20160331, 07:27  #1 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
7221_{10} Posts 
Playing with CADO's individual polyselect binaries
Since I haven't been able to get the regular Python scripts running correctly, and since even if I could their operation seems extraordinarily inflexible to me, I've taken PZ's suggestion of manually using the polyselect binaries that the scripts delegate to.
Here's my first attempt on the A4788_C195: Code:
~/cado/build/Gravemind/polyselect ∰∂ nice n 19 ./polyselect degree 5 P 5000000 admax 50000000 nq 1000 keep 1000 v t 8 N $(cat num) # (17c31b8) ./polyselect degree 5 P 5000000 admax 50000000 nq 1000 keep 1000 v t 8 N 105720747827131650775565137946594727648048676926428801477497713261333062158444658783837181718187127016255169032147325982158719006483898971407998273736975091062494070213867530300194317862973608499 # Compiled with gcc 4.9.2 # Compilation flags std=c99 g W Wall O2 msse3 mssse3 msse4.1 mpclmul # Info: initializing 316066 P primes took 16ms, nq=1000 # Info: estimated peak memory=1388.00MB (8 thread(s), batch 20 inversions on SQ) # thread 0: ad=60 # thread 1: ad=120 # thread 6: ad=180 # thread 3: ad=240 # thread 4: ad=300 # thread 5: ad=360 # thread 2: ad=420 # thread 7: ad=480 # thread 7: ad=540 # thread 4: ad=600 # thread 2: ad=660 # sopt: start sizeoptimization with polynomials: # sopt: f_raw = 120*x^5 + 37*x^4 + ... # sopt: g_raw = 2157420360827950350617*x^1 + 244903953537066202453401636126542860406*x^0 # sopt: with lognorm = 71.270838 Keeping x = 0.260108, f(x) = 2016795408842364209203141872461793618276549461594849023160013414058503962624.000000, f''(x) = 43184121449821530246129924935985504342081783347318205967447779341609100201112371200.000000 # sopt: qroots of Res(c2,c3) or Res(c2,c3)' = { 0.260108 } # sopt: 8 values for the translations were computed and added in list_k # sopt: k = 0 was added list_k # sopt: It remains 9 values after sorting and removing duplicates # sopt: Calling improve_list_k with sopt_effort = 0 # sopt: skew0 = 4275.446290 # sopt: skew[0] = 65 # sopt: skew[1] = 529 # sopt: skew[2] = 4275 # sopt: skew[3] = 34572 # sopt: skew[4] = 279558 # sopt: Start processing all k in list_k of length 9 # sopt: better lognorm 65.28 (previous was 71.27) for skew[2] = 4275 # sopt: better lognorm 65.23 (previous was 65.28) for skew[3] = 34572 # sopt: better lognorm 64.54 (previous was 65.23) for skew[4] = 279558 # sopt: better lognorm 64.17 (previous was 64.54) for skew[3] = 34572 # sopt: better lognorm 63.84 (previous was 64.17) for skew[3] = 34572 # sopt: better lognorm 63.72 (previous was 63.84) for skew[3] = 34572 # sopt: end of sizeoptimization, best polynomial are # sopt: f_opt = 2760*x^5 + 500106045506149*x^4 + ... # sopt: g_opt = 2157420360827950350617*x^1 + 244903875353083220572872777923498836651*x^0 # sopt: with lognorm = 63.724256 # Raw polynomial: # n: 105720747827131650775565137946594727648048676926428801477497713261333062158444658783837181718187127016255169032147325982158719006483898971407998273736975091062494070213867530300194317862973608499 # Y1: 2157420360827950350617 # Y0: 244903953537066202453401636126542860406 # c5: 120 # c4: 37 # c3: 1188753689271031975437528 # c2: 63701574612453595484553171865323265035 # c1: 5231971310990810577211204041041772504 # c0: 39181211010549708386751205216207022495 # raw lognorm 71.27, skew 372185759744.00, alpha 0.09 (proj: 1.21), E 71.36, exp_E 63.14, 1 rroots # Sizeoptimized polynomial: n: 105720747827131650775565137946594727648048676926428801477497713261333062158444658783837181718187127016255169032147325982158719006483898971407998273736975091062494070213867530300194317862973608499 Y1: 2157420360827950350617 Y0: 244903875353083220572872777923498836651 c5: 2760 c4: 500106045506149 c3: 63601533977108612470151786 c2: 2972736829782803317901917056 c1: 77606935545503482645832413970733012323 c0: 556082758789900711444681471769664993163 # lognorm 63.72, skew 1493504.00, alpha 0.76 (proj: 1.34), E 64.49, exp_E 60.24, 3 rroots It might be interesting to combine (e.g.) RichD's GPU sizeopted output with polyselect_ropt and see what we can come up with. Given how modular CADO's binaries are (if not the scripts), mayhaps it's worth hacking GPUMsieve to work with sopt and polyselect_ropt? (It seems that polyselect delegates to sopt? Or are they totally separate somehow...?) Last fiddled with by Dubslow on 20160331 at 07:30 
20160415, 06:25  #2 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
7221_{10} Posts 
It finally completed. Looks like somewhere on the order or 1214 days of a hyper threaded Sandy Bridge quad core... I may have bitten off more than I could truly chew. Oh well, it's complete now.
Next stage: backups and root opt Code:
# sopt: start sizeoptimization with polynomials: # sopt: f_raw = 49999980*x^5 + 87342730*x^4 + ... # sopt: g_raw = 75531706090637747253061*x^1 + 18409334084348638436044486591897373801*x^0 # sopt: with lognorm = 71.191531 # sopt: find_translations_extra 49394349.452506 # sopt: find_translations_extra 49394329.184788 Not keeping x = 0.236905, f(x) = 881266452414298567385496367451512255442834743137534323397114924012974975049793536.000000, f''(x) = 42362913788293809589383387284727357529134974824061360749448886093185664868476268579334914048.000000 # sopt: qroots of Res(c2,c3) or Res(c2,c3)' = { 0.236899, 0.236912 } # sopt: 50 values for the translations were computed and added in list_k # sopt: k = 0 was added list_k # sopt: It remains 27 values after sorting and removing duplicates # sopt: Calling improve_list_k with sopt_effort = 0 # sopt: skew0 = 904.912995 # sopt: skew[0] = 30 # sopt: skew[1] = 165 # sopt: skew[2] = 905 # sopt: skew[3] = 4963 # sopt: skew[4] = 27221 # sopt: Start processing all k in list_k of length 27 # sopt: better lognorm 70.30 (previous was 71.19) for skew[2] = 905 # sopt: better lognorm 70.20 (previous was 70.30) for skew[2] = 905 # sopt: better lognorm 65.96 (previous was 70.20) for skew[3] = 4963 # sopt: better lognorm 65.31 (previous was 65.96) for skew[3] = 4963 # sopt: better lognorm 65.28 (previous was 65.31) for skew[3] = 4963 # sopt: better lognorm 64.25 (previous was 65.28) for skew[2] = 905 # sopt: better lognorm 63.67 (previous was 64.25) for skew[4] = 27221 # sopt: better lognorm 62.84 (previous was 63.67) for skew[2] = 905 # sopt: end of sizeoptimization, best polynomial are # sopt: f_opt = 324399870240*x^5 + 80029460397523177360*x^4 + ... # sopt: g_opt = 75531706090637747253061*x^1 + 18409337811083621201759661159905138289*x^0 # sopt: with lognorm = 62.837342 # Raw polynomial: # n: 105720747827131650775565137946594727648048676926428801477497713261333062158444658783837181718187127016255169032147325982158719006483898971407998273736975091062494070213867530300194317862973608499 # Y1: 75531706090637747253061 # Y0: 18409334084348638436044486591897373801 # c5: 49999980 # c4: 87342730 # c3: 1202006018615283019865612 # c2: 4361271323601108006810005241882801604 # c1: 5777297089772007359416979193471163928 # c0: 1364051122127173272601888644114195017 # raw lognorm 71.19, skew 2042101760.00, alpha 0.07 (proj: 1.40), E 71.26, exp_E 63.99, 3 rroots # Sizeoptimized polynomial: n: 105720747827131650775565137946594727648048676926428801477497713261333062158444658783837181718187127016255169032147325982158719006483898971407998273736975091062494070213867530300194317862973608499 Y1: 75531706090637747253061 Y0: 18409337811083621201759661159905138289 c5: 324399870240 c4: 80029460397523177360 c3: 17398904458268124477723493 c2: 22144827537958081761266148134238 c1: 888071204935334410586667012400944573 c0: 256020541443086763599669214408591268137446 # lognorm 62.84, skew 361088.00, alpha 1.25 (proj: 1.47), E 61.59, exp_E 59.67, 5 rroots # Stat: potential collisions=750929.12 (1.55e01/s) # Stat: raw lognorm (nr/min/av/max/std): 756882/58.91/70.98/71.82/0.83 # Stat: optimized lognorm (nr/min/av/max/std): 756882/58.91/64.02/67.26/0.76 # Stat: tried 833333 advalue(s), found 756882 polynomial(s), 756882 sizeoptimized, 0 rootsieved # Stat: best logmu after size optimization: 58.91 59.05 59.05 59.23 59.25 59.26 59.33 59.47 59.48 59.54 59.57 59.60 59.62 59.64 59.64 59.69 59.70 59.74 59.78 59.78 59.80 59.81 59.82 59.84 59.85 59.86 59.87 59.88 59.88 59.91 59.92 59.94 59.99 60.00 60.01 60.02 60.02 60.03 60.05 60.06 60.07 60.09 60.09 60.10 60.10 60.10 60.11 60.11 60.11 60.12 60.13 60.13 60.14 60.14 60.15 60.15 60.16 60.17 60.17 60.19 60.19 60.21 60.21 60.22 60.22 60.22 60.22 60.23 60.23 60.23 60.24 60.24 60.26 60.26 60.26 60.27 60.27 60.27 60.29 60.29 60.29 60.30 60.30 60.31 60.32 60.33 60.34 60.34 60.34 60.35 60.35 60.35 60.36 60.36 60.37 60.37 60.38 60.38 60.39 60.39 60.39 60.43 60.43 60.43 60.43 60.44 60.44 60.44 60.44 60.44 60.44 60.44 60.45 60.45 60.46 60.46 60.47 60.47 60.48 60.48 60.48 60.48 60.48 60.48 60.48 60.48 60.49 60.51 60.51 60.51 60.51 60.52 60.52 60.53 60.53 60.54 60.54 60.54 60.54 60.54 60.54 60.55 60.55 60.55 60.56 60.56 60.56 60.56 60.56 60.57 60.57 60.57 60.58 60.58 60.58 60.59 60.59 60.59 60.60 60.60 60.60 60.60 60.60 60.60 60.60 60.61 60.61 60.61 60.61 60.62 60.62 60.62 60.62 60.62 60.63 60.63 60.63 60.63 60.63 60.63 60.63 60.63 60.64 60.65 60.65 60.65 60.66 60.66 60.66 60.66 60.67 60.67 60.67 60.67 60.67 60.67 60.67 60.68 60.68 60.68 60.68 60.69 60.69 60.69 60.69 60.69 60.69 60.70 60.70 60.70 60.70 60.70 60.71 60.71 60.71 60.71 60.71 60.72 60.72 60.72 60.72 60.72 60.72 60.72 60.72 60.72 60.73 60.73 60.73 60.73 60.73 60.73 60.74 60.74 60.74 60.74 60.74 60.74 60.74 60.74 60.75 60.75 60.75 60.75 60.75 60.75 60.75 60.76 60.76 60.76 60.76 60.76 60.76 60.77 60.77 60.77 60.77 60.77 60.77 60.77 60.78 60.78 60.78 60.78 60.78 60.78 60.79 60.79 60.79 60.79 60.79 60.79 60.79 60.79 60.79 60.79 60.80 60.80 60.80 60.80 60.80 60.80 60.80 60.80 60.81 60.81 60.81 60.81 60.81 60.81 60.82 60.82 60.82 60.82 60.82 60.82 60.82 60.82 60.83 60.83 60.83 60.83 60.83 60.83 60.84 60.84 60.84 60.84 60.84 60.84 60.84 60.84 60.84 60.85 60.85 60.85 60.85 60.85 60.85 60.85 60.85 60.85 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.86 60.87 60.87 60.87 60.87 60.87 60.87 60.87 60.87 60.88 60.88 60.88 60.88 60.88 60.88 60.88 60.88 60.88 60.88 60.89 60.89 60.89 60.89 60.89 60.89 60.90 60.90 60.90 60.90 60.90 60.90 60.90 60.91 60.91 60.91 60.91 60.91 60.91 60.91 60.91 60.91 60.91 60.91 60.92 60.92 60.92 60.92 60.92 60.92 60.92 60.92 60.92 60.92 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.93 60.94 60.94 60.94 60.94 60.94 60.94 60.94 60.94 60.94 60.94 60.94 60.95 60.95 60.95 60.95 60.95 60.95 60.95 60.95 60.95 60.95 60.95 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.96 60.97 60.97 60.97 60.97 60.97 60.97 60.97 60.97 60.97 60.97 60.97 60.98 60.98 60.98 60.98 60.98 60.98 60.98 60.98 60.98 60.98 60.98 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 60.99 61.00 61.00 61.00 61.00 61.00 61.00 61.00 61.00 61.00 61.00 61.00 61.00 61.01 61.01 61.01 61.01 61.01 61.01 61.01 61.01 61.01 61.01 61.01 61.01 61.01 61.01 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.02 61.03 61.03 61.03 61.03 61.03 61.03 61.03 61.03 61.03 61.04 61.04 61.04 61.04 61.04 61.04 61.04 61.04 61.04 61.04 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.05 61.06 61.06 61.06 61.06 61.06 61.06 61.06 61.06 61.06 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.07 61.08 61.08 61.08 61.08 61.08 61.08 61.08 61.08 61.08 61.08 61.08 61.08 61.08 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.09 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.10 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.11 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.12 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.13 61.14 61.14 61.14 61.14 61.14 61.14 61.14 61.14 61.14 61.14 61.14 61.14 61.14 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.15 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.16 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.17 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.18 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.19 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.20 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.21 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.22 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.23 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.24 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.25 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.26 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 61.27 # Stat: total phase took 4856295.06s # Stat: sizeoptimization took 39902.63s 
20160415, 06:47  #3 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
. It doesn't save them to file unless you specify out (which will get you msieve style output). I did not save the stdout. Only the last 5K lines are saved by my tty, which includes roughly 0.014% of the total output.

20160420, 23:24  #4 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1110000110101_{2} Posts 
Okay, looks like the Python scripts that are otherwise meant to run CADO redirect stdout to file, and then parse said output for the top n lognorm polys itself. That is, the scripts parse out the best n hits, not the polyselect binary itself. The keep parameter is meaningless (except for the stats at the end).
For reference, here is the params.c90 documentation: Code:
########################################################################### # Polynomial selection task with Kleinjung's algorithm (2008) ########################################################################### tasks.polyselect.degree = 4 # degree of the algebraic polynomial #tasks.polyselect.threads = 2 # # How many threads to use per polyselect process tasks.polyselect.P = 10000 # choose lc(g) with two prime factors in [P,2P] # Setting a large value will most likely find better polynomials, # but the number of found polynomials will be smaller. # As a rule of thumb, we want at least 100 found polynomials in total # (without norm limitation, see below). tasks.polyselect.admin = 0 # min value for leading coefficient of f(x) # If not set, the default is 0. tasks.polyselect.admax = 150e3 # max value for leading coefficient of f(x) tasks.polyselect.incr = 60 # increment for leading coefficient of f(x) # This factor is usually a smooth number, which forces projective roots in # the algebraic polynomial. 60 is a good start, 210 is popular as well. # Warning: to ensure lc(f) is divisible by incr, admin should be divisible # by incr too. # The polynomial selection search time is proportional to the # length of the search interval, i.e., (admaxadmin)/incr. tasks.polyselect.nrkeep = 40 tasks.polyselect.adrange = 5000 # size of individual tasks # Polynomial selection is split into several individual tasks. The # complete range from admin to admax has to be covered for the polynomial # selection to complete. The number of individual tasks is # (polsel_admaxpolsel_admin)/polsel_adrange. Each such task is issued as # a workunit to a slave for computation. tasks.polyselect.nq = 256 # Number of small primes in the leading coefficient of the linear polynomial # Safe to leave at the default value # Recommended values are powers of the degree, e.g., 625 for degree 5, # or 1296 for degree 6. Here 256 = 4^4 thus the leading coefficient of # the linear polynomial will be q1*q2*q3*q4*p1*p2 where q1,q2,q3,q4 are # small primes, and P <= p1, p2 < 2*P. Code:
########################################################################### # Polynomial selection ########################################################################### tasks.polyselect.degree = 5 tasks.polyselect.P = 5000000 tasks.polyselect.admax = 5e7 tasks.polyselect.adrange = 5e5 tasks.polyselect.incr = 60 tasks.polyselect.nq = 1000 tasks.polyselect.nrkeep = 1000 Last fiddled with by Dubslow on 20160420 at 23:43 Reason: () 
20160421, 05:32  #5  
"Curtis"
Feb 2005
Riverside, CA
1001001111100_{2} Posts 
Quote:
I can post my top ~500 sizeopt hits from msieve, if you'd like to try rootopting them. But, my best poly was worse than Rich's, so my hits may just not be very good. Lemme know if you'd like them. 

20160421, 05:58  #6  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:
As I recall from the RSA896 experimental poly search, CADO's root siever is noticeably better than Msieve's. Whether or not that's enough to beat RichD's poly, I'm not sure, but I definitely want to try it for posterity's sake, as well as of course trying CADO's first stage/size opt as has so far been the point here. 

20160421, 22:18  #7 
"Curtis"
Feb 2005
Riverside, CA
1001001111100_{2} Posts 
Attached is my top 500 hits from 15 GPUdays. Worst norm is 1.46e26, best 1.33e25. Please post best poly or two from CADO rootopt on this file.
Last fiddled with by VBCurtis on 20160421 at 22:18 
20160421, 23:26  #8 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
jasonp, are the size optimized hit "norms" calculated the same way in Msieve as in CADO? I recall that the Murphy E is definitely different, but it seems that the norms are calculated the same (though CADO gives lognorms, here varying from 6070, where for reference e^65 ~ 1.695e28).
The recorded best 1000 norms from my first run (whose results are lost, but best lognorms are in the second post of this thread) seem to be from 3.84e25  4.97e26. Last fiddled with by Dubslow on 20160421 at 23:29 Reason: second line 
20160422, 00:53  #9 
Tribal Bullet
Oct 2004
2^{4}·13·17 Posts 
The norm (last field in the .ms file) is a rectangular integral very similar to the (now obsolete) GGNFS polynomial selection tool. CADONFS uses the same integral but in radial coordinates, which leads to a different expression to optimize. The two versions will in general not compute the same answer but the hope is the two norms can rank polynomials in approximately the same way.
CADONFS now also uses latticereduction based size optimization techniques that can potentially search a larger space than Msieve does. They took our RSA768 stage 1 dataset and produced a polynomial that was actually better than the one used for the factorization. The Evalues computed by Msieve and CADONFS should be exactly comparable now. Last fiddled with by jasonp on 20160422 at 00:59 
20160422, 09:01  #10  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1110000110101_{2} Posts 
Quote:
2) You mean what Msieve calls stage 1, presizeoptimization, that CADO doesn't bother to separate from size optimization? As in, they used CADO to perform size optimization on Msieve's stage 1 hits? 3) Really? Since when? Which code base changed to match the other? And also I recall that CADO's Murphy E depends on the selected sieve region size, called I in most places? Thanks for the awesome knowledge bombs regardless Last fiddled with by Dubslow on 20160422 at 09:03 

20160422, 15:07  #11 
Tribal Bullet
Oct 2004
2^{4}·13·17 Posts 
1) The value of the integrals would be the same, but remember that we are optimizing very large polynomial expressions, and rectangular vs radial coordinates yield different polynomials that have different gradients and hessians. Our experience is that radial coordinates are better behaved numerically, presumably because polynomial size in the sieving region naturally has radial patterns in it
2) In CADONFS the size optimization is considered part of the initial hashtablebased searching. I think they made an exception for the RSA768 dataset, because all we had was the Msieve stage 1 output and it would have taken quite a while to regenerate it. 3) My memory is hazy on what the difference was; the formula for the Evalue does include the sieving bound and sieve area size as parameters, but those are pretty much always chosen to be the same numbers across the different implementations I know about. Actually I remember now they gave different answers because Dickman's function is computed in segments, and the RSA896 poly search required a few more segments than that version of CADO had tabulated. So we should always have produced the same answers, but in that specific case there was a small bug that they fortunately found quickly Last fiddled with by jasonp on 20160422 at 15:11 
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