[QUOTE=fivemack;134572]To give some idea of the depth of the block-lanczos unparallelisability pit, frmky is not observing speedups with 2 cores over 1 on his matrix, and I get a factor 1.6 on a fairly small matrix with 4 cores over 1.[/QUOTE]Experiments I ran at MSR suggested a scalability of about sqrt(N) for parallel block Lanczos on N processors. A 30-cpu cluster, arranged as a 5x6 torus, was about 5 times faster than a single processor.

I agree this isn't that impressive and that a linear scaling would be wonderful. Nonetheless, it allows us to solver bigger matrices than would be possible on relatively inexpensive hardware. For reasonable values of N, under a few hundred say, it's cost-effective.

The memory layout was reasonable too --- 2GB on each 32-bit address space --- allowed much bigger matrices to be stored than would be possible on a single 32-bit machine. Now that commodity processors have up to 48-bit physical address spaces that may be less of an issue, though filling them remains expensive.


Paul

1/sqrt(N) is what I'd have expected theoretically - the inter-machine communication scales like that, since the length of vector on each machine scales like that, and unless your network is excessively good the communication is the expensive part. It's good to know that it works like that in practice too.

I was hoping for better on a quad-core since the 'network' tying the cores together is excessively good; I ought to apply some profiling tools, though I suspect the hotspot will be the line loading the next matrix entry, and I'd guess that memory bandwidth is saturated.

I seem to recall the Aoki group either doing or proposing something interesting with multi-port network cards and a network topology corresponding to the matrix-multiply communication pattern: the machine at coordinates X,Y needs to communicate only with machines in its row or column, so with two cards in each machine you can build a physical torus and then you don't need a switch. Did MSR use that trick, or a pre-existing cluster which had a switch already?

sqrt(N) is exciting when the matrix doesn't fit on your individual computers; but to do one matrix on four computers in three months rather than four matrices on four computers in six months isn't obviously the trade-off to make if they're the only four computers you've got.

I don't know whether it's easier to get through a proposal to use 144 already-bought cluster nodes for a month or to get a 32GB machine that will sit humming away in your office for a year; depends on status and the time of the financial year, I fear.

[QUOTE=xilman;134588]Experiments I ran at MSR suggested a scalability of about sqrt(N) for parallel block Lanczos on N processors. A 30-cpu cluster, arranged as a 5x6 torus, was about 5 times faster than a single processor.
[/QUOTE]

I would be very happy with that scaling. :smile: As it is now, the best for msieve on this 8-way 32-core computer is to run a single thread on a quad-core cpu by itself, setting it to use the largest cache block Jason's code allows, and allowing the other 3 cores to idle. Putting a second thread on the same CPU, no matter how the cache is arranged, slows it down. Running any other code on the same CPU also slows it down. Putting a second thread on a second CPU does speed it by about 10%, but that's not efficient. So, for now, I'm stuck running up to 8 simultaneous matrices for months, or at least until someone else needs to run something.

We'll soon have a small 10-computer Xeon quadcore Beowulf come online as part of a student project. Hopefully, that will benefit at least somewhat from running 4 threads...

Greg

[QUOTE=frmky;133272] ... The factorization of 12,241- has been completed.
[CODE]
12,241- (C260) = P66 * P194 ...[/CODE]

Bruce completed the ECM pretesting, I did the sieving, and Richard completed the post-processing. A 18.7M^2 matrix was generated and solved successfully. Richard reports that each square root step took about 8 hours, and the factors were found on the third dependency.

Here's the log of the linear algebra & square root steps:
[CODE]Sat Mar 22 01:08:41 2008 commencing linear algebra
Sat Mar 22 01:42:32 2008 building initial matrix
Sat Mar 22 02:26:17 2008 memory use: 6947.3 MB


Sat Mar 22 03:40:43 2008 matrix is 18720804 x 18721052 (5170.3 MB)
with weight 1285924286 (68.69/col)
Sat Mar 22 03:40:43 2008 sparse part has weight 1168145840 (62.40/col)
Sat Mar 22 03:40:43 2008 matrix includes 64 packed rows
Sat Mar 22 03:40:43 2008 using block size 65536 for processor cache
size 4096 kB
Sat Mar 22 03:52:30 2008 commencing Lanczos iteration (4 threads)
Sat Mar 22 03:52:31 2008 memory use: 5547.0 MB
...
Sun May 11 09:27:07 2008 commencing square root phase

Mon May 12 01:06:39 2008 reading relations for dependency 3
Mon May 12 01:07:15 2008 read 9362213 cycles
Mon May 12 01:08:54 2008 cycles contain 32407242 unique relations
Mon May 12 01:30:10 2008 read 32407242 relations
Mon May 12 01:41:20 2008 multiplying 42565700 relations
Mon May 12 04:13:58 2008 multiply complete, coefficients have about
1247.77 million bits
Mon May 12 04:14:25 2008 initial square root is modulo 395611
Mon May 12 09:01:24 2008 prp66 factor:
146879693270660089750065267283010036196682888164682484908678010533
Mon May 12 09:01:24 2008 prp194 factor:
74873107005826461027456840546732017985015839954333825384171460000132499197947734733564329519019603384125346864931519118660986264214961894702863522511201474023708838835354065426450679143708619097
Mon May 12 09:01:24 2008 elapsed time 23:34:20
[/CODE]

Greg[/QUOTE]

Here's 3,536+ c252, which factors as p108*p145 (not an ecm miss!).

[code]
Tue May 27 19:04:01 2008 Msieve v. 1.34
Tue May 27 19:04:01 2008 random seeds: c36751e5 fbff4d69
Tue May 27 19:04:01 2008 factoring 83168008783809316984269306068203448882701078
27518469566923762129753469173952539291575391529776290331560272226037943866861592
46977482486643272231623920710912250092052140352331717544541894673049300930736641
326744186807051373092187580901751625527989694881 (252 digits)
Tue May 27 19:04:04 2008 no P-1/P+1/ECM available, skipping
Tue May 27 19:04:04 2008 commencing number field sieve (252-digit input)
Tue May 27 19:04:04 2008 R0: -2909321189362570808630465826492242446680483
Tue May 27 19:04:04 2008 R1: 1
Tue May 27 19:04:04 2008 A0: 1
Tue May 27 19:04:04 2008 A1: 0
Tue May 27 19:04:04 2008 A2: 0
Tue May 27 19:04:04 2008 A3: 0
Tue May 27 19:04:04 2008 A4: 0
Tue May 27 19:04:04 2008 A5: 0
Tue May 27 19:04:04 2008 A6: 9
Tue May 27 19:04:04 2008 size score = 2.387439e-12, Murphy alpha = 1.425790, co
mbined = 1.588599e-12
Tue May 27 19:04:04 2008
Tue May 27 19:04:04 2008 commencing square root phase
Tue May 27 19:04:04 2008 reading relations for dependency 1
Tue May 27 19:04:17 2008 read 7117913 cycles
Tue May 27 19:04:46 2008
Tue May 27 19:04:46 2008
Tue May 27 19:04:46 2008 Msieve v. 1.34
Tue May 27 19:04:46 2008 random seeds: dd1965a0 0ed1772a
Tue May 27 19:04:46 2008 factoring ...
...
Tue May 27 19:04:49 2008 commencing square root phase
Tue May 27 19:04:49 2008 reading relations for dependency 3
Tue May 27 19:05:37 2008
Tue May 27 19:05:37 2008
Tue May 27 19:05:37 2008 Msieve v. 1.34
Tue May 27 19:05:37 2008 random seeds: 373a08aa 55b35188
Tue May 27 19:05:37 2008 factoring ...
...
Tue May 27 19:05:40 2008 commencing square root phase
Tue May 27 19:05:40 2008 reading relations for dependency 5
Tue May 27 19:05:48 2008 cycles contain 23117957 unique relations
Tue May 27 19:06:06 2008 read 7113593 cycles
Tue May 27 19:06:10 2008 read 7117957 cycles
Tue May 27 19:08:10 2008 cycles contain 23122564 unique relations
Tue May 27 19:08:13 2008 cycles contain 23114684 unique relations
Tue May 27 19:26:58 2008 read 23122564 relations
Tue May 27 19:29:20 2008 read 23114684 relations
Tue May 27 19:30:19 2008 read 23117957 relations
Tue May 27 19:36:35 2008 multiplying 31817592 relations
Tue May 27 19:37:39 2008 multiplying 31806926 relations
Tue May 27 19:38:12 2008 multiplying 31811244 relations
Tue May 27 21:44:14 2008 multiply complete, coefficients have
about 918.77 million bits
Tue May 27 21:44:53 2008 initial square root is modulo 174873547
Tue May 27 22:37:16 2008 multiply complete, coefficients have
about 918.65 million bits
Tue May 27 22:37:42 2008 initial square root is modulo 174444847
Tue May 27 23:03:42 2008 multiply complete, coefficients have
about 918.96 million bits
Tue May 27 23:04:07 2008 initial square root is modulo 175552543
Wed May 28 02:50:55 2008 reading relations for dependency 2
Wed May 28 02:51:03 2008 read 7112914 cycles
Wed May 28 02:52:16 2008 cycles contain 23113644 unique relations
Wed May 28 02:52:32 2008 prp108 factor: 265591638400651141553717281127342456935
823290520029527212347607997785631781314085389028014657466589507185729
Wed May 28 02:52:32 2008 prp145 factor: 313142421518362894896720692414981480884
74906503734383217232267264307789986714150398808485936780724596171367289905259225
23514851174865635120885089
Wed May 28 02:52:32 2008 elapsed time 07:47:46
[/code]

The fifth dependency also failed. The number is easier, and the
dependencies are lighter than for 12,241- c260. -Bruce:smile:

[QUOTE=frmky;133877]Jason,

Here's the output of another large filtering job, 2,949+. Since msieve doesn't thread well on this 8-way quadcore computer I planned to move the matrix to a Core 2 quadcore, but it doesn't fit in 4GB of memory. We will have to do more sieving to get it to fit.

[/QUOTE]

After more sieving, 2,949+ still doesn't fit in 4GB, but at least the time to LA completion has dropped from 6 months to 3 months. That's a number I'm willing to live with. :smile:

[CODE]Sun Jun 1 19:17:51 2008 Msieve v. 1.36
Sun Jun 1 19:17:51 2008 random seeds: 647ccb69 c3852382
Sun Jun 1 19:17:51 2008 factoring 159536541640850482041472347398588297507700248827866272054279599480424280767338982697579495258848375150153519055443517739141989106990625338794428717145409749815953116707251616361046680221057 (189 digits)
Sun Jun 1 19:17:53 2008 no P-1/P+1/ECM available, skipping
Sun Jun 1 19:17:53 2008 commencing number field sieve (189-digit input)
Sun Jun 1 19:17:53 2008 R0: -89202980794122492566142873090593446023921665
Sun Jun 1 19:17:53 2008 R1: 9444732965739290427392
Sun Jun 1 19:17:53 2008 A0: -1
Sun Jun 1 19:17:53 2008 A1: -3
Sun Jun 1 19:17:53 2008 A2: 6
Sun Jun 1 19:17:53 2008 A3: 4
Sun Jun 1 19:17:53 2008 A4: -5
Sun Jun 1 19:17:53 2008 A5: -1
Sun Jun 1 19:17:53 2008 A6: 1
Sun Jun 1 19:17:53 2008 size score = 1.795073e-12, Murphy alpha = 3.125762, combined = 7.348938e-13
Sun Jun 1 19:19:02 2008 restarting with 192941124 relations
Sun Jun 1 19:19:02 2008
Sun Jun 1 19:19:02 2008 commencing relation filtering
Sun Jun 1 19:19:02 2008 commencing duplicate removal, pass 1
... snipped relation errors ...
Sun Jun 1 19:55:33 2008 found 45297067 hash collisions in 192940270 relations
Sun Jun 1 19:55:33 2008 commencing duplicate removal, pass 2
Sun Jun 1 20:21:39 2008 found 1 duplicates and 192940269 unique relations
Sun Jun 1 20:21:39 2008 memory use: 1911.0 MB
Sun Jun 1 20:23:04 2008 ignoring smallest 6177478 rational and 6177931 algebraic ideals
Sun Jun 1 20:23:04 2008 filtering rational ideals above 107675648
Sun Jun 1 20:23:04 2008 filtering algebraic ideals above 107675648
Sun Jun 1 20:23:04 2008 need 18533113 more relations than ideals
Sun Jun 1 20:23:04 2008 commencing singleton removal, pass 1
Sun Jun 1 21:01:55 2008 relations with 0 large ideals: 1664948
Sun Jun 1 21:01:55 2008 relations with 1 large ideals: 11683523
Sun Jun 1 21:01:55 2008 relations with 2 large ideals: 37358163
Sun Jun 1 21:01:55 2008 relations with 3 large ideals: 63292886
Sun Jun 1 21:01:55 2008 relations with 4 large ideals: 56895693
Sun Jun 1 21:01:55 2008 relations with 5 large ideals: 22045056
Sun Jun 1 21:01:55 2008 relations with 6 large ideals: 0
Sun Jun 1 21:01:55 2008 relations with 7+ large ideals: 0
Sun Jun 1 21:01:55 2008 192940269 relations and about 95583338 large ideals
Sun Jun 1 21:01:55 2008 commencing singleton removal, pass 2
Sun Jun 1 21:40:44 2008 found 14423906 singletons
Sun Jun 1 21:40:44 2008 current dataset: 178516363 relations and about 80730295 large ideals
Sun Jun 1 21:40:44 2008 commencing singleton removal, pass 3
Sun Jun 1 22:16:59 2008 relations with 0 large ideals: 1664948
Sun Jun 1 22:16:59 2008 relations with 1 large ideals: 11381179
Sun Jun 1 22:16:59 2008 relations with 2 large ideals: 35478301
Sun Jun 1 22:16:59 2008 relations with 3 large ideals: 58703264
Sun Jun 1 22:16:59 2008 relations with 4 large ideals: 51641221
Sun Jun 1 22:16:59 2008 relations with 5 large ideals: 19647450
Sun Jun 1 22:16:59 2008 relations with 6 large ideals: 0
Sun Jun 1 22:16:59 2008 relations with 7+ large ideals: 0
Sun Jun 1 22:16:59 2008 178516363 relations and about 114546610 large ideals
Sun Jun 1 22:16:59 2008 commencing singleton removal, pass 4
Sun Jun 1 22:53:16 2008 found 21874235 singletons
Sun Jun 1 22:53:16 2008 current dataset: 156642128 relations and about 91568659 large ideals
Sun Jun 1 22:53:16 2008 commencing singleton removal, pass 5
Sun Jun 1 23:25:32 2008 relations with 0 large ideals: 1664948
Sun Jun 1 23:25:32 2008 relations with 1 large ideals: 10878333
Sun Jun 1 23:25:32 2008 relations with 2 large ideals: 32476751
Sun Jun 1 23:25:32 2008 relations with 3 large ideals: 51635591
Sun Jun 1 23:25:32 2008 relations with 4 large ideals: 43812757
Sun Jun 1 23:25:32 2008 relations with 5 large ideals: 16173748
Sun Jun 1 23:25:32 2008 relations with 6 large ideals: 0
Sun Jun 1 23:25:32 2008 relations with 7+ large ideals: 0
Sun Jun 1 23:25:32 2008 156642128 relations and about 111213433 large ideals
Sun Jun 1 23:25:32 2008 commencing singleton removal, pass 6
Sun Jun 1 23:57:54 2008 found 17122305 singletons
Sun Jun 1 23:57:54 2008 current dataset: 139519823 relations and about 93329979 large ideals
Sun Jun 1 23:57:54 2008 commencing singleton removal, pass 7
Mon Jun 2 00:26:54 2008 found 3495691 singletons
Mon Jun 2 00:26:54 2008 current dataset: 136024132 relations and about 89797966 large ideals
Mon Jun 2 00:26:54 2008 commencing singleton removal, pass 8
Mon Jun 2 00:55:12 2008 found 620259 singletons
Mon Jun 2 00:55:12 2008 current dataset: 135403873 relations and about 89176512 large ideals
Mon Jun 2 00:55:12 2008 commencing singleton removal, pass 9
Mon Jun 2 01:23:24 2008 found 102472 singletons
Mon Jun 2 01:23:24 2008 current dataset: 135301401 relations and about 89074002 large ideals
Mon Jun 2 01:23:24 2008 commencing singleton removal, final pass
Mon Jun 2 02:03:00 2008 memory use: 2605.8 MB
Mon Jun 2 02:03:01 2008 commencing in-memory singleton removal
Mon Jun 2 02:03:34 2008 begin with 135301401 relations and 101526579 unique ideals
Mon Jun 2 02:12:02 2008 reduce to 126610758 relations and 92713502 ideals in 13 passes
Mon Jun 2 02:12:02 2008 max relations containing the same ideal: 38
Mon Jun 2 02:14:58 2008 removing 3423500 relations and 3023500 ideals in 400000 cliques
Mon Jun 2 02:15:03 2008 commencing in-memory singleton removal
Mon Jun 2 02:15:33 2008 begin with 123187258 relations and 92713502 unique ideals
Mon Jun 2 02:19:51 2008 reduce to 123139731 relations and 89642279 ideals in 7 passes
Mon Jun 2 02:19:51 2008 max relations containing the same ideal: 36
Mon Jun 2 02:22:31 2008 removing 2580275 relations and 2180275 ideals in 400000 cliques
Mon Jun 2 02:22:35 2008 commencing in-memory singleton removal
Mon Jun 2 02:23:04 2008 begin with 120559456 relations and 89642279 unique ideals
Mon Jun 2 02:26:39 2008 reduce to 120529782 relations and 87432232 ideals in 6 passes
Mon Jun 2 02:26:39 2008 max relations containing the same ideal: 36
Mon Jun 2 02:29:15 2008 removing 2302241 relations and 1902241 ideals in 400000 cliques
Mon Jun 2 02:29:19 2008 commencing in-memory singleton removal
Mon Jun 2 02:29:47 2008 begin with 118227541 relations and 87432232 unique ideals
Mon Jun 2 02:33:16 2008 reduce to 118202947 relations and 85505320 ideals in 6 passes
Mon Jun 2 02:33:16 2008 max relations containing the same ideal: 36
Mon Jun 2 02:35:47 2008 removing 2135737 relations and 1735737 ideals in 400000 cliques
Mon Jun 2 02:35:52 2008 commencing in-memory singleton removal
Mon Jun 2 02:36:19 2008 begin with 116067210 relations and 85505320 unique ideals
Mon Jun 2 02:40:17 2008 reduce to 116045014 relations and 83747306 ideals in 7 passes
Mon Jun 2 02:40:17 2008 max relations containing the same ideal: 35
Mon Jun 2 02:42:45 2008 removing 2025825 relations and 1625825 ideals in 400000 cliques
Mon Jun 2 02:42:49 2008 commencing in-memory singleton removal
Mon Jun 2 02:43:15 2008 begin with 114019189 relations and 83747306 unique ideals
Mon Jun 2 02:47:08 2008 reduce to 113999598 relations and 82101815 ideals in 7 passes
Mon Jun 2 02:47:08 2008 max relations containing the same ideal: 35
Mon Jun 2 02:49:32 2008 removing 1936439 relations and 1536439 ideals in 400000 cliques
Mon Jun 2 02:49:36 2008 commencing in-memory singleton removal
Mon Jun 2 02:50:02 2008 begin with 112063159 relations and 82101815 unique ideals
Mon Jun 2 02:53:16 2008 reduce to 112044483 relations and 80546633 ideals in 6 passes
Mon Jun 2 02:53:16 2008 max relations containing the same ideal: 35
Mon Jun 2 02:55:38 2008 removing 1864602 relations and 1464602 ideals in 400000 cliques
Mon Jun 2 02:55:42 2008 commencing in-memory singleton removal
Mon Jun 2 02:56:07 2008 begin with 110179881 relations and 80546633 unique ideals
Mon Jun 2 02:58:45 2008 reduce to 110161629 relations and 79063720 ideals in 5 passes
Mon Jun 2 02:58:45 2008 max relations containing the same ideal: 35
Mon Jun 2 03:01:03 2008 removing 1814805 relations and 1414805 ideals in 400000 cliques
Mon Jun 2 03:01:07 2008 commencing in-memory singleton removal
Mon Jun 2 03:01:31 2008 begin with 108346824 relations and 79063720 unique ideals
Mon Jun 2 03:04:06 2008 reduce to 108329136 relations and 77631180 ideals in 5 passes
Mon Jun 2 03:04:06 2008 max relations containing the same ideal: 34
Mon Jun 2 03:06:21 2008 removing 1759405 relations and 1359405 ideals in 400000 cliques
Mon Jun 2 03:06:25 2008 commencing in-memory singleton removal
Mon Jun 2 03:06:49 2008 begin with 106569731 relations and 77631180 unique ideals
Mon Jun 2 03:09:21 2008 reduce to 106552900 relations and 76254879 ideals in 5 passes
Mon Jun 2 03:09:21 2008 max relations containing the same ideal: 34
Mon Jun 2 03:11:34 2008 removing 1722332 relations and 1322332 ideals in 400000 cliques
Mon Jun 2 03:11:38 2008 commencing in-memory singleton removal
Mon Jun 2 03:12:01 2008 begin with 104830568 relations and 76254879 unique ideals
Mon Jun 2 03:14:30 2008 reduce to 104814420 relations and 74916339 ideals in 5 passes
Mon Jun 2 03:14:30 2008 max relations containing the same ideal: 34
Mon Jun 2 03:16:40 2008 removing 1686820 relations and 1286820 ideals in 400000 cliques
Mon Jun 2 03:16:43 2008 commencing in-memory singleton removal
Mon Jun 2 03:17:06 2008 begin with 103127600 relations and 74916339 unique ideals
Mon Jun 2 03:19:32 2008 reduce to 103111631 relations and 73613510 ideals in 5 passes
Mon Jun 2 03:19:32 2008 max relations containing the same ideal: 34
Mon Jun 2 03:21:40 2008 removing 1659293 relations and 1259293 ideals in 400000 cliques
Mon Jun 2 03:21:44 2008 commencing in-memory singleton removal
Mon Jun 2 03:22:06 2008 begin with 101452338 relations and 73613510 unique ideals
Mon Jun 2 03:24:28 2008 reduce to 101436041 relations and 72337868 ideals in 5 passes
Mon Jun 2 03:24:28 2008 max relations containing the same ideal: 34
Mon Jun 2 03:26:33 2008 removing 1621092 relations and 1221092 ideals in 400000 cliques
Mon Jun 2 03:26:36 2008 commencing in-memory singleton removal
Mon Jun 2 03:26:59 2008 begin with 99814949 relations and 72337868 unique ideals
Mon Jun 2 03:29:19 2008 reduce to 99797652 relations and 71099412 ideals in 5 passes
Mon Jun 2 03:29:19 2008 max relations containing the same ideal: 33
Mon Jun 2 03:31:22 2008 removing 1622058 relations and 1222058 ideals in 400000 cliques
Mon Jun 2 03:31:25 2008 commencing in-memory singleton removal
Mon Jun 2 03:31:47 2008 begin with 98175594 relations and 71099412 unique ideals
Mon Jun 2 03:34:03 2008 reduce to 98161944 relations and 69863660 ideals in 5 passes
Mon Jun 2 03:34:03 2008 max relations containing the same ideal: 33
Mon Jun 2 03:36:03 2008 removing 1574026 relations and 1174026 ideals in 400000 cliques
Mon Jun 2 03:36:07 2008 commencing in-memory singleton removal
Mon Jun 2 03:36:28 2008 begin with 96587918 relations and 69863660 unique ideals
Mon Jun 2 03:38:42 2008 reduce to 96573216 relations and 68674881 ideals in 5 passes
Mon Jun 2 03:38:42 2008 max relations containing the same ideal: 33
Mon Jun 2 03:40:39 2008 removing 1555136 relations and 1155136 ideals in 400000 cliques
Mon Jun 2 03:40:42 2008 commencing in-memory singleton removal
Mon Jun 2 03:41:03 2008 begin with 95018080 relations and 68674881 unique ideals
Mon Jun 2 03:43:15 2008 reduce to 95002386 relations and 67503990 ideals in 5 passes
Mon Jun 2 03:43:15 2008 max relations containing the same ideal: 33
Mon Jun 2 03:45:10 2008 removing 1545868 relations and 1145868 ideals in 400000 cliques
Mon Jun 2 03:45:13 2008 commencing in-memory singleton removal
Mon Jun 2 03:45:33 2008 begin with 93456518 relations and 67503990 unique ideals
Mon Jun 2 03:47:42 2008 reduce to 93441019 relations and 66342573 ideals in 5 passes
Mon Jun 2 03:47:42 2008 max relations containing the same ideal: 32
Mon Jun 2 03:49:35 2008 removing 1527738 relations and 1127738 ideals in 400000 cliques
Mon Jun 2 03:49:38 2008 commencing in-memory singleton removal
Mon Jun 2 03:49:58 2008 begin with 91913281 relations and 66342573 unique ideals
Mon Jun 2 03:52:04 2008 reduce to 91897941 relations and 65199447 ideals in 5 passes
Mon Jun 2 03:52:04 2008 max relations containing the same ideal: 32
Mon Jun 2 03:53:54 2008 removing 1513413 relations and 1113413 ideals in 400000 cliques
Mon Jun 2 03:53:57 2008 commencing in-memory singleton removal
Mon Jun 2 03:54:17 2008 begin with 90384528 relations and 65199447 unique ideals
Mon Jun 2 03:56:20 2008 reduce to 90368982 relations and 64070419 ideals in 5 passes
Mon Jun 2 03:56:20 2008 max relations containing the same ideal: 32
Mon Jun 2 03:58:08 2008 removing 1490387 relations and 1090387 ideals in 400000 cliques
Mon Jun 2 03:58:12 2008 commencing in-memory singleton removal
Mon Jun 2 03:58:31 2008 begin with 88878595 relations and 64070419 unique ideals
Mon Jun 2 04:00:32 2008 reduce to 88861957 relations and 62963335 ideals in 5 passes
Mon Jun 2 04:00:32 2008 max relations containing the same ideal: 32
Mon Jun 2 04:02:18 2008 removing 1473569 relations and 1073569 ideals in 400000 cliques
Mon Jun 2 04:02:21 2008 commencing in-memory singleton removal
Mon Jun 2 04:02:40 2008 begin with 87388388 relations and 62963335 unique ideals
Mon Jun 2 04:04:37 2008 reduce to 87370740 relations and 61872047 ideals in 5 passes
Mon Jun 2 04:04:37 2008 max relations containing the same ideal: 32
Mon Jun 2 04:06:22 2008 removing 1472098 relations and 1072098 ideals in 400000 cliques
Mon Jun 2 04:06:25 2008 commencing in-memory singleton removal
Mon Jun 2 04:06:43 2008 begin with 85898642 relations and 61872047 unique ideals
Mon Jun 2 04:08:39 2008 reduce to 85882808 relations and 60784047 ideals in 5 passes
Mon Jun 2 04:08:39 2008 max relations containing the same ideal: 32
Mon Jun 2 04:10:21 2008 removing 1454122 relations and 1054122 ideals in 400000 cliques
Mon Jun 2 04:10:24 2008 commencing in-memory singleton removal
Mon Jun 2 04:10:42 2008 begin with 84428686 relations and 60784047 unique ideals
Mon Jun 2 04:12:58 2008 reduce to 84413523 relations and 59714681 ideals in 6 passes
Mon Jun 2 04:12:58 2008 max relations containing the same ideal: 32
Mon Jun 2 04:14:37 2008 removing 1433278 relations and 1033278 ideals in 400000 cliques
Mon Jun 2 04:14:40 2008 commencing in-memory singleton removal
Mon Jun 2 04:14:58 2008 begin with 82980245 relations and 59714681 unique ideals
Mon Jun 2 04:16:49 2008 reduce to 82964032 relations and 58665115 ideals in 5 passes
Mon Jun 2 04:16:49 2008 max relations containing the same ideal: 32
Mon Jun 2 04:18:27 2008 removing 1431268 relations and 1031268 ideals in 400000 cliques
Mon Jun 2 04:18:29 2008 commencing in-memory singleton removal
Mon Jun 2 04:18:47 2008 begin with 81532764 relations and 58665115 unique ideals
Mon Jun 2 04:20:13 2008 reduce to 81516884 relations and 57617892 ideals in 4 passes
Mon Jun 2 04:20:13 2008 max relations containing the same ideal: 31
Mon Jun 2 04:21:49 2008 removing 1422202 relations and 1022202 ideals in 400000 cliques
Mon Jun 2 04:21:52 2008 commencing in-memory singleton removal
Mon Jun 2 04:22:09 2008 begin with 80094682 relations and 57617892 unique ideals
Mon Jun 2 04:23:54 2008 reduce to 80078274 relations and 56579203 ideals in 5 passes
Mon Jun 2 04:23:54 2008 max relations containing the same ideal: 31
Mon Jun 2 04:25:28 2008 removing 1409819 relations and 1009819 ideals in 400000 cliques
Mon Jun 2 04:25:31 2008 commencing in-memory singleton removal
Mon Jun 2 04:25:47 2008 begin with 78668455 relations and 56579203 unique ideals
Mon Jun 2 04:27:31 2008 reduce to 78651156 relations and 55551983 ideals in 5 passes
Mon Jun 2 04:27:31 2008 max relations containing the same ideal: 31
Mon Jun 2 04:29:03 2008 removing 1400578 relations and 1000578 ideals in 400000 cliques
Mon Jun 2 04:29:06 2008 commencing in-memory singleton removal
Mon Jun 2 04:29:22 2008 begin with 77250578 relations and 55551983 unique ideals
Mon Jun 2 04:31:03 2008 reduce to 77232545 relations and 54533260 ideals in 5 passes
Mon Jun 2 04:31:03 2008 max relations containing the same ideal: 31
Mon Jun 2 04:32:33 2008 removing 1406523 relations and 1006523 ideals in 400000 cliques
Mon Jun 2 04:32:36 2008 commencing in-memory singleton removal
Mon Jun 2 04:32:51 2008 begin with 75826022 relations and 54533260 unique ideals
Mon Jun 2 04:34:30 2008 reduce to 75808989 relations and 53509606 ideals in 5 passes
Mon Jun 2 04:34:30 2008 max relations containing the same ideal: 31
Mon Jun 2 04:35:58 2008 removing 1395940 relations and 995940 ideals in 400000 cliques
Mon Jun 2 04:36:01 2008 commencing in-memory singleton removal
Mon Jun 2 04:36:17 2008 begin with 74413049 relations and 53509606 unique ideals
Mon Jun 2 04:37:53 2008 reduce to 74396070 relations and 52496602 ideals in 5 passes
Mon Jun 2 04:37:53 2008 max relations containing the same ideal: 31
Mon Jun 2 04:39:19 2008 removing 1387639 relations and 987639 ideals in 400000 cliques
Mon Jun 2 04:39:21 2008 commencing in-memory singleton removal
Mon Jun 2 04:39:36 2008 begin with 73008431 relations and 52496602 unique ideals
Mon Jun 2 04:41:11 2008 reduce to 72991100 relations and 51491524 ideals in 5 passes
Mon Jun 2 04:41:11 2008 max relations containing the same ideal: 30
Mon Jun 2 04:42:35 2008 removing 1381133 relations and 981133 ideals in 400000 cliques
Mon Jun 2 04:42:38 2008 commencing in-memory singleton removal
Mon Jun 2 04:42:52 2008 begin with 71609967 relations and 51491524 unique ideals
Mon Jun 2 04:44:24 2008 reduce to 71592325 relations and 50492630 ideals in 5 passes
Mon Jun 2 04:44:24 2008 max relations containing the same ideal: 30
Mon Jun 2 04:45:47 2008 removing 1370087 relations and 970087 ideals in 400000 cliques
Mon Jun 2 04:45:49 2008 commencing in-memory singleton removal
Mon Jun 2 04:46:04 2008 begin with 70222238 relations and 50492630 unique ideals
Mon Jun 2 04:47:33 2008 reduce to 70203024 relations and 49503184 ideals in 5 passes
Mon Jun 2 04:47:33 2008 max relations containing the same ideal: 29
Mon Jun 2 04:48:54 2008 removing 1375142 relations and 975142 ideals in 400000 cliques
Mon Jun 2 04:48:56 2008 commencing in-memory singleton removal
Mon Jun 2 04:49:10 2008 begin with 68827882 relations and 49503184 unique ideals
Mon Jun 2 04:50:38 2008 reduce to 68808681 relations and 48508721 ideals in 5 passes
Mon Jun 2 04:50:38 2008 max relations containing the same ideal: 28
Mon Jun 2 04:51:57 2008 removing 1367315 relations and 967315 ideals in 400000 cliques
Mon Jun 2 04:51:59 2008 commencing in-memory singleton removal
Mon Jun 2 04:52:13 2008 begin with 67441366 relations and 48508721 unique ideals
Mon Jun 2 04:53:38 2008 reduce to 67421776 relations and 47521657 ideals in 5 passes
Mon Jun 2 04:53:38 2008 max relations containing the same ideal: 27
Mon Jun 2 04:54:55 2008 removing 1362284 relations and 962284 ideals in 400000 cliques
Mon Jun 2 04:54:57 2008 commencing in-memory singleton removal
Mon Jun 2 04:55:10 2008 begin with 66059492 relations and 47521657 unique ideals
Mon Jun 2 04:56:34 2008 reduce to 66039794 relations and 46539513 ideals in 5 passes
Mon Jun 2 04:56:34 2008 max relations containing the same ideal: 27
Mon Jun 2 04:57:49 2008 removing 1354475 relations and 954475 ideals in 400000 cliques
Mon Jun 2 04:57:51 2008 commencing in-memory singleton removal
Mon Jun 2 04:58:04 2008 begin with 64685319 relations and 46539513 unique ideals
Mon Jun 2 04:59:25 2008 reduce to 64664363 relations and 45563933 ideals in 5 passes
Mon Jun 2 04:59:25 2008 max relations containing the same ideal: 26
Mon Jun 2 05:00:39 2008 removing 1358598 relations and 958598 ideals in 400000 cliques
Mon Jun 2 05:00:41 2008 commencing in-memory singleton removal
Mon Jun 2 05:00:53 2008 begin with 63305765 relations and 45563933 unique ideals
Mon Jun 2 05:02:13 2008 reduce to 63284535 relations and 44583924 ideals in 5 passes
Mon Jun 2 05:02:13 2008 max relations containing the same ideal: 26
Mon Jun 2 05:03:24 2008 removing 652473 relations and 484976 ideals in 167497 cliques
Mon Jun 2 05:03:26 2008 commencing in-memory singleton removal
Mon Jun 2 05:03:38 2008 begin with 62632062 relations and 44583924 unique ideals
Mon Jun 2 05:04:41 2008 reduce to 62628640 relations and 44095519 ideals in 4 passes
Mon Jun 2 05:04:41 2008 max relations containing the same ideal: 25
Mon Jun 2 05:04:54 2008 filtering rational ideals above 720000
Mon Jun 2 05:04:54 2008 filtering algebraic ideals above 720000
Mon Jun 2 05:04:54 2008 need 116164 more relations than ideals
Mon Jun 2 05:04:54 2008 commencing singleton removal, final pass
Mon Jun 2 08:27:56 2008 keeping 95290273 ideals with weight <= 20, new excess is 9778600
Mon Jun 2 08:32:58 2008 memory use: 3655.8 MB
Mon Jun 2 08:33:00 2008 commencing in-memory singleton removal
Mon Jun 2 08:33:33 2008 begin with 126610759 relations and 95290273 unique ideals
Mon Jun 2 08:39:02 2008 reduce to 126610086 relations and 95289599 ideals in 8 passes
Mon Jun 2 08:39:02 2008 max relations containing the same ideal: 20
Mon Jun 2 08:42:11 2008 removing 3423754 relations and 3023754 ideals in 400000 cliques
Mon Jun 2 08:42:17 2008 commencing in-memory singleton removal
Mon Jun 2 08:42:49 2008 begin with 123186332 relations and 95289599 unique ideals
Mon Jun 2 08:47:30 2008 reduce to 123138805 relations and 92218122 ideals in 7 passes
Mon Jun 2 08:47:30 2008 max relations containing the same ideal: 20
Mon Jun 2 08:50:25 2008 removing 2580631 relations and 2180631 ideals in 400000 cliques
Mon Jun 2 08:50:30 2008 commencing in-memory singleton removal
Mon Jun 2 08:51:02 2008 begin with 120558174 relations and 92218122 unique ideals
Mon Jun 2 08:54:56 2008 reduce to 120528560 relations and 90007780 ideals in 6 passes
Mon Jun 2 08:54:56 2008 max relations containing the same ideal: 20
Mon Jun 2 08:57:45 2008 removing 2302330 relations and 1902330 ideals in 400000 cliques
Mon Jun 2 08:57:50 2008 commencing in-memory singleton removal
Mon Jun 2 08:58:20 2008 begin with 118226230 relations and 90007780 unique ideals
Mon Jun 2 09:02:09 2008 reduce to 118201558 relations and 88080702 ideals in 6 passes
Mon Jun 2 09:02:09 2008 max relations containing the same ideal: 20
Mon Jun 2 09:04:54 2008 removing 2136493 relations and 1736493 ideals in 400000 cliques
Mon Jun 2 09:04:59 2008 commencing in-memory singleton removal
Mon Jun 2 09:05:29 2008 begin with 116065065 relations and 88080702 unique ideals
Mon Jun 2 09:09:50 2008 reduce to 116042879 relations and 86321946 ideals in 7 passes
Mon Jun 2 09:09:50 2008 max relations containing the same ideal: 20
Mon Jun 2 09:12:32 2008 removing 2025315 relations and 1625315 ideals in 400000 cliques
Mon Jun 2 09:12:36 2008 commencing in-memory singleton removal
Mon Jun 2 09:13:06 2008 begin with 114017564 relations and 86321946 unique ideals
Mon Jun 2 09:17:21 2008 reduce to 113997906 relations and 84676900 ideals in 7 passes
Mon Jun 2 09:17:21 2008 max relations containing the same ideal: 20
Mon Jun 2 09:19:59 2008 removing 1936953 relations and 1536953 ideals in 400000 cliques
Mon Jun 2 09:20:03 2008 commencing in-memory singleton removal
Mon Jun 2 09:20:32 2008 begin with 112060953 relations and 84676900 unique ideals
Mon Jun 2 09:24:06 2008 reduce to 112042257 relations and 83121186 ideals in 6 passes
Mon Jun 2 09:24:06 2008 max relations containing the same ideal: 20
Mon Jun 2 09:26:40 2008 removing 1864736 relations and 1464736 ideals in 400000 cliques
Mon Jun 2 09:26:45 2008 commencing in-memory singleton removal
Mon Jun 2 09:27:12 2008 begin with 110177521 relations and 83121186 unique ideals
Mon Jun 2 09:30:07 2008 reduce to 110159273 relations and 81638135 ideals in 5 passes
Mon Jun 2 09:30:07 2008 max relations containing the same ideal: 20
Mon Jun 2 09:32:38 2008 removing 1814962 relations and 1414962 ideals in 400000 cliques
Mon Jun 2 09:32:42 2008 commencing in-memory singleton removal
Mon Jun 2 09:33:09 2008 begin with 108344311 relations and 81638135 unique ideals
Mon Jun 2 09:36:00 2008 reduce to 108326621 relations and 80205434 ideals in 5 passes
Mon Jun 2 09:36:00 2008 max relations containing the same ideal: 20
Mon Jun 2 09:38:28 2008 removing 1760851 relations and 1360851 ideals in 400000 cliques
Mon Jun 2 09:38:32 2008 commencing in-memory singleton removal
Mon Jun 2 09:38:59 2008 begin with 106565770 relations and 80205434 unique ideals
Mon Jun 2 09:41:47 2008 reduce to 106549050 relations and 78827798 ideals in 5 passes
Mon Jun 2 09:41:47 2008 max relations containing the same ideal: 20
Mon Jun 2 09:44:12 2008 removing 1721987 relations and 1321987 ideals in 400000 cliques
Mon Jun 2 09:44:16 2008 commencing in-memory singleton removal
Mon Jun 2 09:44:42 2008 begin with 104827063 relations and 78827798 unique ideals
Mon Jun 2 09:47:59 2008 reduce to 104810737 relations and 77489434 ideals in 6 passes
Mon Jun 2 09:47:59 2008 max relations containing the same ideal: 20
Mon Jun 2 09:50:21 2008 removing 1687490 relations and 1287490 ideals in 400000 cliques
Mon Jun 2 09:50:25 2008 commencing in-memory singleton removal
Mon Jun 2 09:50:50 2008 begin with 103123247 relations and 77489434 unique ideals
Mon Jun 2 09:53:31 2008 reduce to 103107337 relations and 76185991 ideals in 5 passes
Mon Jun 2 09:53:31 2008 max relations containing the same ideal: 20
Mon Jun 2 09:55:51 2008 removing 1661446 relations and 1261446 ideals in 400000 cliques
Mon Jun 2 09:55:55 2008 commencing in-memory singleton removal
Mon Jun 2 09:56:20 2008 begin with 101445891 relations and 76185991 unique ideals
Mon Jun 2 09:58:56 2008 reduce to 101429750 relations and 74908348 ideals in 5 passes
Mon Jun 2 09:58:56 2008 max relations containing the same ideal: 20
Mon Jun 2 10:01:13 2008 removing 1621945 relations and 1221945 ideals in 400000 cliques
Mon Jun 2 10:01:17 2008 commencing in-memory singleton removal
Mon Jun 2 10:01:41 2008 begin with 99807805 relations and 74908348 unique ideals
Mon Jun 2 10:04:46 2008 reduce to 99790569 relations and 73669094 ideals in 6 passes
Mon Jun 2 10:04:46 2008 max relations containing the same ideal: 20
Mon Jun 2 10:07:01 2008 removing 1619072 relations and 1219072 ideals in 400000 cliques
Mon Jun 2 10:07:05 2008 commencing in-memory singleton removal
Mon Jun 2 10:07:29 2008 begin with 98171497 relations and 73669094 unique ideals
Mon Jun 2 10:10:30 2008 reduce to 98157635 relations and 72436117 ideals in 6 passes
Mon Jun 2 10:10:30 2008 max relations containing the same ideal: 20
Mon Jun 2 10:12:41 2008 removing 1578934 relations and 1178934 ideals in 400000 cliques
Mon Jun 2 10:12:45 2008 commencing in-memory singleton removal
Mon Jun 2 10:13:08 2008 begin with 96578701 relations and 72436117 unique ideals
Mon Jun 2 10:15:36 2008 reduce to 96564373 relations and 71242805 ideals in 5 passes
Mon Jun 2 10:15:36 2008 max relations containing the same ideal: 20
Mon Jun 2 10:17:46 2008 removing 1554867 relations and 1154867 ideals in 400000 cliques
Mon Jun 2 10:17:50 2008 commencing in-memory singleton removal
Mon Jun 2 10:18:13 2008 begin with 95009506 relations and 71242805 unique ideals
Mon Jun 2 10:20:38 2008 reduce to 94993731 relations and 70072106 ideals in 5 passes
Mon Jun 2 10:20:38 2008 max relations containing the same ideal: 20
Mon Jun 2 10:22:44 2008 removing 1543322 relations and 1143322 ideals in 400000 cliques
Mon Jun 2 10:22:48 2008 commencing in-memory singleton removal
Mon Jun 2 10:23:10 2008 begin with 93450409 relations and 70072106 unique ideals
Mon Jun 2 10:25:32 2008 reduce to 93434687 relations and 68913012 ideals in 5 passes
Mon Jun 2 10:25:32 2008 max relations containing the same ideal: 20
Mon Jun 2 10:27:36 2008 removing 1532282 relations and 1132282 ideals in 400000 cliques
Mon Jun 2 10:27:40 2008 commencing in-memory singleton removal
Mon Jun 2 10:28:02 2008 begin with 91902405 relations and 68913012 unique ideals
Mon Jun 2 10:29:53 2008 reduce to 91887221 relations and 67765490 ideals in 4 passes
Mon Jun 2 10:29:53 2008 max relations containing the same ideal: 20
Mon Jun 2 10:31:54 2008 removing 1511138 relations and 1111138 ideals in 400000 cliques
Mon Jun 2 10:31:58 2008 commencing in-memory singleton removal
Mon Jun 2 10:32:20 2008 begin with 90376083 relations and 67765490 unique ideals
Mon Jun 2 10:34:36 2008 reduce to 90360325 relations and 66638535 ideals in 5 passes
Mon Jun 2 10:34:36 2008 max relations containing the same ideal: 20
Mon Jun 2 10:36:35 2008 removing 1493411 relations and 1093411 ideals in 400000 cliques
Mon Jun 2 10:36:38 2008 commencing in-memory singleton removal
Mon Jun 2 10:36:59 2008 begin with 88866914 relations and 66638535 unique ideals
Mon Jun 2 10:39:13 2008 reduce to 88850561 relations and 65528710 ideals in 5 passes
Mon Jun 2 10:39:13 2008 max relations containing the same ideal: 20
Mon Jun 2 10:41:10 2008 removing 1474295 relations and 1074295 ideals in 400000 cliques
Mon Jun 2 10:41:13 2008 commencing in-memory singleton removal
Mon Jun 2 10:41:34 2008 begin with 87376266 relations and 65528710 unique ideals
Mon Jun 2 10:43:45 2008 reduce to 87358673 relations and 64436736 ideals in 5 passes
Mon Jun 2 10:43:45 2008 max relations containing the same ideal: 20
Mon Jun 2 10:45:40 2008 removing 1470062 relations and 1070062 ideals in 400000 cliques
Mon Jun 2 10:45:43 2008 commencing in-memory singleton removal
Mon Jun 2 10:46:03 2008 begin with 85888611 relations and 64436736 unique ideals
Mon Jun 2 10:48:11 2008 reduce to 85872366 relations and 63350342 ideals in 5 passes
Mon Jun 2 10:48:11 2008 max relations containing the same ideal: 20
Mon Jun 2 10:50:03 2008 removing 1457759 relations and 1057759 ideals in 400000 cliques
Mon Jun 2 10:50:06 2008 commencing in-memory singleton removal
Mon Jun 2 10:50:26 2008 begin with 84414607 relations and 63350342 unique ideals
Mon Jun 2 10:52:31 2008 reduce to 84399172 relations and 62277072 ideals in 5 passes
Mon Jun 2 10:52:31 2008 max relations containing the same ideal: 20
Mon Jun 2 10:54:20 2008 removing 1429838 relations and 1029838 ideals in 400000 cliques
Mon Jun 2 10:54:24 2008 commencing in-memory singleton removal
Mon Jun 2 10:54:43 2008 begin with 82969334 relations and 62277072 unique ideals
Mon Jun 2 10:56:45 2008 reduce to 82952916 relations and 61230740 ideals in 5 passes
Mon Jun 2 10:56:45 2008 max relations containing the same ideal: 20
Mon Jun 2 10:58:33 2008 removing 1439482 relations and 1039482 ideals in 400000 cliques
Mon Jun 2 10:58:37 2008 commencing in-memory singleton removal
Mon Jun 2 10:58:56 2008 begin with 81513434 relations and 61230740 unique ideals
Mon Jun 2 11:01:19 2008 reduce to 81497594 relations and 60175345 ideals in 6 passes
Mon Jun 2 11:01:19 2008 max relations containing the same ideal: 20
Mon Jun 2 11:03:05 2008 removing 1418949 relations and 1018949 ideals in 400000 cliques
Mon Jun 2 11:03:08 2008 commencing in-memory singleton removal
Mon Jun 2 11:03:26 2008 begin with 80078645 relations and 60175345 unique ideals
Mon Jun 2 11:05:23 2008 reduce to 80062009 relations and 59139686 ideals in 5 passes
Mon Jun 2 11:05:23 2008 max relations containing the same ideal: 20
Mon Jun 2 11:07:06 2008 removing 1415084 relations and 1015084 ideals in 400000 cliques
Mon Jun 2 11:07:10 2008 commencing in-memory singleton removal
Mon Jun 2 11:07:28 2008 begin with 78646925 relations and 59139686 unique ideals
Mon Jun 2 11:09:22 2008 reduce to 78629492 relations and 58107068 ideals in 5 passes
Mon Jun 2 11:09:22 2008 max relations containing the same ideal: 20
Mon Jun 2 11:11:03 2008 removing 1404084 relations and 1004084 ideals in 400000 cliques
Mon Jun 2 11:11:06 2008 commencing in-memory singleton removal
Mon Jun 2 11:11:24 2008 begin with 77225408 relations and 58107068 unique ideals
Mon Jun 2 11:13:15 2008 reduce to 77207785 relations and 57085274 ideals in 5 passes
Mon Jun 2 11:13:15 2008 max relations containing the same ideal: 20
Mon Jun 2 11:14:55 2008 removing 1396775 relations and 996775 ideals in 400000 cliques
Mon Jun 2 11:14:58 2008 commencing in-memory singleton removal
Mon Jun 2 11:15:15 2008 begin with 75811010 relations and 57085274 unique ideals
Mon Jun 2 11:17:05 2008 reduce to 75792877 relations and 56070281 ideals in 5 passes
Mon Jun 2 11:17:05 2008 max relations containing the same ideal: 20
Mon Jun 2 11:18:41 2008 removing 1406308 relations and 1006308 ideals in 400000 cliques
Mon Jun 2 11:18:45 2008 commencing in-memory singleton removal
Mon Jun 2 11:19:01 2008 begin with 74386569 relations and 56070281 unique ideals
Mon Jun 2 11:20:49 2008 reduce to 74369860 relations and 55047167 ideals in 5 passes
Mon Jun 2 11:20:49 2008 max relations containing the same ideal: 20
Mon Jun 2 11:22:23 2008 removing 1388543 relations and 988543 ideals in 400000 cliques
Mon Jun 2 11:22:26 2008 commencing in-memory singleton removal
Mon Jun 2 11:22:43 2008 begin with 72981317 relations and 55047167 unique ideals
Mon Jun 2 11:24:27 2008 reduce to 72963997 relations and 54041189 ideals in 5 passes
Mon Jun 2 11:24:27 2008 max relations containing the same ideal: 20
Mon Jun 2 11:26:00 2008 removing 1383285 relations and 983285 ideals in 400000 cliques
Mon Jun 2 11:26:03 2008 commencing in-memory singleton removal
Mon Jun 2 11:26:19 2008 begin with 71580712 relations and 54041189 unique ideals
Mon Jun 2 11:28:01 2008 reduce to 71562802 relations and 53039873 ideals in 5 passes
Mon Jun 2 11:28:01 2008 max relations containing the same ideal: 20
Mon Jun 2 11:29:31 2008 removing 1379064 relations and 979064 ideals in 400000 cliques
Mon Jun 2 11:29:34 2008 commencing in-memory singleton removal
Mon Jun 2 11:29:50 2008 begin with 70183738 relations and 53039873 unique ideals
Mon Jun 2 11:31:30 2008 reduce to 70165315 relations and 52042278 ideals in 5 passes
Mon Jun 2 11:31:30 2008 max relations containing the same ideal: 20
Mon Jun 2 11:33:00 2008 removing 1370506 relations and 970506 ideals in 400000 cliques
Mon Jun 2 11:33:02 2008 commencing in-memory singleton removal
Mon Jun 2 11:33:18 2008 begin with 68794809 relations and 52042278 unique ideals
Mon Jun 2 11:34:56 2008 reduce to 68775228 relations and 51052063 ideals in 5 passes
Mon Jun 2 11:34:56 2008 max relations containing the same ideal: 20
Mon Jun 2 11:36:23 2008 removing 1367443 relations and 967443 ideals in 400000 cliques
Mon Jun 2 11:36:25 2008 commencing in-memory singleton removal
Mon Jun 2 11:36:40 2008 begin with 67407785 relations and 51052063 unique ideals
Mon Jun 2 11:38:16 2008 reduce to 67387847 relations and 50064539 ideals in 5 passes
Mon Jun 2 11:38:16 2008 max relations containing the same ideal: 20
Mon Jun 2 11:39:40 2008 removing 1369138 relations and 969138 ideals in 400000 cliques
Mon Jun 2 11:39:43 2008 commencing in-memory singleton removal
Mon Jun 2 11:39:58 2008 begin with 66018709 relations and 50064539 unique ideals
Mon Jun 2 11:41:30 2008 reduce to 65998505 relations and 49075024 ideals in 5 passes
Mon Jun 2 11:41:30 2008 max relations containing the same ideal: 20
Mon Jun 2 11:42:53 2008 removing 1363523 relations and 963523 ideals in 400000 cliques
Mon Jun 2 11:42:56 2008 commencing in-memory singleton removal
Mon Jun 2 11:43:10 2008 begin with 64634982 relations and 49075024 unique ideals
Mon Jun 2 11:44:40 2008 reduce to 64614398 relations and 48090763 ideals in 5 passes
Mon Jun 2 11:44:40 2008 max relations containing the same ideal: 20
Mon Jun 2 11:46:01 2008 removing 1356656 relations and 956656 ideals in 400000 cliques
Mon Jun 2 11:46:04 2008 commencing in-memory singleton removal
Mon Jun 2 11:46:18 2008 begin with 63257742 relations and 48090763 unique ideals
Mon Jun 2 11:47:46 2008 reduce to 63236311 relations and 47112495 ideals in 5 passes
Mon Jun 2 11:47:46 2008 max relations containing the same ideal: 20
Mon Jun 2 11:49:05 2008 removing 1355234 relations and 955234 ideals in 400000 cliques
Mon Jun 2 11:49:08 2008 commencing in-memory singleton removal
Mon Jun 2 11:49:21 2008 begin with 61881077 relations and 47112495 unique ideals
Mon Jun 2 11:50:47 2008 reduce to 61859213 relations and 46135220 ideals in 5 passes
Mon Jun 2 11:50:47 2008 max relations containing the same ideal: 20
Mon Jun 2 11:52:04 2008 removing 1350334 relations and 950334 ideals in 400000 cliques
Mon Jun 2 11:52:07 2008 commencing in-memory singleton removal
Mon Jun 2 11:52:20 2008 begin with 60508879 relations and 46135220 unique ideals
Mon Jun 2 11:53:43 2008 reduce to 60485913 relations and 45161698 ideals in 5 passes
Mon Jun 2 11:53:43 2008 max relations containing the same ideal: 20
Mon Jun 2 11:54:58 2008 removing 1354807 relations and 954807 ideals in 400000 cliques
Mon Jun 2 11:55:01 2008 commencing in-memory singleton removal
Mon Jun 2 11:55:13 2008 begin with 59131106 relations and 45161698 unique ideals
Mon Jun 2 11:56:34 2008 reduce to 59108410 relations and 44183973 ideals in 5 passes
Mon Jun 2 11:56:34 2008 max relations containing the same ideal: 20
Mon Jun 2 11:57:47 2008 removing 1349456 relations and 949456 ideals in 400000 cliques
Mon Jun 2 11:57:50 2008 commencing in-memory singleton removal
Mon Jun 2 11:58:02 2008 begin with 57758954 relations and 44183973 unique ideals
Mon Jun 2 11:59:21 2008 reduce to 57734866 relations and 43210238 ideals in 5 passes
Mon Jun 2 11:59:21 2008 max relations containing the same ideal: 20
Mon Jun 2 12:00:33 2008 removing 1348382 relations and 948382 ideals in 400000 cliques
Mon Jun 2 12:00:35 2008 commencing in-memory singleton removal
Mon Jun 2 12:00:47 2008 begin with 56386484 relations and 43210238 unique ideals
Mon Jun 2 12:02:04 2008 reduce to 56361873 relations and 42237011 ideals in 5 passes
Mon Jun 2 12:02:04 2008 max relations containing the same ideal: 19
Mon Jun 2 12:03:13 2008 removing 1348760 relations and 948760 ideals in 400000 cliques
Mon Jun 2 12:03:16 2008 commencing in-memory singleton removal
Mon Jun 2 12:03:28 2008 begin with 55013113 relations and 42237011 unique ideals
Mon Jun 2 12:04:42 2008 reduce to 54987591 relations and 41262457 ideals in 5 passes
Mon Jun 2 12:04:42 2008 max relations containing the same ideal: 19
Mon Jun 2 12:05:50 2008 removing 1348654 relations and 948654 ideals in 400000 cliques
Mon Jun 2 12:05:52 2008 commencing in-memory singleton removal
Mon Jun 2 12:06:03 2008 begin with 53638937 relations and 41262457 unique ideals
Mon Jun 2 12:07:16 2008 reduce to 53612737 relations and 40287331 ideals in 5 passes
Mon Jun 2 12:07:16 2008 max relations containing the same ideal: 19
Mon Jun 2 12:08:21 2008 removing 1349030 relations and 949030 ideals in 400000 cliques
Mon Jun 2 12:08:23 2008 commencing in-memory singleton removal
Mon Jun 2 12:08:34 2008 begin with 52263707 relations and 40287331 unique ideals
Mon Jun 2 12:09:44 2008 reduce to 52236490 relations and 39310816 ideals in 5 passes
Mon Jun 2 12:09:44 2008 max relations containing the same ideal: 19
Mon Jun 2 12:10:48 2008 removing 1352158 relations and 952158 ideals in 400000 cliques
Mon Jun 2 12:10:50 2008 commencing in-memory singleton removal
Mon Jun 2 12:11:01 2008 begin with 50884332 relations and 39310816 unique ideals
Mon Jun 2 12:12:08 2008 reduce to 50856355 relations and 38330402 ideals in 5 passes
Mon Jun 2 12:12:08 2008 max relations containing the same ideal: 18
Mon Jun 2 12:13:10 2008 removing 1353875 relations and 953875 ideals in 400000 cliques
Mon Jun 2 12:13:12 2008 commencing in-memory singleton removal
Mon Jun 2 12:13:23 2008 begin with 49502480 relations and 38330402 unique ideals
Mon Jun 2 12:14:28 2008 reduce to 49473522 relations and 37347260 ideals in 5 passes
Mon Jun 2 12:14:28 2008 max relations containing the same ideal: 18
Mon Jun 2 12:15:28 2008 removing 1355709 relations and 955709 ideals in 400000 cliques
Mon Jun 2 12:15:31 2008 commencing in-memory singleton removal
Mon Jun 2 12:15:41 2008 begin with 48117813 relations and 37347260 unique ideals
Mon Jun 2 12:16:44 2008 reduce to 48088344 relations and 36361770 ideals in 5 passes
Mon Jun 2 12:16:44 2008 max relations containing the same ideal: 18
Mon Jun 2 12:17:43 2008 removing 1314203 relations and 930806 ideals in 383397 cliques
Mon Jun 2 12:17:45 2008 commencing in-memory singleton removal
Mon Jun 2 12:17:54 2008 begin with 46774141 relations and 36361770 unique ideals
Mon Jun 2 12:18:56 2008 reduce to 46745785 relations and 35402329 ideals in 5 passes
Mon Jun 2 12:18:56 2008 max relations containing the same ideal: 18
Mon Jun 2 12:19:58 2008 relations with 0 large ideals: 1050168
Mon Jun 2 12:19:58 2008 relations with 1 large ideals: 5498032
Mon Jun 2 12:19:58 2008 relations with 2 large ideals: 12739384
Mon Jun 2 12:19:58 2008 relations with 3 large ideals: 15051315
Mon Jun 2 12:19:58 2008 relations with 4 large ideals: 9351724
Mon Jun 2 12:19:58 2008 relations with 5 large ideals: 2797939
Mon Jun 2 12:19:58 2008 relations with 6 large ideals: 247017
Mon Jun 2 12:19:58 2008 relations with 7+ large ideals: 10206
Mon Jun 2 12:19:58 2008 commencing 2-way merge
Mon Jun 2 12:21:07 2008 reduce to 33307706 relation sets and 21964250 unique ideals
Mon Jun 2 12:21:07 2008 commencing full merge
Mon Jun 2 12:31:29 2008 memory use: 2002.7 MB
Mon Jun 2 12:31:33 2008 found 17478935 cycles, need 15914450
Mon Jun 2 12:31:48 2008 weight of 15914450 cycles is about 1114125375 (70.01/cycle)
Mon Jun 2 12:31:48 2008 distribution of cycle lengths:
Mon Jun 2 12:31:48 2008 1 relations: 1760789
Mon Jun 2 12:31:48 2008 2 relations: 1886876
Mon Jun 2 12:31:48 2008 3 relations: 2133405
Mon Jun 2 12:31:48 2008 4 relations: 2123936
Mon Jun 2 12:31:48 2008 5 relations: 2022155
Mon Jun 2 12:31:48 2008 6 relations: 1789898
Mon Jun 2 12:31:48 2008 7 relations: 1513242
Mon Jun 2 12:31:48 2008 8 relations: 1208841
Mon Jun 2 12:31:48 2008 9 relations: 907862
Mon Jun 2 12:31:48 2008 10+ relations: 567446
Mon Jun 2 12:31:48 2008 heaviest cycle: 11 relations
Mon Jun 2 12:31:55 2008 commencing cycle optimization
Mon Jun 2 12:34:19 2008 start with 75400994 relations
Mon Jun 2 12:39:06 2008 pruned 1598366 relations
Mon Jun 2 12:39:08 2008 memory use: 2563.5 MB
Mon Jun 2 12:39:08 2008 distribution of cycle lengths:
Mon Jun 2 12:39:08 2008 1 relations: 1760789
Mon Jun 2 12:39:08 2008 2 relations: 1927586
Mon Jun 2 12:39:08 2008 3 relations: 2211760
Mon Jun 2 12:39:08 2008 4 relations: 2184131
Mon Jun 2 12:39:08 2008 5 relations: 2090179
Mon Jun 2 12:39:08 2008 6 relations: 1829507
Mon Jun 2 12:39:08 2008 7 relations: 1527422
Mon Jun 2 12:39:08 2008 8 relations: 1169714
Mon Jun 2 12:39:08 2008 9 relations: 804129
Mon Jun 2 12:39:08 2008 10+ relations: 409233
Mon Jun 2 12:39:08 2008 heaviest cycle: 11 relations
Mon Jun 2 12:40:10 2008
Mon Jun 2 12:40:26 2008 commencing linear algebra
Mon Jun 2 12:40:30 2008 read 15914450 cycles
Mon Jun 2 12:46:50 2008 cycles contain 42366523 unique relations
Mon Jun 2 12:55:50 2008 read 42366523 relations
Mon Jun 2 12:59:09 2008 using 32 quadratic characters above 2147483078
Mon Jun 2 13:09:55 2008 building initial matrix
Mon Jun 2 13:47:43 2008 memory use: 5420.8 MB
Mon Jun 2 13:48:00 2008 read 15914450 cycles
Mon Jun 2 13:48:19 2008 matrix is 15913838 x 15914450 (4768.3 MB) with weight 1448473860 (91.02/col)
Mon Jun 2 13:48:19 2008 sparse part has weight 1074910624 (67.54/col)
Mon Jun 2 14:02:57 2008 filtering completed in 3 passes
Mon Jun 2 14:03:05 2008 matrix is 15875803 x 15876003 (4763.5 MB) with weight 1446794676 (91.13/col)
Mon Jun 2 14:03:05 2008 sparse part has weight 1074088286 (67.65/col)
Mon Jun 2 14:06:25 2008 read 15876003 cycles
Mon Jun 2 14:06:45 2008 matrix is 15875803 x 15876003 (4763.5 MB) with weight 1446794676 (91.13/col)
Mon Jun 2 14:06:45 2008 sparse part has weight 1074088286 (67.65/col)
Mon Jun 2 14:06:45 2008 saving the first 48 matrix rows for later
Mon Jun 2 14:07:01 2008 matrix is 15875755 x 15876003 (4555.3 MB) with weight 1114396697 (70.19/col)
Mon Jun 2 14:07:02 2008 sparse part has weight 1035382087 (65.22/col)
Mon Jun 2 14:07:02 2008 matrix includes 64 packed rows
Mon Jun 2 14:07:02 2008 using block size 65536 for processor cache size 2048 kB
Mon Jun 2 14:09:31 2008 commencing Lanczos iteration
Mon Jun 2 14:09:31 2008 memory use: 4483.8 MB
[/CODE]

Greg

This is my first time using the newest version of the msieve filtering. It looked like the matrix was going to build:

Mon Jun 09 19:33:33 2008 reduce to 21661437 relations and 15105465 ideals in 22 passes

At this point I expected some clique removal, but instead the code did something different:

Mon Jun 09 19:40:12 2008 keeping 21684767 ideals with weight <= 20, new excess is 1668663

and the filtering came up a little short. I just wanted to double-check that this is expected while I do some more sieving. Thanks.



[code]
Mon Jun 09 18:26:31 2008 Msieve v. 1.36
Mon Jun 09 18:26:31 2008 random seeds: 6e188440 ab6649d3
Mon Jun 09 18:26:31 2008 factoring 24891507626244406120480497383985472681305924731801184706322368928780665216062688549532304713344794061905695890812821414304746944292502195893893185976748433282143972451856610060708867729 (185 digits)
Mon Jun 09 18:26:33 2008 no P-1/P+1/ECM available, skipping
Mon Jun 09 18:26:33 2008 commencing number field sieve (185-digit input)
Mon Jun 09 18:26:33 2008 R0: -107006904423598033356356300384937784807
Mon Jun 09 18:26:33 2008 R1: 1
Mon Jun 09 18:26:33 2008 A0: 49
Mon Jun 09 18:26:33 2008 A1: 0
Mon Jun 09 18:26:33 2008 A2: 0
Mon Jun 09 18:26:33 2008 A3: 0
Mon Jun 09 18:26:33 2008 A4: 0
Mon Jun 09 18:26:33 2008 A5: 0
Mon Jun 09 18:26:33 2008 A6: 1
Mon Jun 09 18:26:33 2008 size score = 4.006126e-011, Murphy alpha = 1.379935, combined = 2.700825e-011
Mon Jun 09 18:29:11 2008 restarting with 89974016 relations
Mon Jun 09 18:29:16 2008 added 46015 free relations
Mon Jun 09 18:29:17 2008
Mon Jun 09 18:29:17 2008 commencing relation filtering
Mon Jun 09 18:29:17 2008 commencing duplicate removal, pass 1
Mon Jun 09 18:30:24 2008 error -11 reading relation 9680747
Mon Jun 09 18:30:55 2008 error -11 reading relation 14287221
Mon Jun 09 18:32:25 2008 error -11 reading relation 27247783
Mon Jun 09 18:32:26 2008 error -11 reading relation 27343215
Mon Jun 09 18:34:03 2008 error -11 reading relation 41228705
Mon Jun 09 18:34:49 2008 error -11 reading relation 47615346
Mon Jun 09 18:39:40 2008 found 23180592 hash collisions in 90020025 relations
Mon Jun 09 18:39:40 2008 commencing duplicate removal, pass 2
Mon Jun 09 18:42:33 2008 found 22540256 duplicates and 67479769 unique relations
Mon Jun 09 18:42:33 2008 memory use: 504.8 MB
Mon Jun 09 18:43:01 2008 ignoring smallest 4172044 rational and 4168512 algebraic ideals
Mon Jun 09 18:43:01 2008 filtering rational ideals above 70975488
Mon Jun 09 18:43:01 2008 filtering algebraic ideals above 70975488
Mon Jun 09 18:43:01 2008 need 12510834 more relations than ideals
Mon Jun 09 18:43:01 2008 commencing singleton removal, pass 1
Mon Jun 09 18:51:37 2008 relations with 0 large ideals: 2117672
Mon Jun 09 18:51:37 2008 relations with 1 large ideals: 10885484
Mon Jun 09 18:51:37 2008 relations with 2 large ideals: 22501129
Mon Jun 09 18:51:37 2008 relations with 3 large ideals: 21784610
Mon Jun 09 18:51:37 2008 relations with 4 large ideals: 9093355
Mon Jun 09 18:51:37 2008 relations with 5 large ideals: 1097519
Mon Jun 09 18:51:37 2008 relations with 6 large ideals: 0
Mon Jun 09 18:51:37 2008 relations with 7+ large ideals: 0
Mon Jun 09 18:51:37 2008 67479769 relations and about 54399451 large ideals
Mon Jun 09 18:51:37 2008 commencing singleton removal, pass 2
Mon Jun 09 19:00:18 2008 found 18937049 singletons
Mon Jun 09 19:00:18 2008 current dataset: 48542720 relations and about 33069757 large ideals
Mon Jun 09 19:00:18 2008 commencing singleton removal, pass 3
Mon Jun 09 19:06:46 2008 relations with 0 large ideals: 2117672
Mon Jun 09 19:06:46 2008 relations with 1 large ideals: 9404864
Mon Jun 09 19:06:46 2008 relations with 2 large ideals: 16848762
Mon Jun 09 19:06:46 2008 relations with 3 large ideals: 14256246
Mon Jun 09 19:06:46 2008 relations with 4 large ideals: 5319856
Mon Jun 09 19:06:46 2008 relations with 5 large ideals: 595320
Mon Jun 09 19:06:46 2008 relations with 6 large ideals: 0
Mon Jun 09 19:06:46 2008 relations with 7+ large ideals: 0
Mon Jun 09 19:06:46 2008 48542720 relations and about 41699688 large ideals
Mon Jun 09 19:06:46 2008 commencing singleton removal, pass 4
Mon Jun 09 19:13:28 2008 found 13902565 singletons
Mon Jun 09 19:13:28 2008 current dataset: 34640155 relations and about 25993581 large ideals
Mon Jun 09 19:13:28 2008 commencing singleton removal, pass 5
Mon Jun 09 19:18:33 2008 found 4260941 singletons
Mon Jun 09 19:18:33 2008 current dataset: 30379214 relations and about 21511404 large ideals
Mon Jun 09 19:18:33 2008 commencing singleton removal, pass 6
Mon Jun 09 19:23:18 2008 found 1418837 singletons
Mon Jun 09 19:23:18 2008 current dataset: 28960377 relations and about 20064971 large ideals
Mon Jun 09 19:23:18 2008 commencing singleton removal, pass 7
Mon Jun 09 19:27:50 2008 found 491745 singletons
Mon Jun 09 19:27:50 2008 current dataset: 28468632 relations and about 19569882 large ideals
Mon Jun 09 19:27:50 2008 commencing singleton removal, final pass
Mon Jun 09 19:32:51 2008 memory use: 484.8 MB
Mon Jun 09 19:32:51 2008 commencing in-memory singleton removal
Mon Jun 09 19:32:53 2008 begin with 28468632 relations and 22152067 unique ideals
Mon Jun 09 19:33:33 2008 reduce to 21661437 relations and 15105465 ideals in 22 passes
Mon Jun 09 19:33:33 2008 max relations containing the same ideal: 23
Mon Jun 09 19:33:37 2008 filtering rational ideals above 720000
Mon Jun 09 19:33:37 2008 filtering algebraic ideals above 720000
Mon Jun 09 19:33:37 2008 need 115613 more relations than ideals
Mon Jun 09 19:33:37 2008 commencing singleton removal, final pass
Mon Jun 09 19:40:12 2008 keeping 21684767 ideals with weight <= 20, new excess is 1668663
Mon Jun 09 19:40:42 2008 memory use: 693.9 MB
Mon Jun 09 19:40:42 2008 commencing in-memory singleton removal
Mon Jun 09 19:40:45 2008 begin with 21661437 relations and 21684767 unique ideals
Mon Jun 09 19:41:48 2008 reduce to 20537046 relations and 20554229 ideals in 22 passes
Mon Jun 09 19:41:48 2008 max relations containing the same ideal: 20
Mon Jun 09 19:41:52 2008 filtering wants 1000000 more relations
Mon Jun 09 19:41:52 2008 elapsed time 01:15:21
[/code]

[QUOTE=bdodson;134622]Here's 3,536+ c252, which factors as p108*p145 (not an ecm miss!).
...
The number is easier, and the
dependencies are lighter than for 12,241- c260. -Bruce:smile:[/QUOTE]

By contrast, 10,257- was a near ecm-miss at p54*p86*p102. Dependencies
were lighter yet; there were eight used, with coef in 815.3M-816.05M bits.
Details are deferred to another subform (ecm or Cunningham?), as there
wasn't any msieve news [except for another successful completion; thanks
Jason!]. An update on the current Childers/Dodson matrices running here,
10,257- C208 is at 75%, and seems to need another 10 days or so; and the
hardest 3,547- C242 is at 54%. Sounds like there's space here for 7,311+
c258, but we've switched to over-sieving (filtering may be interesting), and
hope for a more tractible matrix.

Sounds like 6*t50 = c. t55 works out to something like 30% of the sievetime
(on the same x86-64 clusters, with a bit of over-sieving), so this p54
isn't evidence that ecm pre-testing past the current 7*t50 level would
be optimal use of cputime. Near-miss; not miss. Sieving for 7,313+ c264
starts tomorrow.

-Bruce (factoring report dated the morning of June 4)

[quote=jbristow;135582]... I just wanted to double-check that this is expected while I do some more sieving. Thanks.

[/quote]

Well, I can't tell you what exactly it's doing, but both 1.35 and 1.36 appear to have this behavior. I saw similar things when building the matrix for 2,799+ (now at 31.5%), and scrolling through various of Greg's posting's using 1.36 I see the same line.

- ben.

This is the new filtering behaviour (introduced at 1.34, I think), which tries to combine the matrix-size advantages of filtering with a very small large-prime bound with the memory advantages of using a larger large-prime bound. There's a load of discussion about it around [url]http://www.mersenneforum.org/showpost.php?p=125767&postcount=192[/url]

Yes, latter-day versions perform one pass with a huge filtering bound to delete most of the singletons, then perform at least one more pass with a very small bound. To avoid the explosion of memory use in the second pass, relations are written to disk, and then ideals that occur too often are skipped when they are read back into memory. Having only two passes is much faster than before, when sometimes five or six were needed, and produces a better matrix because it exposes more ideals to the algorithms in the merge phase.

That being said, the clique removal is deferred until the second pass, because I didn't want to run the risk of deleting too much excess early on, so that the second pass is needlessly painful. However, this makes the second pass typically take 50% more memory than the first pass. Right now it's a wash because I think the linear algebra takes more memory than the filtering, but this might need rethinking to allow the filtering to run on smaller machines.

A side effect of the two-pass model is that if you have just enough excess, removing the dense ideals could make the code think you don't have enough excess to proceed. I should rethink that too.

[QUOTE=frmky;134591]I would be very happy with that scaling. :smile: As it is now, the best for msieve on this 8-way 32-core computer is to run a single thread on a quad-core cpu by itself, setting it to use the largest cache block Jason's code allows, and allowing the other 3 cores to idle. Putting a second thread on the same CPU, no matter how the cache is arranged, slows it down. Running any other code on the same CPU also slows it down. Putting a second thread on a second CPU does speed it by about 10%, but that's not efficient. So, for now, I'm stuck running up to 8 simultaneous matrices for months, or at least until someone else needs to run something.
[/QUOTE]

All the above is wrong. Thanks to Tom's observations, I now know that clock() measures total CPU time, not real time elapsed. BIG difference when using multiple threads. The patch in an earlier thread ... ignore it! On this computer, msieve's LA does scale as about the sqrt of the number of threads up to 8 threads. Above 8 threads, it slows down.

Greg