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error: attempted to heapify an empty ideal

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  • Bob Backstrom
    Hi All, I was trying SNFS with msieve postprocessing, and got the above on-screen message. What a great new word! ... commencing 2-way merge reduce to 2398492
    Message 1 of 1 , Dec 23, 2012
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      Hi All,

      I was trying SNFS with msieve postprocessing, and got the above on-screen message. What a great new word!

      ...
      commencing 2-way merge
      reduce to 2398492 relation sets and 2354441 unique ideals
      ignored 15 oversize relation sets
      commencing full merge
      error: attempted to heapify an empty ideal
      /home/bob/ggnfs/tests/a00-4-4>

      See the full logs, below.

      I could either run the whole job again, or sieve a little more and hope that the "random seeds: c3d73543 46781ae5" make a difference.

      Whew - it factorized OK, but why? And how did an empty ideal appear anyway?

      [ The number was the c157 from 28^127 - 1 ]

      --Puzzled,
      --Bob.

      1st Msieve log:

      Sun Dec 23 18:39:05 2012 Msieve v. 1.44
      Sun Dec 23 18:39:05 2012 random seeds: c3d73543 46781ae5
      Sun Dec 23 18:39:05 2012 factoring 8282721070354851188453168612923435315564541945272663987157778308152769811494993757432168341389819864203275331228417922079441705962309512160923635534221961579 (157 digits)
      Sun Dec 23 18:39:06 2012 no P-1/P+1/ECM available, skipping
      Sun Dec 23 18:39:06 2012 commencing number field sieve (157-digit input)
      Sun Dec 23 18:39:06 2012 R0: -3019818067898448875963258769439195136
      Sun Dec 23 18:39:06 2012 R1: 1
      Sun Dec 23 18:39:06 2012 A0: -2
      Sun Dec 23 18:39:06 2012 A1: 0
      Sun Dec 23 18:39:06 2012 A2: 0
      Sun Dec 23 18:39:06 2012 A3: 0
      Sun Dec 23 18:39:06 2012 A4: 0
      Sun Dec 23 18:39:06 2012 A5: 49
      Sun Dec 23 18:39:06 2012 skew 1.00, size 1.025584e-12, alpha 1.143488, combined = 8.280126e-11
      Sun Dec 23 18:39:06 2012
      Sun Dec 23 18:39:06 2012 commencing relation filtering
      Sun Dec 23 18:39:06 2012 estimated available RAM is 3926.0 MB
      Sun Dec 23 18:39:06 2012 commencing duplicate removal, pass 1
      Sun Dec 23 18:39:57 2012 error -11 reading relation 7849272
      Sun Dec 23 18:42:08 2012 found 4255928 hash collisions in 27771090 relations
      Sun Dec 23 18:42:37 2012 added 717243 free relations
      Sun Dec 23 18:42:37 2012 commencing duplicate removal, pass 2
      Sun Dec 23 18:42:51 2012 found 3672478 duplicates and 24815855 unique relations
      Sun Dec 23 18:42:51 2012 memory use: 165.2 MB
      Sun Dec 23 18:42:51 2012 reading ideals above 6750208
      Sun Dec 23 18:42:52 2012 commencing singleton removal, initial pass
      Sun Dec 23 18:46:11 2012 memory use: 753.0 MB
      Sun Dec 23 18:46:11 2012 reading all ideals from disk
      Sun Dec 23 18:46:13 2012 memory use: 458.6 MB
      Sun Dec 23 18:46:16 2012 commencing in-memory singleton removal
      Sun Dec 23 18:46:18 2012 begin with 24815855 relations and 28305365 unique ideals
      Sun Dec 23 18:46:36 2012 reduce to 5813452 relations and 4798213 ideals in 22 passes
      Sun Dec 23 18:46:36 2012 max relations containing the same ideal: 18
      Sun Dec 23 18:46:37 2012 reading ideals above 100000
      Sun Dec 23 18:46:37 2012 commencing singleton removal, initial pass
      Sun Dec 23 18:47:36 2012 memory use: 172.2 MB
      Sun Dec 23 18:47:37 2012 reading all ideals from disk
      Sun Dec 23 18:47:38 2012 memory use: 215.9 MB
      Sun Dec 23 18:47:39 2012 keeping 5772938 ideals with weight <= 200, target excess is 36972
      Sun Dec 23 18:47:40 2012 commencing in-memory singleton removal
      Sun Dec 23 18:47:40 2012 begin with 5829112 relations and 5772938 unique ideals
      Sun Dec 23 18:47:52 2012 reduce to 5802228 relations and 5669755 ideals in 12 passes
      Sun Dec 23 18:47:52 2012 max relations containing the same ideal: 200
      Sun Dec 23 18:47:57 2012 removing 655496 relations and 610703 ideals in 44793 cliques
      Sun Dec 23 18:47:57 2012 commencing in-memory singleton removal
      Sun Dec 23 18:47:58 2012 begin with 5146732 relations and 5669755 unique ideals
      Sun Dec 23 18:48:10 2012 reduce to 5081599 relations and 4993137 ideals in 13 passes
      Sun Dec 23 18:48:10 2012 max relations containing the same ideal: 189
      Sun Dec 23 18:48:14 2012 removing 470974 relations and 426181 ideals in 44793 cliques
      Sun Dec 23 18:48:14 2012 commencing in-memory singleton removal
      Sun Dec 23 18:48:15 2012 begin with 4610625 relations and 4993137 unique ideals
      Sun Dec 23 18:48:26 2012 reduce to 4571577 relations and 4527511 ideals in 13 passes
      Sun Dec 23 18:48:26 2012 max relations containing the same ideal: 176
      Sun Dec 23 18:48:31 2012 relations with 0 large ideals: 822
      Sun Dec 23 18:48:31 2012 relations with 1 large ideals: 90
      Sun Dec 23 18:48:31 2012 relations with 2 large ideals: 1430
      Sun Dec 23 18:48:31 2012 relations with 3 large ideals: 18954
      Sun Dec 23 18:48:31 2012 relations with 4 large ideals: 131254
      Sun Dec 23 18:48:31 2012 relations with 5 large ideals: 508658
      Sun Dec 23 18:48:31 2012 relations with 6 large ideals: 1132777
      Sun Dec 23 18:48:31 2012 relations with 7+ large ideals: 2777592
      Sun Dec 23 18:48:31 2012 commencing 2-way merge
      Sun Dec 23 18:48:36 2012 reduce to 2398492 relation sets and 2354441 unique ideals
      Sun Dec 23 18:48:36 2012 ignored 15 oversize relation sets
      Sun Dec 23 18:48:36 2012 commencing full merge

      ( No more in the log file )

      error: attempted to heapify an empty ideal ( ON SCREEN - error output )

      2nd Msieve log:

      Sun Dec 23 19:19:48 2012 Msieve v. 1.44
      Sun Dec 23 19:19:48 2012 random seeds: afc59ba8 ffe95570
      Sun Dec 23 19:19:48 2012 factoring 8282721070354851188453168612923435315564541945272663987157778308152769811494993757432168341389819864203275331228417922079441705962309512160923635534221961579 (157 digits)
      Sun Dec 23 19:19:49 2012 no P-1/P+1/ECM available, skipping
      Sun Dec 23 19:19:49 2012 commencing number field sieve (157-digit input)
      Sun Dec 23 19:19:49 2012 R0: -3019818067898448875963258769439195136
      Sun Dec 23 19:19:49 2012 R1: 1
      Sun Dec 23 19:19:49 2012 A0: -2
      Sun Dec 23 19:19:49 2012 A1: 0
      Sun Dec 23 19:19:49 2012 A2: 0
      Sun Dec 23 19:19:49 2012 A3: 0
      Sun Dec 23 19:19:49 2012 A4: 0
      Sun Dec 23 19:19:49 2012 A5: 49
      Sun Dec 23 19:19:49 2012 skew 1.00, size 1.025584e-12, alpha 1.143488, combined = 8.280126e-11
      Sun Dec 23 19:19:49 2012
      Sun Dec 23 19:19:49 2012 commencing relation filtering
      Sun Dec 23 19:19:49 2012 estimated available RAM is 3926.0 MB
      Sun Dec 23 19:19:49 2012 commencing duplicate removal, pass 1
      Sun Dec 23 19:20:39 2012 error -11 reading relation 7849272
      Sun Dec 23 19:23:03 2012 found 4415982 hash collisions in 28940568 relations
      Sun Dec 23 19:23:29 2012 added 595 free relations
      Sun Dec 23 19:23:29 2012 commencing duplicate removal, pass 2
      Sun Dec 23 19:23:41 2012 found 3767776 duplicates and 25173387 unique relations
      Sun Dec 23 19:23:41 2012 memory use: 165.2 MB
      Sun Dec 23 19:23:41 2012 reading ideals above 6750208
      Sun Dec 23 19:23:43 2012 commencing singleton removal, initial pass
      Sun Dec 23 19:27:03 2012 memory use: 753.0 MB
      Sun Dec 23 19:27:03 2012 reading all ideals from disk
      Sun Dec 23 19:27:05 2012 memory use: 465.3 MB
      Sun Dec 23 19:27:08 2012 commencing in-memory singleton removal
      Sun Dec 23 19:27:10 2012 begin with 25173387 relations and 28508919 unique ideals
      Sun Dec 23 19:27:29 2012 reduce to 6179586 relations and 5083166 ideals in 22 passes
      Sun Dec 23 19:27:29 2012 max relations containing the same ideal: 18
      Sun Dec 23 19:27:30 2012 reading ideals above 100000
      Sun Dec 23 19:27:30 2012 commencing singleton removal, initial pass
      Sun Dec 23 19:28:31 2012 memory use: 172.2 MB
      Sun Dec 23 19:28:33 2012 reading all ideals from disk
      Sun Dec 23 19:28:33 2012 memory use: 229.1 MB
      Sun Dec 23 19:28:34 2012 keeping 5967310 ideals with weight <= 200, target excess is 39306
      Sun Dec 23 19:28:35 2012 commencing in-memory singleton removal
      Sun Dec 23 19:28:36 2012 begin with 6180182 relations and 5967310 unique ideals
      Sun Dec 23 19:28:55 2012 reduce to 6171057 relations and 5955223 ideals in 18 passes
      Sun Dec 23 19:28:55 2012 max relations containing the same ideal: 200
      Sun Dec 23 19:29:00 2012 removing 967993 relations and 882873 ideals in 85120 cliques
      Sun Dec 23 19:29:00 2012 commencing in-memory singleton removal
      Sun Dec 23 19:29:01 2012 begin with 5203064 relations and 5955223 unique ideals
      Sun Dec 23 19:29:11 2012 reduce to 5076282 relations and 4943063 ideals in 12 passes
      Sun Dec 23 19:29:11 2012 max relations containing the same ideal: 183
      Sun Dec 23 19:29:15 2012 removing 704740 relations and 619620 ideals in 85120 cliques
      Sun Dec 23 19:29:16 2012 commencing in-memory singleton removal
      Sun Dec 23 19:29:16 2012 begin with 4371542 relations and 4943063 unique ideals
      Sun Dec 23 19:29:24 2012 reduce to 4287296 relations and 4237645 ideals in 11 passes
      Sun Dec 23 19:29:24 2012 max relations containing the same ideal: 159
      Sun Dec 23 19:29:29 2012 relations with 0 large ideals: 874
      Sun Dec 23 19:29:29 2012 relations with 1 large ideals: 95
      Sun Dec 23 19:29:29 2012 relations with 2 large ideals: 1746
      Sun Dec 23 19:29:29 2012 relations with 3 large ideals: 21732
      Sun Dec 23 19:29:29 2012 relations with 4 large ideals: 142270
      Sun Dec 23 19:29:29 2012 relations with 5 large ideals: 521790
      Sun Dec 23 19:29:29 2012 relations with 6 large ideals: 1102612
      Sun Dec 23 19:29:29 2012 relations with 7+ large ideals: 2496177
      Sun Dec 23 19:29:29 2012 commencing 2-way merge
      Sun Dec 23 19:29:33 2012 reduce to 2285321 relation sets and 2235685 unique ideals
      Sun Dec 23 19:29:33 2012 ignored 15 oversize relation sets
      Sun Dec 23 19:29:33 2012 commencing full merge
      Sun Dec 23 19:30:13 2012 memory use: 244.6 MB
      Sun Dec 23 19:30:13 2012 found 1185378 cycles, need 1177885
      Sun Dec 23 19:30:13 2012 weight of 1177885 cycles is about 82678098 (70.19/cycle)
      Sun Dec 23 19:30:13 2012 distribution of cycle lengths:
      Sun Dec 23 19:30:13 2012 1 relations: 145721
      Sun Dec 23 19:30:13 2012 2 relations: 153420
      Sun Dec 23 19:30:13 2012 3 relations: 148322
      Sun Dec 23 19:30:13 2012 4 relations: 130034
      Sun Dec 23 19:30:13 2012 5 relations: 116114
      Sun Dec 23 19:30:13 2012 6 relations: 97026
      Sun Dec 23 19:30:13 2012 7 relations: 80294
      Sun Dec 23 19:30:13 2012 8 relations: 64922
      Sun Dec 23 19:30:13 2012 9 relations: 53508
      Sun Dec 23 19:30:13 2012 10+ relations: 188524
      Sun Dec 23 19:30:13 2012 heaviest cycle: 24 relations
      Sun Dec 23 19:30:14 2012 commencing cycle optimization
      Sun Dec 23 19:30:16 2012 start with 6569279 relations
      Sun Dec 23 19:30:24 2012 pruned 83077 relations
      Sun Dec 23 19:30:24 2012 memory use: 239.4 MB
      Sun Dec 23 19:30:24 2012 distribution of cycle lengths:
      Sun Dec 23 19:30:24 2012 1 relations: 145721
      Sun Dec 23 19:30:24 2012 2 relations: 155573
      Sun Dec 23 19:30:24 2012 3 relations: 151626
      Sun Dec 23 19:30:24 2012 4 relations: 131331
      Sun Dec 23 19:30:24 2012 5 relations: 117173
      Sun Dec 23 19:30:24 2012 6 relations: 97007
      Sun Dec 23 19:30:24 2012 7 relations: 80069
      Sun Dec 23 19:30:24 2012 8 relations: 64459
      Sun Dec 23 19:30:24 2012 9 relations: 52951
      Sun Dec 23 19:30:24 2012 10+ relations: 181975
      Sun Dec 23 19:30:24 2012 heaviest cycle: 24 relations
      Sun Dec 23 19:30:26 2012 RelProcTime: 637
      Sun Dec 23 19:30:26 2012
      Sun Dec 23 19:30:26 2012 commencing linear algebra
      Sun Dec 23 19:30:27 2012 read 1177885 cycles
      Sun Dec 23 19:30:29 2012 cycles contain 4173643 unique relations
      Sun Dec 23 19:30:59 2012 read 4173643 relations
      Sun Dec 23 19:31:04 2012 using 20 quadratic characters above 536868224
      Sun Dec 23 19:31:24 2012 building initial matrix
      Sun Dec 23 19:32:07 2012 memory use: 507.5 MB
      Sun Dec 23 19:32:08 2012 read 1177885 cycles
      Sun Dec 23 19:32:09 2012 matrix is 1177705 x 1177885 (357.4 MB) with weight 104765164 (88.94/col)
      Sun Dec 23 19:32:09 2012 sparse part has weight 80724118 (68.53/col)
      Sun Dec 23 19:32:22 2012 filtering completed in 2 passes
      Sun Dec 23 19:32:22 2012 matrix is 1173880 x 1174059 (357.1 MB) with weight 104646653 (89.13/col)
      Sun Dec 23 19:32:22 2012 sparse part has weight 80684359 (68.72/col)
      Sun Dec 23 19:32:29 2012 read 1174059 cycles
      Sun Dec 23 19:32:30 2012 matrix is 1173880 x 1174059 (357.1 MB) with weight 104646653 (89.13/col)
      Sun Dec 23 19:32:30 2012 sparse part has weight 80684359 (68.72/col)
      Sun Dec 23 19:32:30 2012 saving the first 48 matrix rows for later
      Sun Dec 23 19:32:30 2012 matrix is 1173832 x 1174059 (337.7 MB) with weight 83373112 (71.01/col)
      Sun Dec 23 19:32:30 2012 sparse part has weight 76795448 (65.41/col)
      Sun Dec 23 19:32:30 2012 matrix includes 64 packed rows
      Sun Dec 23 19:32:30 2012 using block size 65536 for processor cache size 6144 kB
      Sun Dec 23 19:32:35 2012 commencing Lanczos iteration (4 threads)
      Sun Dec 23 19:32:35 2012 memory use: 356.4 MB
      Sun Dec 23 19:32:39 2012 linear algebra at 0.1%, ETA 1h42m
      Sun Dec 23 20:59:15 2012 lanczos halted after 18565 iterations (dim = 1173829)
      Sun Dec 23 20:59:17 2012 recovered 36 nontrivial dependencies
      Sun Dec 23 20:59:17 2012 BLanczosTime: 5331
      Sun Dec 23 20:59:17 2012
      Sun Dec 23 20:59:17 2012 commencing square root phase
      Sun Dec 23 20:59:17 2012 reading relations for dependency 1
      Sun Dec 23 20:59:17 2012 read 586874 cycles
      Sun Dec 23 20:59:18 2012 cycles contain 2086230 unique relations
      Sun Dec 23 20:59:38 2012 read 2086230 relations
      Sun Dec 23 20:59:48 2012 multiplying 2086230 relations
      Sun Dec 23 21:03:17 2012 multiply complete, coefficients have about 57.71 million bits
      Sun Dec 23 21:03:17 2012 initial square root is modulo 192953161
      Sun Dec 23 21:10:16 2012 reading relations for dependency 2
      Sun Dec 23 21:10:16 2012 read 587695 cycles
      Sun Dec 23 21:10:17 2012 cycles contain 2087606 unique relations
      Sun Dec 23 21:10:35 2012 read 2087606 relations
      Sun Dec 23 21:10:45 2012 multiplying 2087606 relations
      Sun Dec 23 21:14:14 2012 multiply complete, coefficients have about 57.75 million bits
      Sun Dec 23 21:14:14 2012 initial square root is modulo 195235921
      Sun Dec 23 21:21:13 2012 sqrtTime: 1316
      Sun Dec 23 21:21:13 2012 prp60 factor: 344447951127378870001590288205144270684880590492124834263903
      Sun Dec 23 21:21:13 2012 prp98 factor: 24046364750452100726517334931146788058289966764118423304371309159373377082258966093080527537746293
      Sun Dec 23 21:21:13 2012 elapsed time 02:01:25

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