Mersenne Digest Thursday, June 17 1999 Volume 01 : Number 582
----------------------------------------------------------------------
Date: Wed, 16 Jun 1999 21:19:43 -0400
From: Brian Beuning <[EMAIL PROTECTED]>
Subject: Re: Mersenne: $1000 supercomputer
They seem to be developing a line of machines. I assume
the $1000 price is for the low-end machine and the 10^11
BIPS rating is for the high-end machine. It would be interesting
to see the BIPS of the low-end and the price of the high-end
machines.
Brian Beuning
Gary Diehl wrote:
> I thought this was interesting...
>
> http://www.cnn.com/TECH/computing/9906/15/supercomp.idg/index.html
>
> If you don't have time to read it, here are some quotes:
>
> "Within 18 months, you may be able to put the equivalent of today's
> supercomputer on your desktop--for about $1000"
>
> "The new computer will be able to process 100 billion instructions per
> second, according to Kent Gilson, chief technical officer of Star Bridge
> Systems."
>
> "HAL-300GrW1, a "hypercomputer" that is said to be 60,000 times as fast
> as a 350-MHz Pentium, and many times as fast as IBM's supercomputer
> Pacific Blue."
>
> ...
>
> Goodness, if we could get one of these for GIMPS...
>
> Gary Diehl
> ________________________________________________________________
> Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
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Date: Thu, 17 Jun 1999 13:36:43 +1200
From: "Halliday, Ian" <[EMAIL PROTECTED]>
Subject: Mersenne: Finite or infinite?
Some considerable while back, there was a lively discussion as to the
_total_ number of Mersenne primes. I still believe that the number is
finite, in contrast to what appears to be the majority view: that there is
an infinity of Mersenne primes out there waiting to be discovered.
One correspondent at that time postulated that there were no further
Mersenne primes to be discovered and that the 37th was also the last. In the
light of recent events, does anybody have an update on this view? So far as
I am aware, M38 has not been confirmed yet. No flames, please: I am _not_
posting this as an "I told you so" but as a genuine enquiry.
Regards,
Ian
Ian W Halliday
Wellington, New Zealand
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Date: Wed, 16 Jun 1999 18:56:44 -0700
From: Luke Welsh <[EMAIL PROTECTED]>
Subject: Re: Mersenne: interesting Mathematicians
At 04:09 PM 6/16/99 -0400, lrwiman wrote:
>Taken verbatim from the Linux fortune file:
>Norbert Weiner was the subject of many dotty professor stories.
<snip>
Version by Weiner's daughter:
http://www.tiac.net/users/cri/weiner.hrml
I guess she doesn't run Linux ;-)
- --Luke
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Date: Wed, 16 Jun 1999 20:50:59 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Re: NTPrime and proth
At 11:13 PM 6/16/99 +0200, Steinar H. Gunderson wrote:
>I'm not sure why you want to run two different projects. I'm afraid you'll
>have to choose -- running them both at the same time will make _both_ slower
>(due to increased OS overhead).
I don't think it hurts much. I've had both running at the same tie, with
little overhead ( < 1%).
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| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Wed, 16 Jun 1999 20:52:19 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Thoughts on Merced / IA-64
At 03:52 PM 6/16/99 -0600, Aaron Blosser wrote:
>- 82bit FPU (??)
82 bits? It is time to go to 128 bits!
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| Jud "program first and think later" McCranie |
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Date: Wed, 16 Jun 1999 22:25:26 -0400
From: Leo Feret <[EMAIL PROTECTED]>
Subject: Re: Mersenne: interesting Mathematicians
I suppose it's obvious, but the referenced link should be
http://www.tiac.net/users/cri/weiner.html
Luke Welsh wrote:
> At 04:09 PM 6/16/99 -0400, lrwiman wrote:
> >Taken verbatim from the Linux fortune file:
> >Norbert Weiner was the subject of many dotty professor stories.
> <snip>
> Version by Weiner's daughter:
> http://www.tiac.net/users/cri/weiner.hrml
>
> I guess she doesn't run Linux ;-)
>
> --Luke
>
> ________________________________________________________________
> Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
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Date: Wed, 16 Jun 1999 22:26:51 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Finite or infinite?
At 01:36 PM 6/17/99 +1200, Halliday, Ian wrote:
>Some considerable while back, there was a lively discussion as to the
>_total_ number of Mersenne primes.
In all likelihood, there are an infinite number of Mersenne primes.
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Date: Wed, 16 Jun 1999 22:53:16 EDT
From: [EMAIL PROTECTED]
Subject: Mersenne: Z80s Are Everywhere!
<<guess you might even be able to find the odd one [Z80 processor] still in
use somewhere>>
Actually, the Z80 is still alive and kicking. You might even have one in your
pocket right now. Texas Instruments uses the Z80 in many of its calculators,
including the wildly successful TI-85.
S.T.L.
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Date: Thu, 17 Jun 1999 03:08:52 +0000 (GMT)
From: Henrik Olsen <[EMAIL PROTECTED]>
Subject: Re: Mersenne: $1000 supercomputer
On Wed, 16 Jun 1999, Gary Diehl wrote:
> I thought this was interesting...
>
> http://www.cnn.com/TECH/computing/9906/15/supercomp.idg/index.html
>
> If you don't have time to read it, here are some quotes:
>
> "Within 18 months, you may be able to put the equivalent of today's
> supercomputer on your desktop--for about $1000"
>
> "The new computer will be able to process 100 billion instructions per
> second, according to Kent Gilson, chief technical officer of Star Bridge
> Systems."
>
> "HAL-300GrW1, a "hypercomputer" that is said to be 60,000 times as fast
> as a 350-MHz Pentium, and many times as fast as IBM's supercomputer
> Pacific Blue."
>
> ...
>
> Goodness, if we could get one of these for GIMPS...
>From the same article:
is on its high-end hypercomputer line, HAL. The HAL-300GrW1 has a price
tag of about $26 million, so it doesn't take a hypercomputer to
understand why Star Bridge Systems has chosen to direct its attention
to the HAL line first.
If we could get one of these, we could use the money better for 60,000
PII-350's anyway:)
>
> Gary Diehl
> ________________________________________________________________
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>
- --
Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/
Animal behaviour is best described by the four F's
Food, Fight, Flee and Reproduce
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Date: Wed, 16 Jun 1999 21:32:23 -0600
From: "Aaron Blosser" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Z80s Are Everywhere!
> <<guess you might even be able to find the odd one [Z80
> processor] still in use somewhere>>
>
> Actually, the Z80 is still alive and kicking. You might even have
> one in your
> pocket right now. Texas Instruments uses the Z80 in many of its
> calculators,
> including the wildly successful TI-85.
Okay, I don't know about anyone else, but I'm not so bad off that I carry my
TI calculator in my pocket wherever I go!
No offense to those who do. :-)
Aaron
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Date: Thu, 17 Jun 1999 00:37:04 -0400 (EDT)
From: "Roger M. Levasseur" <[EMAIL PROTECTED]>
Subject: RE: OT: Mersenne: ARM Licenses
> I know a lot of Z80s were manufactured, and I guess you might even be
> able to find the odd one still in use somewhere (NASA's immensely
> successful Voyager spacecraft use an even more primitive
> microprocessor), but I reckon that, for LL tests, the combined power
> of all the Z80s ever manufactured is less than that of a couple of
> today's standard desktop PCs.
I believe that they've made over a billion Z80s already. I know they
were still making them a few years ago for embedded application use.
In fact, I have one in my 486...located on the Adaptec 1542C scsi
adapter. I know, not the same as being in a TRS-80.
> Based on the fact that Intel are apparently holding back the 100MHz
> FSB versions of the Celeron until Feb 2000 (according to August's
> "Personal Computer World" which arrived with me today) - the theory
> is that Intel don't want to undermine the PII/PIII market - I would
133 MHz FSB PIII machines are expected later this year. Celerons
will always be a step down from PIII (and plain PIII will always be
a step down from the Xeon models).
-roger
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Date: Wed, 16 Jun 1999 21:51:43 -0700
From: "Scott Kurowski" <[EMAIL PROTECTED]>
Subject: Mersenne: RE: Mersenne Digest V1 #581
> Would a doublecheck with v17 on an exponent >4.2M result in the same (wrong)
> residue as the first (wrong) test?
Yes.
> Now, I when I check in the Internet PrimeNet Individual Account,
> it gives me no credit for that work. Where theses exponents given to
> someone else or is there another place to go to check?
[snip]
> I do not want to bother Georges with these small details (but
> important to me!) so I decide to send it to the list. But I sure
> want to know if my PC at home is computing for nothing.
You can bother us for answers. :-) <[EMAIL PROTECTED]> I've forwarded your
message to our support guy, Brad, who will review your account history with you.
Off the top, please bear in mind PrimeNet does not credit work submitted on the
manual testing page. Even so, the test results are collected and tracked by
George and the work done is useful. In practically every case we can account
for apparent discrepancies, and easily correct the very few that are real.
> So long as double-checking assignments have exponents less than 2^22,
> the server-imposed rule is OK. But we're starting to close in on 2^22
> - - Scott, this rule may need to be looked at in a month or two!
Yup. They will probably be put to factoring.
> SETI@Home brought positive effects to GIMPS? Wow, this thing must be bigger
> than we thought, considering the people who left us.
Many that registered for newsletters said they went to the seti@home web site,
saw the GIMPS link and joined GIMPS instead.
> Radio ads? Is somebody paying to get out `join GIMPS' on everybody's radio?
Entropia.com, Inc. paid for a few spots on a local S.F. Bay Area PBS station in
mid May. Seemed to have brought around 1600 new GIMPS folks in about a week,
but that's only a *very* rough figure. We can't correct for unknown events, but
if we (liberally) assume airtime was the only significant attention-getting
event during that period, the correlation is reasonably strong. It was a fun
experiment.
> Do you mean the `v17 bug' newsletter, or has there been one (with M?38) that
> I didn't get? I _have_ signed up for the newsletter on the web page.
Yes - the v17 bug and $50k prize newsletter. Roughly 1100 new accounts joined
within a few days of that. Some of that was undoubtedly due to the EFF's own
press releases, but either way, it smacked of prize motivation.
> [...] (What FBI quote, BTW?)
Aaron's unfortunate search warrant quotes an Arthur Anderson estimate for the
cost of 8 P90 CPU years.
> "Within 18 months, you may be able to put the equivalent of today's
> supercomputer on your desktop--for about $1000"
Keep your Internet services... :-)
Regards,
scott
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Date: Wed, 16 Jun 1999 23:36:40 -0700
From: "John R Pierce" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Thoughts on Merced / IA-64
> >- 82bit FPU (??)
>
> 82 bits? It is time to go to 128 bits!
*If* the IA64 has a fast pipelineable 64 bit * 64 bit -> 128 bit integer
multiply capability, perhaps the FPU is no longer needed? I guess I'd
better dig into that Architecture document a bit more. Ah, sigh. It has
64*64 but it only generates a single 64 bit high *or* low result in one
instruction, you get to chose which. There's also Fixed-Point Multiply and
Add.
Hmm. I wonder if two fixed point multiplies can be done in the same
instruction cycle? Yeee-hah.
- -jrp
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Date: Thu, 17 Jun 1999 10:31:11 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Thoughts on Merced / IA-64
At 11:36 PM 6/16/99 -0700, John R Pierce wrote:
>*If* the IA64 has a fast pipelineable 64 bit * 64 bit -> 128 bit integer
>multiply capability, perhaps the FPU is no longer needed?
You still need floating point numbers and that's probably better handled with
FPU hardware.
+----------------------------------------------+
| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Thu, 17 Jun 1999 08:31:12 -0600
From: "Blosser, Jeremy" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Z80s Are Everywhere!
> -----Original Message-----
> From: Aaron Blosser [mailto:[EMAIL PROTECTED]]
> Sent: Wednesday, June 16, 1999 10:32 PM
> To: Mersenne@Base. Com
> Subject: RE: Mersenne: Z80s Are Everywhere!
>
>
> > <<guess you might even be able to find the odd one [Z80
> > processor] still in use somewhere>>
> >
> > Actually, the Z80 is still alive and kicking. You might even have
> > one in your
> > pocket right now. Texas Instruments uses the Z80 in many of its
> > calculators,
> > including the wildly successful TI-85.
>
> Okay, I don't know about anyone else, but I'm not so bad off
> that I carry my
> TI calculator in my pocket wherever I go!
>
> No offense to those who do. :-)
>
So what if I carry my TI-81 around with me wherever I go. Its got a whopping
2Mhz Z80 in it. And you never know when you're gonna need to figure out some
equation that pops in your head as you drive to work in the morning or
something.
Actually, I wrote a program on it last night even... Not terribly fast at
finding primes I found tho. ;)
Too bad the precision isn't enough to really do... anything...
- -Jeremy
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Date: Thu, 17 Jun 1999 09:48:57 -0600
From: "Blosser, Jeremy" <[EMAIL PROTECTED]>
Subject: Mersenne: CPUs and BigOs
First, I'm wondering what the big O is on the LL test. I'm wondering really
just how many operations are performed on a typical M(6000000) test or
whatnot. Or is it a matter of multiplying your 'P' times the FFT size?
Then, I realized to my amazement that the AS/400 I have sitting around doing
nothing here has 4 A35 CPUs in it (AKA RS64 and Apache). Which is the
predecessor to the Power3. So anyway, I'm reading thru the documentation on
the A35 last night, and it _appears_ to claim to do all FPU ops in 1 cycle.
So I'm beginning to think a port is in order... Then I go on to read that it
has only 8k L1 cache, but huge L2 caches (4-8MB)...
Supposedly the chip runs at 125 mhz, so...
Of course, it being an AS/400, the really annoying part about the whole
thing is that there are absolutely NO useful benchmarks. They have some
weird one called CPW, and there are some TPC benchmarks. But for some odd
reason, IBM didn't release any Spec benchmarks on the danged thang... Maybe
it sucks.
Oh, and that Russian company is called Elbrus, and the chip is the E2K.
>From their press-release:
Russian company Elbrus International has disclosed the technical details of
its revolutionary new microprocessor E2K. The microprocessor will function 3
to 5 times more quickly than Intel Merced while still running all legacy MS
DOS and Windows software. Fabricated in a 0.18-micron process, the chip
would run at 1.2GHz and deliver 135 SPECint95 and 350 SPECfp95, yet require
only 35 Watts of power and occupy 126 mm2 of silicon. By contrast, Intel's
forthcoming processor, which will be manufactured in the same process, would
operate at 800MHz, occupy 300 mm2, consume 60 Watts, and score only 45
SPECint95 and 70 SPECfp95. Elbrus technology does not infringe on any
Western intellectual property and it is protected by 70 US patent
applications
Man, a SPECfp of 350!!!! Yowza!
No mention of a release date or anything tho... hmmm...
- -Jeremy
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Date: Thu, 17 Jun 1999 10:56:09 -0500
From: "Willmore, David" <[EMAIL PROTECTED]>
Subject: RE: OT: Mersenne: Z80s Are Everywhere!
> > From: Aaron Blosser [mailto:[EMAIL PROTECTED]]
> > Okay, I don't know about anyone else, but I'm not so bad off
> > that I carry my
> > TI calculator in my pocket wherever I go!
> >
> > No offense to those who do. :-)
> >
>
> So what if I carry my TI-81 around with me wherever I go. Its got a
> whopping
> 2Mhz Z80 in it. And you never know when you're gonna need to figure out
> some
> equation that pops in your head as you drive to work in the morning or
> something.
>
> Actually, I wrote a program on it last night even... Not terribly fast at
> finding primes I found tho. ;)
>
> Too bad the precision isn't enough to really do... anything...
>
Boys, boys, please, keep it civil. (brothers, sheesh...)
Anyone remember back several years, wasn't an LL code for the HP calculators
mentioned? After all, they have 64 bit ALUs. :)
Cheers,
David
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Date: Thu, 17 Jun 1999 11:02:05 -0500
From: "Willmore, David" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Thoughts on Merced / IA-64
> From: Jud McCranie[SMTP:[EMAIL PROTECTED]]
> At 11:36 PM 6/16/99 -0700, John R Pierce wrote:
> >*If* the IA64 has a fast pipelineable 64 bit * 64 bit -> 128 bit integer
> >multiply capability, perhaps the FPU is no longer needed?
>
> You still need floating point numbers and that's probably better handled
> with
> FPU hardware.
>
>
No, no, no, no. :) Georges code uses the FPU of intel chips because the
early ones had very poor integer processing capabilities--small number of
small registers, non-pipelined multiply, darn *slow* multiply, etc. There
was the FPU sitting right next to it with 8 80 bit registers, nice multiply
instruction, etc... When the pentium came along, it pipelines the FPU and
things really got fun. Didn't hurt that the C&F DWT paper came out about
that time.
But, you can do it in integer if you have a processor with 1) enough integer
registers 2) wide registers and 3) fast/pipelined multiply--which IA-64 is
supposed to have. The floating point version was a cluge to make up for an,
uhhh, *interesting* processor archetecture. It shouldn't make everyone
think that it's always the best way to do things.
Well, keep in mind I'm wrong frequently, but I think this sums up the
development of the arguement--four or six years ago. It's been a while and
I don't remember all that well.
Cheers,
David
> +----------------------------------------------+
> | Jud "program first and think later" McCranie |
> +----------------------------------------------+
>
*laugh* Uh, hmmm, think now? :)
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Date: Thu, 17 Jun 1999 09:21:57 -0700
From: "John R Pierce" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Thoughts on Merced / IA-64
> At 11:36 PM 6/16/99 -0700, John R Pierce wrote:
> >*If* the IA64 has a fast pipelineable 64 bit * 64 bit -> 128 bit integer
> >multiply capability, perhaps the FPU is no longer needed?
>
> You still need floating point numbers and that's probably better handled
with
> FPU hardware.
Do you? I thought the only reason the FFT was using FP numbers was most
current generation processors have a faster and higher precision FP multiply
than fixed point. With a 64*64 bit fixed point multiply that generates a
higher precision result, you can quickly do exact fixed point multiplies of
any length.
example, multiplying 2 128 bit integers X * Y where Xh and Xl are the high
and low half of the X argument takes 4 multiples plus a few adds.
Z = XhXl * YhYl
Z = Xl * Yl
Z += (Xl * Yh) << 64
Z += (Xh * Yl) << 64
Z += (Xh * Yh) << 128
where Z is a 256 bit 'accumulator'...
- -jrp
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Date: Thu, 17 Jun 1999 13:46:56 -0300 (EST)
From: "Nicolau C. Saldanha" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Finite or infinite?
On Thu, 17 Jun 1999, Halliday, Ian wrote:
> Some considerable while back, there was a lively discussion as to the
> _total_ number of Mersenne primes. I still believe that the number is
> finite, in contrast to what appears to be the majority view: that there is
> an infinity of Mersenne primes out there waiting to be discovered.
Forgive me if this has been asked M38 times already, but why do you
believe there are only finitely many Mersenne primes?
I know several arguments in favor of there being infinitely many
of them but have never seen an argument for the opposite point of view.
[]s, N.
http://www.mat.puc-rio.br/~nicolau
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Date: Thu, 17 Jun 1999 13:11:09 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Thoughts on Merced / IA-64
At 11:02 AM 6/17/99 -0500, Willmore, David wrote:
>No, no, no, no. :)
I'm speaking that in general you need FP hardware.
> Georges code uses the FPU of intel chips because the
>early ones had very poor integer processing capabilities
The Intel FPU is still better at handling 64-bit integers than using two 32-bit
doublewords.
>But, you can do it in integer if you have a processor with 1) enough integer
>registers 2) wide registers and 3) fast/pipelined multiply--which IA-64 is
>supposed to have.
The IA-64 sounds like a monster. I'll want one, but they'll probably be too
expensive for a few years. (It happens over and over - "no person will need
that much on their desktop.")
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| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Thu, 17 Jun 1999 13:25:15 -0400
From: Jud McCranie <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Thoughts on Merced / IA-64
At 09:21 AM 6/17/99 -0700, John R Pierce wrote:
>>
>> You still need floating point numbers and that's probably better handled
>with
>> FPU hardware.
>
>Do you?
Yes. You absolutely need FP numbers, and in all cases that I know of, FP
numbers are better handled by FP hardware.
+----------------------------------------------+
| Jud "program first and think later" McCranie |
+----------------------------------------------+
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Date: Thu, 17 Jun 1999 12:15:52 -0600
From: "Blosser, Jeremy" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Thoughts on Merced / IA-64
> -----Original Message-----
> From: Jud McCranie [mailto:[EMAIL PROTECTED]]
> Sent: Thursday, June 17, 1999 12:25 PM
> To: John R Pierce
> Cc: Mersenne discussion list
> Subject: Re: Mersenne: Thoughts on Merced / IA-64
>
>
> At 09:21 AM 6/17/99 -0700, John R Pierce wrote:
> >>
> >> You still need floating point numbers and that's probably
> better handled
> >with
> >> FPU hardware.
> >
> >Do you?
>
> Yes. You absolutely need FP numbers, and in all cases that I
> know of, FP
> numbers are better handled by FP hardware.
>
You could go with a NTT instead of a FFT. Thus foregoing any double
precision floats. Going with an NTT would also eliminate any precision
problems...
Of course, NTTs right now are a bit slower than FFTs, but who knows maybe w/
MMX instructions you could get a NTT to perform on par with an FFT...
I need to look into that... hmm...
Jeremy
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Date: Thu, 17 Jun 1999 19:18:12 +0100
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Finite or infinite?
On 17 Jun 99, at 13:36, Halliday, Ian wrote:
> Some considerable while back, there was a lively discussion as to the
> _total_ number of Mersenne primes. I still believe that the number is
> finite, in contrast to what appears to be the majority view: that there is
> an infinity of Mersenne primes out there waiting to be discovered.
You're entitled to your viewpoint, there is no proof one way or the
other. But the circumstantial evidence seems to point to the number
of Mersenne primes being infinite - if you take any integer n, where
the exponents up to 2n have been searched completely, the "best fit"
model is that there as many Mersenne primes between 2^n and 2^(2n)
as there are between 2^(n/2) and 2^n. The "expected number" in an
"octave" is about 1. Now there are an infinite number of "octaves",
so ...
> One correspondent at that time postulated that there were no further
> Mersenne primes to be discovered and that the 37th was also the last. In the
> light of recent events, does anybody have an update on this view?
Bearing the above in mind, even if the number of Mersenne primes _is_
finite, I'd be very surprised if we've found even half of them yet.
I vaguely recall the message, my recollection is that its author
disagreed with conventional mathematicians over the meaning of
"infinity". If he's right, a lot of text books need pulping...
> So far as
> I am aware, M38 has not been confirmed yet. No flames, please: I am _not_
> posting this as an "I told you so" but as a genuine enquiry.
So far as I know, M38 is, at the moment, unconfirmed. But, again so
far as I know, this is because the verification run has not finished,
not because it has finished but proved "unsuccessful". And, again,
the verification run could fail for some reason - in which case, at
least one more double-check/verification run would be needed to
decide the status of the "unverified prime", one way or the other.
Please bear in mind that the chance of a "false positive" being
output from a LL test program is _minute_ - exactly 1 in 2^p-1, in
fact, if the error was a random bit-flip event. It's far more
probable that the "unverified prime" is a consequence of someone
"nobbling" the server. But, seeing that you couldn't possibly lay
hands on any prize money that way, I can't see any reason why a sane
person would want to do that.
Regards
Brian Beesley
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Date: Thu, 17 Jun 1999 15:21:02 -0400
From: Pierre Abbat <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Thoughts on Merced / IA-64
> Do you? I thought the only reason the FFT was using FP numbers was most
> current generation processors have a faster and higher precision FP multiply
> than fixed point. With a 64*64 bit fixed point multiply that generates a
> higher precision result, you can quickly do exact fixed point multiplies of
> any length.
In an FFT you are multiplying by sines and cosines of binary fractions of a
circle, most of which are irrational numbers, so exact fixed point multiplies
are irrelevant for it.
phma
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Date: Thu, 17 Jun 1999 15:24:23 -0400
From: Pierre Abbat <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Thoughts on Merced / IA-64
> You could go with a NTT instead of a FFT. Thus foregoing any double
> precision floats. Going with an NTT would also eliminate any precision
> problems...
What's NTT? And is DWT Discrete Walsh Transform?
phma
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Date: Thu, 17 Jun 1999 19:48:03 +0000
From: "David L. Nicol" <[EMAIL PROTECTED]>
Subject: Re: OT: Mersenne: ARM Licenses
Aaron Blosser wrote:
> BTW - Read http://www.cnn.com/TECH/computing/9906/15/supercomp.idg/
I am reminded of hype over the "thinking machines" parallel computer.
How difficult is it to write for an FPGA array? Do tools exist to
compile a C program into an FPGA configuration? Has BEos been ported
to it?
(Have just posted the URL to the egcs developers mailing list, expecting
heavy jihads to result)
________________________________________________________________________
David Nicol 816.235.1187 UMKC Network Operations [EMAIL PROTECTED]
"It is a computer under my desk, nobody but me uses it" -- J. Levine
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Date: Thu, 17 Jun 1999 14:24:45 -0600
From: "Blosser, Jeremy" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Thoughts on Merced / IA-64
> -----Original Message-----
> From: Pierre Abbat [mailto:[EMAIL PROTECTED]]
> Sent: Thursday, June 17, 1999 2:24 PM
> To: Blosser, Jeremy; Mersenne discussion list
> Subject: RE: Mersenne: Thoughts on Merced / IA-64
>
>
> > You could go with a NTT instead of a FFT. Thus foregoing any double
> > precision floats. Going with an NTT would also eliminate
> any precision
> > problems...
>
> What's NTT? And is DWT Discrete Walsh Transform?
>
NTT = Number Theoretic Transform (Wow, my fingers got twisted)
See: http://www.hut.fi/~mtommila/ntt.html for a decent explanation of an NTT
and how it relates to FFTs. At some point GIMPS would either have to move to
quad precision primes or an NTT algorithm because of round-off errors (not
enough bits... I think it'll die around 32-bit? And right now we're at 19 or
something?)
DWT is the discrete walsh transform... of which there is of course the FWHT
(Fast Walsh-Hadamard Tranform). Which is considered a "poor man's FFT" a lot
of the time. Its faster than an FFT, but I think the issue is that there is
no real way to do a convolution via FWHT (that has been found yet?)
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Date: Thu, 17 Jun 1999 14:08:29 -0700
From: Luke Welsh <[EMAIL PROTECTED]>
Subject: Re: Mersenne: Thoughts on Merced / IA-64
At 09:21 AM 6/17/99 -0700, jrp wrote:
>[...]multiplying 2 128 bit integers X * Y where Xh and Xl are the high
>and low half of the X argument takes 4 multiples plus a few adds.
It can be done in fewer than 4 muliplies. See Karatsuba's Method in
Knuth's TAOCP, Vol 2, Section 4.3.3, "How Fast Can We Multiply?"
Not as sexy as it used to be because multiplication is sooo fast
now-a-days. But it still might come in handy.
BTW, has anybody investigated this package:
http://clisp.cons.org/~haible/packages-cln-README.html
- --Luke
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Date: Thu, 17 Jun 1999 17:14:07 -0400 (EDT)
From: Jason Stratos Papadopoulos <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Thoughts on Merced / IA-64
On Thu, 17 Jun 1999, Blosser, Jeremy wrote:
> See: http://www.hut.fi/~mtommila/ntt.html for a decent explanation of an NTT
> and how it relates to FFTs. At some point GIMPS would either have to move to
> quad precision primes or an NTT algorithm because of round-off errors (not
> enough bits... I think it'll die around 32-bit? And right now we're at 19 or
> something?)
With the discrete weighted transforms GIMPS uses now, you can simply
perform a larger FFT and keep the number of bits per double the same.
> DWT is the discrete walsh transform... of which there is of course the FWHT
> (Fast Walsh-Hadamard Tranform). Which is considered a "poor man's FFT" a lot
> of the time. Its faster than an FFT, but I think the issue is that there is
> no real way to do a convolution via FWHT (that has been found yet?)
Richard Crandall's book "Topics in Advanced Scientific Computation" has a
way to do convolutions via fast Walsh transforms, but it's somewhat
complicated and for large sizes the FFT is still faster (at least from an
operation count point of view)
jasonp
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Date: Thu, 17 Jun 1999 14:32:58 -0700
From: Will Edgington <[EMAIL PROTECTED]>
Subject: Mersenne: Mers beta release; minor milestone achieved
While updating my web pages the other day, I noticed a bug in the
contents of the DATABASE file; it turned out to be a sign extension
bug in extract's handling of exponents above 2^31 (~2 billion). I've
made a fix and built a new:
http://www.garlic.com/~wedgingt/beta.tgz
beta.tar.gz
... several days ago. These might be some other, very small,
improvements over the "regular" release, but nothing else that really
qualifies as a bug fix or speed up.
I also updated my web pages that day to fix the DATABASE file itself,
which should have included a minor milestone: all Mersenne numbers
with exponents less than 20,000 have now had pseudo-prime tests of
their remaining cofactors.
http://www.garlic.com/~wedgingt/mersdata.tgz
mersdata.zip
See mersenne.html and mersfmt.txt there for more info.
I now automatically get data from Dr. Wagstaff's web site at Purdue as
well as from George Woltman's and Paul Leyland's sites.
The local disk space I can use for Mersenne stuffs has nearly doubled,
to about 3 GB, so feel free to send me new factoring data, Factor98
and Factor95 save files, etc., even more than before. I already
update automatically from a few personal web pages with factoring
data, beyond those mentioned above, as well.
Will
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Date: Thu, 17 Jun 1999 23:09:12 +0100
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: RE: Mersenne: Thoughts on Merced / IA-64
On 17 Jun 99, at 12:15, Blosser, Jeremy wrote:
> You could go with a NTT instead of a FFT. Thus foregoing any double
> precision floats. Going with an NTT would also eliminate any precision
> problems...
This is true.
>
> Of course, NTTs right now are a bit slower than FFTs, but who knows maybe w/
> MMX instructions you could get a NTT to perform on par with an FFT...
>
> I need to look into that... hmm...
Ah. I think that might be less of a good idea than you think.
When you do your NTT, you're going to need at least twice as many
bits in the elements of the transform as there are bits in the number
you're testing (because you're going to want to square the values in
the elements, without any bits falling off the more significant end).
If you're working into millions of bits, I think this forces you to
use (at least) 64-bit elements. That scuppers any plans to use MMX
instructions.
Still, if Merced has parallel integer execution pipes which can do
all instructions (instead of some being done in one pipe & some in
another, a la Pentium), then maybe you don't need MMX to get the same
total performance as a floating-point FFT.
Regards
Brian Beesley
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Date: Thu, 17 Jun 1999 23:09:12 +0100
From: "Brian J. Beesley" <[EMAIL PROTECTED]>
Subject: Re: OT: Mersenne: ARM Licenses
On 17 Jun 99, at 19:48, David L. Nicol wrote:
> How difficult is it to write for an FPGA array? Do tools exist to
> compile a C program into an FPGA configuration? Has BEos been ported
> to it?
Basically what you have to do is to feed instructions which the FPGA
can execute from firmware (EPROM, or static RAM). But you write your
own instructions, so you can have the FPGA execute any instruction
set you want.
You define the CPU architecture you want by putting voltages onto the
FPGA pins.
Having done that, use a "standard" compiler with the opcode generator
replaced by one that corresponds to your target architecture.
People who try these stunts are sometimes successful, but one notices
that they tend to have splinters in their fingers from scratching
their heads trying to figure out what went wrong, and that bad
language frequently is to be heard from the labs in which they're
working. Getting the hardware to execute one instruction correctly is
a major milestone, usually the project is pretty well cracked by
then.
The labs where these toys are played with probably haven't heard of
any OS except unix. Unless the supervisor vaguely remembers AppleDOS
or CP/M.
Regards
Brian Beesley
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End of Mersenne Digest V1 #582
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