Mersenne Digest Friday, June 18 1999 Volume 01 : Number 583 ---------------------------------------------------------------------- Date: Thu, 17 Jun 1999 23:38:11 +0100 From: Nick Craig-Wood <[EMAIL PROTECTED]> Subject: Re: Mersenne: Thoughts on Merced / IA-64 On Thu, Jun 17, 1999 at 02:08:29PM -0700, Luke Welsh wrote: > BTW, has anybody investigated this package: > > http://clisp.cons.org/~haible/packages-cln-README.html Yes I have. It is a very thorough C++ class library for number manipulation. It has an O(n log n) multiply. You could implement a Lucas Lehmer tester using it in about a dozen lines of code but you'd find that it was some factor slower than Prime95 (3 rings a bell but I may be wrong). - -- Nick Craig-Wood [EMAIL PROTECTED] http://www.axis.demon.co.uk/ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 23:51:19 +0100 From: Nick Craig-Wood <[EMAIL PROTECTED]> Subject: Re: Mersenne: Thoughts on Merced / IA-64 On Thu, Jun 17, 1999 at 11:09:12PM +0100, Brian J. Beesley wrote: > 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. That is correct - for any reasonable length FFT or NTT you will need at least 64 bit elements. You can synthesise these elements by doing two or three 32 bit transforms and combining them with the chinese remainder theorem. I experimented with this on the ARM and came to the conclusion that doing it like this was slower because the operation count was larger. However if there is a really significant speed up by using the MMX instructions then it may be practical to combine these single precision NTTs. - -- Nick Craig-Wood [EMAIL PROTECTED] http://www.axis.demon.co.uk/ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 16:50:41 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Thoughts on Merced / IA-64 > 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. That's kind of what I was driving at. With 128 64 bit multi-purpose registers, register rotation, etc. The register rotation should help by not making you unroll *all* your loops *all* the time. I'm sure it'd still help to unroll them anyway, but that's an opinion. Oh...sure enough, there's an example where they show that you get a speedup in an unrolled loop, but you do save even more cycles in a partially unrolled loop using register rotation. I notice that the imul actually uses the FPU which makes me wonder if imul would really be any better than fpmul (which can be parallelized - fpmpy). Fused-multiply-and-add commands (fma) could help with some code, but that's a guess on my part. On the other hand, I do see that IA-64 *does* do 64bit*64bit=128bit imul, though they do indeed use the FP registers, and it's the FPU core doing all the work. "The product of 2 64bit significands is added to the third 64bit significand (zero extended) to produce a 128bit result." Additionally, there is support for quad-precision FP "in software" (just above the microcode I'd guess? Or do they mean in ASM?). Certainly quad-precision (128bits), if it were fast enough, would be a lot better than extended double (80bits). I wonder about the speed of that though, and what they mean by "in software". Lost my train of thought...the power went where I work for a couple hours just now....and I think I'd better end it here! :-) Aaron ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 17:07:01 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: Mersenne: Custom FPGA design > > 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? Well...with today's newest FPGA's in the range of 2 million gates, you can certainly do WONDERFUL things with them. I had been discussing this off the list and came up with the idea that it's not entirely strange to think that perhaps I could design a custom FPGA to do high-speed FFT work. I ordered an eval softare package from Viewlogic, and now if I could just find my old Xilinx test bed...crud. Anyway, one big problem with using FPGA's "on the fly" is that you'd really need to have a "precompiled" library of routes for what you want, and you'd really have to be REALLY good at designing logic flow. It's basically (quite literally) like designing your own CPU. I had the distinct pleasure of designing my own CPU (albeit, a 4 bit doodad) some years ago, and one major hurdle to any real-time use is that it can take hours to route your design to a device. Even on the latest fast computers, you might still only get 100,000 gates per hour during the routing phase of the design. Then you have to "burn" (program) the routes to the device, and usually there's a lot of testing using JEDEC and what not before you're sure the thing will actually work right. Designing your own chips is GREAT if you have the upfront time, but there is so much work involved (even with my 4 bit CPU) that you'd really need to have an EE degree to do any of that (good thing I do! :-P ) Anyway, I'll have to get my eval of Viewlogic and see what it would take to do an FFT hardware device. Or, if it'd be easier, use my bro's idea of NTT to do the same thing, since designing an FPU unit would be intense. After my experience with logic design on a small scale, I have MUCH more respect for the folks at Intel/AMD/etc. who design the CPU's. Far out stuff. Aaron ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 20:09:38 -0400 (EDT) From: "David A. Miller" <[EMAIL PROTECTED]> Subject: Mersenne: Windows NT question Here at the University of Michigan, there are computer labs with Dell Pentium II systems running Windows NT 4.0. Each student has a little online file space connected to the Sun login machines; I believe it uses the Andrew File System (AFS). This file space is made available as a network drive on the Windows NT systems, and can be used as an ordinary drive by most Windows programs. But when I try to run Prime95 directly from a directory in my online file space, I get this error message: "The application failed to initialize properly (0xc0000022). Click on OK to terminate the application." Sometimes the program starts without error, but usually I get the message above, and so to get ECM work done while I'm at the computer lab I have to create a directory on the hard drive and move everything back when I'm done, which is inconvenient. Does anyone know what the problem might be? David A. Miller Rumors of my existence have been greatly exaggerated. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 20:46:31 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Mersenne Primes - what'd you expect? <<I still believe that the number is finite, in contrast to what appears to be the majority view>> The "majority view" is the way it is because a number of Darn Good (TM) heuristic arguments have been made that the number of Mersenne Primes is infinite, just like Darn Good (TM) heuristic arguments exist that the number of Fermat primes is finite (and probably =4). TI-81s run on 2MHz Z80s, but TI-85s run on 6MHz Z80s. And it is possible to overclock them something like 6x. Whoo! Now, you couldn't run a LL test program on a TI-85, but it might just be possible on a TI-92+. They have a 10 MHz Motorola 68000 processor, and something like 512K of memory. You could build yourself one of those memory expanders that have been designed for the TI-92+, and BOOM, instant LL tester. Or even factoring machine. Could you factor a Mersenne number without storing it in memory? (Answer: I don't *think* so....) Ptoo bad. If we could factor Mersenne numbers on an unmodified TI-92+, then there'd be a lot of people who'd run that program. TIs actually aren't that useless. You can do RSA cryptography on a TI-92, 92+, or 89. <<I'm not so bad off>> My TI-85 goes with me wherever I go - got a problem with that? :-D Well, that's it. S.T.L. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 13:00:20 +1200 From: "Halliday, Ian" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Finite or infinite? Merely expressing an opinion as to whether or not you think there are an infinite or finite number of Mersenne primes doesn't add anything to the discussion unless you can furnish some argument one way or the other. As with many issues in pure mathematics, it is unlikely (but not impossible) that a proof will be found one way or the other. I acknowledge Euclid's proof of an infinity of primes, cited by Michael Clark, but do not see any compelling evidence in this pointing towards an infinity of Mersenne primes. The rarity of these numbers is part of what leads me to suppose that they are finite in number, but I concede that numerical evidence does not carry much weight. For example, if I were to claim that all integers are below 2 raised to the power of M37, I could exhibit a huge number of examples of integers supporting this point of view, but anybody could furnish as many counterexamples as needed to refute this extraordinary claim. As we know, one counterexample suffices. Nevertheless, my view is that the rarity of Mersenne primes points towards finiteness. If we look at Mersenne primes as a subset of the integers, we have a fraction which is truly minuscule. If we look at them as a fraction of all primes, we're not much better off. Progressively considering them as a proportion of { 2^n - 1 } and { 2^p - 1 } they start to become slightly noticeable. I suppose that the view of finite v infinite is partly related to what one sees Mersenne primes as a subset or special case of. Brian Beesley wrote intelligently on the subject: I thank him for conceding that this is probably a matter for viewpoint rather than proof at the moment. He is citing circumstantial evidence just as much as I am, however. Certainly the earlier correspondent seemed to have eccentric ideas in many areas of mathematics. Infinity is hard for us to understand because we are, in some ways, only finite ourselves. I am aware that the chances of a false positive are extremely small and look forward with eagerness to somebody being able to tell us the value of M38. I mentioned the possibility only to pre-empt any claim "there are only 37 of the things - you haven't proved M38 yet". I don't see why anybody would try to nobble the server either, since such a person would indeed be found out. Personally, I participate in the search for mathematical reasons and not for the money. Winning the Mersenne prize offers much less money than the average state lottery, but more long-term acknowledgement. The average reader of this list can probably name several Mersenne discoverers but probably not the winners of recent lotteries. I've been looking for Mersenne primes through GIMPS since before there was any mention of prizes, recalling the "good old days" when I checked the whole range of 928,000 to 929,000, mailed the results to George and visited a website at ourworld.compuserve.com, the full URL of which nobody ever seemed to remember. Now I'm in the same boat as S Gunderson, who has switched to double checking because he doesn't like having to wait months for a result. It's encouraging to know I'm not the only one who thinks like that. Regards, Ian Ian W Halliday, BA Hons, MIMIS, ANZCS, CTM P O Box 5472, Wellington 6040, New Zealand ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 21:24:36 EDT From: Foghorn Leghorn <[EMAIL PROTECTED]> Subject: Re: Mersenne: Mersenne Primes - what'd you expect? Could you >factor a Mersenne number without storing it in memory? (Answer: I don't >*think* so....) Ptoo bad. If we could factor Mersenne numbers on an >unmodified TI-92+, then there'd be a lot of people who'd run that program. Uh, that's exactly what Prime95 does. To test whether a potential factor f divides 2^p-1, we use a standard binary powering algorithm to compute 2^p modulo f; it requires roughly log2(p) operations on numbers no bigger than f, and we never have to store the full representation of 2^p-1. I'm sure that this could be done on a TI. I don't know about ECM though. _______________________________________________________________ Get Free Email and Do More On The Web. Visit http://www.msn.com ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 22:16:46 -0400 (EDT) From: lrwiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Mersenne Primes - what'd you expect? >You could build yourself one of those memory expanders that have been designed >for the TI-92+, and BOOM, instant LL tester. Or even factoring machine. Could >you factor a Mersenne number without storing it in memory? (Answer: I don't >*think* so....) Ptoo bad. Yes, actually you can. By using an algorithm (I think Donald Knuth invented it, but it *is* in TAOCP vol II). Its not all that complex here is a calc program to find a^b mod c (which I think explains things better than 2 pages of mathematical ranting) define modpow(a,b,c) { local res; res=1; while (b>0) { if (odd(b)) { res=a*res; /* res=res*(a^(2^n)) whenever the nth binary digit of b is 1 everything mod c*/ if (res>c) res=res%c; } a=a^2; if (a>c) a=a%c; b=(b-odd(b))/2; } ; return res; } Note that if 2^p==1 mod c then c is a factor. Also note that no number ever gets bigger than c^2 (keen huh?) So it is not only possible to find a factor without holding the mersenne number in memory, but it is considerably faster. However, I cannot think of any way to do an LL test without storing the number in memory. Is there way? - -Lucas Wiman ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 22:13:58 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: Mersenne Primes - what'd you expect? At 08:46 PM 6/17/99 -0400, [EMAIL PROTECTED] wrote: >The "majority view" is the way it is because a number of Darn Good (TM) >heuristic arguments have been made that the number of Mersenne Primes is >infinite, Furthermore, I haven't seen any (good) argument at all as to why they should be only a finite number of Mersenne primes. +----------------------------------------------+ | Jud "program first and think later" McCranie | +----------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 22:46:42 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: Finite or infinite? At 01:00 PM 6/18/99 +1200, Halliday, Ian wrote: >Merely expressing an opinion as to whether or not you think there are an >infinite or finite number of Mersenne primes doesn't add anything to the >discussion unless you can furnish some argument one way or the other. There are two main reasons: (1) if you consider the prime number theorem to approximate the probability that 2^p-1 is prime and sum that over all primes p, you get an infinite number which means that you expect an infinite number of Mersenne primes. (2) there are several conjectures concerning the growth rate of successive Mersenne primes. They all suggest that on average, one exponent resulting in a Mersenne prime is no more than twice the previous one. This implies an infinite number of Mersenne primes. The known Mersenne primes are in very good agreement with the conjecture that, on the average, an exponent resulting in a Mersenne prime is about 3/2 as large as the previous one. That, of course, would imply an infinite number of Mersenne primes. +----------------------------------------------+ | Jud "program first and think later" McCranie | +----------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 22:58:59 -0500 (CDT) From: Robert Stalzer <[EMAIL PROTECTED]> Subject: Mersenne: Team Reports Once I've 'Cleared' an unwanted exponent from my to-do list ('oops, didn't want to do double-checks') how do I banish the outcast exponent from my team's report? Can another volunteer be assigned the exponent automatically or must we wait for the exponent to expire (a lengthy wait)? Robert Stalzer [EMAIL PROTECTED] ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 00:08:42 -0400 (EDT) From: lrwiman <[EMAIL PROTECTED]> Subject: Re: Mersenne: Finite or infinite? >(1) if you consider the prime number theorem to approximate the probability >that 2^p-1 is prime and sum that over all primes p, you get an infinite number >which means that you expect an infinite number of Mersenne primes. True, the probability of a given n being prime is ~1/log(n), and the sum from 1 to infinity of 1/log(2^p-1)~=log(2)*sum from 1 to infinity 1/p which euler proved is infinite. I think that the probability of 2^p-1 being prime is considerably higher than most numbers that big, because they can only be divisable by numbers of the form 2*k*p+1, and they must be ==+/-1 mod 8. Thus 1/4*(1/(2*p))*sqrt(2^p-1)~=2^(p/2-3)/p possible divisors (less when you look at the probability that 2*k*p+1 is prime) as opposed to ~sqrt(2^p)/log(sqrt(2^p))=2^(p/2)/(log(2)*p/2) which is 2^3*2/log(2)~=23 times fewer possible factors than a normal number that size (it's not much, but hey, it's something). >(2) there are several conjectures concerning the growth rate of successive >Mersenne primes. They all suggest that on average, one exponent resulting in >a Mersenne prime is no more than twice the previous one. This implies an >infinite number of Mersenne primes. The known Mersenne primes are in very good >agreement with the conjecture that, on the average, an exponent resulting in a >Mersenne prime is about 3/2 as large as the previous one. That, of course, >would imply an infinite number of Mersenne primes. Well, I don't know about that. Using conjectured behavior of mersenne primes to argue other conjectures... We must tread carefully... - -Lucas Wiman ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 00:38:54 -0400 From: "Rick Pali" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Team Reports From: Robert Stalzer > Once I've 'Cleared' an unwanted exponent from my to-do list > ('oops, didn't want to do double-checks') how do I banish the > outcast exponent from my team's report? The easiest way is to make sure that your instance of the prime software has as many days of work as you've specified, close the software, then add the unwanted exponent at the *end* of your worktodo.ini file. When you restart the software it will see that it's got 'too much work' and dump the last one on the list. That's the way I've always done it. Though my days of work setting is set to '1' so it's really easy. :-) > Can another volunteer be assigned the exponent automatically > or must we wait for the exponent to expire (a lengthy wait)? As long as the exponent appears on your team's individual report, it's signed out to you and cannot be reassigned. Rick. - ----- [EMAIL PROTECTED] http://www.alienshore.com/ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Thu, 17 Jun 1999 23:09:07 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: Mersenne: Team Reports > Once I've 'Cleared' an unwanted exponent from my to-do list ('oops, didn't > want to do double-checks') how do I banish the outcast exponent from my > team's report? Can another volunteer be assigned the exponent > automatically or must we wait for the exponent to expire (a lengthy wait)? Go to http://entropia.com/ips/manualtests.shtml and manually release the exponent. Simple matter of putting in your account and password, then the exponent you want cleared, or the whole "DoubleCheck=xxx" or "Test=xxx" will work also. Aaron ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 00:30:19 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Thoughts on Merced / IA-64 >What's NTT? And is DWT Discrete Walsh Transform? I don't have a clue about how NTTs actually are done, but I think the words `Numerical' and `Transform' accounts for one N and one T. (I could always look it up in the list archives, but I'm too lazy.) DWT does as far as I know stand for `Discrete Weighted Transform', discovered by our great heroes Crandall and Fagin. (Of course, George is the greatest hero for all our GIMPSers, perhaps we need to make a `worship list'. OK, OK, I'm tired. Don't listen to me.) /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 00:24:46 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Thoughts on Merced / IA-64 On Thu, Jun 17, 1999 at 01:11:09PM -0400, Jud McCranie wrote: >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.") In the case of the 386, there was "no person will need that at all" :-) That's why FRACTINT (a DOS fractal program, also ported to Windows, Linux/Unix, and I believe some other platforms too) introduced arbitrary precision zooming: To keep processors busy in the days where they could look back at `Grandpa's days where they *only* had Pentium processors'. /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 00:33:55 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: OT: Mersenne: ARM Licenses On Thu, Jun 17, 1999 at 07:48:03PM +0000, David L. Nicol wrote: >How difficult is it to write for an FPGA array? I would guess not so difficult, as long as the task _is_ easily parallelizable. >Do tools exist to compile a C program into an FPGA configuration? I would guess that you couldn't run _any_ program into it and get mass- parallelization out, but, as a wild guess, I would believe they've made a C compiler with hooks into the right libraries. >Has BEos been ported to it? What a funny question :-) (Perhaps I'm only thinking so because I'm a Linux user, and more used to that porting of open-source stuff is easier than closed- source stuff. Of course, since all I've ever _heard_ of BeOS is its name, it might be open-sourced for all I know.) To answer your question: That would be very unlikely. /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 00:03:49 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Thoughts on Merced / IA-64 On Thu, Jun 17, 1999 at 11:02:05AM -0500, Willmore, David wrote: >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. Perhaps not. Not to take any sides in this discussion, but when I first joined GIMPS, I had a Cyrix 6x86 CPU. It was (is) _really_ poor for FPU work, so I tried to make George include an integer algorithm. His answer was that even though he _had_ an old integer version, it was rougly _seven_ times as slow as the FPU version. Now, we must try to find out how much the difference is (and of course, in `whose' favour (excuse me if my English is bad at the time of writing) it is) on the IA-64. I think I've read about Intel's plans. Quick summary: 1. Merced comes out. So expensive, it's targetted at the server market only. 2. Foster comes out. Still being IA-32 compatible, it _matches_ the performance of the Merced! 3. Next generation IA-64 (can't remember the name) comes out. The price is now reasonable enough for desktop markets. (Although I would guess still rather expensive, and targetted at the high-end desktop market...) That was just some facts to educate you all ;-) >> +----------------------------------------------+ >> | Jud "program first and think later" McCranie | >> +----------------------------------------------+ >*laugh* Uh, hmmm, think now? :) I think that resembles to a great deal my own programming style. I happen to write things not `top-down' or 'bottom-up', but more `left-right'. When I happen to get an idea I must think about, I actually have to stand up from the chair and walk about, so I can think of the idea instead of spitting out even more low-quality code... Good George is programming this thing, and not me :-) /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 00:22:40 +0200 From: "Steinar H. Gunderson" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Thoughts on Merced / IA-64 On Thu, Jun 17, 1999 at 09:21:57AM -0700, John R Pierce wrote: >where Z is a 256 bit 'accumulator'... And where are you going to find a 256 bit add instruction? :-) /* Steinar */ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 08:10:13 +0000 (GMT) From: Henrik Olsen <[EMAIL PROTECTED]> Subject: RE: Mersenne: Team Reports On Fri, 18 Jun 1999, Rick Pali wrote: > From: Robert Stalzer > > > Once I've 'Cleared' an unwanted exponent from my to-do list > > ('oops, didn't want to do double-checks') how do I banish the > > outcast exponent from my team's report? > > The easiest way is to make sure that your instance of the prime software > has as many days of work as you've specified, close the software, then add > the unwanted exponent at the *end* of your worktodo.ini file. When you > restart the software it will see that it's got 'too much work' and dump > the last one on the list. > > That's the way I've always done it. Though my days of work setting is set > to '1' so it's really easy. :-) > > > > Can another volunteer be assigned the exponent automatically > > or must we wait for the exponent to expire (a lengthy wait)? > > As long as the exponent appears on your team's individual report, it's > signed out to you and cannot be reassigned. > > Rick. Signed out to your team that is. If you add it to the worktodo.ini file of another machine in your team, it will happily start churning on it, since it's still assigned to your team, the only real result will be that the next time it reports in, the exponent will get reported as assigned to the new machine. I've used this technique before, to get a batch of exponents in one gulp, with one machine, then distribute the work between my different machines as I consider best. - -- Henrik Olsen, Dawn Solutions I/S URL=http://www.iaeste.dk/~henrik/ Animal behaviour is best described by the four F's Feed, Fight, Flee and Reproduce ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 10:51:35 -0400 From: Jeff Woods <[EMAIL PROTECTED]> Subject: Mersenne: AMD K7 to be king of the hill? Will v18.1 run on an AMD K7 at appropriately fast speeds without modification? Looks like the K7 will be the heat for at least several months.... http://www.news.com/News/Item/0,4,38021,00.html?st.ne.fd.gif.d Excerpts: The delay to Coppermine--a high-performance version of the Pentium III--means that the Intel chip will not appear until November. That may mean that the chip won't appear in many PCs in 1999, since new systems don't often come out so late in the year. - ------------------- Under different circumstances, the delays might be irrelevant, but AMD is currently preparing to release its K7 processor. The chip will be announced later this month and start to roll out in volumes later in the summer at speeds of 500 MHz, 550 MHz, and 600 MHz, said several sources. Benchmarks released by AMD recently show that the chip will outperform the Pentium III and even the more-upscale Xeon processor on certain benchmarks. "It does seem likely that the K7 will be no slower than the Pentium III. It is also clear that, unlike the situation with the K6, the K7 will be no laggard in floating point and multimedia performance," wrote Michael Slater in a recent Microprocessor Watch newsletter. ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 12:08:17 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: Finite or infinite? At 12:08 AM 6/18/99 -0400, lrwiman wrote: > >True, the probability of a given n being prime is ~1/log(n), and >the sum from 1 to infinity of 1/log(2^p-1)~=log(2)*sum from 1 to infinity 1/p >which euler proved is infinite. I think that the probability of 2^p-1 being >prime is considerably higher than most numbers that big, because they can >only be divisable by numbers of the form 2*k*p+1, That's true, so Mersenne numbers are even more likely to be prime, due to the limited number of potential factors. >Well, I don't know about that. Using conjectured behavior of Mersenne primes >to argue other conjectures... They fit the formula that the nth Mersenne exponent is approximately (3/2)^n pretty well. That isn't a proof, of course, but it is a strong suggestion. +----------------------------------------------+ | Jud "program first and think later" McCranie | +----------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 12:05:41 -0400 From: Jud McCranie <[EMAIL PROTECTED]> Subject: Re: Mersenne: Finite or infinite? At 01:00 PM 6/18/99 +1200, Halliday, Ian wrote: > >I acknowledge Euclid's proof of an infinity of primes, cited by Michael >Clark, but do not see any compelling evidence in this pointing towards an >infinity of Mersenne primes. The rarity of these numbers is part of what >leads me to suppose that they are finite in number, That doesn't make much sense. Numbers of the form 10^10^n are much more rare than Mersenne primes, but there are an infinite number of them. > Infinity is hard for us to understand because we are, >in some ways, only finite ourselves. Have you been talking to my grandfather? (below) +------------------------------------------------------------+ | Jud McCranie | | | | "The mind is finite so it cannot understand the infinite." | | -- G. F. McCranie, Jr. | | "It depends on how finite your mind is." -- Jud McCranie | +------------------------------------------------------------+ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 12:34:24 -0700 (PDT) From: poke <[EMAIL PROTECTED]> Subject: Re: OT: Mersenne: ARM Licenses My understanding is that it comes with a language of its own. My impression is that it is an icon based language. Kind of like connect the blocks into a flow chart of some sort and hit "GO". - -Chuck On Thu, 17 Jun 1999, David L. Nicol wrote: > 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 > ________________________________________________________________ > Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm > -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : WWW: http://www.silverlink.net/poke : : E-Mail: [EMAIL PROTECTED] : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : Ask Mike! Aviation's response to Dear : : Abby. http://www.avstarair.com : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 22:04:58 +0200 From: Sylvain PEREZ <[EMAIL PROTECTED]> Subject: Mersenne: Hello from Paris - France I'm Sylvain Perez, I do take care of the French version of GIMPS. If any of you need francophone support, please visit http://www.entropia.com/gimps/fr, or send me an email. About cool guys that like hot chips, what do you think about those pages : http://www.agaweb.com/coolcpu/, it seems to me to have good info for cpu cooling. OK, now take care of you and of your prime95s. Sylvain Participer à la recherche de très grands Nombres Premiers, sérieusement, pour le plaisir, ou les prix ! ... <http://www.entropia.com/gimps/fr> ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ Date: Fri, 18 Jun 1999 14:45:45 -0600 From: "Aaron Blosser" <[EMAIL PROTECTED]> Subject: RE: OT: Mersenne: ARM Licenses > My understanding is that it comes with a language of its own. My > impression is that it is an icon based language. Kind of like connect the > blocks into a flow chart of some sort and hit "GO". I'll try and give a cursory explanation of what you can do with FPGA's. Bear in mind, I haven't done FPGA work in nearly 5 years, but not much could change. I'm sure we all understand boolean logic...and, or, not, etc. (as well as their counterparts nand, nor, xor, etc). You can do all sorts of wonderful logic designs using handfuls of "74" chips, the basic building blocks of logic design. You can even design memory cells using latches and the sort. An FPGA is essentially a WHOLE bunch of logic gates on a single chip, and furthermore, they are programmable. You can talk about FPGA's in terms of the number of gates and numbers of pads (I/O connects for instance) and such. These gates are grouped into CLB's (configurable logic block I think?). On a chip with 1M gates, you maybe have around 27-28 thousand of these CLB's. Each CLB can be configured as basically any kind of logic gate you want. Configure it as a nand gate, or a xor, or whatever. Besides the CLB's and I/O stuff, you also need to worry about routing. On an FPGA, there are all these CLB's, but there are limited ways to route signals between them. One problem I used to have (on occasion) was that my design would work great on a simulator, but when it came time to actually route the design, I'd find that I'd run out of routes. I might have to "move" certain functions to other parts of the chip that had more interconnects available. Other designs like PLD's have n-way routing, so each block can connect to any other one...simplifies the routing but there are generally less blocks available. Hmmm... What you can do is configure some of the gates as memory cells (J-K or S-R latches), or use external RAM (which I did in my design...we had Xilinx chips with very few blocks) to hold data. Then configure the rest of the blocks as your logic. Another part of the routing process is determining the load on "bus" signals, like the system clock for instance. Too many devices running off the clock means you're waveform will distort and you'll wind up with a bad signal. This routing part can take a while...be prepared to go grab a snack or two while it churns out the design. Programming of the device is done serially, but it's generally not too much of a wait for that part. Then when you first run it, non-simulated, you get to find out if you screwed up any timings (registers loading in the wrong order, bus collisions, etc.). VERY fun stuff! :-) When doing FPGA design, you need to work out your timing signals, design your own registers, generally a good idea to build a state machine for the timings (kind of the master control), be sure and grey code everything in the timings to prevent race conditions, etc. It really isn't easy, but you can do AMAZING things. If you wanted to build a 256 bit multiplier, well, it could be done. The real trick is to KNOW how to optimize logic tables and design. Any Joe Schmoe can build an n-bit multiplier, but getting it done optimally is something else entirely. That's the tricky part, and there are all sorts of cool tricks (the same ones that programmers would know about in their psuedo-code) for getting it done. The fun part is that since you're designing the hardware, you can put in your own clever "cheats" in hardware. For a ROR, for instance, instead of actually reading in each bit and moving it over to the right one, and using a temporary bit to hold the extra along the way, you could just copy the byte to another register with a 1-bit offset, then rename the registers, making it faster (that's just a dumb example, but you get the idea). Doing something like an add in hardware is quite easy. I'm still not entirely sure how a "real" CPU does multiplies and divides so DARN FAST in the hardware though... I mean, I could do a multiply by simply doing multiple adds, but that would be pretty slow. Anyone who has ever delved into advanced microprocessor designs probably knows what I'm talking about. Intel uses some pretty clever stuff to get extra speed from their design, at the price of using more silicon. It took me a good 2 months to design a 4 bit CPU (with 3 registers, A, B and an accumulator) that could do only 8 instructions like add, sub, jmp, etc. Sure, I was learning at the time, but it's complicated stuff! (PS, I cheated on some parts by using the bus as a "temporary" register. It really sped up a few parts without adding another register. My prof. thought it was clever, though he wasn't terribly crazy about it...I had to rearrange some timings to avoid bus collisions and at that point, the examples he gave in class no longer applied to my design. Still, I'm bragging here, but my design was faster than the others.) I would still like to see just how hard it would be to design an n-bit multiply with add or something in an FPGA...just send the data from the computer to the FPGA and get the result back, maybe using the PCI bus. I sure wish I had my computers back so I could go over my old designs and "refresh" my brain cells! :-) The beauty is that once you have a small bit design figured out, it's not terribly more complicated to add more bits to the data design. And if it were a dedicated device that only did one instruction, but did it fast, that would simplify the state machine design greatly! Aaron ________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm ------------------------------ End of Mersenne Digest V1 #583 ******************************
