^2-2 % 2^P-1
sequence... Do you think N ever repeats itself? Has anyone checked this?

I checked it some years ago. It doesn't seem to. (But Mandelbrot fractals
do, that's where I got the idea from originally.) But don't take my word for
it, I was merely playing with Java's BigInteger class, and I don't think I
tested it extensively.

---snip---

Well, could anybody explain me the FFT-Algorithm. I'd be very pleased about
it, because I've not found any usefull stuff in the NET

If you read George's source, he gives you an excellent advice: Go buy a book :-)
FFTs are (I guess) really serious maths, and you will need both a good
background _and_ a good textbook. Honestly, the Net doesn't contain very much
advanced material such as this.

/* Steinar */

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Re: Mersenne: Java Prime and lotsa questions

1999-05-05 Thread Nick Craig-Wood

In URL:news:local.mersenne on Tue 04 May, Brian J Beesley wrote:
 I'm still "rather hazy" (read, totally baffled) on exactly how  the
 Crandall-Fagin procedure works, so I don't know if you could  adapt NTT to
 do the mod 2^p-1 automatically. But my gut feeling is  that it ought to be
 possible.

It is possible.  That is how my StrongARM code works.  The maths for the
irrational base transform all works out provided the relevant fractional
powers of 2 exist in the field you are using  (ie for a transform of length n
there must exists a number x so that x^n = 2).  Whether this is the complex
field or some other Galois field it doesn't matter.  This puts some
constraints on which modulus you can use...  My code uses GF(2^64-2^32+1)
which works for DWTs up to 2^26 bits (67 million).  The 'interesting' binary
representation of this number makes for lots of short cuts when taking the
modulus also.

-- 
Nick Craig-Wood
[EMAIL PROTECTED]
http://www.axis.demon.co.uk/


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Mersenne: ECM question

1999-05-05 Thread Foghorn Leghorn

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?


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Mersenne Digest V1 #552

1999-05-05 Thread Mersenne Digest


Mersenne Digest Wednesday, May 5 1999 Volume 01 : Number 552




--

Date: Mon, 3 May 1999 14:31:52 -0400
From: "Ernst W. Mayer" [EMAIL PROTECTED]
Subject: Mersenne: IA-64

I got an announcement in today's mail advertising "Intel's Merced
and IA-64: Technology and Market Forecast," by Linley Gwennap, editor
of Microprocessor Report, and to be published by MicroDesign Resources
(www.mdronline.com). MDR claims the above to be

"The authoritative analysis of Intel's new microprocessor
architecture from the industry's most trusted source."

They also drop tantalizing hints about

"...the fledgling chip's strengths and its critical weaknesses."

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. This raises several questions:

1) How does Intel expect to be able to maintain anything approaching their
current price advantage over other (already existing) high-end chips with
this much Silicon in the IA-64?

2) What use are so many registers without a major increase in the number
of functional units? (I believe IA-64 still has 1 FP adder, 1FP multiplier,
perhaps 2 64-bit integer units, the latter having been a longstanding feature
of e.g. Alpha and MIPS, which both have excellent integer functionality
and neither has 128 integer registers.)

Sure, lots of registers is nice for out-of-order execution (OOE), but even
an OOE monster like the Alpha 21264 has "just" 80 FP registers, each of just
64 bits - IA-64 will have double the silicon here!


The aforementioned book is pricey: $995 before 31 May, but additional
copies are "only" $295. Microprocessor Report subscribers get $100 off
either of these figures. At a potential $195 a copy, perhaps if one of
the readers of this list is a subscriber, there might be enough interest
for a volume order?

Or, perhaps there's a better/cheaper place to obtain the relevant technical
information?

- -Ernst

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--

Date: Mon, 3 May 1999 13:58:44 -0600
From: "Aaron Blosser" [EMAIL PROTECTED]
Subject: RE: Mersenne: IA-64

 The aforementioned book is pricey: $995 before 31 May, but additional
 copies are "only" $295. Microprocessor Report subscribers get $100 off
 either of these figures. At a potential $195 a copy, perhaps if one of
 the readers of this list is a subscriber, there might be enough interest
 for a volume order?

 Or, perhaps there's a better/cheaper place to obtain the relevant
 technical
 information?

In the past, I've been blessed to see some Intel demos, but I had to sign an
NDA, so I'm not always sure what I can and cannot say.

But if you can get yourself into an Intel demo or seminar, they pass out all
sorts of literature.  I'll be going to another one in August sometime, and
Intel will be there.  I should be able to get alot more detail on IA-64 and
Merced then.

But from what I can recall, there are multiple FPU pipelines to take
advantage of all those yummy registers...that and the fact that the core is
really a RISC design now anyways...register renaming, etc.


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Date: Mon, 3 May 1999 15:04:25 -0500 
From: "Griffith, Shaun" [EMAIL PROTECTED]
Subject: Mersenne: Java Prime and lotsa questions

Since the heavyweights here seem to be involved with finals and such, let me
get you started on your answers...

a) [skipping, I don't know]
b1) Using "properly sized" FFT: Yes, I believe using properly sized FFT's
saves some time. How much depends on the programmer, the data, the
language/compiler, and the hardware. Non-power-of-2 FFT's can even be
useful, but it seems that coding up all (or most) of the possible sizes may
be more trouble than it's worth.

b2) Recurring pattern in "N=N^2-2 % (2^P-1)": I don't recall anyone here
mentioning any interesting repeats, even for composite P. I'm sure many have
looked, and were disappointed.

c1) DB Lookup: If you are in the 2^8,000,000 range, that is 8 million bits,
or ~1MB. A database of all possible results of "N=N^2-2 % (2^P-1)" would
take 1MB * 2^8,000,000 ~= 10^3,500,000MB. This is larger than the number of
particles in the universe, by something like 10^35,000. If instead you meant
to lookup all of the "N=N^2-2" values, and compute the "%(2^P-1)" at
runtime, then P~=8,000,000 gives the last number in the sequence ~=
2^(2^8,000,000), which again runs up against the universal limit.

c2) The LL test does not adapt well