Re: Mersenne: difference between LL and double check
Hi, At 05:19 AM 10/25/99 +0200, Robert van der Peijl wrote: Why is there a difference in iteration time between the LL test and a double test. There isn't - other than double-checking is working on smaller exponents. For the same FFT-size, the double checking code has to perform a bit extra work per iteration: it multiplies by 2 before the DWT, and divides by 4 afterward. This isn't quite how double-checking works. What happens is the initial Lucas value, 4, is shifted left a random number of bits. We remember this shift count in the variable called units_bit. Each iteration does a squaring, then computes the new location of the units bit (old_units_bit * 2 modulo exponent_being_tested). Now that we know where the units bit is, it is easy to subtract two. This has the same property of having the FFT deal with different data, but without the cost of a multiply by 2 and divide by 4 on every iteration. BTW, the above is done on first-time tests too. Regards, George _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: More Schlag
- Original Message - From: Bob Margulies [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, October 24, 1999 9:15 AM Subject: Mersenne: More Schlag In reading the numerous postings about Liouville numbers and patterned transcendentals, I notice that there has been a careful avoidance of the definition of the term 'pattern.' If the Liouville Transcendental Number is expressed in a base other than 10, I would guess that there's still a pattern, but I don't know how to see it. Perhaps a pattern is something that sets the 'I see a pattern' bit in my head. Sounds ok by me. I would accept as a 'pattern' for a (possibly transcendental) number ANY closed form expression giving a general term. That is, there is some function f(n) for (positive) integers n such that a number with 'pattern' is given by the infinite sum f(1)+f(2)+f(3)+...+f(n)+... The Liouville number I remembered was f(n) = (0.1)^(n!) for n=1,2,3,... A simpler (and larger) number used f(n) = (0.1) ^ (n^2) As I recall, either of these definitions can use any rational number (between 0 and 1) in place of 0.1 and we get a transcendental number. Using something convenient in base 10 is not the critical point. The critical question is the form of f(n) -- in this case the kind of exponent grows faster than a linear function. I seem to recall a non-intuititive theorem about rational approximations to numbers (this is from c. 1968). If you can approximate a number too closely, then it is transcendental. S.Lang wrote a book on trancendental numbers and degrees around 1973 and a precise statement might be there. Does anyone recall this? JT _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: mprime v19 release factoring
mprime v19 sep23 version: Factoring M8632699 to 2^64 is 92.2286% complete. 5.531 sec. (3042241006 clocks) Factoring M8632699 to 2^64 is 92.2378% complete. 5.532 sec. (3042454084 clocks) mprime v19 oct3 version: Factoring M8632699 to 2^64 is 92.2476% complete. 15.946 sec. (8770110717 clocks) Factoring M8632699 to 2^64 is 92.2568% complete. 15.930 sec. (8761602607 clocks) Why the difference in speed? Also, neither version will let me download anymore assignments while I have factoring assignments in worktodo.ini. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: ReCache for Windoze (was: mprime startup at boot-time)
I have 256 MB of memory (about 30 gig of hard drive space). Will this process assist me? At 07:23 PM 10/25/99 +0100, you wrote: On 24 Oct 99, at 18:23, Bruce A Metcalf wrote: Hello, I must have missed the discussion of ReCache the last time around. Would someone be willing to explain where this can be obtained, how to install, and the likely benefits to Prime95? Brian Beesley responded: ftp://lettuce.edsc.ulst.ac.uk/gimps/software/ReCache.zip To install: Unzip the file place the executable in a directory referenced in the search path. [Or in the same directory as Prime95] Read the other file. To run: from DOS command prompt: change directory to the folder containing Prime95 then issue the command "ReCache nn Prime95.exe" where nn is the amount of physical memory in the system in megabytes. Can easily be set up as a Windows shortcut. Benefits: the ReCache program forces unused DLLs out to swap space causes a general "tidy up" of the whole Windows memory space. This makes any compute-intensive program launched using it operate a little more efficiently. Speed up of 1% or 2% is usual. I'd also be particularly interested in an automatic routine, as my Windoze box crashes 3 or 4 times a day. (Yes, I know -- but I've only read through chapter 3 in "Linus for Dummies" so far.) Place a shortcut to Prime95 (or to launch Prime95 using ReCache) in your startup folder, using "Start/Settings/Taskbar/Start Menu/Add" But you probably should find out why windoze crashes so often. If you're on a busy LAN, it does help to have a full set of LAN security patches installed! Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Error 2250 using Linux mprime
Hi all, This was just reported to me. Others may find it useful. Regards, George I took the liberty of looking at this. It appears that even w/ "gcc -static", the new glibc name resolution stuff contains explicit uses of several dynamic libraries. If these libraries aren't present, gethostbyname(3) will silently fail, yielding the 2250 errors. There's a discussion of this in the usenet archives at: http://x35.deja.com/getdoc.xp?AN=414019916CONTEXT=940892973.188547100hitnu m=0 I worked around this by moving the following .so's to my bootdisk for my ips machines: libc.so.6 ld-linux.so.2 libnss_dns.so.2 libresolv.so.2 This may not be ideal for everyone. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
