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 2018-06-25, 14:14 #1 VictordeHolland     "Victor de Hollander" Aug 2011 the Netherlands 2·587 Posts Factoring on a ARM board (Odroid-U2) with Cortex A9 These little ARM boards are a lot of fun . Hint: They're not particularly fast GMP-ECM 7.0.5-dev http://mersenneforum.org/showthread.php?t=23070 CADO-NFS 3.0-dev (factoring RSA-100 in about 3.5h) http://mersenneforum.org/showpost.ph...&postcount=129 and now also Msieve (SVN1022) Quadratic sieve: Code: odroid@odroid-u2:~/Documents/msieve-SVN1022$./msieve -v 482023953171263179598463399469620779294192640218599890595570781655655552082529 Msieve v. 1.54 (SVN Unversioned directory) Mon Jun 25 14:41:10 2018 random seeds: 93cbf29d 83c8d2b2 factoring 482023953171263179598463399469620779294192640218599890595570781655655552082529 (78 digits) searching for 15-digit factors commencing quadratic sieve (78-digit input) using multiplier of 3 using generic 32kb sieve core sieve interval: 12 blocks of size 32768 processing polynomials in batches of 17 using a sieve bound of 952381 (37824 primes) using large prime bound of 95238100 (26 bits) using trial factoring cutoff of 27 bits polynomial 'A' values have 10 factors sieving in progress (press Ctrl-C to pause) 38137 relations (19841 full + 18296 combined from 204445 partial), need 37920 38137 relations (19841 full + 18296 combined from 204445 partial), need 37920 sieving complete, commencing postprocessing begin with 224286 relations reduce to 54111 relations in 2 passes attempting to read 54111 relations recovered 54111 relations recovered 42193 polynomials attempting to build 38137 cycles found 38137 cycles in 1 passes distribution of cycle lengths: length 1 : 19841 length 2 : 18296 largest cycle: 2 relations matrix is 37824 x 38137 (5.0 MB) with weight 1145593 (30.04/col) sparse part has weight 1145593 (30.04/col) filtering completed in 4 passes matrix is 26555 x 26619 (3.8 MB) with weight 893449 (33.56/col) sparse part has weight 893449 (33.56/col) saving the first 48 matrix rows for later matrix includes 64 packed rows matrix is 26507 x 26619 (2.4 MB) with weight 655532 (24.63/col) sparse part has weight 470989 (17.69/col) commencing Lanczos iteration memory use: 2.4 MB lanczos halted after 421 iterations (dim = 26505) recovered 16 nontrivial dependencies p1 factor: 3 p33 factor: 300704334686783305051368312538631 p45 factor: 534327685114509832669825288562536388785831453 elapsed time 00:13:22 Next I did polysearch+sieve of RSA100 on a computer (x86_64) and copied the relations and poly to the ARM board and did the filtering/LA and SQR with msieve there: Code: Sun Jun 24 13:42:13 2018 Sun Jun 24 13:42:13 2018 Sun Jun 24 13:42:13 2018 Msieve v. 1.54 (SVN Unversioned directory) Sun Jun 24 13:42:13 2018 random seeds: 3202ded0 6ba54a8e Sun Jun 24 13:42:13 2018 factoring 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 (100 digits) Sun Jun 24 13:42:16 2018 searching for 15-digit factors Sun Jun 24 13:42:18 2018 commencing number field sieve (100-digit input) Sun Jun 24 13:42:18 2018 R0: -1500948764646399765833785 Sun Jun 24 13:42:18 2018 R1: 4412959449373 Sun Jun 24 13:42:18 2018 A0: 58495626606615351512386040384 Sun Jun 24 13:42:18 2018 A1: -5772374246691267911604 Sun Jun 24 13:42:18 2018 A2: -8833629323103645 Sun Jun 24 13:42:18 2018 A3: 595383944 Sun Jun 24 13:42:18 2018 A4: 300 Sun Jun 24 13:42:18 2018 skew 4593762.87, size 1.165e-13, alpha -4.779, combined = 1.277e-08 rroots = 2 Sun Jun 24 13:42:18 2018 Sun Jun 24 13:42:18 2018 commencing relation filtering Sun Jun 24 13:42:18 2018 estimated available RAM is 2023.1 MB Sun Jun 24 13:42:18 2018 commencing duplicate removal, pass 1 Sun Jun 24 13:47:23 2018 found 364484 hash collisions in 4508009 relations Sun Jun 24 13:48:46 2018 commencing duplicate removal, pass 2 Sun Jun 24 13:48:50 2018 found 255001 duplicates and 4253008 unique relations Sun Jun 24 13:48:50 2018 memory use: 16.3 MB Sun Jun 24 13:48:50 2018 reading ideals above 100000 Sun Jun 24 13:48:50 2018 commencing singleton removal, initial pass Sun Jun 24 13:51:25 2018 memory use: 94.1 MB Sun Jun 24 13:51:25 2018 reading all ideals from disk Sun Jun 24 13:51:25 2018 memory use: 130.9 MB Sun Jun 24 13:51:27 2018 keeping 4582269 ideals with weight <= 200, target excess is 21260 Sun Jun 24 13:51:30 2018 commencing in-memory singleton removal Sun Jun 24 13:51:31 2018 begin with 4253008 relations and 4582269 unique ideals Sun Jun 24 13:51:44 2018 reduce to 1675157 relations and 1462630 ideals in 13 passes Sun Jun 24 13:51:44 2018 max relations containing the same ideal: 106 Sun Jun 24 13:51:47 2018 removing 422012 relations and 328079 ideals in 93933 cliques Sun Jun 24 13:51:47 2018 commencing in-memory singleton removal Sun Jun 24 13:51:48 2018 begin with 1253145 relations and 1462630 unique ideals Sun Jun 24 13:51:53 2018 reduce to 1170153 relations and 1045619 ideals in 9 passes Sun Jun 24 13:51:53 2018 max relations containing the same ideal: 83 Sun Jun 24 13:51:55 2018 removing 338525 relations and 244592 ideals in 93933 cliques Sun Jun 24 13:51:55 2018 commencing in-memory singleton removal Sun Jun 24 13:51:55 2018 begin with 831628 relations and 1045619 unique ideals Sun Jun 24 13:51:58 2018 reduce to 756925 relations and 720072 ideals in 9 passes Sun Jun 24 13:51:58 2018 max relations containing the same ideal: 61 Sun Jun 24 13:52:00 2018 removing 71580 relations and 59389 ideals in 12191 cliques Sun Jun 24 13:52:00 2018 commencing in-memory singleton removal Sun Jun 24 13:52:00 2018 begin with 685345 relations and 720072 unique ideals Sun Jun 24 13:52:02 2018 reduce to 680615 relations and 655865 ideals in 7 passes Sun Jun 24 13:52:02 2018 max relations containing the same ideal: 57 Sun Jun 24 13:52:02 2018 relations with 0 large ideals: 423 Sun Jun 24 13:52:02 2018 relations with 1 large ideals: 268 Sun Jun 24 13:52:02 2018 relations with 2 large ideals: 3711 Sun Jun 24 13:52:02 2018 relations with 3 large ideals: 25970 Sun Jun 24 13:52:02 2018 relations with 4 large ideals: 92954 Sun Jun 24 13:52:02 2018 relations with 5 large ideals: 186499 Sun Jun 24 13:52:02 2018 relations with 6 large ideals: 198741 Sun Jun 24 13:52:02 2018 relations with 7+ large ideals: 172049 Sun Jun 24 13:52:02 2018 commencing 2-way merge Sun Jun 24 13:52:04 2018 reduce to 399836 relation sets and 375086 unique ideals Sun Jun 24 13:52:04 2018 commencing full merge Sun Jun 24 13:52:21 2018 memory use: 39.2 MB Sun Jun 24 13:52:21 2018 found 194290 cycles, need 191286 Sun Jun 24 13:52:22 2018 weight of 191286 cycles is about 13654981 (71.39/cycle) Sun Jun 24 13:52:22 2018 distribution of cycle lengths: Sun Jun 24 13:52:22 2018 1 relations: 16617 Sun Jun 24 13:52:22 2018 2 relations: 17228 Sun Jun 24 13:52:22 2018 3 relations: 17888 Sun Jun 24 13:52:22 2018 4 relations: 17484 Sun Jun 24 13:52:22 2018 5 relations: 16784 Sun Jun 24 13:52:22 2018 6 relations: 15926 Sun Jun 24 13:52:22 2018 7 relations: 14859 Sun Jun 24 13:52:22 2018 8 relations: 13350 Sun Jun 24 13:52:22 2018 9 relations: 11803 Sun Jun 24 13:52:22 2018 10+ relations: 49347 Sun Jun 24 13:52:22 2018 heaviest cycle: 23 relations Sun Jun 24 13:52:22 2018 commencing cycle optimization Sun Jun 24 13:52:23 2018 start with 1310580 relations Sun Jun 24 13:52:28 2018 pruned 36004 relations Sun Jun 24 13:52:28 2018 memory use: 32.9 MB Sun Jun 24 13:52:28 2018 distribution of cycle lengths: Sun Jun 24 13:52:28 2018 1 relations: 16617 Sun Jun 24 13:52:28 2018 2 relations: 17555 Sun Jun 24 13:52:28 2018 3 relations: 18514 Sun Jun 24 13:52:28 2018 4 relations: 17903 Sun Jun 24 13:52:28 2018 5 relations: 17390 Sun Jun 24 13:52:28 2018 6 relations: 16354 Sun Jun 24 13:52:28 2018 7 relations: 15270 Sun Jun 24 13:52:28 2018 8 relations: 13614 Sun Jun 24 13:52:28 2018 9 relations: 11896 Sun Jun 24 13:52:28 2018 10+ relations: 46173 Sun Jun 24 13:52:28 2018 heaviest cycle: 23 relations Sun Jun 24 13:52:29 2018 RelProcTime: 611 Sun Jun 24 13:52:29 2018 Sun Jun 24 13:52:29 2018 commencing linear algebra Sun Jun 24 13:52:29 2018 read 191286 cycles Sun Jun 24 13:52:30 2018 cycles contain 662298 unique relations Sun Jun 24 13:52:48 2018 read 662298 relations Sun Jun 24 13:52:50 2018 using 20 quadratic characters above 4294917295 Sun Jun 24 13:53:00 2018 building initial matrix Sun Jun 24 13:53:30 2018 memory use: 74.0 MB Sun Jun 24 13:53:31 2018 read 191286 cycles Sun Jun 24 13:53:31 2018 matrix is 191105 x 191286 (54.7 MB) with weight 18411203 (96.25/col) Sun Jun 24 13:53:31 2018 sparse part has weight 12990646 (67.91/col) Sun Jun 24 13:53:40 2018 filtering completed in 2 passes Sun Jun 24 13:53:40 2018 matrix is 191010 x 191191 (54.7 MB) with weight 18406796 (96.27/col) Sun Jun 24 13:53:40 2018 sparse part has weight 12989219 (67.94/col) Sun Jun 24 13:53:46 2018 matrix starts at (0, 0) Sun Jun 24 13:53:46 2018 matrix is 191010 x 191191 (54.7 MB) with weight 18406796 (96.27/col) Sun Jun 24 13:53:46 2018 sparse part has weight 12989219 (67.94/col) Sun Jun 24 13:53:46 2018 saving the first 48 matrix rows for later Sun Jun 24 13:53:46 2018 matrix includes 64 packed rows Sun Jun 24 13:53:46 2018 matrix is 190962 x 191191 (52.4 MB) with weight 14528553 (75.99/col) Sun Jun 24 13:53:46 2018 sparse part has weight 12576621 (65.78/col) Sun Jun 24 13:53:46 2018 using block size 8192 and superblock size 49152 for processor cache size 512 kB Sun Jun 24 13:53:48 2018 commencing Lanczos iteration Sun Jun 24 13:53:48 2018 memory use: 41.9 MB Sun Jun 24 13:54:57 2018 linear algebra at 6.3%, ETA 0h16m Sun Jun 24 14:11:54 2018 lanczos halted after 3021 iterations (dim = 190962) Sun Jun 24 14:11:55 2018 recovered 34 nontrivial dependencies Sun Jun 24 14:11:55 2018 BLanczosTime: 1166 Sun Jun 24 14:11:55 2018 Sun Jun 24 14:11:55 2018 commencing square root phase Sun Jun 24 14:11:55 2018 reading relations for dependency 1 Sun Jun 24 14:11:55 2018 read 95430 cycles Sun Jun 24 14:11:56 2018 cycles contain 330468 unique relations Sun Jun 24 14:12:06 2018 read 330468 relations Sun Jun 24 14:12:11 2018 multiplying 330468 relations Sun Jun 24 14:13:02 2018 multiply complete, coefficients have about 12.85 million bits Sun Jun 24 14:13:03 2018 initial square root is modulo 24181847 Sun Jun 24 14:14:23 2018 GCD is N, no factor found Sun Jun 24 14:14:23 2018 reading relations for dependency 2 Sun Jun 24 14:14:23 2018 read 95866 cycles Sun Jun 24 14:14:23 2018 cycles contain 331562 unique relations Sun Jun 24 14:14:34 2018 read 331562 relations Sun Jun 24 14:14:38 2018 multiplying 331562 relations Sun Jun 24 14:15:30 2018 multiply complete, coefficients have about 12.89 million bits Sun Jun 24 14:15:31 2018 initial square root is modulo 25612739 Sun Jun 24 14:16:51 2018 GCD is 1, no factor found Sun Jun 24 14:16:51 2018 reading relations for dependency 3 Sun Jun 24 14:16:51 2018 read 95879 cycles Sun Jun 24 14:16:51 2018 cycles contain 330932 unique relations Sun Jun 24 14:17:02 2018 read 330932 relations Sun Jun 24 14:17:07 2018 multiplying 330932 relations Sun Jun 24 14:17:58 2018 multiply complete, coefficients have about 12.87 million bits Sun Jun 24 14:18:00 2018 initial square root is modulo 24799387 Sun Jun 24 14:19:20 2018 GCD is N, no factor found Sun Jun 24 14:19:20 2018 reading relations for dependency 4 Sun Jun 24 14:19:20 2018 read 95523 cycles Sun Jun 24 14:19:21 2018 cycles contain 331356 unique relations Sun Jun 24 14:19:31 2018 read 331356 relations Sun Jun 24 14:19:36 2018 multiplying 331356 relations Sun Jun 24 14:20:27 2018 multiply complete, coefficients have about 12.88 million bits Sun Jun 24 14:20:28 2018 initial square root is modulo 25307939 Sun Jun 24 14:21:47 2018 GCD is 1, no factor found Sun Jun 24 14:21:47 2018 reading relations for dependency 5 Sun Jun 24 14:21:47 2018 read 95805 cycles Sun Jun 24 14:21:48 2018 cycles contain 331526 unique relations Sun Jun 24 14:21:58 2018 read 331526 relations Sun Jun 24 14:22:03 2018 multiplying 331526 relations Sun Jun 24 14:22:55 2018 multiply complete, coefficients have about 12.89 million bits Sun Jun 24 14:22:56 2018 initial square root is modulo 25568393 Sun Jun 24 14:24:16 2018 sqrtTime: 741 Sun Jun 24 14:24:16 2018 p50 factor: 37975227936943673922808872755445627854565536638199 Sun Jun 24 14:24:16 2018 p50 factor: 40094690950920881030683735292761468389214899724061 Sun Jun 24 14:24:16 2018 elapsed time 00:42:03 I could not find a pure-c version of the lasieve4 sievers (they all use ASM and/or intrinsics and requires cweb??), so If anybody knows where to get that please let me know (and some basic compile instructions if there is no makefile)! So I went the Msieve --> las (CADO-NFS siever) --> Msieve route for a full NFS factorization Poly search with Msieve -np 1,1000 Code: Sun Jun 24 14:27:34 2018 Sun Jun 24 14:27:34 2018 Sun Jun 24 14:27:34 2018 Msieve v. 1.54 (SVN Unversioned directory) Sun Jun 24 14:27:34 2018 random seeds: 4f90fbf4 d86a5791 Sun Jun 24 14:27:34 2018 factoring 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 (100 digits) Sun Jun 24 14:27:37 2018 searching for 15-digit factors Sun Jun 24 14:27:39 2018 commencing number field sieve (100-digit input) Sun Jun 24 14:27:39 2018 commencing number field sieve polynomial selection Sun Jun 24 14:27:39 2018 polynomial degree: 4 Sun Jun 24 14:27:39 2018 max stage 1 norm: 1.36e+17 Sun Jun 24 14:27:39 2018 max stage 2 norm: 3.19e+15 Sun Jun 24 14:27:39 2018 min E-value: 9.14e-09 Sun Jun 24 14:27:39 2018 poly select deadline: 1286 Sun Jun 24 14:27:39 2018 time limit set to 0.36 CPU-hours Sun Jun 24 14:27:39 2018 expecting poly E from 1.29e-08 to > 1.49e-08 Sun Jun 24 14:27:39 2018 searching leading coefficients from 1 to 1000 Sun Jun 24 14:35:08 2018 polynomial selection complete Sun Jun 24 14:35:08 2018 R0: -1160318224499030718294235 Sun Jun 24 14:35:08 2018 R1: 378654317647 Sun Jun 24 14:35:08 2018 A0: -12084851459361393651319621216 Sun Jun 24 14:35:08 2018 A1: -1180605682597027204428 Sun Jun 24 14:35:08 2018 A2: -8614727289369279 Sun Jun 24 14:35:08 2018 A3: -2848466002 Sun Jun 24 14:35:08 2018 A4: 840 Sun Jun 24 14:35:08 2018 skew 3254900.80, size 9.828e-14, alpha -5.221, combined = 1.210e-08 rroots = 2 Sun Jun 24 14:35:08 2018 elapsed time 00:07:34 Which resulted in the msieve.poly (which I renamed to rsa100.poly) Code: n: 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 skew: 3254900.80 c0 -12084851459361393651319621216 c1 -1180605682597027204428 c2 -8614727289369279 c3 -2848466002 c4 840 Y0: -1160318224499030718294235 Y1: 378654317647 Created a factorbase for the las siever with makefb (from the CADO-NFS suite), I had no idea what to put with the -maxbits (if anybody can explain if or how the -maxbits corresponds to the siever ( -I) or the lpb I'd appreciate that. Code: odroid@odroid-u2:~/Documents/makefb$ ./makefb -poly rsa100.poly -lim 650000 -maxbits 12 -out rsa100factorbase.fb started las with (I looked at the CADO-NFS logs of RSA100 on how it start it): Code: ./las -I 12 -poly rsa100.poly -q0 400000 -q1 500000 -lim0 650000 -lim1 650000 -lpb0 25 -lpb1 25 -mfb0 50 -mfb1 50 -ncurves0 11 -ncurves1 16 -fb rsa100factorbase.fb -out rsa100.q400k-500k.gz -stats-stderr At first it looked like it failed, but somehow corrected (probably because of my stupid parameters): Code: madvise failed: Invalid argument # redoing q=400277, rho=5345 because buckets are full # Fullest level-1s bucket #44, wrote 23894/23855 # Maybe you have too many threads compared to the size of the factor bases. # Please try less threads, or a larger -bkmult parameter (at some cost!). # The code will now try to adapt by allocating more memory for buckets. # Average J=1517 for 7765 special-q's, max bucket fill -bkmult 1,1s:1.1018 # Discarded 0 special-q's out of 7765 pushed # Total cpu time 6710.98s [norm 9.25+77.0, sieving 3548.4 (1294.4 + 396.3 + 1857.7), factor 3076.4 (2740.1 + 336.3)] # Total elapsed time 6869.65s, per special-q 0.884694s, per relation 0.0101343s # PeakMemusage (MB) = 56 # Total 677859 reports [0.0099s/r, 87.3r/sq] So it produced relations (about 100/s) and after 100k special Q I got about 677,000 relations, which took almost 2h (on a single core) After Q 400k-500k I did 500k-600k the same way (up to 1000k) I unzipped the relations and put them together in a single file with the cat (miauw!): Code: odroid@odroid-u2:~/Documents/msieve-SVN1022$cat rsa100.q400k-500k rsa100.q500k-600k rsa100.q600k-700k rsa100.q700k-800k rsa100.q800k-900k rsa100.q900k-1000k > msieve.dat I had to open the msieve.dat file and put Code: N 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 in as the first line to get msieve to recognize the relations. Convert the .poly to a .fb file for use with Msieve (there should be a program available somewhere in Msieve or CADO-NFS, but I couldn't find it, so I did it manually). Code: N 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 SKEW 3254900.80 A4 840 A3 -2848466002 A2 -8614727289369279 A1 -1180605682597027204428 A0 -12084851459361393651319621216 R1 378654317647 R0 -1160318224499030718294235 FAMAX 650000 FRMAX 650000 and it worked!!!! Code: Mon Jun 25 00:20:30 2018 Mon Jun 25 00:20:30 2018 Mon Jun 25 00:20:30 2018 Msieve v. 1.54 (SVN Unversioned directory) Mon Jun 25 00:20:30 2018 random seeds: 6c9d5866 1efb149a Mon Jun 25 00:20:30 2018 factoring 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 (100 digits) Mon Jun 25 00:20:33 2018 searching for 15-digit factors Mon Jun 25 00:20:35 2018 commencing number field sieve (100-digit input) Mon Jun 25 00:20:35 2018 R0: -1160318224499030718294235 Mon Jun 25 00:20:35 2018 R1: 378654317647 Mon Jun 25 00:20:35 2018 A0: -12084851459361393651319621216 Mon Jun 25 00:20:35 2018 A1: -1180605682597027204428 Mon Jun 25 00:20:35 2018 A2: -8614727289369279 Mon Jun 25 00:20:35 2018 A3: -2848466002 Mon Jun 25 00:20:35 2018 A4: 840 Mon Jun 25 00:20:35 2018 skew 3254900.80, size 9.828e-14, alpha -5.221, combined = 1.210e-08 rroots = 2 Mon Jun 25 00:20:35 2018 Mon Jun 25 00:20:35 2018 commencing relation filtering Mon Jun 25 00:20:35 2018 estimated available RAM is 2023.1 MB Mon Jun 25 00:20:35 2018 commencing duplicate removal, pass 1 Mon Jun 25 00:24:36 2018 found 542632 hash collisions in 4243088 relations Mon Jun 25 00:25:34 2018 added 1544 free relations Mon Jun 25 00:25:34 2018 commencing duplicate removal, pass 2 Mon Jun 25 00:25:42 2018 found 571058 duplicates and 3673574 unique relations Mon Jun 25 00:25:42 2018 memory use: 41.3 MB Mon Jun 25 00:25:42 2018 reading ideals above 100000 Mon Jun 25 00:25:42 2018 commencing singleton removal, initial pass Mon Jun 25 00:27:11 2018 memory use: 94.1 MB Mon Jun 25 00:27:11 2018 reading all ideals from disk Mon Jun 25 00:27:11 2018 memory use: 110.1 MB Mon Jun 25 00:27:13 2018 keeping 3374382 ideals with weight <= 200, target excess is 20465 Mon Jun 25 00:27:16 2018 commencing in-memory singleton removal Mon Jun 25 00:27:17 2018 begin with 3673574 relations and 3374382 unique ideals Mon Jun 25 00:27:31 2018 reduce to 2235657 relations and 1751368 ideals in 12 passes Mon Jun 25 00:27:31 2018 max relations containing the same ideal: 147 Mon Jun 25 00:27:35 2018 removing 729096 relations and 498821 ideals in 230275 cliques Mon Jun 25 00:27:36 2018 commencing in-memory singleton removal Mon Jun 25 00:27:36 2018 begin with 1506561 relations and 1751368 unique ideals Mon Jun 25 00:27:41 2018 reduce to 1356738 relations and 1083362 ideals in 8 passes Mon Jun 25 00:27:41 2018 max relations containing the same ideal: 103 Mon Jun 25 00:27:44 2018 removing 601706 relations and 371431 ideals in 230275 cliques Mon Jun 25 00:27:44 2018 commencing in-memory singleton removal Mon Jun 25 00:27:46 2018 begin with 755032 relations and 1083362 unique ideals Mon Jun 25 00:27:48 2018 reduce to 627990 relations and 565221 ideals in 8 passes Mon Jun 25 00:27:48 2018 max relations containing the same ideal: 57 Mon Jun 25 00:27:49 2018 removing 141279 relations and 102250 ideals in 39029 cliques Mon Jun 25 00:27:49 2018 commencing in-memory singleton removal Mon Jun 25 00:27:49 2018 begin with 486711 relations and 565221 unique ideals Mon Jun 25 00:27:50 2018 reduce to 456187 relations and 430334 ideals in 8 passes Mon Jun 25 00:27:50 2018 max relations containing the same ideal: 50 Mon Jun 25 00:27:51 2018 relations with 0 large ideals: 368 Mon Jun 25 00:27:51 2018 relations with 1 large ideals: 307 Mon Jun 25 00:27:51 2018 relations with 2 large ideals: 4539 Mon Jun 25 00:27:51 2018 relations with 3 large ideals: 27250 Mon Jun 25 00:27:51 2018 relations with 4 large ideals: 83283 Mon Jun 25 00:27:51 2018 relations with 5 large ideals: 137570 Mon Jun 25 00:27:51 2018 relations with 6 large ideals: 120688 Mon Jun 25 00:27:51 2018 relations with 7+ large ideals: 82182 Mon Jun 25 00:27:51 2018 commencing 2-way merge Mon Jun 25 00:27:52 2018 reduce to 284206 relation sets and 258353 unique ideals Mon Jun 25 00:27:52 2018 commencing full merge Mon Jun 25 00:28:05 2018 memory use: 28.5 MB Mon Jun 25 00:28:05 2018 found 137264 cycles, need 132553 Mon Jun 25 00:28:05 2018 weight of 132553 cycles is about 9600137 (72.42/cycle) Mon Jun 25 00:28:05 2018 distribution of cycle lengths: Mon Jun 25 00:28:05 2018 1 relations: 9273 Mon Jun 25 00:28:05 2018 2 relations: 11186 Mon Jun 25 00:28:05 2018 3 relations: 12585 Mon Jun 25 00:28:05 2018 4 relations: 12807 Mon Jun 25 00:28:05 2018 5 relations: 12657 Mon Jun 25 00:28:05 2018 6 relations: 11770 Mon Jun 25 00:28:05 2018 7 relations: 11054 Mon Jun 25 00:28:05 2018 8 relations: 9737 Mon Jun 25 00:28:05 2018 9 relations: 8417 Mon Jun 25 00:28:05 2018 10+ relations: 33067 Mon Jun 25 00:28:05 2018 heaviest cycle: 22 relations Mon Jun 25 00:28:05 2018 commencing cycle optimization Mon Jun 25 00:28:06 2018 start with 904230 relations Mon Jun 25 00:28:10 2018 pruned 32551 relations Mon Jun 25 00:28:10 2018 memory use: 22.0 MB Mon Jun 25 00:28:10 2018 distribution of cycle lengths: Mon Jun 25 00:28:10 2018 1 relations: 9273 Mon Jun 25 00:28:10 2018 2 relations: 11434 Mon Jun 25 00:28:10 2018 3 relations: 13045 Mon Jun 25 00:28:10 2018 4 relations: 13348 Mon Jun 25 00:28:10 2018 5 relations: 13212 Mon Jun 25 00:28:10 2018 6 relations: 12248 Mon Jun 25 00:28:10 2018 7 relations: 11603 Mon Jun 25 00:28:10 2018 8 relations: 10001 Mon Jun 25 00:28:10 2018 9 relations: 8490 Mon Jun 25 00:28:10 2018 10+ relations: 29899 Mon Jun 25 00:28:10 2018 heaviest cycle: 21 relations Mon Jun 25 00:28:10 2018 RelProcTime: 455 Mon Jun 25 00:28:10 2018 elapsed time 00:07:40 Mon Jun 25 00:30:42 2018 Mon Jun 25 00:30:42 2018 Mon Jun 25 00:30:42 2018 Msieve v. 1.54 (SVN Unversioned directory) Mon Jun 25 00:30:42 2018 random seeds: e81300e3 2b61f139 Mon Jun 25 00:30:42 2018 factoring 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 (100 digits) Mon Jun 25 00:30:45 2018 searching for 15-digit factors Mon Jun 25 00:30:47 2018 commencing number field sieve (100-digit input) Mon Jun 25 00:30:47 2018 R0: -1160318224499030718294235 Mon Jun 25 00:30:47 2018 R1: 378654317647 Mon Jun 25 00:30:47 2018 A0: -12084851459361393651319621216 Mon Jun 25 00:30:47 2018 A1: -1180605682597027204428 Mon Jun 25 00:30:47 2018 A2: -8614727289369279 Mon Jun 25 00:30:47 2018 A3: -2848466002 Mon Jun 25 00:30:47 2018 A4: 840 Mon Jun 25 00:30:47 2018 skew 3254900.80, size 9.828e-14, alpha -5.221, combined = 1.210e-08 rroots = 2 Mon Jun 25 00:30:47 2018 Mon Jun 25 00:30:47 2018 commencing linear algebra Mon Jun 25 00:30:47 2018 read 132553 cycles Mon Jun 25 00:30:47 2018 cycles contain 430159 unique relations Mon Jun 25 00:30:56 2018 read 430159 relations Mon Jun 25 00:30:57 2018 using 20 quadratic characters above 4294917295 Mon Jun 25 00:31:03 2018 building initial matrix Mon Jun 25 00:31:22 2018 memory use: 48.8 MB Mon Jun 25 00:31:22 2018 read 132553 cycles Mon Jun 25 00:31:22 2018 matrix is 132373 x 132553 (38.0 MB) with weight 13013892 (98.18/col) Mon Jun 25 00:31:22 2018 sparse part has weight 9028499 (68.11/col) Mon Jun 25 00:31:27 2018 filtering completed in 2 passes Mon Jun 25 00:31:27 2018 matrix is 132295 x 132475 (38.0 MB) with weight 13009752 (98.21/col) Mon Jun 25 00:31:27 2018 sparse part has weight 9026861 (68.14/col) Mon Jun 25 00:31:29 2018 matrix starts at (0, 0) Mon Jun 25 00:31:29 2018 matrix is 132295 x 132475 (38.0 MB) with weight 13009752 (98.21/col) Mon Jun 25 00:31:29 2018 sparse part has weight 9026861 (68.14/col) Mon Jun 25 00:31:29 2018 saving the first 48 matrix rows for later Mon Jun 25 00:31:29 2018 matrix includes 64 packed rows Mon Jun 25 00:31:29 2018 matrix is 132247 x 132475 (36.6 MB) with weight 10287295 (77.65/col) Mon Jun 25 00:31:29 2018 sparse part has weight 8790586 (66.36/col) Mon Jun 25 00:31:29 2018 using block size 8192 and superblock size 49152 for processor cache size 512 kB Mon Jun 25 00:31:30 2018 commencing Lanczos iteration Mon Jun 25 00:31:30 2018 memory use: 28.8 MB Mon Jun 25 00:32:16 2018 linear algebra at 9.2%, ETA 0h 7m Mon Jun 25 00:39:47 2018 lanczos halted after 2093 iterations (dim = 132246) Mon Jun 25 00:39:48 2018 recovered 33 nontrivial dependencies Mon Jun 25 00:39:48 2018 BLanczosTime: 541 Mon Jun 25 00:39:48 2018 elapsed time 00:09:06 Mon Jun 25 00:40:39 2018 Mon Jun 25 00:40:39 2018 Mon Jun 25 00:40:39 2018 Msieve v. 1.54 (SVN Unversioned directory) Mon Jun 25 00:40:39 2018 random seeds: be7f2f8d e1df76bb Mon Jun 25 00:40:39 2018 factoring 1522605027922533360535618378132637429718068114961380688657908494580122963258952897654000350692006139 (100 digits) Mon Jun 25 00:40:41 2018 searching for 15-digit factors Mon Jun 25 00:40:44 2018 commencing number field sieve (100-digit input) Mon Jun 25 00:40:44 2018 R0: -1160318224499030718294235 Mon Jun 25 00:40:44 2018 R1: 378654317647 Mon Jun 25 00:40:44 2018 A0: -12084851459361393651319621216 Mon Jun 25 00:40:44 2018 A1: -1180605682597027204428 Mon Jun 25 00:40:44 2018 A2: -8614727289369279 Mon Jun 25 00:40:44 2018 A3: -2848466002 Mon Jun 25 00:40:44 2018 A4: 840 Mon Jun 25 00:40:44 2018 skew 3254900.80, size 9.828e-14, alpha -5.221, combined = 1.210e-08 rroots = 2 Mon Jun 25 00:40:44 2018 Mon Jun 25 00:40:44 2018 commencing square root phase Mon Jun 25 00:40:44 2018 reading relations for dependency 1 Mon Jun 25 00:40:44 2018 read 66295 cycles Mon Jun 25 00:40:44 2018 cycles contain 215178 unique relations Mon Jun 25 00:40:49 2018 read 215178 relations Mon Jun 25 00:40:53 2018 multiplying 215178 relations Mon Jun 25 00:41:23 2018 multiply complete, coefficients have about 8.63 million bits Mon Jun 25 00:41:24 2018 initial square root is modulo 91577 Mon Jun 25 00:42:12 2018 GCD is N, no factor found Mon Jun 25 00:42:12 2018 reading relations for dependency 2 Mon Jun 25 00:42:12 2018 read 66301 cycles Mon Jun 25 00:42:13 2018 cycles contain 214640 unique relations Mon Jun 25 00:42:18 2018 read 214640 relations Mon Jun 25 00:42:21 2018 multiplying 214640 relations Mon Jun 25 00:42:52 2018 multiply complete, coefficients have about 8.61 million bits Mon Jun 25 00:42:53 2018 initial square root is modulo 88951 Mon Jun 25 00:43:41 2018 sqrtTime: 177 Mon Jun 25 00:43:41 2018 p50 factor: 37975227936943673922808872755445627854565536638199 Mon Jun 25 00:43:41 2018 p50 factor: 40094690950920881030683735292761468389214899724061 Mon Jun 25 00:43:41 2018 elapsed time 00:03:02  2018-06-25, 14:42 #2 paulunderwood Sep 2002 Database er0rr 65668 Posts Were you using 4 cores on both the X86_64 and the ARM? What is the power usage of the 2 systems and what was each system's total time?  2018-06-25, 15:28 #3 henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 131448 Posts lasieve4 should compile with no asm. You should copy the generic folder and call it asm. I have had it running on a raspberry pi 2b. It is worth bearing in mind that you would probably get a factor of several improvement in speed on a modern arm chip such as a A57. How does msieve qs compare with c code to yafu qs with c code? 2018-06-25, 17:10 #4 bsquared "Ben" Feb 2007 2·17·97 Posts Quote:  Originally Posted by henryzz How does msieve qs compare with c code to yafu qs with c code? I'm actually not sure if it is possible to compile yafu qs without any x86 assembly or sse2 code. defining FORCE_GENERIC somewhere globally might work, but without looking I can't remember if I've guarded all assembly sections with that symbol. However with that defined the speed is pretty similar through c75 or so. After that yafu starts to get slightly faster (10 to 20%). If anyone does manage to get yafu working on an ARM I'd like to hear about it 2018-06-26, 00:53 #5 VictordeHolland "Victor de Hollander" Aug 2011 the Netherlands 2·587 Posts Quote:  Originally Posted by henryzz lasieve4 should compile with no asm. You should copy the generic folder and call it asm. I have had it running on a raspberry pi 2b. Thanks for the tip! It still took me more than 2 hours to fix all the errors (note errors, not warnings) I was getting (undefined variables, problems with header files and of course the cweb/ctangle/cweave stuff and a little editing of the makefile in the mix). I don't understand why they used the cweb stuff??? But persistence pays of (the Odroid-U2:) 10k special-Q Code: odroid@odroid-u2:~/Documents/ggnfs-source/bin/testing$ ./gnfs-lasieve4I12e -a -v -o testRels testPoly
gnfs-lasieve4I12e: L1_BITS=15, SVN $Revision$
FBsize 89232+0 (deg 4), 169510+0 (deg 1)
total yield: 79211, q=2310019 (0.01136 sec/rel)
648 Special q, 974 reduction iterations
reports: 294157337->26568664->24297997->5506929->5506836->5140364
Number of relations with k rational and l algebraic primes for (k,l)=:

Total yield: 79211
0/0 mpqs failures, 42287/41995 vain mpqs
milliseconds total: Sieve 45468 Sched 0 medsched 31
TD 234474 (Init 0, MPQS 47318) Sieve-Change 210096
TD side 0: init/small/medium/large/search: 0 0 0 0 0
sieve: init/small/medium/large/search: 0 0 0 23372 0
TD side 1: init/small/medium/large/search: 0 0 0 0 124656
sieve: init/small/medium/large/search: 0 0 0 21900 196
Intel Xeon E5-2650 (Sandy-bridge based Xeon) generic

Code:
./gnfs-lasieve4I12e -a -v -o testRels testPoly
gnfs-lasieve4I12e: L1_BITS=15, SVN $Revision$
FBsize 89232+0 (deg 4), 169510+0 (deg 1)
total yield: 79211, q=2310019 (0.00380 sec/rel)
648 Special q, 974 reduction iterations
reports: 294157337->26568664->24297997->5506929->5506836->5140364
Number of relations with k rational and l algebraic primes for (k,l)=:

Total yield: 79211
0/0 mpqs failures, 42287/41995 vain mpqs
milliseconds total: Sieve 15557 Sched 0 medsched 0
TD 10260 (Init 0, MPQS 0) Sieve-Change 81015
TD side 0: init/small/medium/large/search: 0 0 0 0 0
sieve: init/small/medium/large/search: 0 0 0 7780 0
TD side 1: init/small/medium/large/search: 0 0 0 0 3211
sieve: init/small/medium/large/search: 0 0 0 7777 0
Intel Xeon E5-2650 (Sandy-bridge based Xeon) asm64 (downloaded somewhere from the forum)

Code:
./gnfs-lasieve4I12e -a -v -o testRels testPoly
gnfs-lasieve4I12e (with asm64): L1_BITS=15, SVN $Revision: 399$
FBsize 89232+0 (deg 4), 169510+0 (deg 1)
total yield: 79211, q=2310019 (0.00189 sec/rel)
648 Special q, 974 reduction iterations
reports: 199726752->18930110->17344713->5507541->5507448->5140389
Number of relations with k rational and l algebraic primes for (k,l)=:

Total yield: 79211
0/0 mpqs failures, 42287/41995 vain mpqs
milliseconds total: Sieve 37300 Sched 0 medsched 23990
TD 53880 (Init 2820, MPQS 32270) Sieve-Change 34440
TD side 0: init/small/medium/large/search: 780 2330 960 1030 4930
sieve: init/small/medium/large/search: 2260 10750 940 4340 2440
TD side 1: init/small/medium/large/search: 320 2080 910 1090 4050
sieve: init/small/medium/large/search: 880 6210 880 4210 4390
Intel Xeon E5-2650 (Sandy-bridge based Xeon) asm64 (compiled on the machine)

Code:
./gnfs-lasieve4I12e -a -v -o testRels testPoly
gnfs-lasieve4I12e (with asm64): L1_BITS=15, SVN $Revision$
FBsize 89232+0 (deg 4), 169510+0 (deg 1)
total yield: 79211, q=2310019 (0.00178 sec/rel)
648 Special q, 974 reduction iterations
reports: 199726752->18930110->17344713->5507541->5507448->5140389
Number of relations with k rational and l algebraic primes for (k,l)=:

Total yield: 79211
0/0 mpqs failures, 42287/41995 vain mpqs
milliseconds total: Sieve 34144 Sched 0 medsched 24430
TD 47818 (Init 2512, MPQS 27253) Sieve-Change 34580
TD side 0: init/small/medium/large/search: 770 2264 960 1034 4545
sieve: init/small/medium/large/search: 1644 9387 954 4325 2375
TD side 1: init/small/medium/large/search: 314 2164 907 1118 3643
sieve: init/small/medium/large/search: 849 5945 932 4329 3404
Quote:
 It is worth bearing in mind that you would probably get a factor of several improvement in speed on a modern arm chip such as a A57.
I know, it is mostly just for the fun of it. I sometimes have no idea what I'm doing .

Quote:
 How does msieve qs compare with c code to yafu qs with c code?
The YAFU code is full of ASM intrinsics and files (SSE2, SSE4.1, AVX2, AVX-512) so I'm going nowhere near that. That stuff is way above my head/skill. If it doesn't work after 'make' or editing the makefile to point to the libs I just scream for help .

 2018-06-26, 08:36 #6 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 22×1,433 Posts A factor of 4 difference isn't much given the difference in power draw. I wonder how it would perform on a more modern ARM chip. It looks like you might get better performance by optimizing parameters differently.
2018-06-26, 09:47   #7
VictordeHolland

"Victor de Hollander"
Aug 2011
the Netherlands

2×587 Posts

Quote:
 Originally Posted by paulunderwood Were you using 4 cores on both the X86_64 and the ARM? What is the power usage of the 2 systems and what was each system's total time?
The results are in for RSA-100

Odroid-U2
<1 W idle (my wattmeter is not accurate enough)
Code:
Tue Jun 26 03:04:52 2018 -> factmsieve.py (v0.86)
Tue Jun 26 03:04:52 2018 -> This is client 1 of 1
Tue Jun 26 03:04:52 2018 -> Running on 4 Cores with 1 hyper-thread per Core
Tue Jun 26 03:04:52 2018 -> Working with NAME = RSA100
...
Tue Jun 26 06:16:43 2018  p50 factor: 37975227936943673922808872755445627854565536638199
Tue Jun 26 06:16:43 2018  p50 factor: 40094690950920881030683735292761468389214899724061
3:11:51

(which is comparable to the 3:31:18 it took with CADO-NFS 3.0-dev)

A reference point:
Intel Core i7 3770k @3.5GHz (80+ Gold PSU)
Using the pythonscript+lasieve4+msieve
54.5W idle
88-89W - 4core/4thread sieve - 25:12
96-97.5W - 4core/8thread sieve - 21:17

Some other RSA100 times:
Dual Intel Xeon E5-2650 (16core/32thread) - YAFU (NFS) - 10:25
Dual Intel Xeon E5-2650 (16core/32thread) - lasieve4+msieve+py - 11:20
KNL 7210 (256-thread) AVX512 SIQS - 6:08
from
http://mersenneforum.org/showpost.ph...&postcount=241
and

Last fiddled with by VictordeHolland on 2018-06-26 at 09:50 Reason: somehow the forum adds extra newlines to my posts...

 2018-07-19, 13:19 #8 VictordeHolland     "Victor de Hollander" Aug 2011 the Netherlands 2·587 Posts I bought myself a little present: Raspberry Pi 3B+ It was only 35 euros :) Should have some CADO-NFS and Msieve results soon.
2018-07-20, 10:36   #9
VictordeHolland

"Victor de Hollander"
Aug 2011
the Netherlands

2·587 Posts

Quote:
 Originally Posted by VictordeHolland I bought myself a little present: Raspberry Pi 3B+ It was only 35 euros :) Should have some CADO-NFS and Msieve results soon.
Factmsieve v0.86 + Msieve SVN1022 + Lasieve4 (generic)

Code:
Thu Jul 19 09:49:47 2018 -> factmsieve.py (v0.86)
Thu Jul 19 09:49:47 2018 -> This is client 1 of 1
Thu Jul 19 09:49:47 2018 -> Running on 4 Cores with 1 hyper-thread per Core
Thu Jul 19 09:49:47 2018 -> Working with NAME = RSA100
...
Thu Jul 19 13:41:11 2018  p50 factor: 37975227936943673922808872755445627854565536638199
Thu Jul 19 13:41:11 2018  p50 factor: 40094690950920881030683735292761468389214899724061
3:51:24

Code:
Info:Square Root: Factors: 37975227936943673922808872755445627854565536638199 40094690950920881030683735292761468389214899724061
Info:Square Root: Total cpu/real time for sqrt: 514.38/159.773
Info:Polynomial Selection (size optimized): Aggregate statistics:
Info:Polynomial Selection (size optimized): potential collisions: 1867.92
Info:Polynomial Selection (size optimized): raw lognorm (nr/min/av/max/std): 3725/33.340/37.848/38.690/0.707
Info:Polynomial Selection (size optimized): optimized lognorm (nr/min/av/max/std): 3725/32.980/37.005/38.680/1.127
Info:Polynomial Selection (size optimized): Total time: 1634.75
Info:Polynomial Selection (root optimized): Aggregate statistics:
Info:Polynomial Selection (root optimized): Total time: 460.95
Info:Polynomial Selection (root optimized): Rootsieve time: 457.98
Info:Generate Factor Base: Total cpu/real time for makefb: 7.48/2.16876
Info:Lattice Sieving: Aggregate statistics:
Info:Lattice Sieving: Total number of relations: 2362062
Info:Lattice Sieving: Average J: 1019.58 for 69667 special-q, max bucket fill -bkmult 1.0,1s:1.204870
Info:Lattice Sieving: Total time: 19829.4s
Info:Filtering - Duplicate Removal, splitting pass: Total cpu/real time for dup1: 22.71/51.1323
Info:Filtering - Duplicate Removal, splitting pass: Aggregate statistics:
Info:Filtering - Duplicate Removal, splitting pass: CPU time for dup1: 50.7s
Info:Filtering - Duplicate Removal, removal pass: Total cpu/real time for dup2: 90.65/73.286
Info:Filtering - Duplicate Removal, removal pass: Aggregate statistics:
Info:Filtering - Duplicate Removal, removal pass: CPU time for dup2: 68.4s
Info:Filtering - Singleton removal: Total cpu/real time for purge: 70.99/55.5308
Info:Filtering - Merging: Total cpu/real time for merge: 346.7/329.282
Info:Filtering - Merging: Total cpu/real time for replay: 33.93/32.8305
Info:Linear Algebra: Total cpu/real time for bwc: 18085.5/4799.38
Info:Linear Algebra: Aggregate statistics:
Info:Linear Algebra: Krylov: WCT time 2911.73, iteration CPU time 0.45, COMM 0.01, cpu-wait 0.02, comm-wait 0.0 (6000 iterations)
Info:Linear Algebra: Lingen CPU time 712.82, WCT time 189.49
Info:Linear Algebra: Mksol: WCT time 1482.32, iteration CPU time 0.47, COMM 0.01, cpu-wait 0.02, comm-wait 0.0 (3000 iterations)
Info:Quadratic Characters: Total cpu/real time for characters: 21.5/10.3837
Info:Square Root: Total cpu/real time for sqrt: 514.38/159.773
Info:HTTP server: Shutting down HTTP server
Info:Complete Factorization: Total cpu/elapsed time for entire factorization: 51928.4/16344.8
CPU time: 51928.4 Elapsed time: 16344.8

4:32:25

 2018-07-20, 10:44 #10 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 131448 Posts Where is the qs/gnfs border on systems like this? Also how does the raspberry pi 3b compare powerwise to your Odroid U2? It looks like arm is more efficient for nfs sieving than x86 according to your power report a few posts ago.
2018-07-20, 14:56   #11
VictordeHolland

"Victor de Hollander"
Aug 2011
the Netherlands

2·587 Posts

Quote:
 Originally Posted by henryzz Where is the qs/gnfs border on systems like this? Also how does the raspberry pi 3b compare powerwise to your Odroid U2? It looks like arm is more efficient for nfs sieving than x86 according to your power report a few posts ago.
Yes, but the differences are not that shockingly big.

Quote:
 Originally Posted by VictordeHolland Odroid-U2 <1 W idle (my wattmeter is not accurate enough) 7.2W sieveing with 4 threads 3:11:51
Factoring RSA100 using the Odroid-U2 works out to roughly:
11,511 seconds * 7.2W = 82,879 Joules

Quote:
 A reference point: Intel Core i7 3770k @3.5GHz (80+ Gold PSU) Using the pythonscript+lasieve4+msieve 54.5W idle 88-89W - 4core/4thread sieve - 25:12 96-97.5W - 4core/8thread sieve - 21:17
And for a quadcore of a few generations old, then factoring RSA100 takes:
1,277 seconds * 97.5W = 124,508 Joules

Somehow the Raspberry Pi 3B+ takes longer than the ODROID-U2
(wombatman got similar timings on his Pi3B+) see:
http://mersenneforum.org/showpost.ph...&postcount=273
it is using about ~6.7W (fluctuates a lot, so eye-balling it a bit)

3:51:24
13,884 seconds * 6.7W = 93,023 Joules

The biggest obstacle with using these ARM boards for any useful factorizations is their severely limited memory (1GB for the RPi3B+ and 2GB for the ODROID-U2)

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