mersenneforum.org - Running Msieve

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- Msieve (https://www.mersenneforum.org/forumdisplay.php?f=83)

- - Running Msieve (https://www.mersenneforum.org/showthread.php?t=10168)

[quote=jasonp;124981]Probably the FFT's were too large after the changes in v1.33

Keep trying dependencies, each has a 50% chance of completing the job as long as there are no errors reported.

Let me know if you want to help isolate the problem, I have a few ideas.[/quote]

Once again many thanks for the program. All has turned out. Assembly msieve1.32 vc2005sp1 64bit. Sergey Miklin

[code]
Wed Feb 06 12:49:21 2008 Msieve v. 1.32
Wed Feb 06 12:49:21 2008 random seeds: 5080a248 7d842fc3
Wed Feb 06 12:49:21 2008 factoring 8266309047181022405353777302426117907484231464195030961205492983304640804057155643239818038225508173250310696877219392691052751978838088765473026049013959 (154 digits)
Wed Feb 06 12:49:23 2008 no P-1/P+1/ECM available, skipping
Wed Feb 06 12:49:23 2008 commencing number field sieve (154-digit input)
Wed Feb 06 12:49:23 2008 R0: -259180767284417684872274319851
Wed Feb 06 12:49:23 2008 R1: 130576890561073429
Wed Feb 06 12:49:23 2008 A0: 321734774100366992493104066152882456
Wed Feb 06 12:49:23 2008 A1: 2324280139698946250758568017311
Wed Feb 06 12:49:23 2008 A2: -12665674762234440961836116
Wed Feb 06 12:49:23 2008 A3: -7047205438924859234
Wed Feb 06 12:49:23 2008 A4: 40087789172148
Wed Feb 06 12:49:23 2008 A5: 7068000
Wed Feb 06 12:49:23 2008 size score = 6.079972e-016, Murphy alpha = -6.022094, combined = 4.525734e-015
Wed Feb 06 12:49:23 2008
Wed Feb 06 12:49:23 2008 commencing square root phase
Wed Feb 06 12:49:23 2008 reading relations for dependency 1
Wed Feb 06 12:49:40 2008 read 1889906 cycles
Wed Feb 06 12:49:46 2008 cycles contain 5628669 unique relations
Wed Feb 06 13:05:01 2008 read 5628669 relations
Wed Feb 06 13:06:16 2008 multiplying 8501850 relations
Wed Feb 06 14:02:00 2008 multiply complete, coefficients have about 502.23 million bits
Wed Feb 06 14:02:36 2008 initial square root is modulo 1027042309
Wed Feb 06 16:18:09 2008 reading relations for dependency 2
Wed Feb 06 16:18:24 2008 read 1890135 cycles
Wed Feb 06 16:18:31 2008 cycles contain 5629806 unique relations
Wed Feb 06 16:33:22 2008 read 5629806 relations
Wed Feb 06 16:34:36 2008 multiplying 8503188 relations
Wed Feb 06 17:30:32 2008 multiply complete, coefficients have about 502.31 million bits
Wed Feb 06 17:31:12 2008 initial square root is modulo 1030465937
Wed Feb 06 19:49:22 2008 prp77 factor: 75417034474736472180545669587118172545185589128341834187697792613778214227723
Wed Feb 06 19:49:22 2008 prp78 factor: 109607983193108802733249399107977613000240701053334983022316126562062175191733
Wed Feb 06 19:49:22 2008 elapsed time 07:00:01[/code]

[QUOTE=miklin;124983]Jasonp, Thanks huge. Keys are received, now I know that the spent two months have not passed gift. This program simply fairy tale. I am sorry for bad English, I simply do not know it.
[/QUOTE]
Excellent. Don't worry, your english is far better than my Russian :)

In the v1.33 source, could you replace gnfs/sqrt/sqrt_a.c with the version from v1.32, then recompile and retry the square root, looking for errors? If you do not get errors this will help isolate what is happening.

[quote=jasonp;124987]Excellent. Don't worry, your english is far better than my Russian :)

In the v1.33 source, could you replace gnfs/sqrt/sqrt_a.c with the version from v1.32, then recompile and retry the square root, looking for errors? If you do not get errors this will help isolate what is happening.[/quote]

Here not that has copied.

[code]
Wed Feb 06 21:49:49 2008 Msieve v. 1.33
Wed Feb 06 21:49:49 2008 random seeds: ce1869a0 8c0362b8
Wed Feb 06 21:49:49 2008 factoring 8266309047181022405353777302426117907484231464195030961205492983304640804057155643239818038225508173250310696877219392691052751978838088765473026049013959 (154 digits)
Wed Feb 06 21:49:51 2008 no P-1/P+1/ECM available, skipping
Wed Feb 06 21:49:51 2008 commencing number field sieve (154-digit input)
Wed Feb 06 21:49:51 2008 R0: -259180767284417684872274319851
Wed Feb 06 21:49:51 2008 R1: 130576890561073429
Wed Feb 06 21:49:51 2008 A0: 321734774100366992493104066152882456
Wed Feb 06 21:49:51 2008 A1: 2324280139698946250758568017311
Wed Feb 06 21:49:51 2008 A2: -12665674762234440961836116
Wed Feb 06 21:49:51 2008 A3: -7047205438924859234
Wed Feb 06 21:49:51 2008 A4: 40087789172148
Wed Feb 06 21:49:51 2008 A5: 7068000
Wed Feb 06 21:49:51 2008 size score = 6.079972e-016, Murphy alpha = -5.836125, combined = 4.253703e-015
Wed Feb 06 21:49:51 2008
Wed Feb 06 21:49:51 2008 commencing square root phase
Wed Feb 06 21:49:51 2008 reading relations for dependency 1
Wed Feb 06 21:50:03 2008 read 1889906 cycles
Wed Feb 06 21:50:09 2008 cycles contain 5628669 unique relations
Wed Feb 06 22:00:19 2008 read 5628669 relations
Wed Feb 06 22:01:32 2008 multiplying 8501850 relations
Wed Feb 06 22:57:30 2008 multiply complete, coefficients have about 502.23 million bits
Wed Feb 06 22:57:39 2008 error: relation product is incorrect; if this is a debug binary, make sure that NDEBUG is not defined
Wed Feb 06 22:57:39 2008 algebraic square root failed
Wed Feb 06 22:57:39 2008 reading relations for dependency 2
Wed Feb 06 22:57:41 2008 read 1890135 cycles
Wed Feb 06 22:57:48 2008 cycles contain 5629806 unique relations[/code]

[QUOTE=miklin;125012]Here such result has received. Speak what to try, I shall make.
[/QUOTE]
Okay, now start with v1.33 and on line 561 of common/fastmult.c change the function get_log2_fhtsize() to
[code]
static int32 get_log2_fhtsize(int32 nwords, int32 *log2_base) {

int32 i;
int32 runlength;
int32 bits;

/* begin by assuming base 2^16 for the FHT multiply */

bits = 16;
runlength = 1;
while ((1 << runlength) < 2 * nwords)
runlength++;

*log2_base = bits;
return runlength;
}
[/code]
then recompile and rerun the square root. Any difference?

[quote=jasonp;125023]Okay, now start with v1.33 and on line 561 of common/fastmult.c change the function get_log2_fhtsize() to
then recompile and rerun the square root. Any difference?[/quote]

Has corrected, we wait result.
Can on mail we shall pass???
And which at you there now hour???

[EMAIL="miklin@diakom.ru"]miklin@diakom.ru[/EMAIL]
Sergey Miklin

[quote=jasonp;125023]Okay, now start with v1.33 and on line 561 of common/fastmult.c change the function get_log2_fhtsize() to
then recompile and rerun the square root. Any difference?[/quote]

This change too has not helped.

[code]
Thu Feb 07 00:30:06 2008 commencing square root phase
Thu Feb 07 00:30:06 2008 reading relations for dependency 1
Thu Feb 07 00:30:08 2008 read 1889906 cycles
Thu Feb 07 00:30:14 2008 cycles contain 5628669 unique relations
Thu Feb 07 00:40:29 2008 read 5628669 relations
Thu Feb 07 00:41:42 2008 multiplying 8501850 relations
Thu Feb 07 01:38:50 2008 multiply complete, coefficients have about 502.23 million bits
Thu Feb 07 01:38:59 2008 error: relation product is incorrect; if this is a debug binary, make sure that NDEBUG is not defined
Thu Feb 07 01:38:59 2008 algebraic square root failed
Thu Feb 07 01:38:59 2008 reading relations for dependency 2
Thu Feb 07 01:39:01 2008 read 1890135 cycles
Thu Feb 07 01:39:08 2008 cycles contain 5629806 unique relations
Thu Feb 07 01:49:19 2008 read 5629806 relations
Thu Feb 07 01:50:32 2008 multiplying 8503188 relations[/code]

Help for newbie: using msieve and ggnfs

I decided to investigate msieve in earnest, having heard so many good things about its NFS post-processing. Previously I'd used it only for MPQS on small integers.

I'd like advice on two matters, if possible.

First, how in practice do I use it for the post processing? I've a ggnfs siever busy creating relations into a file spairs.out. I also fired up msieve to get the polynomial file and produce some relations from its line siever. These appear in msieve.dat. (Yes, I've read the doc where it's said that the ggnfs polynomial finder may be better, but this is a toy factorization of a C118 as a learning exercise.) When the ggnfs siever crashes after running a batch (the subject of the second question), I've been appending spairs.out to msieve.dat. Is this the right thing to do, and what must I do when there are enough relations in it?

The second matter concerns the ggnfs siever. It fires up fine and runs a batch of special-q in a range of 100K. However, each job crashes as follows:[code]Attempt 50 / 50 for: 1860275116805366835360883350634230901440647651446421083579260567272044334669573697107233781966234371079653406546373061
Monic polynomial: T=-433537265046439130785134915151590456362713515720057710368441977804976253184000000000000-10783833185000965790015287955584003256887059019893082649706624000000000X-29100662953302191018121148275402779971380760416000000X^2 + 290293756100973932442482108633256000X^3-861398521692980001X^4 + 1X^5
Obtained integral basis:
W =
121915830631347063321569789508142702722517248000000000 0 0 60957915315673531660784894754071351361258624000000000 91436872973510297491177342131107027041887936000000000
0 40638610210449021107189929836047567574172416000000000 2779227567407944813460117943759304551590622528000000 37368091772074993803490031804373580149167570880000000 16743628413329954526125570650157436240812446704000000
0 0 562903328421084622898571809472000000 6416051303723462998429547256696000 530183519029528744482244985293836000
0 0 0 1299503745767304000 221521266446439999
0 0 0 0 1
denominator = 121915830631347063321569789508142702722517248000000000
Checking file rels.bin.0 ...
Largest prel file size is 0 versus max allowed of 128000000.
Warning: Could not stat processed file rels.bin.0. Is this the first run?.
New file is 53.39263MB.
New file appears to have 494487 relations.
Building (a,b) hash table...0..makeABList() Failed to open rels.bin.0 for read!

makeABLookup() : Sorting abList...Done.
Before processing new relations, there are 0 total.
Return value 11. Terminating...ns from spairs.out... (at 11459.88 rels/sec)
[/code]I've tried "touch rels.bin.0" to create the file but the crash still happens.

I've Googled the error message and found 3 or 4 complaints from others about the crash but no answer was forthcoming.

Thanks for any assistance.

Paul

[QUOTE=xilman;125262]I decided to investigate msieve in earnest, having heard so many good things about its NFS post-processing. Previously I'd used it only for MPQS on small integers.[/QUOTE]

Greg Childers created the script factMsieve.pl to be used in place of factLat.pl. It uses the ggnfs suite for polynomial selection and sieving and msieve for the rest. I've used it a few times and it has worked very well. [URL="http://tech.groups.yahoo.com/group/ggnfs/message/2208"]This post[/URL] from Greg explains how to use factMsieve.pl to complete a factorization started by factLat.pl.

[QUOTE=rogue;125265]Greg Childers created the script factMsieve.pl to be used in place of factLat.pl. It uses the ggnfs suite for polynomial selection and sieving and msieve for the rest. I've used it a few times and it has worked very well. [URL="http://tech.groups.yahoo.com/group/ggnfs/message/2208"]This post[/URL] from Greg explains how to use factMsieve.pl to complete a factorization started by factLat.pl.[/QUOTE]

Thanks Mark. I'll give it a try when the current sieving job ends.

Paul

[QUOTE=xilman;125269]Thanks Mark. I'll give it a try when the current sieving job ends.

Paul[/QUOTE]Hmmm.[code]pcl@imhotep ~/msieve-1.33/tmp $ factMsieve.pl
This Perl has neither ithreads nor 5005threads at /usr/lib64/perl5/5.8.8/Thread.pm line 335
BEGIN failed--compilation aborted at /usr/lib64/perl5/5.8.8/Thread.pm line 335.
Compilation failed in require at /home/pcl/bin/factMsieve.pl line 65.
BEGIN failed--compilation aborted at /home/pcl/bin/factMsieve.pl line 65.
pcl@imhotep ~/msieve-1.33/tmp $ [/code]Oh well, time to start hacking Perl and/or factMsieve.pl I guess.

Paul

[QUOTE=xilman;125271]Oh well, time to start hacking Perl and/or factMsieve.pl I guess.

Paul[/QUOTE]This change[code]

=for comment
if ($NUM_THREADS != 1) {
use Config;
if (!($Config{usethreads})) {
printf "This version of Perl doesn't support multiple threads. Only using 1 thread.";
$NUM_THREADS=1;
}
else {
use Thread qw(async);
}
}
=cut
[/code] may be brutal, but it seems to have let the siever start. It remains to be seen what else will die in the future.

Paul

[QUOTE=xilman;125273]
(cut) may be brutal, but it seems to have let the siever start. It remains to be seen what else will die in the future.

Paul[/QUOTE]

That'll work. Or just set NUM_THREADS to 1 before that section.

As for the crashing, the GGNFS lattice siever likes to do that. I've found it very mysterious. Compiling with -fomit-frame-pointer seems to be a recipe to create a broken binary every time. Even without that tho, I've had a few binaries that crash frequently, and others that never seem to crash. It seems to depend on the compiler you use, and perhaps even on the day of the week and whether it's raining or not. :smile:

Greg

[quote=xilman;125262]The second matter concerns the ggnfs siever. It fires up fine and runs a batch of special-q in a range of 100K. However, each job crashes as follows:

[/quote]

The crash you describe is happening in the procrels program, not the siever. Perhaps something is corrupted with the spairs.out file, or it is too big? I've had procrels crash when spairs.out is big, on the order of 1GB.

[quote=xilman;125262]
... how in practice do I use it for the post processing?
[/quote]

My scheme to use ggnfs/msieve is to run a simple modified version of factLat.pl, where the modification is to stick an exit 0 right before it starts the matrix process. Then I do a

[code]procrels -prel rels.bin -fb input.fb -dump[/code]

to dump the relations in a format msieve can handle. then:

[code]
make_msieve.pl input.poly spairs.dump.*
[/code]

to build up msieve.dat the factorbase (with poly), and worktodo.ini

and finally

[code]
msieve -v -nc -i worktodo.ini
[/code]

I got make_msieve.pl from this forum somewhere. I think it came from fivemack. I've attached it as well, if you are interested in this approach.

These 4 commands can go in a simple shell script for fire-n-forget NFS.

Sometimes factLat.pl doesn't work so well with SNFS jobs, in which case I run the lattice siever and procrels manually until there are enough relations to do the rest of the steps and start msieve.

Can't you just avoid procrels entirely?

If you're going to perform post-processing with msieve, then procrels is really only useful as a sequence of samples to see where you are with your sieving, right?

Is there a way of performing this test on your raw relations, using some means other than procrels? Doesn't "msieve -v -nc1" tell you you're a few relations short of a matrix (:missingteeth:) if you show up without enough? Or is procrels much quicker as a meter of progress?

If you have not yet used msieve for NFS post-processing, then you're in for a treat.

[quote=FactorEyes;125312]If you're going to perform post-processing with msieve, then procrels is really only useful as a sequence of samples to see where you are with your sieving, right?
[/quote]

If you're using factLat.pl, which uses procrels, then procrels is useful to dump out the relations in the various rels.bin* files that are created.

For big factorizations, I don't use factLat but I've always used procrels and make_msieve.pl to get the files msieve needs. I'm sure there are other ways to do it as well.

[quote=FactorEyes;125312]If you have not yet used msieve for NFS post-processing, then you're in for a treat.[/quote]

Agreed!

[QUOTE=FactorEyes;125312]If you have not yet used msieve for NFS post-processing, then you're in for a treat.[/QUOTE]I hope to find out within a day or to. So far, I've been satisfied with the CWI post-processing suite.

Paul

[QUOTE=xilman;125359]I hope to find out within a day or to. So far, I've been satisfied with the CWI post-processing suite.

Paul[/QUOTE]

Once you have got the relations in the following form, so that the lines look like this (I guess that's what you get when dumping the relations out with procrels):

[code]-20924856703,65467:C757,9485B,4A4893,2761C91,1D,191,5C9,2F,2F,2:3fce4b69,4488703,13A6B,1AC0F,2A59DD,5B5E51,151F,3,3,3,3,7,3D,269,5,B,8583B29
1612784043,81091:f5d08ab,40d594f3,21979,97051,17,6B,139,2,2,2,2,2:259DF,65E25,4F9C13,5B882F,1779CF1,1B91,5,5,5,5,7,11,3D,43,6D,F1,199,3,3,3,8583B29
-26779529009,296087:DB55,1C10F3,13CB25D,140387F,B,E5,397,509,2,2,2,2:2901f587,6876fdfd,6079,6947,754C1,1A4EF9,1471,3,3,3,5,7,1F,3B,97,1F3,8583B29
-653208684,3377:21004c21,8CFCB,B471F,771E27,B,277,779:924ca57,11081,79165,B367B9,1587DED,160F,959,5,7,2F,3,3,3,2,2,2,2,2,8583B29
[/code]

1.) Concatenate all files to one big file named msieve.dat and add "N <number to factorize>" as first line to msieve.dat.

2.) Create a msieve.fb file which looks like this (of course using your polynomial instead of mine)

[code]N 230380135646168002240144238096238189782429580465812519176892278271650463794969643225877877269156894108094881082195219664775471894182470295616143804362949333632033489
R0 -7253635851193924156735160443739
R1 2391424041494417171
A0 547440910672314203689898814059115360
A1 33277562211750204806364306268284
A2 107677876784557388243547221
A3 -2612363701552248486716
A4 -3795305047120954
A5 11472718320
[/code]

...with N is the number to factorize.

3.) create a worktodo.ini file which contains the number to factorize.

4.) copy these three files to your msieve directory.

5.) from the command line type "msieve -v -nc -t <number of threads>"

I hope this works.

[QUOTE=xilman;125359]I hope to find out within a day or to. So far, I've been satisfied with the CWI post-processing suite.[/QUOTE]Rather longer than a day or two, but the machine has been rather busy proving the primality of over 30 thousand integers in the range P13 through P250.

The linear algebra started about 35 minutes ago, plenty long enough for me to estimate that it's close to 2.2 times faster than the CWI implementation of blocked Lanczos. Assuming it finishes and that the sqrt phase is well-behaved it seems likely I'll be using msieve in future.

My thanks to everyone who helped.

Paul

Trouble with 1.33

I've now had two large jobs which have run the linear algebra without reported error but finding only trivial dependencies. These are both running on a machine of whose reliability I am confident. One is sieved just barely up to the point of making a matrix, the other is enormously oversieved.

I'm rerunning the 151-digit job with msieve-1.29 (from before the threading modifications), which will take another three days.

[code]
Wed Feb 13 21:03:30 2008 Msieve v. 1.33
Wed Feb 13 21:03:30 2008 random seeds: b4e9a7d6 1f21cb0b
Wed Feb 13 21:03:30 2008 factoring 6217523082758401556030460236402809630656994359423664008236740148265533840342530861439938963095458807452655685629643666716576581773404701260451369712951 (151 digits)
Wed Feb 13 21:03:32 2008 no P-1/P+1/ECM available, skipping
Wed Feb 13 21:03:32 2008 commencing number field sieve (151-digit input)
Wed Feb 13 21:03:32 2008 R0: -66862108170409256564279521485
Wed Feb 13 21:03:32 2008 R1: 323116668946615313
Wed Feb 13 21:03:32 2008 A0: 23907870192659903038552206588349732
Wed Feb 13 21:03:32 2008 A1: 703126393841859924006025666960
Wed Feb 13 21:03:32 2008 A2: 2767149157482587319179015
Wed Feb 13 21:03:32 2008 A3: -3838229760711724000
Wed Feb 13 21:03:32 2008 A4: -23001392760552
Wed Feb 13 21:03:32 2008 A5: 4652940
Wed Feb 13 21:03:33 2008 size score = 1.232009e-15, Murphy alpha = -6.418885, combined = 1.046749e-14
Wed Feb 13 21:08:30 2008 restarting with 48131793 relations
Wed Feb 13 21:08:30 2008
Wed Feb 13 21:08:30 2008 commencing relation filtering
Wed Feb 13 21:08:30 2008 commencing duplicate removal, pass 1
Wed Feb 13 21:16:03 2008 found 8086405 hash collisions in 48131793 relations
Wed Feb 13 21:16:04 2008 commencing duplicate removal, pass 2
Wed Feb 13 21:21:11 2008 found 6162724 duplicates and 41969069 unique relations
Wed Feb 13 21:21:11 2008 memory use: 270.4 MB
Wed Feb 13 21:21:34 2008 ignoring smallest 2971685 rational and 2973397 algebraic ideals
Wed Feb 13 21:21:34 2008 filtering rational ideals above 49479680
Wed Feb 13 21:21:34 2008 filtering algebraic ideals above 49479680
Wed Feb 13 21:21:34 2008 need 10106639 more relations than ideals
Wed Feb 13 21:21:34 2008 commencing singleton removal, pass 1
Wed Feb 13 21:28:44 2008 relations with 0 large ideals: 1802844
Wed Feb 13 21:28:44 2008 relations with 1 large ideals: 8159953
Wed Feb 13 21:28:44 2008 relations with 2 large ideals: 14625261
Wed Feb 13 21:28:44 2008 relations with 3 large ideals: 12293453
Wed Feb 13 21:28:44 2008 relations with 4 large ideals: 4587390
Wed Feb 13 21:28:44 2008 relations with 5 large ideals: 500168
Wed Feb 13 21:28:44 2008 relations with 6 large ideals: 0
Wed Feb 13 21:28:44 2008 relations with 7+ large ideals: 0
Wed Feb 13 21:28:44 2008 41969069 relations and about 33002452 large ideals
Wed Feb 13 21:28:44 2008 commencing singleton removal, pass 2
Wed Feb 13 21:35:56 2008 found 11602604 singletons
Wed Feb 13 21:35:56 2008 current dataset: 30366465 relations and about 19926913 large ideals
Wed Feb 13 21:35:57 2008 commencing singleton removal, pass 3
Wed Feb 13 21:42:06 2008 found 2520768 singletons
Wed Feb 13 21:42:06 2008 current dataset: 27845697 relations and about 17318061 large ideals
Wed Feb 13 21:42:07 2008 commencing singleton removal, pass 4
Wed Feb 13 21:47:33 2008 found 566221 singletons
Wed Feb 13 21:47:33 2008 current dataset: 27279476 relations and about 16746794 large ideals
Wed Feb 13 21:47:33 2008 commencing singleton removal, pass 5
Wed Feb 13 21:52:07 2008 found 124874 singletons
Wed Feb 13 21:52:07 2008 current dataset: 27154602 relations and about 16621667 large ideals
Wed Feb 13 21:52:07 2008 commencing singleton removal, final pass
Wed Feb 13 21:57:52 2008 memory use: 418.9 MB
Wed Feb 13 21:58:07 2008 commencing in-memory singleton removal
Wed Feb 13 21:58:11 2008 begin with 27154602 relations and 20271707 unique ideals
Wed Feb 13 21:58:57 2008 reduce to 20611471 relations and 13406838 ideals in 16 passes
Wed Feb 13 21:58:57 2008 max relations containing the same ideal: 34
Wed Feb 13 21:59:03 2008 dataset has 21.2% excess relations
Wed Feb 13 21:59:23 2008 ignoring smallest 2691524 rational and 2693652 algebraic ideals
Wed Feb 13 21:59:23 2008 filtering rational ideals above 44531712
Wed Feb 13 21:59:23 2008 filtering algebraic ideals above 44531712
Wed Feb 13 21:59:23 2008 need 6484169 more relations than ideals
Wed Feb 13 21:59:23 2008 commencing singleton removal, final pass
Wed Feb 13 22:04:05 2008 memory use: 322.6 MB
Wed Feb 13 22:04:16 2008 commencing in-memory singleton removal
Wed Feb 13 22:04:19 2008 begin with 20611471 relations and 13955645 unique ideals
Wed Feb 13 22:04:51 2008 reduce to 20524886 relations and 13868999 ideals in 12 passes
Wed Feb 13 22:04:51 2008 max relations containing the same ideal: 34
Wed Feb 13 22:05:11 2008 removing 948017 relations and 862158 ideals in 85859 cliques
Wed Feb 13 22:05:11 2008 commencing in-memory singleton removal
Wed Feb 13 22:05:14 2008 begin with 19576869 relations and 13868999 unique ideals
Wed Feb 13 22:05:34 2008 reduce to 19552847 relations and 12982682 ideals in 8 passes
Wed Feb 13 22:05:34 2008 max relations containing the same ideal: 33
Wed Feb 13 22:05:49 2008 removing 687302 relations and 601443 ideals in 85859 cliques
Wed Feb 13 22:05:50 2008 commencing in-memory singleton removal
Wed Feb 13 22:05:53 2008 begin with 18865545 relations and 12982682 unique ideals
Wed Feb 13 22:06:09 2008 reduce to 18851820 relations and 12367443 ideals in 7 passes
Wed Feb 13 22:06:09 2008 max relations containing the same ideal: 32
Wed Feb 13 22:06:27 2008 dataset has 9.1% excess relations
Wed Feb 13 22:06:28 2008 relations with 0 large ideals: 1329807
Wed Feb 13 22:06:28 2008 relations with 1 large ideals: 4704885
Wed Feb 13 22:06:28 2008 relations with 2 large ideals: 6636860
Wed Feb 13 22:06:28 2008 relations with 3 large ideals: 4517177
Wed Feb 13 22:06:28 2008 relations with 4 large ideals: 1477055
Wed Feb 13 22:06:28 2008 relations with 5 large ideals: 186036
Wed Feb 13 22:06:28 2008 relations with 6 large ideals: 0
Wed Feb 13 22:06:28 2008 relations with 7+ large ideals: 0
Wed Feb 13 22:06:28 2008 commencing 2-way merge
Wed Feb 13 22:06:45 2008 reduce to 12026039 relation sets and 5541662 unique ideals
Wed Feb 13 22:06:45 2008 commencing full merge
Wed Feb 13 22:08:42 2008 memory use: 514.7 MB
Wed Feb 13 22:08:42 2008 found 6339499 cycles, need 5416876
Wed Feb 13 22:08:46 2008 weight of 5416876 cycles is about 342597479 (63.25/cycle)
Wed Feb 13 22:08:46 2008 distribution of cycle lengths:
Wed Feb 13 22:08:46 2008 1 relations: 1332169
Wed Feb 13 22:08:46 2008 2 relations: 759189
Wed Feb 13 22:08:46 2008 3 relations: 590631
Wed Feb 13 22:08:46 2008 4 relations: 481540
Wed Feb 13 22:08:46 2008 5 relations: 409674
Wed Feb 13 22:08:46 2008 6 relations: 349215
Wed Feb 13 22:08:46 2008 7 relations: 302740
Wed Feb 13 22:08:46 2008 8 relations: 261779
Wed Feb 13 22:08:46 2008 9 relations: 229409
Wed Feb 13 22:08:46 2008 10+ relations: 700530
Wed Feb 13 22:08:46 2008 heaviest cycle: 15 relations
Wed Feb 13 22:08:47 2008 commencing cycle optimization
Wed Feb 13 22:08:59 2008 start with 25045770 relations
Wed Feb 13 22:10:12 2008 pruned 1134955 relations
Wed Feb 13 22:10:12 2008 memory use: 793.9 MB
Wed Feb 13 22:10:12 2008 distribution of cycle lengths:
Wed Feb 13 22:10:12 2008 1 relations: 1332169
Wed Feb 13 22:10:12 2008 2 relations: 788850
Wed Feb 13 22:10:12 2008 3 relations: 625793
Wed Feb 13 22:10:12 2008 4 relations: 500893
Wed Feb 13 22:10:12 2008 5 relations: 429357
Wed Feb 13 22:10:12 2008 6 relations: 361645
Wed Feb 13 22:10:12 2008 7 relations: 313246
Wed Feb 13 22:10:12 2008 8 relations: 267379
Wed Feb 13 22:10:12 2008 9 relations: 230371
Wed Feb 13 22:10:12 2008 10+ relations: 567173
Wed Feb 13 22:10:12 2008 heaviest cycle: 15 relations
Wed Feb 13 22:10:22 2008
Wed Feb 13 22:10:22 2008 commencing linear algebra
Wed Feb 13 22:10:36 2008 read 5416876 cycles
Wed Feb 13 22:11:13 2008 cycles contain 13464663 unique relations
Wed Feb 13 22:15:19 2008 read 13464663 relations
Wed Feb 13 22:15:58 2008 using 32 quadratic characters above 536870612
Wed Feb 13 22:18:13 2008 building initial matrix
Wed Feb 13 22:24:26 2008 memory use: 1879.5 MB
Wed Feb 13 22:24:30 2008 read 5416876 cycles
Wed Feb 13 22:24:44 2008 matrix is 5360072 x 5416876 (1462.9 MB) with weight 490510854 (90.55/col)
Wed Feb 13 22:24:44 2008 sparse part has weight 318480484 (58.79/col)
Wed Feb 13 22:28:35 2008 filtering completed in 3 passes
Wed Feb 13 22:28:37 2008 matrix is 5026035 x 5026229 (1360.6 MB) with weight 455825733 (90.69/col)
Wed Feb 13 22:28:37 2008 sparse part has weight 296365900 (58.96/col)
Wed Feb 13 22:30:05 2008 read 5026229 cycles
Wed Feb 13 22:30:18 2008 matrix is 5026035 x 5026229 (1360.6 MB) with weight 455825733 (90.69/col)
Wed Feb 13 22:30:18 2008 sparse part has weight 296365900 (58.96/col)
Wed Feb 13 22:30:18 2008 saving the first 48 matrix rows for later
Wed Feb 13 22:30:22 2008 matrix is 5025987 x 5026229 (1294.7 MB) with weight 349634052 (69.56/col)
Wed Feb 13 22:30:22 2008 sparse part has weight 279094804 (55.53/col)
Wed Feb 13 22:30:22 2008 matrix includes 128 packed rows
Wed Feb 13 22:30:22 2008 using block size 65536 for processor cache size 4096 kB
Wed Feb 13 22:30:52 2008 commencing Lanczos iteration (2 threads)
Wed Feb 13 22:30:52 2008 memory use: 1319.4 MB
Sun Feb 17 03:28:48 2008 lanczos halted after 79479 iterations (dim = 5025576)
Sun Feb 17 03:29:01 2008 lanczos error: only trivial dependencies found
[/code]

and

[code]
Fri Feb 1 18:41:19 2008 Msieve v. 1.33
Fri Feb 1 18:41:19 2008 random seeds: cbb1d6bd 5b11044a
Fri Feb 1 18:41:19 2008 factoring 230380135646168002240144238096238189782429580465812519176892278271650463794969643225877877269156894108094881082195219664775471894182470295616143804362949333632033489 (165 digits)
Fri Feb 1 18:41:20 2008 no P-1/P+1/ECM available, skipping
Fri Feb 1 18:41:20 2008 commencing number field sieve (165-digit input)
Fri Feb 1 18:41:20 2008 R0: -7253635851193924156735160443739
Fri Feb 1 18:41:20 2008 R1: 2391424041494417171
Fri Feb 1 18:41:20 2008 A0: 547440910672314203689898814059115360
Fri Feb 1 18:41:20 2008 A1: 33277562211750204806364306268284
Fri Feb 1 18:41:20 2008 A2: 107677876784557388243547221
Fri Feb 1 18:41:20 2008 A3: -2612363701552248486716
Fri Feb 1 18:41:20 2008 A4: -3795305047120954
Fri Feb 1 18:41:20 2008 A5: 11472718320
Fri Feb 1 18:41:20 2008 size score = 4.400513e-17, Murphy alpha = -7.122525, combined = 4.727096e-16
Fri Feb 1 19:13:20 2008 restarting with 228057828 relations
Fri Feb 1 19:13:20 2008
Fri Feb 1 19:13:20 2008 commencing relation filtering
[errors reading relation]
Fri Feb 1 20:01:36 2008 found 68940645 hash collisions in 227965000 relations
Fri Feb 1 20:01:36 2008 commencing duplicate removal, pass 2
Fri Feb 1 20:33:18 2008 found 43495997 duplicates and 184469003 unique relations
Fri Feb 1 20:33:18 2008 memory use: 1911.0 MB
Fri Feb 1 20:34:21 2008 ignoring smallest 7907833 rational and 7909147 algebraic ideals
Fri Feb 1 20:34:21 2008 filtering rational ideals above 139919360
Fri Feb 1 20:34:21 2008 filtering algebraic ideals above 139919360
Fri Feb 1 20:34:21 2008 need 26888866 more relations than ideals
Fri Feb 1 20:34:21 2008 commencing singleton removal, pass 1
Fri Feb 1 21:13:34 2008 relations with 0 large ideals: 7060370
Fri Feb 1 21:13:34 2008 relations with 1 large ideals: 34969288
Fri Feb 1 21:13:34 2008 relations with 2 large ideals: 67164031
Fri Feb 1 21:13:34 2008 relations with 3 large ideals: 57050919
Fri Feb 1 21:13:34 2008 relations with 4 large ideals: 18176795
Fri Feb 1 21:13:34 2008 relations with 5 large ideals: 47592
Fri Feb 1 21:13:34 2008 relations with 6 large ideals: 8
Fri Feb 1 21:13:34 2008 relations with 7+ large ideals: 0
Fri Feb 1 21:13:34 2008 184469003 relations and about 91212880 large ideals
Fri Feb 1 21:13:34 2008 commencing singleton removal, pass 2
Fri Feb 1 21:50:50 2008 found 17752850 singletons
Fri Feb 1 21:50:51 2008 current dataset: 166716153 relations and about 72783284 large ideals
Fri Feb 1 21:50:52 2008 commencing singleton removal, pass 3
Fri Feb 1 22:26:08 2008 relations with 0 large ideals: 7060370
Fri Feb 1 22:26:08 2008 relations with 1 large ideals: 33444844
Fri Feb 1 22:26:08 2008 relations with 2 large ideals: 61387319
Fri Feb 1 22:26:08 2008 relations with 3 large ideals: 49701411
Fri Feb 1 22:26:08 2008 relations with 4 large ideals: 15082229
Fri Feb 1 22:26:08 2008 relations with 5 large ideals: 39973
Fri Feb 1 22:26:08 2008 relations with 6 large ideals: 7
Fri Feb 1 22:26:08 2008 relations with 7+ large ideals: 0
Fri Feb 1 22:26:08 2008 166716153 relations and about 103590738 large ideals
Fri Feb 1 22:26:08 2008 commencing singleton removal, pass 4
Fri Feb 1 23:07:12 2008 found 24652189 singletons
Fri Feb 1 23:07:12 2008 current dataset: 142063964 relations and about 77434141 large ideals
Fri Feb 1 23:07:12 2008 commencing singleton removal, pass 5
Fri Feb 1 23:37:51 2008 relations with 0 large ideals: 7060370
Fri Feb 1 23:37:51 2008 relations with 1 large ideals: 31100390
Fri Feb 1 23:37:51 2008 relations with 2 large ideals: 53029094
Fri Feb 1 23:37:51 2008 relations with 3 large ideals: 39711529
Fri Feb 1 23:37:51 2008 relations with 4 large ideals: 11132819
Fri Feb 1 23:37:51 2008 relations with 5 large ideals: 29756
Fri Feb 1 23:37:51 2008 relations with 6 large ideals: 6
Fri Feb 1 23:37:51 2008 relations with 7+ large ideals: 0
Fri Feb 1 23:37:51 2008 142063964 relations and about 93534301 large ideals
Fri Feb 1 23:37:51 2008 commencing singleton removal, pass 6
Sat Feb 2 00:08:20 2008 found 17505340 singletons
Sat Feb 2 00:08:20 2008 current dataset: 124558624 relations and about 75155405 large ideals
Sat Feb 2 00:08:21 2008 commencing singleton removal, pass 7
Sat Feb 2 00:36:15 2008 found 3747152 singletons
Sat Feb 2 00:36:15 2008 current dataset: 120811472 relations and about 71361086 large ideals
Sat Feb 2 00:36:16 2008 commencing singleton removal, pass 8
Sat Feb 2 01:09:40 2008 found 711486 singletons
Sat Feb 2 01:09:40 2008 current dataset: 120099986 relations and about 70647739 large ideals
Sat Feb 2 01:09:41 2008 commencing singleton removal, pass 9
Sat Feb 2 01:37:50 2008 found 126821 singletons
Sat Feb 2 01:37:50 2008 current dataset: 119973165 relations and about 70520867 large ideals
Sat Feb 2 01:37:51 2008 commencing singleton removal, final pass
Sat Feb 2 02:09:45 2008 memory use: 1847.4 MB
Sat Feb 2 02:11:26 2008 commencing in-memory singleton removal
Sat Feb 2 02:11:39 2008 begin with 119973165 relations and 79045425 unique ideals
Sat Feb 2 02:14:18 2008 reduce to 112705469 relations and 71683219 ideals in 12 passes
Sat Feb 2 02:14:18 2008 max relations containing the same ideal: 69
Sat Feb 2 02:15:44 2008 removing 3362193 relations and 2962193 ideals in 400000 cliques
Sat Feb 2 02:15:47 2008 commencing in-memory singleton removal
Sat Feb 2 02:15:59 2008 begin with 109343276 relations and 71683219 unique ideals
Sat Feb 2 02:17:24 2008 reduce to 109296016 relations and 68673568 ideals in 7 passes
Sat Feb 2 02:17:24 2008 max relations containing the same ideal: 65
Sat Feb 2 02:18:28 2008 removing 2516523 relations and 2116523 ideals in 400000 cliques
Sat Feb 2 02:18:31 2008 commencing in-memory singleton removal
Sat Feb 2 02:18:42 2008 begin with 106779493 relations and 68673568 unique ideals
Sat Feb 2 02:19:53 2008 reduce to 106750234 relations and 66527684 ideals in 6 passes
Sat Feb 2 02:19:53 2008 max relations containing the same ideal: 63
Sat Feb 2 02:20:55 2008 removing 2242829 relations and 1842829 ideals in 400000 cliques
Sat Feb 2 02:20:57 2008 commencing in-memory singleton removal
Sat Feb 2 02:21:08 2008 begin with 104507405 relations and 66527684 unique ideals
Sat Feb 2 02:22:29 2008 reduce to 104483539 relations and 64660914 ideals in 7 passes
Sat Feb 2 02:22:29 2008 max relations containing the same ideal: 63
Sat Feb 2 02:23:29 2008 removing 2073230 relations and 1673230 ideals in 400000 cliques
Sat Feb 2 02:23:31 2008 commencing in-memory singleton removal
Sat Feb 2 02:23:42 2008 begin with 102410309 relations and 64660914 unique ideals
Sat Feb 2 02:24:49 2008 reduce to 102388657 relations and 62965953 ideals in 6 passes
Sat Feb 2 02:24:49 2008 max relations containing the same ideal: 61
Sat Feb 2 02:25:47 2008 removing 1960237 relations and 1560237 ideals in 400000 cliques
Sat Feb 2 02:25:49 2008 commencing in-memory singleton removal
Sat Feb 2 02:25:59 2008 begin with 100428420 relations and 62965953 unique ideals
Sat Feb 2 02:27:05 2008 reduce to 100409198 relations and 61386440 ideals in 6 passes
Sat Feb 2 02:27:05 2008 max relations containing the same ideal: 60
Sat Feb 2 02:28:01 2008 removing 1871974 relations and 1471974 ideals in 400000 cliques
Sat Feb 2 02:28:04 2008 commencing in-memory singleton removal
Sat Feb 2 02:28:14 2008 begin with 98537224 relations and 61386440 unique ideals
Sat Feb 2 02:29:17 2008 reduce to 98518901 relations and 59896081 ideals in 6 passes
Sat Feb 2 02:29:17 2008 max relations containing the same ideal: 59
Sat Feb 2 02:30:12 2008 removing 1800539 relations and 1400539 ideals in 400000 cliques
Sat Feb 2 02:30:14 2008 commencing in-memory singleton removal
Sat Feb 2 02:30:24 2008 begin with 96718362 relations and 59896081 unique ideals
Sat Feb 2 02:31:16 2008 reduce to 96700186 relations and 58477295 ideals in 5 passes
Sat Feb 2 02:31:16 2008 max relations containing the same ideal: 59
Sat Feb 2 02:32:09 2008 removing 1736333 relations and 1336333 ideals in 400000 cliques
Sat Feb 2 02:32:11 2008 commencing in-memory singleton removal
Sat Feb 2 02:32:21 2008 begin with 94963853 relations and 58477295 unique ideals
Sat Feb 2 02:33:11 2008 reduce to 94946533 relations and 57123572 ideals in 5 passes
Sat Feb 2 02:33:11 2008 max relations containing the same ideal: 59
Sat Feb 2 02:34:04 2008 removing 1701647 relations and 1301647 ideals in 400000 cliques
Sat Feb 2 02:34:06 2008 commencing in-memory singleton removal
Sat Feb 2 02:34:15 2008 begin with 93244886 relations and 57123572 unique ideals
Sat Feb 2 02:35:04 2008 reduce to 93229008 relations and 55805997 ideals in 5 passes
Sat Feb 2 02:35:04 2008 max relations containing the same ideal: 57
Sat Feb 2 02:35:55 2008 removing 1646287 relations and 1246287 ideals in 400000 cliques
Sat Feb 2 02:35:57 2008 commencing in-memory singleton removal
Sat Feb 2 02:36:06 2008 begin with 91582721 relations and 55805997 unique ideals
Sat Feb 2 02:36:54 2008 reduce to 91564682 relations and 54541598 ideals in 5 passes
Sat Feb 2 02:36:54 2008 max relations containing the same ideal: 56
Sat Feb 2 02:37:44 2008 removing 1630159 relations and 1230159 ideals in 400000 cliques
Sat Feb 2 02:37:46 2008 commencing in-memory singleton removal
Sat Feb 2 02:37:55 2008 begin with 89934523 relations and 54541598 unique ideals
Sat Feb 2 02:38:42 2008 reduce to 89920991 relations and 53297855 ideals in 5 passes
Sat Feb 2 02:38:42 2008 max relations containing the same ideal: 54
Sat Feb 2 02:39:30 2008 removing 1573058 relations and 1173058 ideals in 400000 cliques
Sat Feb 2 02:39:33 2008 commencing in-memory singleton removal
Sat Feb 2 02:39:41 2008 begin with 88347933 relations and 53297855 unique ideals
Sat Feb 2 02:40:27 2008 reduce to 88332948 relations and 52109743 ideals in 5 passes
Sat Feb 2 02:40:27 2008 max relations containing the same ideal: 54
Sat Feb 2 02:41:14 2008 removing 1563378 relations and 1163378 ideals in 400000 cliques
Sat Feb 2 02:41:16 2008 commencing in-memory singleton removal
Sat Feb 2 02:41:25 2008 begin with 86769570 relations and 52109743 unique ideals
Sat Feb 2 02:42:09 2008 reduce to 86755283 relations and 50932023 ideals in 5 passes
Sat Feb 2 02:42:09 2008 max relations containing the same ideal: 54
Sat Feb 2 02:42:55 2008 removing 1534319 relations and 1134319 ideals in 400000 cliques
Sat Feb 2 02:42:57 2008 commencing in-memory singleton removal
Sat Feb 2 02:43:05 2008 begin with 85220964 relations and 50932023 unique ideals
Sat Feb 2 02:43:49 2008 reduce to 85205994 relations and 49782672 ideals in 5 passes
Sat Feb 2 02:43:49 2008 max relations containing the same ideal: 54
Sat Feb 2 02:44:34 2008 removing 1503446 relations and 1103446 ideals in 400000 cliques
Sat Feb 2 02:44:36 2008 commencing in-memory singleton removal
Sat Feb 2 02:44:44 2008 begin with 83702548 relations and 49782672 unique ideals
Sat Feb 2 02:45:26 2008 reduce to 83686012 relations and 48662625 ideals in 5 passes
Sat Feb 2 02:45:26 2008 max relations containing the same ideal: 54
Sat Feb 2 02:46:10 2008 removing 1486477 relations and 1086477 ideals in 400000 cliques
Sat Feb 2 02:46:12 2008 commencing in-memory singleton removal
Sat Feb 2 02:46:20 2008 begin with 82199535 relations and 48662625 unique ideals
Sat Feb 2 02:47:02 2008 reduce to 82184256 relations and 47560798 ideals in 5 passes
Sat Feb 2 02:47:02 2008 max relations containing the same ideal: 53
Sat Feb 2 02:47:44 2008 removing 1458695 relations and 1058695 ideals in 400000 cliques
Sat Feb 2 02:47:46 2008 commencing in-memory singleton removal
Sat Feb 2 02:47:54 2008 begin with 80725561 relations and 47560798 unique ideals
Sat Feb 2 02:48:35 2008 reduce to 80711890 relations and 46488351 ideals in 5 passes
Sat Feb 2 02:48:35 2008 max relations containing the same ideal: 52
Sat Feb 2 02:49:16 2008 removing 1432791 relations and 1032791 ideals in 400000 cliques
Sat Feb 2 02:49:18 2008 commencing in-memory singleton removal
Sat Feb 2 02:49:26 2008 begin with 79279099 relations and 46488351 unique ideals
Sat Feb 2 02:50:05 2008 reduce to 79264864 relations and 45441264 ideals in 5 passes
Sat Feb 2 02:50:05 2008 max relations containing the same ideal: 51
Sat Feb 2 02:50:46 2008 removing 1406061 relations and 1006061 ideals in 400000 cliques
Sat Feb 2 02:50:48 2008 commencing in-memory singleton removal
Sat Feb 2 02:50:55 2008 begin with 77858803 relations and 45441264 unique ideals
Sat Feb 2 02:51:41 2008 reduce to 77842951 relations and 44419272 ideals in 6 passes
Sat Feb 2 02:51:41 2008 max relations containing the same ideal: 50
Sat Feb 2 02:52:21 2008 removing 1420018 relations and 1020018 ideals in 400000 cliques
Sat Feb 2 02:52:23 2008 commencing in-memory singleton removal
Sat Feb 2 02:52:30 2008 begin with 76422933 relations and 44419272 unique ideals
Sat Feb 2 02:53:00 2008 reduce to 76408633 relations and 43384876 ideals in 4 passes
Sat Feb 2 02:53:00 2008 max relations containing the same ideal: 49
Sat Feb 2 02:53:39 2008 removing 1385105 relations and 985105 ideals in 400000 cliques
Sat Feb 2 02:53:41 2008 commencing in-memory singleton removal
Sat Feb 2 02:53:48 2008 begin with 75023528 relations and 43384876 unique ideals
Sat Feb 2 02:54:25 2008 reduce to 75008306 relations and 42384466 ideals in 5 passes
Sat Feb 2 02:54:25 2008 max relations containing the same ideal: 47
Sat Feb 2 02:55:03 2008 removing 1386688 relations and 986688 ideals in 400000 cliques
Sat Feb 2 02:55:04 2008 commencing in-memory singleton removal
Sat Feb 2 02:55:11 2008 begin with 73621618 relations and 42384466 unique ideals
Sat Feb 2 02:55:47 2008 reduce to 73606900 relations and 41382984 ideals in 5 passes
Sat Feb 2 02:55:47 2008 max relations containing the same ideal: 47
Sat Feb 2 02:56:24 2008 removing 1367535 relations and 967535 ideals in 400000 cliques
Sat Feb 2 02:56:26 2008 commencing in-memory singleton removal
Sat Feb 2 02:56:32 2008 begin with 72239365 relations and 41382984 unique ideals
Sat Feb 2 02:57:01 2008 reduce to 72223753 relations and 40399755 ideals in 4 passes
Sat Feb 2 02:57:01 2008 max relations containing the same ideal: 46
Sat Feb 2 02:57:37 2008 removing 1351460 relations and 951460 ideals in 400000 cliques
Sat Feb 2 02:57:38 2008 commencing in-memory singleton removal
Sat Feb 2 02:57:45 2008 begin with 70872293 relations and 40399755 unique ideals
Sat Feb 2 02:58:19 2008 reduce to 70855135 relations and 39431032 ideals in 5 passes
Sat Feb 2 02:58:19 2008 max relations containing the same ideal: 45
Sat Feb 2 02:58:54 2008 removing 1340482 relations and 940482 ideals in 400000 cliques
Sat Feb 2 02:58:56 2008 commencing in-memory singleton removal
Sat Feb 2 02:59:02 2008 begin with 69514653 relations and 39431032 unique ideals
Sat Feb 2 02:59:36 2008 reduce to 69496474 relations and 38472235 ideals in 5 passes
Sat Feb 2 02:59:36 2008 max relations containing the same ideal: 45
Sat Feb 2 03:00:10 2008 removing 1328477 relations and 928477 ideals in 400000 cliques
Sat Feb 2 03:00:12 2008 commencing in-memory singleton removal
Sat Feb 2 03:00:18 2008 begin with 68167997 relations and 38472235 unique ideals
Sat Feb 2 03:00:51 2008 reduce to 68152003 relations and 37527626 ideals in 5 passes
Sat Feb 2 03:00:51 2008 max relations containing the same ideal: 45
Sat Feb 2 03:01:24 2008 removing 1306587 relations and 906587 ideals in 400000 cliques
Sat Feb 2 03:01:26 2008 commencing in-memory singleton removal
Sat Feb 2 03:01:32 2008 begin with 66845416 relations and 37527626 unique ideals
Sat Feb 2 03:02:04 2008 reduce to 66830237 relations and 36605742 ideals in 5 passes
Sat Feb 2 03:02:04 2008 max relations containing the same ideal: 45
Sat Feb 2 03:02:36 2008 removing 1298668 relations and 898668 ideals in 400000 cliques
Sat Feb 2 03:02:38 2008 commencing in-memory singleton removal
Sat Feb 2 03:02:44 2008 begin with 65531569 relations and 36605742 unique ideals
Sat Feb 2 03:03:15 2008 reduce to 65516826 relations and 35692229 ideals in 5 passes
Sat Feb 2 03:03:15 2008 max relations containing the same ideal: 45
Sat Feb 2 03:03:46 2008 removing 1285876 relations and 885876 ideals in 400000 cliques
Sat Feb 2 03:03:48 2008 commencing in-memory singleton removal
Sat Feb 2 03:03:53 2008 begin with 64230950 relations and 35692229 unique ideals
Sat Feb 2 03:04:30 2008 reduce to 64215889 relations and 34791183 ideals in 6 passes
Sat Feb 2 03:04:30 2008 max relations containing the same ideal: 44
Sat Feb 2 03:05:00 2008 removing 1276314 relations and 876314 ideals in 400000 cliques
Sat Feb 2 03:05:02 2008 commencing in-memory singleton removal
Sat Feb 2 03:05:07 2008 begin with 62939575 relations and 34791183 unique ideals
Sat Feb 2 03:05:31 2008 reduce to 62924457 relations and 33899638 ideals in 4 passes
Sat Feb 2 03:05:31 2008 max relations containing the same ideal: 44
Sat Feb 2 03:06:01 2008 removing 1266553 relations and 866553 ideals in 400000 cliques
Sat Feb 2 03:06:02 2008 commencing in-memory singleton removal
Sat Feb 2 03:06:08 2008 begin with 61657904 relations and 33899638 unique ideals
Sat Feb 2 03:06:36 2008 reduce to 61642021 relations and 33017093 ideals in 5 passes
Sat Feb 2 03:06:36 2008 max relations containing the same ideal: 44
Sat Feb 2 03:07:05 2008 removing 1269571 relations and 869571 ideals in 400000 cliques
Sat Feb 2 03:07:07 2008 commencing in-memory singleton removal
Sat Feb 2 03:07:12 2008 begin with 60372450 relations and 33017093 unique ideals
Sat Feb 2 03:07:45 2008 reduce to 60357820 relations and 32132801 ideals in 6 passes
Sat Feb 2 03:07:45 2008 max relations containing the same ideal: 41
Sat Feb 2 03:08:13 2008 removing 1264461 relations and 864461 ideals in 400000 cliques
Sat Feb 2 03:08:15 2008 commencing in-memory singleton removal
Sat Feb 2 03:08:20 2008 begin with 59093359 relations and 32132801 unique ideals
Sat Feb 2 03:08:47 2008 reduce to 59079551 relations and 31254448 ideals in 5 passes
Sat Feb 2 03:08:47 2008 max relations containing the same ideal: 41
Sat Feb 2 03:09:14 2008 removing 1246120 relations and 846120 ideals in 400000 cliques
Sat Feb 2 03:09:15 2008 commencing in-memory singleton removal
Sat Feb 2 03:09:20 2008 begin with 57833431 relations and 31254448 unique ideals
Sat Feb 2 03:09:47 2008 reduce to 57818623 relations and 30393423 ideals in 5 passes
Sat Feb 2 03:09:47 2008 max relations containing the same ideal: 41
Sat Feb 2 03:10:13 2008 removing 1249893 relations and 849893 ideals in 400000 cliques
Sat Feb 2 03:10:14 2008 commencing in-memory singleton removal
Sat Feb 2 03:10:19 2008 begin with 56568730 relations and 30393423 unique ideals
Sat Feb 2 03:10:45 2008 reduce to 56554433 relations and 29529107 ideals in 5 passes
Sat Feb 2 03:10:45 2008 max relations containing the same ideal: 41
Sat Feb 2 03:11:10 2008 removing 487390 relations and 350931 ideals in 136459 cliques
Sat Feb 2 03:11:11 2008 commencing in-memory singleton removal
Sat Feb 2 03:11:16 2008 begin with 56067043 relations and 29529107 unique ideals
Sat Feb 2 03:11:36 2008 reduce to 56064949 relations and 29176081 ideals in 4 passes
Sat Feb 2 03:11:36 2008 max relations containing the same ideal: 41
Sat Feb 2 03:11:51 2008 dataset has 70.0% excess relations
Sat Feb 2 03:12:48 2008 ignoring smallest 7159917 rational and 7160002 algebraic ideals
Sat Feb 2 03:12:48 2008 filtering rational ideals above 125927424
Sat Feb 2 03:12:48 2008 filtering algebraic ideals above 125927424
Sat Feb 2 03:12:48 2008 need 24199981 more relations than ideals
Sat Feb 2 03:12:48 2008 commencing singleton removal, final pass
Sat Feb 2 03:36:17 2008 memory use: 800.1 MB
Sat Feb 2 03:37:08 2008 commencing in-memory singleton removal
Sat Feb 2 03:37:13 2008 begin with 56064949 relations and 30649971 unique ideals
Sat Feb 2 03:37:42 2008 reduce to 55942514 relations and 30527459 ideals in 6 passes
Sat Feb 2 03:37:42 2008 max relations containing the same ideal: 44
Sat Feb 2 03:38:17 2008 removing 1250788 relations and 850788 ideals in 400000 cliques
Sat Feb 2 03:38:19 2008 commencing in-memory singleton removal
Sat Feb 2 03:38:23 2008 begin with 54691726 relations and 30527459 unique ideals
Sat Feb 2 03:38:46 2008 reduce to 54668862 relations and 29653415 ideals in 5 passes
Sat Feb 2 03:38:46 2008 max relations containing the same ideal: 43
Sat Feb 2 03:39:10 2008 removing 1242032 relations and 842032 ideals in 400000 cliques
Sat Feb 2 03:39:11 2008 commencing in-memory singleton removal
Sat Feb 2 03:39:15 2008 begin with 53426830 relations and 29653415 unique ideals
Sat Feb 2 03:39:34 2008 reduce to 53410290 relations and 28794675 ideals in 4 passes
Sat Feb 2 03:39:34 2008 max relations containing the same ideal: 42
Sat Feb 2 03:39:56 2008 removing 1232023 relations and 832023 ideals in 400000 cliques
Sat Feb 2 03:39:58 2008 commencing in-memory singleton removal
Sat Feb 2 03:40:02 2008 begin with 52178267 relations and 28794675 unique ideals
Sat Feb 2 03:40:24 2008 reduce to 52161123 relations and 27945366 ideals in 5 passes
Sat Feb 2 03:40:24 2008 max relations containing the same ideal: 41
Sat Feb 2 03:40:46 2008 removing 69595 relations and 53820 ideals in 15775 cliques
Sat Feb 2 03:40:47 2008 commencing in-memory singleton removal
Sat Feb 2 03:40:51 2008 begin with 52091528 relations and 27945366 unique ideals
Sat Feb 2 03:41:04 2008 reduce to 52091468 relations and 27891486 ideals in 3 passes
Sat Feb 2 03:41:04 2008 max relations containing the same ideal: 41
Sat Feb 2 03:41:17 2008 dataset has 53.0% excess relations
Sat Feb 2 03:42:07 2008 ignoring smallest 6407562 rational and 6407473 algebraic ideals
Sat Feb 2 03:42:07 2008 filtering rational ideals above 111935488
Sat Feb 2 03:42:07 2008 filtering algebraic ideals above 111935488
Sat Feb 2 03:42:07 2008 need 19359985 more relations than ideals
Sat Feb 2 03:42:07 2008 commencing singleton removal, final pass
Sat Feb 2 04:05:31 2008 memory use: 771.3 MB
Sat Feb 2 04:06:27 2008 commencing in-memory singleton removal
Sat Feb 2 04:06:31 2008 begin with 52091468 relations and 29376445 unique ideals
Sat Feb 2 04:06:55 2008 reduce to 51980098 relations and 29265023 ideals in 5 passes
Sat Feb 2 04:06:55 2008 max relations containing the same ideal: 41
Sat Feb 2 04:07:28 2008 removing 1280663 relations and 880663 ideals in 400000 cliques
Sat Feb 2 04:07:29 2008 commencing in-memory singleton removal
Sat Feb 2 04:07:33 2008 begin with 50699435 relations and 29265023 unique ideals
Sat Feb 2 04:07:55 2008 reduce to 50675789 relations and 28360376 ideals in 5 passes
Sat Feb 2 04:07:55 2008 max relations containing the same ideal: 40
Sat Feb 2 04:08:18 2008 removing 1234184 relations and 834184 ideals in 400000 cliques
Sat Feb 2 04:08:19 2008 commencing in-memory singleton removal
Sat Feb 2 04:08:23 2008 begin with 49441605 relations and 28360376 unique ideals
Sat Feb 2 04:08:44 2008 reduce to 49422269 relations and 27506635 ideals in 5 passes
Sat Feb 2 04:08:44 2008 max relations containing the same ideal: 40
Sat Feb 2 04:09:06 2008 removing 1221500 relations and 821500 ideals in 400000 cliques
Sat Feb 2 04:09:07 2008 commencing in-memory singleton removal
Sat Feb 2 04:09:11 2008 begin with 48200769 relations and 27506635 unique ideals
Sat Feb 2 04:09:32 2008 reduce to 48181209 relations and 26665385 ideals in 5 passes
Sat Feb 2 04:09:32 2008 max relations containing the same ideal: 40
Sat Feb 2 04:09:53 2008 removing 1215025 relations and 815025 ideals in 400000 cliques
Sat Feb 2 04:09:54 2008 commencing in-memory singleton removal
Sat Feb 2 04:09:58 2008 begin with 46966184 relations and 26665385 unique ideals
Sat Feb 2 04:10:17 2008 reduce to 46945582 relations and 25829526 ideals in 5 passes
Sat Feb 2 04:10:17 2008 max relations containing the same ideal: 39
Sat Feb 2 04:10:38 2008 removing 1208649 relations and 808649 ideals in 400000 cliques
Sat Feb 2 04:10:39 2008 commencing in-memory singleton removal
Sat Feb 2 04:10:43 2008 begin with 45736933 relations and 25829526 unique ideals
Sat Feb 2 04:11:02 2008 reduce to 45715487 relations and 24999189 ideals in 5 passes
Sat Feb 2 04:11:02 2008 max relations containing the same ideal: 39
Sat Feb 2 04:11:22 2008 removing 1200712 relations and 800712 ideals in 400000 cliques
Sat Feb 2 04:11:23 2008 commencing in-memory singleton removal
Sat Feb 2 04:11:26 2008 begin with 44514775 relations and 24999189 unique ideals
Sat Feb 2 04:11:41 2008 reduce to 44492252 relations and 24175675 ideals in 4 passes
Sat Feb 2 04:11:41 2008 max relations containing the same ideal: 38
Sat Feb 2 04:12:00 2008 removing 1183772 relations and 783772 ideals in 400000 cliques
Sat Feb 2 04:12:02 2008 commencing in-memory singleton removal
Sat Feb 2 04:12:05 2008 begin with 43308480 relations and 24175675 unique ideals
Sat Feb 2 04:12:19 2008 reduce to 43283180 relations and 23366236 ideals in 4 passes
Sat Feb 2 04:12:19 2008 max relations containing the same ideal: 38
Sat Feb 2 04:12:38 2008 removing 1206714 relations and 806714 ideals in 400000 cliques
Sat Feb 2 04:12:39 2008 commencing in-memory singleton removal
Sat Feb 2 04:12:42 2008 begin with 42076466 relations and 23366236 unique ideals
Sat Feb 2 04:12:56 2008 reduce to 42058239 relations and 22540970 ideals in 4 passes
Sat Feb 2 04:12:56 2008 max relations containing the same ideal: 37
Sat Feb 2 04:13:14 2008 removing 513254 relations and 355971 ideals in 157283 cliques
Sat Feb 2 04:13:15 2008 commencing in-memory singleton removal
Sat Feb 2 04:13:18 2008 begin with 41544985 relations and 22540970 unique ideals
Sat Feb 2 04:13:31 2008 reduce to 41541162 relations and 22181149 ideals in 4 passes
Sat Feb 2 04:13:31 2008 max relations containing the same ideal: 37
Sat Feb 2 04:13:43 2008 dataset has 22.4% excess relations
Sat Feb 2 04:14:27 2008 ignoring smallest 5649956 rational and 5649937 algebraic ideals
Sat Feb 2 04:14:27 2008 filtering rational ideals above 97943552
Sat Feb 2 04:14:27 2008 filtering algebraic ideals above 97943552
Sat Feb 2 04:14:27 2008 need 17082338 more relations than ideals
Sat Feb 2 04:14:27 2008 commencing singleton removal, final pass
Sat Feb 2 04:37:06 2008 memory use: 625.6 MB
Sat Feb 2 04:37:53 2008 commencing in-memory singleton removal
Sat Feb 2 04:37:57 2008 begin with 41541162 relations and 23670875 unique ideals
Sat Feb 2 04:38:18 2008 reduce to 41407975 relations and 23537597 ideals in 6 passes
Sat Feb 2 04:38:18 2008 max relations containing the same ideal: 37
Sat Feb 2 04:38:44 2008 removing 1201538 relations and 807518 ideals in 394020 cliques
Sat Feb 2 04:38:45 2008 commencing in-memory singleton removal
Sat Feb 2 04:38:49 2008 begin with 40206437 relations and 23537597 unique ideals
Sat Feb 2 04:39:06 2008 reduce to 40174424 relations and 22697365 ideals in 5 passes
Sat Feb 2 04:39:06 2008 max relations containing the same ideal: 37
Sat Feb 2 04:39:23 2008 removing 1172909 relations and 778889 ideals in 394020 cliques
Sat Feb 2 04:39:24 2008 commencing in-memory singleton removal
Sat Feb 2 04:39:27 2008 begin with 39001515 relations and 22697365 unique ideals
Sat Feb 2 04:39:43 2008 reduce to 38977233 relations and 21893800 ideals in 5 passes
Sat Feb 2 04:39:43 2008 max relations containing the same ideal: 36
Sat Feb 2 04:40:07 2008 dataset has 8.0% excess relations
Sat Feb 2 04:40:10 2008 relations with 0 large ideals: 2989715
Sat Feb 2 04:40:10 2008 relations with 1 large ideals: 11010656
Sat Feb 2 04:40:10 2008 relations with 2 large ideals: 14303313
Sat Feb 2 04:40:10 2008 relations with 3 large ideals: 8291833
Sat Feb 2 04:40:10 2008 relations with 4 large ideals: 2173298
Sat Feb 2 04:40:10 2008 relations with 5 large ideals: 208418
Sat Feb 2 04:40:10 2008 relations with 6 large ideals: 0
Sat Feb 2 04:40:10 2008 relations with 7+ large ideals: 0
Sat Feb 2 04:40:10 2008 commencing 2-way merge
Sat Feb 2 04:40:34 2008 reduce to 28878604 relation sets and 11795171 unique ideals
Sat Feb 2 04:40:34 2008 commencing full merge
Sat Feb 2 04:43:45 2008 memory use: 1177.2 MB
Sat Feb 2 04:43:45 2008 found 17171528 cycles, need 11399371
Sat Feb 2 04:43:54 2008 weight of 11399371 cycles is about 519435201 (45.57/cycle)
Sat Feb 2 04:43:54 2008 distribution of cycle lengths:
Sat Feb 2 04:43:54 2008 1 relations: 3006558
Sat Feb 2 04:43:54 2008 2 relations: 1935993
Sat Feb 2 04:43:54 2008 3 relations: 1751058
Sat Feb 2 04:43:54 2008 4 relations: 1591526
Sat Feb 2 04:43:54 2008 5 relations: 1423816
Sat Feb 2 04:43:54 2008 6 relations: 1156684
Sat Feb 2 04:43:54 2008 7 relations: 533590
Sat Feb 2 04:43:54 2008 8 relations: 146
Sat Feb 2 04:43:54 2008 9 relations: 0
Sat Feb 2 04:43:54 2008 10+ relations: 0
Sat Feb 2 04:43:54 2008 heaviest cycle: 8 relations
Sat Feb 2 04:43:56 2008 matrix not dense enough, retrying
Sat Feb 2 04:43:58 2008 dataset has 8.0% excess relations
Sat Feb 2 04:44:42 2008 ignoring smallest 4886474 rational and 4886641 algebraic ideals
Sat Feb 2 04:44:42 2008 filtering rational ideals above 83951616
Sat Feb 2 04:44:42 2008 filtering algebraic ideals above 83951616
Sat Feb 2 04:44:42 2008 need 17082338 more relations than ideals
Sat Feb 2 04:44:42 2008 commencing singleton removal, final pass
Sat Feb 2 05:06:09 2008 memory use: 616.0 MB
Sat Feb 2 05:06:54 2008 commencing in-memory singleton removal
Sat Feb 2 05:06:58 2008 begin with 38977233 relations and 23401261 unique ideals
Sat Feb 2 05:07:16 2008 reduce to 38864938 relations and 23288900 ideals in 5 passes
Sat Feb 2 05:07:16 2008 max relations containing the same ideal: 36
Sat Feb 2 05:07:26 2008 dataset has -1.5% excess relations
Sat Feb 2 05:07:29 2008 relations with 0 large ideals: 2068760
Sat Feb 2 05:07:29 2008 relations with 1 large ideals: 8814134
Sat Feb 2 05:07:29 2008 relations with 2 large ideals: 13888356
Sat Feb 2 05:07:29 2008 relations with 3 large ideals: 10189875
Sat Feb 2 05:07:29 2008 relations with 4 large ideals: 3462233
Sat Feb 2 05:07:29 2008 relations with 5 large ideals: 441580
Sat Feb 2 05:07:29 2008 relations with 6 large ideals: 0
Sat Feb 2 05:07:29 2008 relations with 7+ large ideals: 0
Sat Feb 2 05:07:29 2008 commencing 2-way merge
Sat Feb 2 05:07:55 2008 reduce to 28634130 relation sets and 13058092 unique ideals
Sat Feb 2 05:07:55 2008 commencing full merge
Sat Feb 2 05:11:50 2008 memory use: 1215.2 MB
Sat Feb 2 05:11:50 2008 found 16223504 cycles, need 10430315
Sat Feb 2 05:11:59 2008 weight of 10430315 cycles is about 514662887 (49.34/cycle)
Sat Feb 2 05:11:59 2008 distribution of cycle lengths:
Sat Feb 2 05:11:59 2008 1 relations: 2237118
Sat Feb 2 05:11:59 2008 2 relations: 1676315
Sat Feb 2 05:11:59 2008 3 relations: 1623758
Sat Feb 2 05:11:59 2008 4 relations: 1535425
Sat Feb 2 05:11:59 2008 5 relations: 1425221
Sat Feb 2 05:11:59 2008 6 relations: 1212911
Sat Feb 2 05:11:59 2008 7 relations: 718760
Sat Feb 2 05:11:59 2008 8 relations: 807
Sat Feb 2 05:11:59 2008 9 relations: 0
Sat Feb 2 05:11:59 2008 10+ relations: 0
Sat Feb 2 05:11:59 2008 heaviest cycle: 8 relations
Sat Feb 2 05:12:01 2008 matrix not dense enough, retrying
Sat Feb 2 05:12:03 2008 dataset has -1.5% excess relations
Sat Feb 2 05:12:41 2008 ignoring smallest 4115855 rational and 4116628 algebraic ideals
Sat Feb 2 05:12:41 2008 filtering rational ideals above 69959680
Sat Feb 2 05:12:41 2008 filtering algebraic ideals above 69959680
Sat Feb 2 05:12:41 2008 need 17082338 more relations than ideals
Sat Feb 2 05:12:41 2008 commencing singleton removal, final pass
Sat Feb 2 05:34:34 2008 memory use: 653.6 MB
Sat Feb 2 05:35:16 2008 commencing in-memory singleton removal
Sat Feb 2 05:35:20 2008 begin with 38864938 relations and 24818311 unique ideals
Sat Feb 2 05:35:40 2008 reduce to 38792132 relations and 24745471 ideals in 5 passes
Sat Feb 2 05:35:40 2008 max relations containing the same ideal: 36
Sat Feb 2 05:35:51 2008 dataset has -11.2% excess relations
Sat Feb 2 05:35:55 2008 relations with 0 large ideals: 1317773
Sat Feb 2 05:35:55 2008 relations with 1 large ideals: 6623437
Sat Feb 2 05:35:55 2008 relations with 2 large ideals: 12797772
Sat Feb 2 05:35:55 2008 relations with 3 large ideals: 11924983
Sat Feb 2 05:35:55 2008 relations with 4 large ideals: 5239424
Sat Feb 2 05:35:55 2008 relations with 5 large ideals: 888743
Sat Feb 2 05:35:55 2008 relations with 6 large ideals: 0
Sat Feb 2 05:35:55 2008 relations with 7+ large ideals: 0
Sat Feb 2 05:35:55 2008 commencing 2-way merge
Sat Feb 2 05:36:23 2008 reduce to 28461160 relation sets and 14414499 unique ideals
Sat Feb 2 05:36:23 2008 commencing full merge
Sat Feb 2 05:41:13 2008 memory use: 1282.0 MB
Sat Feb 2 05:41:13 2008 found 15255948 cycles, need 9469183
Sat Feb 2 05:41:21 2008 weight of 9469183 cycles is about 528705802 (55.83/cycle)
Sat Feb 2 05:41:21 2008 distribution of cycle lengths:
Sat Feb 2 05:41:21 2008 1 relations: 1549848
Sat Feb 2 05:41:21 2008 2 relations: 1365605
Sat Feb 2 05:41:21 2008 3 relations: 1387149
Sat Feb 2 05:41:21 2008 4 relations: 1354489
Sat Feb 2 05:41:21 2008 5 relations: 1302076
Sat Feb 2 05:41:21 2008 6 relations: 1185563
Sat Feb 2 05:41:21 2008 7 relations: 987298
Sat Feb 2 05:41:21 2008 8 relations: 337088
Sat Feb 2 05:41:21 2008 9 relations: 67
Sat Feb 2 05:41:21 2008 10+ relations: 0
Sat Feb 2 05:41:21 2008 heaviest cycle: 9 relations
Sat Feb 2 05:41:23 2008 matrix not dense enough, retrying
Sat Feb 2 05:41:25 2008 dataset has -11.2% excess relations
Sat Feb 2 05:41:56 2008 ignoring smallest 3336478 rational and 3337166 algebraic ideals
Sat Feb 2 05:41:56 2008 filtering rational ideals above 55967743
Sat Feb 2 05:41:56 2008 filtering algebraic ideals above 55967743
Sat Feb 2 05:41:56 2008 need 17082338 more relations than ideals
Sat Feb 2 05:41:56 2008 commencing singleton removal, final pass
Sat Feb 2 06:04:43 2008 memory use: 697.9 MB
Sat Feb 2 06:05:26 2008 commencing in-memory singleton removal
Sat Feb 2 06:05:30 2008 begin with 38792132 relations and 26299310 unique ideals
Sat Feb 2 06:05:52 2008 reduce to 38752473 relations and 26259644 ideals in 5 passes
Sat Feb 2 06:05:52 2008 max relations containing the same ideal: 36
Sat Feb 2 06:06:03 2008 dataset has -21.0% excess relations
Sat Feb 2 06:06:07 2008 relations with 0 large ideals: 737715
Sat Feb 2 06:06:07 2008 relations with 1 large ideals: 4516923
Sat Feb 2 06:06:07 2008 relations with 2 large ideals: 10918249
Sat Feb 2 06:06:07 2008 relations with 3 large ideals: 13190671
Sat Feb 2 06:06:07 2008 relations with 4 large ideals: 7630168
Sat Feb 2 06:06:07 2008 relations with 5 large ideals: 1758747
Sat Feb 2 06:06:07 2008 relations with 6 large ideals: 0
Sat Feb 2 06:06:07 2008 relations with 7+ large ideals: 0
Sat Feb 2 06:06:07 2008 commencing 2-way merge
Sat Feb 2 06:06:38 2008 reduce to 28357840 relation sets and 15865011 unique ideals
Sat Feb 2 06:06:38 2008 commencing full merge
Sat Feb 2 06:12:49 2008 memory use: 1380.3 MB
Sat Feb 2 06:12:50 2008 found 14308470 cycles, need 8575211
Sat Feb 2 06:12:57 2008 weight of 8575211 cycles is about 557692281 (65.04/cycle)
Sat Feb 2 06:12:57 2008 distribution of cycle lengths:
Sat Feb 2 06:12:57 2008 1 relations: 980082
Sat Feb 2 06:12:57 2008 2 relations: 1043152
Sat Feb 2 06:12:57 2008 3 relations: 1124089
Sat Feb 2 06:12:57 2008 4 relations: 1136680
Sat Feb 2 06:12:57 2008 5 relations: 1122920
Sat Feb 2 06:12:57 2008 6 relations: 1072071
Sat Feb 2 06:12:57 2008 7 relations: 982123
Sat Feb 2 06:12:57 2008 8 relations: 815648
Sat Feb 2 06:12:57 2008 9 relations: 298298
Sat Feb 2 06:12:57 2008 10+ relations: 148
Sat Feb 2 06:12:57 2008 heaviest cycle: 10 relations
Sat Feb 2 06:13:00 2008 commencing cycle optimization
Sat Feb 2 06:13:17 2008 start with 39118606 relations
Sat Feb 2 06:14:22 2008 pruned 1215512 relations
Sat Feb 2 06:14:22 2008 memory use: 1338.0 MB
Sat Feb 2 06:14:22 2008 distribution of cycle lengths:
Sat Feb 2 06:14:22 2008 1 relations: 980082
Sat Feb 2 06:14:22 2008 2 relations: 1084860
Sat Feb 2 06:14:22 2008 3 relations: 1197476
Sat Feb 2 06:14:22 2008 4 relations: 1201166
Sat Feb 2 06:14:22 2008 5 relations: 1192699
Sat Feb 2 06:14:22 2008 6 relations: 1105461
Sat Feb 2 06:14:22 2008 7 relations: 950065
Sat Feb 2 06:14:22 2008 8 relations: 661228
Sat Feb 2 06:14:22 2008 9 relations: 202080
Sat Feb 2 06:14:22 2008 10+ relations: 94
Sat Feb 2 06:14:22 2008 heaviest cycle: 10 relations
Sat Feb 2 06:14:40 2008
Sat Feb 2 06:14:40 2008 commencing linear algebra
Sat Feb 2 06:14:59 2008 read 8575211 cycles
Sat Feb 2 06:15:57 2008 cycles contain 22136943 unique relations
Sat Feb 2 06:44:07 2008 read 22136943 relations
Sat Feb 2 06:44:54 2008 using 32 quadratic characters above 2147481360
Sat Feb 2 06:48:47 2008 building initial matrix
Sat Feb 2 06:58:40 2008 memory use: 3033.7 MB
Sat Feb 2 06:59:05 2008 read 8575211 cycles
Sat Feb 2 06:59:28 2008 matrix is 8547933 x 8575211 (2409.0 MB) with weight 805680220 (93.95/col)
Sat Feb 2 06:59:28 2008 sparse part has weight 528595381 (61.64/col)
Sat Feb 2 07:03:53 2008 filtering completed in 3 passes
Sat Feb 2 07:03:56 2008 matrix is 8340443 x 8340634 (2359.4 MB) with weight 788048578 (94.48/col)
Sat Feb 2 07:03:57 2008 sparse part has weight 518418993 (62.16/col)
Sat Feb 2 07:06:26 2008 read 8340634 cycles
Sat Feb 2 07:06:48 2008 matrix is 8340443 x 8340634 (2359.4 MB) with weight 788048578 (94.48/col)
Sat Feb 2 07:06:48 2008 sparse part has weight 518418993 (62.16/col)
Sat Feb 2 07:06:48 2008 saving the first 48 matrix rows for later
Sat Feb 2 07:06:52 2008 matrix is 8340395 x 8340634 (2285.7 MB) with weight 605146918 (72.55/col)
Sat Feb 2 07:06:52 2008 sparse part has weight 515782599 (61.84/col)
Sat Feb 2 07:06:52 2008 matrix includes 64 packed rows
Sat Feb 2 07:06:52 2008 using block size 65536 for processor cache size 4096 kB
Sat Feb 2 07:07:53 2008 commencing Lanczos iteration (4 threads)
Sat Feb 2 07:07:53 2008 memory use: 2402.8 MB
Mon Feb 11 08:37:32 2008 lanczos halted after 131898 iterations (dim = 8340313)
Mon Feb 11 08:37:59 2008 lanczos error: only trivial dependencies found
Mon Feb 11 08:37:59 2008
Mon Feb 11 08:37:59 2008 commencing square root phase
Mon Feb 11 08:37:59 2008 reading relations for dependency 1
[/code]

Have you already restarted 6,383+? I guess this one is the oversieved one - did you try to restart with less relations?

[I just got back from a week-long vacation. Note to those about to take a cruise: the world will sway back and forth for several days afterwards]

The initial filtering bound is chosen as the point where the estimated number of occurrences of a given large ideal drops below a limit (this assumes you're using the patch to v1.33 that was previously posted in this thread). The choice of bound occurs before singleton removal starts, to avoid needing yet another pass through the entire dataset. This means the data is quite noisy, since it includes contributions from relations that will later be pruned, and the initial estimate is usually too conservative. Subsequent removal passes lower the bound by 10% at a time until the amount of excess (relations minus unique ideals) drops below 8% of the number of ideals below the current bound. There is always at least one subsequent pass.

Once the above has happened, the merge phase runs and the density of the resulting matrix is tested. If it's too low, the bound continues to be reduced by 10% at a time. Many of the logs that have been posted here show that the latter step is necessary. When there is a huge amount of oversieving, it looks like additional strictness is needed. I don't want to resort to a fixed-size filtering bound, since a bound that's too high will not do anything and a bound that's too low will consume excessive memory (some of these jobs use gigs of memory with a filtering bound in the tens of millions).

Tom, I also think the threading changes are suspicious. The histograms output during filtering on the C165 definitely indicate the final filtering bound should have been lower.

[QUOTE=jasonp;125974]Tom, I also think the threading changes are suspicious.[/QUOTE]

Jason,

I'm running 1.33 as fetched from your website with "-t 4".
I had to make a few changes to get it to avoid crashing on memory allocation on my Mac running OSX 10.5.

Should I obtain a different version rather than spend another 500 hours on this LA and hope that it works?

I was also wondering if I can stop at a checkpoint and restart with a different "num_threads" ?

[QUOTE=Wacky;126210]Jason,

I'm running 1.33 as fetched from your website with "-t 4".
I had to make a few changes to get it to avoid crashing on memory allocation on my Mac running OSX 10.5.

Should I obtain a different version rather than spend another 500 hours on this LA and hope that it works?

I was also wondering if I can stop at a checkpoint and restart with a different "num_threads" ?[/QUOTE]
It is safe to stop and restart with a different number of threads; the on-disk format does not care about how the matrix is partitioned before running the linear algebra.

I'm not sure what you mean by 'obtain a different version'.

My experience is that the time needed for a matrix multiply, on the same machine, varies approximately linearly with the number of nonzeros in the sparse part of the matrix. I agree that bus speed is likely the limiting factor, since the multithreaded speedup on dual-CPU machines started off much higher than the speedup on dual-core machines (recent patches to the threading code have improved that).

I've also wondered about finding more than 64 nullspace vectors, at least for really big problems. The source changes would be pretty invasive, and the memory use would jump noticeably, but it might be a good idea to try. If you want instead to push the matrix dimension down (and the density up), just increase the value of TARGET_DENSITY in gnfs/filter/merge.c; the main merge code will continue merging ideals until the resulting matrix has more than this many estimated average nonzeros per column.

[QUOTE=jasonp;126233]I'm not sure what you mean by 'obtain a different version'.[/QUOTE]

My concern relates to Tom's report of difficulty and your reply
[QUOTE]Tom, I also think the threading changes are suspicious.[/QUOTE]

I don't want to spend weeks only to find out that the results are worthless.
Greg has certainly been successful using version 1.32

[QUOTE=Wacky;126236]My concern relates to Tom's report of difficulty and your reply

I don't want to spend weeks only to find out that the results are worthless.
Greg has certainly been successful using version 1.32[/QUOTE]
Okay, I follow now. v1.33 has no linear algebra changes compared to v1.32. Tom is due to report back in the next day or two on whether a followup run with an older msieve version succeeded on his C151 GNFS matrix. ISTR that he had trouble on this number before too. Just out of curiosity, what version of gcc is everyone using for linux compiles? (I use 4.1.1 and it's never caused any trouble)

I'm not sure what to make of the recent spate of reports of linear algebra trouble. People have reported both successes and failures with multithreaded runs using versions > 1.30

PS: Richard, what changes to v1.33 did you have to make?

[quote=(I use 4.1.1 and it's never caused any trouble)

[/quote]

Version 1.33 works well without failures on freebsd. Unequivocally. GCC 4.2.1

[EMAIL="admin@relay.diakom.ru"]admin@relay.diakom.ru[/EMAIL] [19:09:48][1][~] >gcc -v
Using built-in specs.
Target: i386-undermydesk-freebsd
Configured with: FreeBSD/i386 system compiler
Thread model: posix
gcc version 4.2.1 20070719 [FreeBSD]

The C151 completed without issue (and with a noticeably smaller matrix than msieve-1.33 was offering me with default settings, about 4.5M^2 rather than 5M^2) using msieve-1.29 this morning after about 60 hours on two cores of a quad-core; I'm leaving it to Chad Davis, who did all the sieving, to post the factors.

I'm running linalg for a C154 SNFS (the last Cunningham-table composite of <512 bits) with msieve-1.29 at the moment, that should again take about 60 hours so I can post something more detailed at the weekend.

[QUOTE=jasonp;126245]Richard, what changes to v1.33 did you have to make?[/QUOTE]

After it aborted with an allocation error when the matrix started getting VERY large (I assume that the "wrong" implementation of malloc had been selected), I wanted to be able to run it from Xcode (the IDE for OSX). It was too much trouble porting your multi-architecture library of sieving "cores" to compile in that environment. So I just stripped out the options that I did not need.

In the process, I think that both __i386__ and __x86_64__ were set.
So in the cpuid code as well as the call to the architecture specific core, I inverted the order of your selection so that the 64 bit code would take precedence.

Another threading datapoint:
Machines were A64 X2 6000+ linux amd64, A64 X2 4800+ linux i386.
GCC versions from 4.1.x to 4.2.2.
msieve versions 1.31+threading patch to 1.33.
sieved with ggnfs lasieve, pp/la/sqrt with msieve -t 2.
gnfs 1 c155, 1 c154, 5+ c120-130.
snfs 1 c198, 10+ c160-c180.
40+ small snfs and gnfs.
no problems with msieve at all, had a bunch of lasieve crashes on the snfs c198.

Hello!

First of all, thank you Jason for such a brilliant piece of software!
When I used Msieve for the first time, I was amazed how fast it was going. Great optimization, nice code, awesome job!

Now I'm trying my first rather "big" job (at least for single man). It's C145 with GNFS. Almost everything went smooth.

After finding good poly and sieving with GGNFS, I switched to Msieve.

When trying to do linear algebra, first problems occured.
Msieve failed few times with the following error:
[code]
commencing linear algebra
read 3432998 cycles
cycles contain 9838531 unique relations
failed to allocate 236124744 bytes
[/code]
I restarted combining and matrix solving for three times. Finally it was OK and matrix was solved in 35 hours.

[code]
Fri Feb 22 15:20:05 2008 commencing Lanczos iteration (2 threads)
Fri Feb 22 15:20:05 2008 memory use: 906.2 MB
Sun Feb 24 02:20:26 2008 lanczos halted after 53238 iterations (dim = 3366183)
Sun Feb 24 02:20:39 2008 recovered 40 nontrivial dependencies
Sun Feb 24 02:20:40 2008 elapsed time 35:13:47
[/code]

The worst problem occured on square root step. I tried to restart it for 10+ times total, but I always get the same error (I tried different depencies by the way).

[code]
Sun Feb 24 18:48:09 2008 Msieve v. 1.33
..skipped..
Sun Feb 24 18:48:13 2008
Sun Feb 24 18:48:13 2008 commencing square root phase
Sun Feb 24 18:48:13 2008 reading relations for dependency 1
Sun Feb 24 18:48:15 2008 read 1682371 cycles
Sun Feb 24 18:48:21 2008 cycles contain 5796302 unique relations
Sun Feb 24 18:51:37 2008 read 5796302 relations
Sun Feb 24 18:52:33 2008 multiplying 8104966 relations
[/code]

My machine has 3 GB of RAM. During first tries swap file was switched off.
I thought this could cause a problem and enabled it.
512 MB of swap for next run. No luck.
1024 MB of swap for next run. No luck.
1536 MB - same. :(
1792 MB - again :piggie::cry:

I think that 3GB RAM + 1,75GB of swap is more than enough for such a thing (matrix building/solving was finished successfully after all).
I tried two versions of Msieve - 1.32 and 1.33. If you request any files needed to find out where error is, I provide any of them.

Looking for help :hello:
Thanks in advance.

WBR,
Craig

[QUOTE=_dc_;126829]
I think that 3GB RAM + 1,75GB of swap is more than enough for such a thing (matrix building/solving was finished successfully after all).
I tried two versions of Msieve - 1.32 and 1.33. If you request any files needed to find out where error is, I provide any of them.
[/QUOTE]
Was this 32-bit windows? A single program is limited to 2GB of virtual memory, and probably a good deal less, no matter how much RAM and swap you have. frmky had better luck compiling his own cygwin binary, but for such a large job you may need a 64-bit OS to complete the square root.

In the past I'd started making changes to the square root that flushed intermediate results to disk, but they turned out to be more difficult than I expected and they are stalled for now.

[quote=jasonp;126852]In the past I'd started making changes to the square root that flushed intermediate results to disk, but they turned out to be more difficult than I expected and they are stalled for now.[/quote]

It certainly your right to do or to not do a conclusion of intermediate data. But on mine it for such project vital. As to appear a certain opportunity of search of mistakes and localizations of problems. Well and the right for you. It simply my opinion.

[quote=jasonp;126852]Was this 32-bit windows? [/quote]
Right, sorry for not including this valuable info in previous post.

[quote]A single program is limited to 2GB of virtual memory, and probably a good deal less, no matter how much RAM and swap you have. frmky had better luck compiling his own cygwin binary, but for such a large job you may need a 64-bit OS to complete the square root.[/quote]
As far as I remember it's possible to set /3GB flag in boot.ini to make 3GB of virtual memory available for applications. But it requires some special flag to be set in PE header as well, I can't recall it's name. I'll try this thing and report about results.

[quote]
In the past I'd started making changes to the square root that flushed intermediate results to disk, but they turned out to be more difficult than I expected and they are stalled for now.[/quote]
Well, square root is something that is computed rather fast (comparing to matrix step). So even in case of power failure or something else it's still OK just to restart a complete thing. So if it requires much effor from you, of course it's a question if it's reasonable enough to implement this feature.

Thanks for your reply, I didn't know square root computation could take more memory than matrix step.

[QUOTE=_dc_;126876]Thanks for your reply, I didn't know square root computation could take more memory than matrix step.[/QUOTE]
See [url="http://mersenneforum.org/showpost.php?p=117348&postcount=279"]this post[/url] for background about why this is an issue. It does need fixing somehow, but any solution would be a good deal of work.

[quote=jasonp;126881]See this post for background about why this is an issue. It does need fixing somehow, but any solution would be a good deal of work.[/quote]
I have read info behind this link. I have to say that I totally agree with you. This trade-off seems to be quite reasonable. I'm programmer and I have to deal with problems like this on daily basis (resource/speed optimization vs time/difficulty of coding).
When I have time and passion I can try harder and produce cute solution that I personally like. But usually one has loads of other problems to solve and he just can't spend time on one of them. It's always your choice and there is no need for excuse to yourself.

/3GB swith solved my issue - I attached logfile. Everything went smooth except I had to reboot once and so stop working copy of Msieve. Non-trivial factors were found on 3rd depency.
To use this switch one just has to put /3GB in boot.ini and then use application linked in special way (/LARGEADDRESSAWARE must be specified for linker).
Then you just run this application and voila - it has 3GB of virtual memory available.
May be you could put both versions on your web page (one .exe linked with /LARGEADDRESSAWARE and another without it)? Msieve is memory-hungry software, so this one could be a good solution.

By the way do you have any plans/ideas about futher development of Msieve?
I'm not sure if it's possible to call this a feature request, but still this could be useful to split sqrt problem on few PCs.
At the moment one could do this by copying all .dat and other files to other PCs and executing Msieve (in my case it's 3.5+ GB in compressed form).
May I introduce the following idea (I'm sorry if something of that is wrong from the point of underlying maths).
As far as I understand you need just a subset of relations to proceed square root step. Is it possible to make a special call to msieve, that would generate only required subset of relations for specific depency to transfer it to another machine and run sqrt procedure there?
I don't know how much effort is required for implementing this feature, because I don't know underlying theory on level. If it takes more than day to implement, then it's probably useless.

Curiouser and curiouser

I am now slightly more suspicious about the threading code in 1.33.

At least, I ran a job with -nc 1000000,1000000 -t4 using 1.33 on my quad-core of unclear reliability, which failed oddly; I've just rerun the same job with -t4 using 1.29, and it's completed without issue.

[QUOTE=fivemack;127120]I am now slightly more suspicious about the threading code in 1.33.

At least, I ran a job with -nc 1000000,1000000 -t4 using 1.33 on my quad-core of unclear reliability, which failed oddly; I've just rerun the same job with -t4 using 1.29, and it's completed without issue.[/QUOTE]
I guess either there is a threading problem in the code that only shows up for multithreaded runs on fast machines, or both your machines are slightly unstable but only for a version of msieve that has high multithreaded concurency. I try not to blame the computer because in general that means making two mistakes (including blaming the computer), but I frankly don't know where to start looking. Is it possible to underclock the memory to see if the problems persist? Failing that, can anyone audit the matrix multiply code?

Well, the LA for "2,841- C245" finally finished.
But the sqrt has failed.
:(

Fri Feb 22 10:16:00 2008 Msieve v. 1.33
Fri Feb 22 10:16:00 2008 random seeds: f602689b 5099f3da
Fri Feb 22 10:16:00 2008 factoring 27312187167948796049898887842782596405655381943670578373120353781997447000328700858938482409418918448758778194857586271196003004729048486053340769161697167767956404785889687728602979284674332324623675660860406658739006337124213538943374972682241 (245 digits)
Fri Feb 22 10:16:03 2008 no P-1/P+1/ECM available, skipping
Fri Feb 22 10:16:03 2008 commencing number field sieve (245-digit input)
Fri Feb 22 10:16:03 2008 R0: -1393796574908163946345982392040522594123776
Fri Feb 22 10:16:03 2008 R1: 1
Fri Feb 22 10:16:03 2008 A0: -1
Fri Feb 22 10:16:03 2008 A1: 0
Fri Feb 22 10:16:03 2008 A2: 0
Fri Feb 22 10:16:03 2008 A3: 0
Fri Feb 22 10:16:03 2008 A4: 0
Fri Feb 22 10:16:03 2008 A5: 0
Fri Feb 22 10:16:03 2008 A6: 2
Fri Feb 22 10:16:03 2008 size score = 4.189742e-12, Murphy alpha = 2.413277, combined = 2.102509e-12
Fri Feb 22 10:16:03 2008
Fri Feb 22 10:16:03 2008 commencing linear algebra
Fri Feb 22 10:16:12 2008 read 13558374 cycles
Fri Feb 22 10:17:01 2008 matrix is 13558175 x 13558374 (3832.4 MB) with weight 1195000318 (88.14/col)
Fri Feb 22 10:17:01 2008 sparse part has weight 855491974 (63.10/col)
Fri Feb 22 10:17:02 2008 saving the first 48 matrix rows for later
Fri Feb 22 10:17:08 2008 matrix is 13558127 x 13558374 (3675.6 MB) with weight 906838153 (66.88/col)
Fri Feb 22 10:17:08 2008 sparse part has weight 827953701 (61.07/col)
Fri Feb 22 10:17:08 2008 matrix includes 64 packed rows
Fri Feb 22 10:17:08 2008 using block size 65536 for processor cache size 4096 kB
Fri Feb 22 10:18:53 2008 commencing Lanczos iteration (4 threads)
Fri Feb 22 10:18:53 2008 memory use: 3945.0 MB
Fri Feb 22 10:19:43 2008 restarting at iteration 26887 (dim = 1700224)
Thu Mar 13 21:27:55 2008 lanczos halted after 214402 iterations (dim = 13558116)
Thu Mar 13 21:28:43 2008 recovered 42 nontrivial dependencies
Thu Mar 13 21:28:47 2008 elapsed time 490:12:47
Thu Mar 13 21:41:39 2008
Thu Mar 13 21:41:39 2008
Thu Mar 13 21:41:39 2008 Msieve v. 1.33
Thu Mar 13 21:41:39 2008 random seeds: 5a79d3c3 d4b0c533
Thu Mar 13 21:41:39 2008 factoring 27312187167948796049898887842782596405655381943670578373120353781997447000328700858938482409418918448758778194857586271196003004729048486053340769161697167767956404785889687728602979284674332324623675660860406658739006337124213538943374972682241 (245 digits)
Thu Mar 13 21:41:42 2008 no P-1/P+1/ECM available, skipping
Thu Mar 13 21:41:42 2008 commencing number field sieve (245-digit input)
Thu Mar 13 21:41:42 2008 R0: -1393796574908163946345982392040522594123776
Thu Mar 13 21:41:42 2008 R1: 1
Thu Mar 13 21:41:42 2008 A0: -1
Thu Mar 13 21:41:42 2008 A1: 0
Thu Mar 13 21:41:42 2008 A2: 0
Thu Mar 13 21:41:42 2008 A3: 0
Thu Mar 13 21:41:42 2008 A4: 0
Thu Mar 13 21:41:42 2008 A5: 0
Thu Mar 13 21:41:42 2008 A6: 2
Thu Mar 13 21:41:42 2008 size score = 4.189742e-12, Murphy alpha = 2.413277, combined = 2.102509e-12
Thu Mar 13 21:41:42 2008
Thu Mar 13 21:41:42 2008 commencing square root phase
Thu Mar 13 21:41:42 2008 reading relations for dependency 1
Thu Mar 13 21:41:45 2008 read 6778074 cycles
Thu Mar 13 21:42:34 2008 cycles contain 21733920 unique relations
Thu Mar 13 21:58:59 2008 read 21733920 relations
Thu Mar 13 22:04:39 2008 multiplying 30208440 relations
Thu Mar 13 23:40:41 2008 multiply complete, coefficients have about 808.62 million bits
Thu Mar 13 23:40:54 2008 error: relation product is incorrect; if this is a debug binary, make sure that NDEBUG is not defined
Thu Mar 13 23:40:54 2008 algebraic square root failed
Thu Mar 13 23:40:54 2008 reading relations for dependency 2
Thu Mar 13 23:41:07 2008 read 6778294 cycles
Thu Mar 13 23:41:57 2008 cycles contain 21741379 unique relations
Thu Mar 13 23:56:52 2008 read 21741379 relations
Fri Mar 14 00:02:32 2008 multiplying 30220600 relations
Fri Mar 14 01:38:36 2008 multiply complete, coefficients have about 808.95 million bits
Fri Mar 14 01:38:48 2008 error: relation product is incorrect; if this is a debug binary, make sure that NDEBUG is not defined
Fri Mar 14 01:38:48 2008 algebraic square root failed
Fri Mar 14 01:38:48 2008 reading relations for dependency 3
Fri Mar 14 01:39:02 2008 read 6778113 cycles
Fri Mar 14 01:39:52 2008 cycles contain 21738263 unique relations
Fri Mar 14 01:55:02 2008 read 21738263 relations
Fri Mar 14 02:00:42 2008 multiplying 30216356 relations
Fri Mar 14 03:36:50 2008 multiply complete, coefficients have about 808.83 million bits
Fri Mar 14 03:37:02 2008 error: relation product is incorrect; if this is a debug binary, make sure that NDEBUG is not defined
Fri Mar 14 03:37:02 2008 algebraic square root failed
Fri Mar 14 03:37:02 2008 reading relations for dependency 4
Fri Mar 14 03:37:16 2008 read 6778859 cycles
Fri Mar 14 03:38:05 2008 cycles contain 21736172 unique relations
Fri Mar 14 03:53:30 2008 read 21736172 relations
Fri Mar 14 03:59:11 2008 multiplying 30215154 relations
Fri Mar 14 05:35:14 2008 multiply complete, coefficients have about 808.79 million bits
Fri Mar 14 05:35:27 2008 error: relation product is incorrect; if this is a debug binary, make sure that NDEBUG is not defined
Fri Mar 14 05:35:27 2008 algebraic square root failed

At me too such was with version 1.33. Use version 1.32.

Just for the records: successful 131 digits postprocessing (was c131 of HP782(81)) with 1.33

[code]Tue Mar 18 06:42:59 2008
Tue Mar 18 06:42:59 2008
Tue Mar 18 06:42:59 2008 Msieve v. 1.33
Tue Mar 18 06:42:59 2008 random seeds: 3d085994 57fd92d4
Tue Mar 18 06:42:59 2008 factoring 43222886169321329059036880032650709108733196405535056581042817111139574013523184223970207895448911636597349075156599534230820924243 (131 digits)
Tue Mar 18 06:43:00 2008 searching for 15-digit factors
Tue Mar 18 06:43:02 2008 commencing number field sieve (131-digit input)
Tue Mar 18 06:43:02 2008 R0: -19064967440603921797335263
Tue Mar 18 06:43:02 2008 R1: 63486192432329
Tue Mar 18 06:43:02 2008 A0: 86517693452891581716471954832800
Tue Mar 18 06:43:02 2008 A1: 826599889106007076977737118
Tue Mar 18 06:43:02 2008 A2: -10804596144270735568004
Tue Mar 18 06:43:02 2008 A3: -11580666747757990
Tue Mar 18 06:43:02 2008 A4: 191514913087
Tue Mar 18 06:43:02 2008 A5: 17160
Tue Mar 18 06:43:02 2008 size score = 1.095187e-013, Murphy alpha = -6.730026, combined = 1.032189e-012
Tue Mar 18 06:43:14 2008 restarting with 13505843 relations
Tue Mar 18 06:43:18 2008 added 3307 free relations
Tue Mar 18 06:43:18 2008
Tue Mar 18 06:43:18 2008 commencing relation filtering
Tue Mar 18 06:43:18 2008 commencing duplicate removal, pass 1
Tue Mar 18 06:46:13 2008 found 1911814 hash collisions in 13509148 relations
Tue Mar 18 06:46:13 2008 commencing duplicate removal, pass 2
Tue Mar 18 06:46:57 2008 found 1818184 duplicates and 11690964 unique relations
Tue Mar 18 06:46:57 2008 memory use: 65.3 MB
Tue Mar 18 06:47:01 2008 ignoring smallest 367531 rational and 368278 algebraic ideals
Tue Mar 18 06:47:01 2008 filtering rational ideals above 5294233
Tue Mar 18 06:47:01 2008 filtering algebraic ideals above 5294233
Tue Mar 18 06:47:01 2008 need 1250875 more relations than ideals
Tue Mar 18 06:47:01 2008 commencing singleton removal, pass 1
Tue Mar 18 06:49:46 2008 relations with 0 large ideals: 3037
Tue Mar 18 06:49:46 2008 relations with 1 large ideals: 178629
Tue Mar 18 06:49:46 2008 relations with 2 large ideals: 1323773
Tue Mar 18 06:49:46 2008 relations with 3 large ideals: 3625483
Tue Mar 18 06:49:46 2008 relations with 4 large ideals: 4363158
Tue Mar 18 06:49:46 2008 relations with 5 large ideals: 2035624
Tue Mar 18 06:49:46 2008 relations with 6 large ideals: 156156
Tue Mar 18 06:49:46 2008 relations with 7+ large ideals: 5104
Tue Mar 18 06:49:46 2008 11690964 relations and about 9685407 large ideals
Tue Mar 18 06:49:46 2008 commencing singleton removal, pass 2
Tue Mar 18 06:52:32 2008 found 3649185 singletons
Tue Mar 18 06:52:32 2008 current dataset: 8041779 relations and about 5662564 large ideals
Tue Mar 18 06:52:32 2008 commencing singleton removal, pass 3
Tue Mar 18 06:54:54 2008 found 542090 singletons
Tue Mar 18 06:54:54 2008 current dataset: 7499689 relations and about 5107285 large ideals
Tue Mar 18 06:54:54 2008 commencing singleton removal, pass 4
Tue Mar 18 06:57:11 2008 found 92584 singletons
Tue Mar 18 06:57:11 2008 current dataset: 7407105 relations and about 5014234 large ideals
Tue Mar 18 06:57:11 2008 commencing singleton removal, final pass
Tue Mar 18 06:59:35 2008 memory use: 155.1 MB
Tue Mar 18 06:59:35 2008 commencing in-memory singleton removal
Tue Mar 18 06:59:36 2008 begin with 7407105 relations and 5310239 unique ideals
Tue Mar 18 06:59:44 2008 reduce to 6995326 relations and 4894051 ideals in 9 passes
Tue Mar 18 06:59:44 2008 max relations containing the same ideal: 56
Tue Mar 18 06:59:50 2008 removing 1453446 relations and 1053446 ideals in 400000 cliques
Tue Mar 18 06:59:51 2008 commencing in-memory singleton removal
Tue Mar 18 06:59:52 2008 begin with 5541880 relations and 4894051 unique ideals
Tue Mar 18 06:59:55 2008 reduce to 5407136 relations and 3698117 ideals in 6 passes
Tue Mar 18 06:59:55 2008 max relations containing the same ideal: 47
Tue Mar 18 06:59:59 2008 removing 1130803 relations and 730803 ideals in 400000 cliques
Tue Mar 18 07:00:00 2008 commencing in-memory singleton removal
Tue Mar 18 07:00:00 2008 begin with 4276333 relations and 3698117 unique ideals
Tue Mar 18 07:00:03 2008 reduce to 4148372 relations and 2830542 ideals in 7 passes
Tue Mar 18 07:00:03 2008 max relations containing the same ideal: 37
Tue Mar 18 07:00:06 2008 removing 254415 relations and 187461 ideals in 66954 cliques
Tue Mar 18 07:00:07 2008 commencing in-memory singleton removal
Tue Mar 18 07:00:07 2008 begin with 3893957 relations and 2830542 unique ideals
Tue Mar 18 07:00:09 2008 reduce to 3887204 relations and 2636221 ideals in 4 passes
Tue Mar 18 07:00:09 2008 max relations containing the same ideal: 36
Tue Mar 18 07:00:12 2008 dataset has 70.0% excess relations
Tue Mar 18 07:00:15 2008 ignoring smallest 333170 rational and 333987 algebraic ideals
Tue Mar 18 07:00:15 2008 filtering rational ideals above 4764809
Tue Mar 18 07:00:15 2008 filtering algebraic ideals above 4764809
Tue Mar 18 07:00:15 2008 need 1125884 more relations than ideals
Tue Mar 18 07:00:15 2008 commencing singleton removal, final pass
Tue Mar 18 07:01:35 2008 memory use: 78.6 MB
Tue Mar 18 07:01:35 2008 commencing in-memory singleton removal
Tue Mar 18 07:01:35 2008 begin with 3887204 relations and 2704807 unique ideals
Tue Mar 18 07:01:38 2008 reduce to 3886580 relations and 2704183 ideals in 6 passes
Tue Mar 18 07:01:38 2008 max relations containing the same ideal: 36
Tue Mar 18 07:01:40 2008 removing 102225 relations and 73969 ideals in 28256 cliques
Tue Mar 18 07:01:40 2008 commencing in-memory singleton removal
Tue Mar 18 07:01:41 2008 begin with 3784355 relations and 2704183 unique ideals
Tue Mar 18 07:01:42 2008 reduce to 3782930 relations and 2628779 ideals in 4 passes
Tue Mar 18 07:01:42 2008 max relations containing the same ideal: 36
Tue Mar 18 07:01:44 2008 removing 92207 relations and 63951 ideals in 28256 cliques
Tue Mar 18 07:01:44 2008 commencing in-memory singleton removal
Tue Mar 18 07:01:44 2008 begin with 3690723 relations and 2628779 unique ideals
Tue Mar 18 07:01:46 2008 reduce to 3689335 relations and 2563430 ideals in 4 passes
Tue Mar 18 07:01:46 2008 max relations containing the same ideal: 36
Tue Mar 18 07:01:47 2008 dataset has 53.0% excess relations
Tue Mar 18 07:01:49 2008 ignoring smallest 298637 rational and 299396 algebraic ideals
Tue Mar 18 07:01:49 2008 filtering rational ideals above 4235386
Tue Mar 18 07:01:49 2008 filtering algebraic ideals above 4235386
Tue Mar 18 07:01:49 2008 need 900724 more relations than ideals
Tue Mar 18 07:01:49 2008 commencing singleton removal, final pass
Tue Mar 18 07:02:53 2008 memory use: 76.6 MB
Tue Mar 18 07:02:53 2008 commencing in-memory singleton removal
Tue Mar 18 07:02:54 2008 begin with 3689335 relations and 2632514 unique ideals
Tue Mar 18 07:02:55 2008 reduce to 3688830 relations and 2632009 ideals in 4 passes
Tue Mar 18 07:02:55 2008 max relations containing the same ideal: 36
Tue Mar 18 07:02:58 2008 removing 230657 relations and 152609 ideals in 78048 cliques
Tue Mar 18 07:02:58 2008 commencing in-memory singleton removal
Tue Mar 18 07:02:58 2008 begin with 3458173 relations and 2632009 unique ideals
Tue Mar 18 07:03:00 2008 reduce to 3450957 relations and 2472060 ideals in 5 passes
Tue Mar 18 07:03:00 2008 max relations containing the same ideal: 33
Tue Mar 18 07:03:02 2008 removing 228818 relations and 150770 ideals in 78048 cliques
Tue Mar 18 07:03:02 2008 commencing in-memory singleton removal
Tue Mar 18 07:03:02 2008 begin with 3222139 relations and 2472060 unique ideals
Tue Mar 18 07:03:04 2008 reduce to 3212412 relations and 2311369 ideals in 5 passes
Tue Mar 18 07:03:04 2008 max relations containing the same ideal: 32
Tue Mar 18 07:03:06 2008 dataset has 22.5% excess relations
Tue Mar 18 07:03:09 2008 ignoring smallest 263796 rational and 264642 algebraic ideals
Tue Mar 18 07:03:09 2008 filtering rational ideals above 3705963
Tue Mar 18 07:03:09 2008 filtering algebraic ideals above 3705963
Tue Mar 18 07:03:09 2008 need 794673 more relations than ideals
Tue Mar 18 07:03:09 2008 commencing singleton removal, final pass
Tue Mar 18 07:04:05 2008 memory use: 68.1 MB
Tue Mar 18 07:04:05 2008 commencing in-memory singleton removal
Tue Mar 18 07:04:05 2008 begin with 3212412 relations and 2380911 unique ideals
Tue Mar 18 07:04:07 2008 reduce to 3211899 relations and 2380398 ideals in 4 passes
Tue Mar 18 07:04:07 2008 max relations containing the same ideal: 32
Tue Mar 18 07:04:09 2008 removing 68550 relations and 50136 ideals in 18414 cliques
Tue Mar 18 07:04:09 2008 commencing in-memory singleton removal
Tue Mar 18 07:04:09 2008 begin with 3143349 relations and 2380398 unique ideals
Tue Mar 18 07:04:11 2008 reduce to 3142656 relations and 2329566 ideals in 4 passes
Tue Mar 18 07:04:11 2008 max relations containing the same ideal: 31
Tue Mar 18 07:04:12 2008 removing 59715 relations and 41301 ideals in 18414 cliques
Tue Mar 18 07:04:12 2008 commencing in-memory singleton removal
Tue Mar 18 07:04:13 2008 begin with 3082941 relations and 2329566 unique ideals
Tue Mar 18 07:04:14 2008 reduce to 3082380 relations and 2287702 ideals in 4 passes
Tue Mar 18 07:04:14 2008 max relations containing the same ideal: 31
Tue Mar 18 07:04:15 2008 dataset has 8.0% excess relations
Tue Mar 18 07:04:15 2008 relations with 0 large ideals: 2167
Tue Mar 18 07:04:15 2008 relations with 1 large ideals: 85369
Tue Mar 18 07:04:15 2008 relations with 2 large ideals: 472717
Tue Mar 18 07:04:15 2008 relations with 3 large ideals: 978271
Tue Mar 18 07:04:15 2008 relations with 4 large ideals: 947586
Tue Mar 18 07:04:15 2008 relations with 5 large ideals: 462670
Tue Mar 18 07:04:15 2008 relations with 6 large ideals: 116505
Tue Mar 18 07:04:15 2008 relations with 7+ large ideals: 17095
Tue Mar 18 07:04:15 2008 commencing 2-way merge
Tue Mar 18 07:04:18 2008 reduce to 2301851 relation sets and 1507173 unique ideals
Tue Mar 18 07:04:18 2008 commencing full merge
Tue Mar 18 07:04:55 2008 memory use: 137.8 MB
Tue Mar 18 07:04:55 2008 found 1201254 cycles, need 935373
Tue Mar 18 07:04:56 2008 weight of 935373 cycles is about 60842890 (65.05/cycle)
Tue Mar 18 07:04:56 2008 distribution of cycle lengths:
Tue Mar 18 07:04:56 2008 1 relations: 71062
Tue Mar 18 07:04:56 2008 2 relations: 106231
Tue Mar 18 07:04:56 2008 3 relations: 123181
Tue Mar 18 07:04:56 2008 4 relations: 126953
Tue Mar 18 07:04:56 2008 5 relations: 125832
Tue Mar 18 07:04:56 2008 6 relations: 117267
Tue Mar 18 07:04:56 2008 7 relations: 104114
Tue Mar 18 07:04:56 2008 8 relations: 87702
Tue Mar 18 07:04:56 2008 9 relations: 63710
Tue Mar 18 07:04:56 2008 10+ relations: 9321
Tue Mar 18 07:04:56 2008 heaviest cycle: 12 relations
Tue Mar 18 07:04:56 2008 commencing cycle optimization
Tue Mar 18 07:04:57 2008 start with 4590689 relations
Tue Mar 18 07:05:08 2008 pruned 87279 relations
Tue Mar 18 07:05:08 2008 memory use: 120.6 MB
Tue Mar 18 07:05:08 2008 distribution of cycle lengths:
Tue Mar 18 07:05:08 2008 1 relations: 71062
Tue Mar 18 07:05:08 2008 2 relations: 107888
Tue Mar 18 07:05:08 2008 3 relations: 127250
Tue Mar 18 07:05:08 2008 4 relations: 130820
Tue Mar 18 07:05:08 2008 5 relations: 130854
Tue Mar 18 07:05:08 2008 6 relations: 120941
Tue Mar 18 07:05:08 2008 7 relations: 105640
Tue Mar 18 07:05:08 2008 8 relations: 82824
Tue Mar 18 07:05:08 2008 9 relations: 51411
Tue Mar 18 07:05:08 2008 10+ relations: 6683
Tue Mar 18 07:05:08 2008 heaviest cycle: 12 relations
Tue Mar 18 07:05:10 2008
Tue Mar 18 07:05:10 2008 commencing linear algebra
Tue Mar 18 07:05:11 2008 read 935373 cycles
Tue Mar 18 07:05:13 2008 cycles contain 2394472 unique relations
Tue Mar 18 07:06:21 2008 read 2394472 relations
Tue Mar 18 07:06:25 2008 using 32 quadratic characters above 134215002
Tue Mar 18 07:06:52 2008 building initial matrix
Tue Mar 18 07:07:31 2008 memory use: 300.9 MB
Tue Mar 18 07:07:33 2008 read 935373 cycles
Tue Mar 18 07:07:57 2008 matrix is 934883 x 935373 (251.4 MB) with weight 90139280 (96.37/col)
Tue Mar 18 07:07:57 2008 sparse part has weight 58407509 (62.44/col)
Tue Mar 18 07:08:11 2008 filtering completed in 3 passes
Tue Mar 18 07:08:11 2008 matrix is 929498 x 929698 (250.4 MB) with weight 89759497 (96.55/col)
Tue Mar 18 07:08:11 2008 sparse part has weight 58213982 (62.62/col)
Tue Mar 18 07:08:28 2008 read 929698 cycles
Tue Mar 18 07:09:51 2008 matrix is 929498 x 929698 (250.4 MB) with weight 89759497 (96.55/col)
Tue Mar 18 07:09:54 2008 sparse part has weight 58213982 (62.62/col)
Tue Mar 18 07:09:54 2008 saving the first 48 matrix rows for later
Tue Mar 18 07:09:55 2008 matrix is 929450 x 929698 (242.0 MB) with weight 69029264 (74.25/col)
Tue Mar 18 07:09:55 2008 sparse part has weight 57857561 (62.23/col)
Tue Mar 18 07:09:55 2008 matrix includes 64 packed rows
Tue Mar 18 07:09:55 2008 using block size 65536 for processor cache size 4096 kB
Tue Mar 18 07:10:04 2008 commencing Lanczos iteration (2 threads)
Tue Mar 18 07:10:04 2008 memory use: 247.7 MB
Tue Mar 18 09:00:48 2008 lanczos halted after 14697 iterations (dim = 929448)
Tue Mar 18 09:00:50 2008 recovered 43 nontrivial dependencies
Tue Mar 18 09:00:51 2008
Tue Mar 18 09:00:51 2008 commencing square root phase
Tue Mar 18 09:00:51 2008 reading relations for dependency 1
Tue Mar 18 09:00:52 2008 read 464618 cycles
Tue Mar 18 09:00:53 2008 cycles contain 1464214 unique relations
Tue Mar 18 09:02:04 2008 read 1464214 relations
Tue Mar 18 09:02:16 2008 multiplying 2245242 relations
Tue Mar 18 09:10:54 2008 multiply complete, coefficients have about 113.04 million bits
Tue Mar 18 09:11:00 2008 initial square root is modulo 130015399
Tue Mar 18 09:25:03 2008 prp56 factor: 32954971892100042977799569415093678837254428701547341173
Tue Mar 18 09:25:03 2008 prp76 factor: 1311574056589704078537800777069018790782839890278845124803308140882436967591
Tue Mar 18 09:25:03 2008 elapsed time 02:42:04
[/code]

Just a guess: Could it be possible, that with huge postprocessing jobs (larger than mine) a variable is overflowing and thus causes these jobs to fail?

[quote=Andi47;129045]Just for the records: successful 131 digits postprocessing (was c131 of HP782(81)) with 1.33
Just a guess: Could it be possible, that with huge postprocessing jobs (larger than mine) a variable is overflowing and thus causes these jobs to fail?[/quote]

It is necessary to read through attentively conference simply.
Since # 409, and further to take version 1.32 and to start SQRT.
I already the fourth key rsa154 consider one and too occurs.
It is assured that all will turn out.
Success.

[QUOTE=miklin;129047]
Since # 409, and further to take version 1.32 and to start SQRT.
I already the fourth key rsa154 consider one and too occurs.
[/QUOTE]
Using the older version has not helped Richard, and at this point I am assuming the job is so large that the FFTs fail due to accumulated roundoff error. If that is true, the only solution is to use all-integer transforms.

[QUOTE=jasonp;129055]Using the older version has not helped Richard, and at this point I am assuming the job is so large that the FFTs fail due to accumulated roundoff error. If that is true, the only solution is to use all-integer transforms.[/QUOTE]

What about using a larger FFT size for larger jobs (like Prime95 does)?
And a roundoff error check (in debug mode, and also prior to doing the "real" calculations to decide whether to switch to a larger FFT size) could give you an answer to the question if the error is accumulated roundoff error or something else - if roundoff errors tend to be not far below 0.5 it is likely, that some of the roundoff errors are in fact somewhat above 0.5.

[quote=jasonp;129055]Using the older version has not helped Richard, and at this point I am assuming the job is so large that the FFTs fail due to accumulated roundoff error. If that is true, the only solution is to use all-integer transforms.[/quote]

Yes you are possible and the rights. To mine most easier to try hours 10 will borrow. As up to sqrt I use 1.33 version, and sqrt I do by version 1.32. You when have suggested it to try me I and itself were surprised. As it is new version on old to change. And all has earned. Why I do not know. Yes all the same the program fine works. The good fellow.

[QUOTE=Andi47;129056]What about using a larger FFT size for larger jobs (like Prime95 does)?
[/QUOTE]
The FFTs here are 30x larger than the ones used in Prime95, and previous experience shows that failure due to roundoff error is pretty much inevitable for convolution products above 512 megabits in size. We've tried switching to fewer bits per convolution element and it doesn't help. I'll do something about it when time allows.

[QUOTE=jasonp;129063]The FFTs here are 30x larger than the ones used in Prime95, and previous experience shows that failure due to roundoff error is pretty much inevitable for convolution products above 512 megabits in size.[/QUOTE]

Prime95 can handle 596 million bit numbers using an FFT size of 32M (about 17.75 bits per double).

Jason, another pair of data points: Mlucas' exponent limit for 28672Kdouble FFTs is 519932856, and for 30720K the limit is 556194824, which bracket your figure of 512 megabits [assuming by that you mean 512 *2^20.]

Are you using balanced digits for these?

You could try a Schönhage-Strassen multiplication on top of the complex FFT. A basic implementation should be very easy to write and yet would be sufficient to eliminate problems with input size. If your complex DWT for multiplication modulo (2^N+1) allows, say, N=2^20, you could use a transform length of 2^22 for Schönhage-Strassen and so should be able to multiply two numbers of up to 2^40 bits each.

[/shame][plug]In case you're interested, I know of a recent publication on the subject. :grin:[/plug][shame]

Alex

Ernst, the code does use balanced representation. I could possibly get an extra power of two by using a complete list of premultiplied twiddle factors, instead of the two-square-root-size-plus-one-multiply table as was used in the F24 code, but that would double the already excessive memory use.

Alex, I've read the paper and was quite impressed. Even easier than implementing Schonhage-Strassen is to make the large-integer portion of msieve depend on GMP :) A middle ground would be to implement something like the nice system of multi-prime NTTs with CRT reconstruction as used in GMP-ECM. It's been something I've wanted to do for a long time, and makes multithreading and saving intermediate results to disk very easy.