Lanczos error

Andi47 · 2009-01-11, 14:10

Just got this error when running a c107 GNFS factorization on my P4:

Code:

Sun Jan 11 13:30:48 2009  Msieve v. 1.39
Sun Jan 11 13:30:48 2009  random seeds: 28de8eac 2089edbe
Sun Jan 11 13:30:48 2009  factoring 49522765289485889233681931153717435991979703139426318174911416089221747128358987182858892932767806807975353 (107 digits)
Sun Jan 11 13:30:49 2009  searching for 15-digit factors
Sun Jan 11 13:30:51 2009  commencing number field sieve (107-digit input)
Sun Jan 11 13:30:51 2009  R0: -438344816114060314814
Sun Jan 11 13:30:51 2009  R1:  132924059497
Sun Jan 11 13:30:51 2009  A0: -111978409899830736166589619
Sun Jan 11 13:30:51 2009  A1:  10900893999882414321130
Sun Jan 11 13:30:51 2009  A2: -73456024489071382
Sun Jan 11 13:30:51 2009  A3: -14805200109600
Sun Jan 11 13:30:51 2009  A4:  94944591
Sun Jan 11 13:30:51 2009  A5:  3060
Sun Jan 11 13:30:51 2009  skew 36845.15, size 5.659998e-011, alpha -5.326807, combined = 3.341570e-010
Sun Jan 11 13:30:51 2009  
Sun Jan 11 13:30:51 2009  commencing relation filtering
Sun Jan 11 13:30:51 2009  commencing duplicate removal, pass 1
Sun Jan 11 13:31:51 2009  found 347118 hash collisions in 4712358 relations
Sun Jan 11 13:32:18 2009  added 31775 free relations
Sun Jan 11 13:32:19 2009  commencing duplicate removal, pass 2
Sun Jan 11 13:32:29 2009  found 324399 duplicates and 4419733 unique relations
Sun Jan 11 13:32:29 2009  memory use: 43.3 MB
Sun Jan 11 13:32:29 2009  reading rational ideals above 2949120
Sun Jan 11 13:32:29 2009  reading algebraic ideals above 2949120
Sun Jan 11 13:32:29 2009  commencing singleton removal, pass 1
Sun Jan 11 13:33:30 2009  relations with 0 large ideals: 110837
Sun Jan 11 13:33:30 2009  relations with 1 large ideals: 695096
Sun Jan 11 13:33:30 2009  relations with 2 large ideals: 1569426
Sun Jan 11 13:33:30 2009  relations with 3 large ideals: 1492049
Sun Jan 11 13:33:30 2009  relations with 4 large ideals: 502184
Sun Jan 11 13:33:30 2009  relations with 5 large ideals: 20134
Sun Jan 11 13:33:30 2009  relations with 6 large ideals: 30007
Sun Jan 11 13:33:30 2009  relations with 7+ large ideals: 0
Sun Jan 11 13:33:30 2009  4419733 relations and about 4338337 large ideals
Sun Jan 11 13:33:30 2009  commencing singleton removal, pass 2
Sun Jan 11 13:34:31 2009  found 1969447 singletons
Sun Jan 11 13:34:31 2009  current dataset: 2450286 relations and about 1970706 large ideals
Sun Jan 11 13:34:31 2009  commencing singleton removal, pass 3
Sun Jan 11 13:35:07 2009  found 462026 singletons
Sun Jan 11 13:35:07 2009  current dataset: 1988260 relations and about 1474077 large ideals
Sun Jan 11 13:35:07 2009  commencing singleton removal, final pass
Sun Jan 11 13:35:39 2009  memory use: 37.3 MB
Sun Jan 11 13:35:39 2009  commencing in-memory singleton removal
Sun Jan 11 13:35:39 2009  begin with 1988260 relations and 1515227 unique ideals
Sun Jan 11 13:35:41 2009  reduce to 1664707 relations and 1182437 ideals in 16 passes
Sun Jan 11 13:35:41 2009  max relations containing the same ideal: 47
Sun Jan 11 13:35:42 2009  reading rational ideals above 720000
Sun Jan 11 13:35:42 2009  reading algebraic ideals above 720000
Sun Jan 11 13:35:42 2009  commencing singleton removal, final pass
Sun Jan 11 13:36:12 2009  keeping 1467428 ideals with weight <= 20, new excess is 187057
Sun Jan 11 13:36:13 2009  memory use: 46.9 MB
Sun Jan 11 13:36:13 2009  commencing in-memory singleton removal
Sun Jan 11 13:36:14 2009  begin with 1672568 relations and 1467428 unique ideals
Sun Jan 11 13:36:17 2009  reduce to 1651369 relations and 1408316 ideals in 15 passes
Sun Jan 11 13:36:17 2009  max relations containing the same ideal: 20
Sun Jan 11 13:36:18 2009  removing 139447 relations and 126414 ideals in 13033 cliques
Sun Jan 11 13:36:18 2009  commencing in-memory singleton removal
Sun Jan 11 13:36:18 2009  begin with 1511922 relations and 1408316 unique ideals
Sun Jan 11 13:36:20 2009  reduce to 1503837 relations and 1273735 ideals in 8 passes
Sun Jan 11 13:36:20 2009  max relations containing the same ideal: 20
Sun Jan 11 13:36:21 2009  removing 101981 relations and 88948 ideals in 13033 cliques
Sun Jan 11 13:36:21 2009  commencing in-memory singleton removal
Sun Jan 11 13:36:21 2009  begin with 1401856 relations and 1273735 unique ideals
Sun Jan 11 13:36:22 2009  reduce to 1396557 relations and 1179452 ideals in 7 passes
Sun Jan 11 13:36:22 2009  max relations containing the same ideal: 20
Sun Jan 11 13:36:23 2009  relations with 0 large ideals: 15119
Sun Jan 11 13:36:23 2009  relations with 1 large ideals: 105699
Sun Jan 11 13:36:23 2009  relations with 2 large ideals: 301464
Sun Jan 11 13:36:23 2009  relations with 3 large ideals: 437317
Sun Jan 11 13:36:23 2009  relations with 4 large ideals: 344432
Sun Jan 11 13:36:23 2009  relations with 5 large ideals: 148754
Sun Jan 11 13:36:23 2009  relations with 6 large ideals: 38263
Sun Jan 11 13:36:23 2009  relations with 7+ large ideals: 5509
Sun Jan 11 13:36:23 2009  commencing 2-way merge
Sun Jan 11 13:36:25 2009  reduce to 826083 relation sets and 608978 unique ideals
Sun Jan 11 13:36:25 2009  commencing full merge
Sun Jan 11 13:36:37 2009  memory use: 46.5 MB
Sun Jan 11 13:36:37 2009  found 385635 cycles, need 359178
Sun Jan 11 13:36:37 2009  weight of 359178 cycles is about 25497695 (70.99/cycle)
Sun Jan 11 13:36:37 2009  distribution of cycle lengths:
Sun Jan 11 13:36:37 2009  1 relations: 41032
Sun Jan 11 13:36:37 2009  2 relations: 37329
Sun Jan 11 13:36:37 2009  3 relations: 36815
Sun Jan 11 13:36:37 2009  4 relations: 33907
Sun Jan 11 13:36:37 2009  5 relations: 31185
Sun Jan 11 13:36:37 2009  6 relations: 27422
Sun Jan 11 13:36:37 2009  7 relations: 24890
Sun Jan 11 13:36:37 2009  8 relations: 21712
Sun Jan 11 13:36:37 2009  9 relations: 18849
Sun Jan 11 13:36:37 2009  10+ relations: 86037
Sun Jan 11 13:36:37 2009  heaviest cycle: 19 relations
Sun Jan 11 13:36:38 2009  commencing cycle optimization
Sun Jan 11 13:36:38 2009  start with 2306192 relations
Sun Jan 11 13:36:46 2009  pruned 71150 relations
Sun Jan 11 13:36:46 2009  memory use: 59.1 MB
Sun Jan 11 13:36:46 2009  distribution of cycle lengths:
Sun Jan 11 13:36:46 2009  1 relations: 41032
Sun Jan 11 13:36:46 2009  2 relations: 38368
Sun Jan 11 13:36:46 2009  3 relations: 38384
Sun Jan 11 13:36:46 2009  4 relations: 35109
Sun Jan 11 13:36:46 2009  5 relations: 32245
Sun Jan 11 13:36:46 2009  6 relations: 28176
Sun Jan 11 13:36:46 2009  7 relations: 25251
Sun Jan 11 13:36:46 2009  8 relations: 21807
Sun Jan 11 13:36:46 2009  9 relations: 19046
Sun Jan 11 13:36:46 2009  10+ relations: 79760
Sun Jan 11 13:36:46 2009  heaviest cycle: 19 relations
Sun Jan 11 13:36:47 2009  
Sun Jan 11 13:36:47 2009  commencing linear algebra
Sun Jan 11 13:36:47 2009  read 359178 cycles
Sun Jan 11 13:36:48 2009  cycles contain 1219899 unique relations
Sun Jan 11 13:37:11 2009  read 1219899 relations
Sun Jan 11 13:37:13 2009  using 20 quadratic characters above 67106504
Sun Jan 11 13:37:29 2009  building initial matrix
Sun Jan 11 13:37:49 2009  memory use: 143.3 MB
Sun Jan 11 13:37:50 2009  read 359178 cycles
Sun Jan 11 13:37:54 2009  matrix is 358916 x 359178 (101.8 MB) with weight 34240490 (95.33/col)
Sun Jan 11 13:37:54 2009  sparse part has weight 24159762 (67.26/col)
Sun Jan 11 13:38:04 2009  filtering completed in 3 passes
Sun Jan 11 13:38:04 2009  matrix is 356391 x 356591 (101.3 MB) with weight 34051114 (95.49/col)
Sun Jan 11 13:38:04 2009  sparse part has weight 24052492 (67.45/col)
Sun Jan 11 13:38:10 2009  read 356591 cycles
Sun Jan 11 13:38:34 2009  matrix is 356391 x 356591 (101.3 MB) with weight 34051114 (95.49/col)
Sun Jan 11 13:38:34 2009  sparse part has weight 24052492 (67.45/col)
Sun Jan 11 13:38:34 2009  saving the first 48 matrix rows for later
Sun Jan 11 13:38:34 2009  matrix is 356343 x 356591 (97.5 MB) with weight 27064086 (75.90/col)
Sun Jan 11 13:38:34 2009  sparse part has weight 23420867 (65.68/col)
Sun Jan 11 13:38:34 2009  matrix includes 64 packed rows
Sun Jan 11 13:38:34 2009  using block size 65536 for processor cache size 2048 kB
Sun Jan 11 13:38:39 2009  commencing Lanczos iteration
Sun Jan 11 13:38:39 2009  memory use: 94.9 MB
Sun Jan 11 14:23:46 2009  lanczos error: submatrix is not invertible
Sun Jan 11 14:23:46 2009  lanczos halted after 8286 iterations (dim = 523979)
Sun Jan 11 14:23:46 2009  linear algebra failed; retrying...
Sun Jan 11 14:23:46 2009  commencing Lanczos iteration
Sun Jan 11 14:23:46 2009  memory use: 94.9 MB
Sun Jan 11 14:54:33 2009  lanczos halted after 5635 iterations (dim = 356340)
Sun Jan 11 14:54:34 2009  recovered 31 nontrivial dependencies
Sun Jan 11 14:54:35 2009  
Sun Jan 11 14:54:35 2009  commencing square root phase
Sun Jan 11 14:54:35 2009  reading relations for dependency 1
Sun Jan 11 14:54:35 2009  read 178125 cycles
Sun Jan 11 14:54:35 2009  cycles contain 748833 unique relations
Sun Jan 11 14:54:56 2009  read 748833 relations
Sun Jan 11 14:55:01 2009  multiplying 607892 relations
Sun Jan 11 14:57:15 2009  multiply complete, coefficients have about 24.15 million bits
Sun Jan 11 14:57:17 2009  initial square root is modulo 8637493
Sun Jan 11 15:00:19 2009  prp48 factor: 432285313041719300052871390761329367297291202031
Sun Jan 11 15:00:19 2009  prp60 factor: 114560369726709893553301074140392913347253937166681264885463
Sun Jan 11 15:00:19 2009  elapsed time 01:29:31

What's that? A hardware glitch / cosmic ray hitting my CPU?

(I reran the factorization starting with the same relations on my C2D and did not get this error.)

Edit: Logfile of my run on the C2D laptop:

Code:

Sun Jan 11 14:33:07 2009  
Sun Jan 11 14:33:07 2009  
Sun Jan 11 14:33:07 2009  Msieve v. 1.39
Sun Jan 11 14:33:07 2009  random seeds: a38734c0 afc5c328
Sun Jan 11 14:33:07 2009  factoring 49522765289485889233681931153717435991979703139426318174911416089221747128358987182858892932767806807975353 (107 digits)
Sun Jan 11 14:33:08 2009  searching for 15-digit factors
Sun Jan 11 14:33:10 2009  commencing number field sieve (107-digit input)
Sun Jan 11 14:33:10 2009  R0: -438344816114060314814
Sun Jan 11 14:33:10 2009  R1:  132924059497
Sun Jan 11 14:33:10 2009  A0: -111978409899830736166589619
Sun Jan 11 14:33:10 2009  A1:  10900893999882414321130
Sun Jan 11 14:33:10 2009  A2: -73456024489071382
Sun Jan 11 14:33:10 2009  A3: -14805200109600
Sun Jan 11 14:33:10 2009  A4:  94944591
Sun Jan 11 14:33:10 2009  A5:  3060
Sun Jan 11 14:33:10 2009  skew 36845.15, size 5.659998e-011, alpha -5.326807, combined = 3.341570e-010
Sun Jan 11 14:33:10 2009  
Sun Jan 11 14:33:10 2009  commencing relation filtering
Sun Jan 11 14:33:10 2009  commencing duplicate removal, pass 1
Sun Jan 11 14:34:04 2009  found 347625 hash collisions in 4744132 relations
Sun Jan 11 14:34:23 2009  added 1 free relations
Sun Jan 11 14:34:23 2009  commencing duplicate removal, pass 2
Sun Jan 11 14:34:33 2009  found 324399 duplicates and 4419734 unique relations
Sun Jan 11 14:34:33 2009  memory use: 43.3 MB
Sun Jan 11 14:34:33 2009  reading rational ideals above 2949120
Sun Jan 11 14:34:33 2009  reading algebraic ideals above 2949120
Sun Jan 11 14:34:33 2009  commencing singleton removal, pass 1
Sun Jan 11 14:35:27 2009  relations with 0 large ideals: 110838
Sun Jan 11 14:35:27 2009  relations with 1 large ideals: 695096
Sun Jan 11 14:35:27 2009  relations with 2 large ideals: 1569426
Sun Jan 11 14:35:27 2009  relations with 3 large ideals: 1492049
Sun Jan 11 14:35:27 2009  relations with 4 large ideals: 502184
Sun Jan 11 14:35:27 2009  relations with 5 large ideals: 20134
Sun Jan 11 14:35:27 2009  relations with 6 large ideals: 30007
Sun Jan 11 14:35:27 2009  relations with 7+ large ideals: 0
Sun Jan 11 14:35:27 2009  4419734 relations and about 4338337 large ideals
Sun Jan 11 14:35:27 2009  commencing singleton removal, pass 2
Sun Jan 11 14:36:19 2009  found 1969447 singletons
Sun Jan 11 14:36:19 2009  current dataset: 2450287 relations and about 1970706 large ideals
Sun Jan 11 14:36:19 2009  commencing singleton removal, pass 3
Sun Jan 11 14:36:50 2009  found 462026 singletons
Sun Jan 11 14:36:50 2009  current dataset: 1988261 relations and about 1474077 large ideals
Sun Jan 11 14:36:50 2009  commencing singleton removal, final pass
Sun Jan 11 14:37:17 2009  memory use: 37.3 MB
Sun Jan 11 14:37:17 2009  commencing in-memory singleton removal
Sun Jan 11 14:37:17 2009  begin with 1988261 relations and 1515227 unique ideals
Sun Jan 11 14:37:19 2009  reduce to 1664708 relations and 1182437 ideals in 16 passes
Sun Jan 11 14:37:19 2009  max relations containing the same ideal: 47
Sun Jan 11 14:37:20 2009  reading rational ideals above 720000
Sun Jan 11 14:37:20 2009  reading algebraic ideals above 720000
Sun Jan 11 14:37:20 2009  commencing singleton removal, final pass
Sun Jan 11 14:37:46 2009  keeping 1421676 ideals with weight <= 20, new excess is 187057
Sun Jan 11 14:37:47 2009  memory use: 46.7 MB
Sun Jan 11 14:37:47 2009  commencing in-memory singleton removal
Sun Jan 11 14:37:48 2009  begin with 1664708 relations and 1421676 unique ideals
Sun Jan 11 14:37:50 2009  reduce to 1651370 relations and 1408316 ideals in 15 passes
Sun Jan 11 14:37:50 2009  max relations containing the same ideal: 20
Sun Jan 11 14:37:51 2009  removing 139455 relations and 126421 ideals in 13034 cliques
Sun Jan 11 14:37:51 2009  commencing in-memory singleton removal
Sun Jan 11 14:37:51 2009  begin with 1511915 relations and 1408316 unique ideals
Sun Jan 11 14:37:52 2009  reduce to 1503826 relations and 1273724 ideals in 8 passes
Sun Jan 11 14:37:52 2009  max relations containing the same ideal: 20
Sun Jan 11 14:37:53 2009  removing 101984 relations and 88950 ideals in 13034 cliques
Sun Jan 11 14:37:53 2009  commencing in-memory singleton removal
Sun Jan 11 14:37:53 2009  begin with 1401842 relations and 1273724 unique ideals
Sun Jan 11 14:37:53 2009  reduce to 1396543 relations and 1179439 ideals in 7 passes
Sun Jan 11 14:37:53 2009  max relations containing the same ideal: 20
Sun Jan 11 14:37:54 2009  relations with 0 large ideals: 15120
Sun Jan 11 14:37:54 2009  relations with 1 large ideals: 105699
Sun Jan 11 14:37:54 2009  relations with 2 large ideals: 301461
Sun Jan 11 14:37:54 2009  relations with 3 large ideals: 437312
Sun Jan 11 14:37:54 2009  relations with 4 large ideals: 344428
Sun Jan 11 14:37:54 2009  relations with 5 large ideals: 148752
Sun Jan 11 14:37:54 2009  relations with 6 large ideals: 38263
Sun Jan 11 14:37:54 2009  relations with 7+ large ideals: 5508
Sun Jan 11 14:37:54 2009  commencing 2-way merge
Sun Jan 11 14:37:56 2009  reduce to 826080 relation sets and 608976 unique ideals
Sun Jan 11 14:37:56 2009  commencing full merge
Sun Jan 11 14:38:07 2009  memory use: 46.5 MB
Sun Jan 11 14:38:07 2009  found 385653 cycles, need 359176
Sun Jan 11 14:38:07 2009  weight of 359176 cycles is about 25500227 (71.00/cycle)
Sun Jan 11 14:38:07 2009  distribution of cycle lengths:
Sun Jan 11 14:38:07 2009  1 relations: 41038
Sun Jan 11 14:38:07 2009  2 relations: 37302
Sun Jan 11 14:38:07 2009  3 relations: 36818
Sun Jan 11 14:38:07 2009  4 relations: 33878
Sun Jan 11 14:38:07 2009  5 relations: 31174
Sun Jan 11 14:38:07 2009  6 relations: 27493
Sun Jan 11 14:38:07 2009  7 relations: 24872
Sun Jan 11 14:38:07 2009  8 relations: 21684
Sun Jan 11 14:38:07 2009  9 relations: 18882
Sun Jan 11 14:38:07 2009  10+ relations: 86035
Sun Jan 11 14:38:07 2009  heaviest cycle: 19 relations
Sun Jan 11 14:38:07 2009  commencing cycle optimization
Sun Jan 11 14:38:08 2009  start with 2306467 relations
Sun Jan 11 14:38:14 2009  pruned 71206 relations
Sun Jan 11 14:38:14 2009  memory use: 59.1 MB
Sun Jan 11 14:38:14 2009  distribution of cycle lengths:
Sun Jan 11 14:38:14 2009  1 relations: 41038
Sun Jan 11 14:38:14 2009  2 relations: 38347
Sun Jan 11 14:38:14 2009  3 relations: 38386
Sun Jan 11 14:38:14 2009  4 relations: 35075
Sun Jan 11 14:38:14 2009  5 relations: 32238
Sun Jan 11 14:38:14 2009  6 relations: 28236
Sun Jan 11 14:38:14 2009  7 relations: 25238
Sun Jan 11 14:38:14 2009  8 relations: 21790
Sun Jan 11 14:38:14 2009  9 relations: 19075
Sun Jan 11 14:38:14 2009  10+ relations: 79753
Sun Jan 11 14:38:14 2009  heaviest cycle: 19 relations
Sun Jan 11 14:38:15 2009  
Sun Jan 11 14:38:15 2009  commencing linear algebra
Sun Jan 11 14:38:15 2009  read 359176 cycles
Sun Jan 11 14:38:16 2009  cycles contain 1219904 unique relations
Sun Jan 11 14:38:37 2009  read 1219904 relations
Sun Jan 11 14:38:39 2009  using 20 quadratic characters above 67106504
Sun Jan 11 14:38:48 2009  building initial matrix
Sun Jan 11 14:39:04 2009  memory use: 143.3 MB
Sun Jan 11 14:39:04 2009  read 359176 cycles
Sun Jan 11 14:39:09 2009  matrix is 358916 x 359176 (101.8 MB) with weight 34242477 (95.34/col)
Sun Jan 11 14:39:09 2009  sparse part has weight 24161895 (67.27/col)
Sun Jan 11 14:39:15 2009  filtering completed in 3 passes
Sun Jan 11 14:39:15 2009  matrix is 356378 x 356578 (101.3 MB) with weight 34051136 (95.49/col)
Sun Jan 11 14:39:15 2009  sparse part has weight 24053165 (67.46/col)
Sun Jan 11 14:39:26 2009  read 356578 cycles
Sun Jan 11 14:39:48 2009  matrix is 356378 x 356578 (101.3 MB) with weight 34051136 (95.49/col)
Sun Jan 11 14:39:48 2009  sparse part has weight 24053165 (67.46/col)
Sun Jan 11 14:39:48 2009  saving the first 48 matrix rows for later
Sun Jan 11 14:39:48 2009  matrix is 356330 x 356578 (97.5 MB) with weight 27064648 (75.90/col)
Sun Jan 11 14:39:48 2009  sparse part has weight 23421599 (65.68/col)
Sun Jan 11 14:39:48 2009  matrix includes 64 packed rows
Sun Jan 11 14:39:48 2009  using block size 65536 for processor cache size 4096 kB
Sun Jan 11 14:39:52 2009  commencing Lanczos iteration
Sun Jan 11 14:39:52 2009  memory use: 94.9 MB
Sun Jan 11 14:59:38 2009  lanczos halted after 5636 iterations (dim = 356328)
Sun Jan 11 14:59:39 2009  recovered 32 nontrivial dependencies
Sun Jan 11 14:59:40 2009  
Sun Jan 11 14:59:40 2009  commencing square root phase
Sun Jan 11 14:59:40 2009  reading relations for dependency 1
Sun Jan 11 14:59:40 2009  read 177839 cycles
Sun Jan 11 14:59:40 2009  cycles contain 747735 unique relations
Sun Jan 11 15:00:00 2009  read 747735 relations
Sun Jan 11 15:00:04 2009  multiplying 606662 relations
Sun Jan 11 15:01:47 2009  multiply complete, coefficients have about 24.10 million bits
Sun Jan 11 15:01:48 2009  initial square root is modulo 8362163
Sun Jan 11 15:04:11 2009  reading relations for dependency 2
Sun Jan 11 15:04:11 2009  read 177507 cycles
Sun Jan 11 15:04:11 2009  cycles contain 747061 unique relations
Sun Jan 11 15:04:31 2009  read 747061 relations
Sun Jan 11 15:04:35 2009  multiplying 606718 relations
Sun Jan 11 15:06:19 2009  multiply complete, coefficients have about 24.10 million bits
Sun Jan 11 15:06:20 2009  initial square root is modulo 8365739
Sun Jan 11 15:08:42 2009  reading relations for dependency 3
Sun Jan 11 15:08:42 2009  read 178069 cycles
Sun Jan 11 15:08:43 2009  cycles contain 748967 unique relations
Sun Jan 11 15:09:03 2009  read 748967 relations
Sun Jan 11 15:09:07 2009  multiplying 608248 relations
Sun Jan 11 15:10:50 2009  multiply complete, coefficients have about 24.16 million bits
Sun Jan 11 15:10:52 2009  initial square root is modulo 8716289
Sun Jan 11 15:13:13 2009  reading relations for dependency 4
Sun Jan 11 15:13:13 2009  read 177853 cycles
Sun Jan 11 15:13:14 2009  cycles contain 748192 unique relations
Sun Jan 11 15:13:35 2009  read 748192 relations
Sun Jan 11 15:13:48 2009  multiplying 607722 relations
Sun Jan 11 15:15:31 2009  multiply complete, coefficients have about 24.15 million bits
Sun Jan 11 15:15:32 2009  initial square root is modulo 8606929
Sun Jan 11 15:17:53 2009  prp48 factor: 432285313041719300052871390761329367297291202031
Sun Jan 11 15:17:53 2009  prp60 factor: 114560369726709893553301074140392913347253937166681264885463
Sun Jan 11 15:17:53 2009  elapsed time 00:44:46

4 dependencies needed to find the factors - vs one in the P4 retry? Why the difference?

jasonp · 2009-01-11, 14:56

This is the first time I've seen a Lanczos run reach >100% and actually terminate (with an error). It appears to happen once in a while, and failures of the sort listed are not impossible according to the theory behind block Lanczos. If, as is more likely, there's a well-hidden bug in the code, I have no clue how to go about fixing it.

Regarding the different number of dependencies, this is because the library chooses a random start vector when performing the linear algebra. Even if the matrix is exactly the same between two machines, this implies that the dependencies found will be different from run to run. When the input has two factors, each dependency has a 2-in-3 chance of being nontrivial but you "reroll the dice" every time a new batch of dependencies is computed.

Andi47 · 2009-01-11, 15:09

Quote:

Originally Posted by jasonp

This is the first time I've seen a Lanczos run reach >100% and actually terminate (with an error). It appears to happen once in a while, and failures of the sort listed are not impossible according to the theory behind block Lanczos. If, as is more likely, there's a well-hidden bug in the code, I have no clue how to go about fixing it.

Regarding the different number of dependencies, this is because the library chooses a random start vector when performing the linear algebra. Even if the matrix is exactly the same between two machines, this implies that the dependencies found will be different from run to run. When the input has two factors, each dependency has a 2-in-3 chance of being nontrivial but you "reroll the dice" every time a new batch of dependencies is computed.

So even when the error is not reproducible between two machines, this is no prove for a hardware error on my first machine?

BTW: about trying to fix a possible elusive bug: What about printing the start vector to the logfile? This might make it somewhat easier to track it down.

Edit: I still have got the matrix - if you want to have it for testing, I could upload it and give you the link. (I assume that you need the msieve.dat.mat file.)

Edit2: About running above 100% and terminating: Fivemack had some matrices to run beyond 100% and AFIK he stopped these runs manually. So possible these ones might have terminated themselves too, but who wants to run a matrix up to 146% when this takes an additional week or two?

10metreh · 2009-01-11, 16:06

Quote:

Originally Posted by Andi47

I assume that you need the msieve.mat.dat file.

And I assume that you need the msieve.dat.mat file.

Andi47 · 2009-01-11, 16:08

Quote:

Originally Posted by 10metreh

And I assume that you need the msieve.dat.mat file.

*grrrr* sorry, mistyped it.

jasonp · 2009-01-11, 17:29

I don't have the time to do more research on this problem. I think automatically quitting with an error when the number of dimensions exceeds maybe 105% of the maximum expected is a good idea.

Andi47 · 2009-01-11, 17:33

Quote:

Originally Posted by jasonp

I don't have the time to do more research on this problem. I think automatically quitting with an error when the number of dimensions exceeds maybe 105% of the maximum expected is a good idea.

Why not 100.5%? Is there any chance for a matrix to succeed when the number of dimensions exceeds 100% of the maximum expected?

This question went unanswered:

Quote:

Originally Posted by Andi47

So even when the error is not reproducible between two machines, this is no prove for a hardware error on my first machine? (addition: i.e. getting an error one time and none the other time could still be caused by software related things like choosing a random starting vector?)

jasonp · 2009-01-11, 19:33

I don't know if it's possible to get a completed matrix solution if the iterations go over 100%; it's never happened but that doesn't mean it's impossible.

Yes, in theory the code could be working perfectly and merely have chosen a bad starting vector. I have seen the 'matrix not invertible' error occur before reaching 100%, and all the times it has happened there was never a question about the stability of the underlying machine. Block Lanczos is not a good stress test for the memory system anyway, because the amount of tuning I've had time to perform on the code is quite minimal.

2009-01-11, 19:33	#8
jasonp Tribal Bullet Oct 2004 2×3×19×31 Posts	I don't know if it's possible to get a completed matrix solution if the iterations go over 100%; it's never happened but that doesn't mean it's impossible. Yes, in theory the code could be working perfectly and merely have chosen a bad starting vector. I have seen the 'matrix not invertible' error occur before reaching 100%, and all the times it has happened there was never a question about the stability of the underlying machine. Block Lanczos is not a good stress test for the memory system anyway, because the amount of tuning I've had time to perform on the code is quite minimal. Last fiddled with by jasonp on 2009-01-11 at 19:34

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Initial vector in Lanczos	Robert Holmes	Miscellaneous Math	4	2010-09-11 01:34
Msieve Lanczos scalability	Jeff Gilchrist	Msieve	1	2009-01-02 09:32

2009-01-11, 14:56	#2
jasonp Tribal Bullet Oct 2004 2·3·19·31 Posts	This is the first time I've seen a Lanczos run reach >100% and actually terminate (with an error). It appears to happen once in a while, and failures of the sort listed are not impossible according to the theory behind block Lanczos. If, as is more likely, there's a well-hidden bug in the code, I have no clue how to go about fixing it. Regarding the different number of dependencies, this is because the library chooses a random start vector when performing the linear algebra. Even if the matrix is exactly the same between two machines, this implies that the dependencies found will be different from run to run. When the input has two factors, each dependency has a 2-in-3 chance of being nontrivial but you "reroll the dice" every time a new batch of dependencies is computed.

2009-01-11, 17:29	#6
jasonp Tribal Bullet Oct 2004 2·3·19·31 Posts	I don't have the time to do more research on this problem. I think automatically quitting with an error when the number of dimensions exceeds maybe 105% of the maximum expected is a good idea.