Faster cofactorization with ECM using mixed representations


Cost of ECM for the values of B1 and B2 used by the default cofactorization strategy implemented in CADO-NFS.
The values of B1 and B2 are listed in the order in which they are used.
(We assume that S = 1 M.)
B1 B2 cado-nfs 2.3.0 Our work
stage 1 stage 2 totalstage 1 stage 2 total
cost ω elliptic op. #mulcost costcost ω elliptic op. #mulcost cost
105 3255 1240 M 210 4 dDBL + 50 dADD 439 759 M 1999 M 1144 M 126 14 dDBL + 36 dADD 448 734 M 1878 M (-6.05%)
315 5355 3900 M 210 5 dDBL + 60 dADD 643 1028 M 4928 M 3491 M 210 15 dDBL + 49 dADD 642 1011 M 4502 M (-8.64%)
115 5775 1415 M 210 6 dDBL + 61 dADD 675 1071 M 2486 M 1297 M 210 16 dDBL + 50 dADD 675 1055 M 2352 M (-5.39%)
125 6195 1460 M 210 6 dDBL + 63 dADD 714 1122 M 2582 M 1339 M 210 17 dDBL + 51 dADD 713 1104 M 2443 M (-5.38%)
137 6825 1652 M 210 6 dDBL + 66 dADD 783 1209 M 2861 M 1499 M 210 19 dDBL + 52 dADD 776 1183 M 2682 M (-6.26%)
148 7455 1715 M 210 6 dDBL + 69 dADD 838 1282 M 2997 M 1557 M 210 20 dDBL + 54 dADD 834 1258 M 2815 M (-6.07%)
161 8085 1907 M 210 8 dDBL + 72 dADD 894 1366 M 3273 M 1722 M 210 21 dDBL + 56 dADD 894 1335 M 3057 M (-6.60%)
173 8715 2128 M 210 8 dDBL + 75 dADD 958 1448 M 3576 M 1917 M 210 22 dDBL + 58 dADD 954 1412 M 3329 M (-6.91%)
187 9345 2258 M 210 8 dDBL + 78 dADD 1021 1529 M 3787 M 2030 M 210 24 dDBL + 59 dADD 1016 1490 M 3520 M (-7.05%)
200 9975 2521 M 210 8 dDBL + 81 dADD 1078 1604 M 4125 M 2262 M 210 25 dDBL + 61 dADD 1075 1566 M 3828 M (-7.20%)
214 10815 2590 M 210 9 dDBL + 86 dADD 1151 1712 M 4302 M 2318 M 210 26 dDBL + 63 dADD 1149 1657 M 3975 M (-7.60%)
229 11445 2800 M 210 9 dDBL + 89 dADD 1211 1790 M 4590 M 2497 M 210 28 dDBL + 64 dADD 1207 1731 M 4228 M (-7.89%)
244 12285 3016 M 210 9 dDBL + 93 dADD 1287 1890 M 4906 M 2682 M 330 19 dDBL + 76 dADD 1269 1820 M 4502 M (-8.23%)
260 12915 3162 M 210 9 dDBL + 95 dADD 1339 1954 M 5116 M 2813 M 330 20 dDBL + 77 dADD 1321 1883 M 4696 M (-8.21%)
276 13755 3372 M 210 9 dDBL + 99 dADD 1425 2064 M 5436 M 3004 M 330 22 dDBL + 78 dADD 1392 1970 M 4974 M (-8.50%)
293 14595 3688 M 210 9 dDBL + 103 dADD 1502 2165 M 5853 M 3284 M 330 23 dDBL + 79 dADD 1454 2043 M 5327 M (-8.99%)
310 15435 3759 M 210 9 dDBL + 106 dADD 1582 2263 M 6022 M 3348 M 330 23 dDBL + 81 dADD 1526 2127 M 5475 M (-9.08%)
327 16485 3971 M 210 9 dDBL + 111 dADD 1682 2393 M 6364 M 3541 M 330 25 dDBL + 82 dADD 1620 2237 M 5778 M (-9.21%)
345 17325 4141 M 210 10 dDBL + 115 dADD 1745 2485 M 6626 M 3682 M 330 25 dDBL + 84 dADD 1678 2307 M 5989 M (-9.61%)
364 18165 4477 M 210 10 dDBL + 119 dADD 1827 2591 M 7068 M 3968 M 330 26 dDBL + 86 dADD 1762 2408 M 6376 M (-9.79%)
383 19215 4784 M 210 10 dDBL + 124 dADD 1912 2706 M 7490 M 4243 M 330 28 dDBL + 87 dADD 1848 2510 M 6753 M (-9.84%)
403 20055 5012 M 210 11 dDBL + 128 dADD 1987 2810 M 7822 M 4436 M 330 28 dDBL + 89 dADD 1923 2597 M 7033 M (-10.09%)
423 21105 5245 M 210 11 dDBL + 133 dADD 2086 2939 M 8184 M 4649 M 330 30 dDBL + 90 dADD 2013 2703 M 7352 M (-10.17%)
443 22155 5549 M 210 11 dDBL + 137 dADD 2173 3050 M 8599 M 4918 M 330 30 dDBL + 92 dADD 2092 2794 M 7712 M (-10.32%)
464 23205 5859 M 210 11 dDBL + 142 dADD 2274 3181 M 9040 M 5187 M 390 27 dDBL + 98 dADD 2166 2889 M 8076 M (-10.66%)
486 24255 6012 M 210 11 dDBL + 146 dADD 2365 3296 M 9308 M 5329 M 330 32 dDBL + 95 dADD 2262 2992 M 8321 M (-10.60%)
508 25515 6323 M 210 11 dDBL + 152 dADD 2473 3440 M 9763 M 5600 M 390 30 dDBL + 101 dADD 2341 3097 M 8697 M (-10.92%)
531 26565 6608 M 210 11 dDBL + 156 dADD 2562 3553 M 10161 M 5843 M 390 31 dDBL + 102 dADD 2428 3195 M 9038 M (-11.05%)
554 27615 6766 M 210 11 dDBL + 161 dADD 2654 3675 M 10441 M 5986 M 390 32 dDBL + 104 dADD 2507 3291 M 9277 M (-11.15%)
577 28875 7174 M 210 11 dDBL + 166 dADD 2762 3813 M 10987 M 6322 M 390 33 dDBL + 105 dADD 2614 3409 M 9731 M (-11.43%)
601 30135 7504 M 210 11 dDBL + 172 dADD 2877 3964 M 11468 M 6601 M 390 34 dDBL + 107 dADD 2711 3523 M 10124 M (-11.72%)
626 31395 7848 M 210 11 dDBL + 177 dADD 2979 4096 M 11944 M 6901 M 390 36 dDBL + 108 dADD 2807 3635 M 10536 M (-11.79%)
651 32655 8177 M 210 11 dDBL + 183 dADD 3090 4243 M 12420 M 7198 M 390 38 dDBL + 110 dADD 2912 3762 M 10960 M (-11.76%)
676 33915 8506 M 210 11 dDBL + 188 dADD 3199 4382 M 12888 M 7478 M 462 29 dDBL + 117 dADD 3026 3873 M 11351 M (-11.93%)
702 35175 8837 M 210 11 dDBL + 194 dADD 3309 4528 M 13365 M 7772 M 462 31 dDBL + 118 dADD 3123 3986 M 11758 M (-12.02%)
729 36435 9094 M 210 12 dDBL + 200 dADD 3413 4673 M 13767 M 7997 M 462 31 dDBL + 121 dADD 3216 4097 M 12094 M (-12.15%)
756 37905 9434 M 210 12 dDBL + 207 dADD 3547 4849 M 14283 M 8280 M 462 32 dDBL + 122 dADD 3327 4219 M 12499 M (-12.49%)
783 39165 9780 M 210 13 dDBL + 213 dADD 3651 4994 M 14774 M 8568 M 462 33 dDBL + 124 dADD 3425 4334 M 12902 M (-12.67%)
811 40635 10120 M 210 13 dDBL + 219 dADD 3773 5152 M 15272 M 8865 M 462 34 dDBL + 125 dADD 3526 4446 M 13311 M (-12.84%)
840 42105 10560 M 210 13 dDBL + 226 dADD 3906 5327 M 15887 M 9243 M 462 35 dDBL + 127 dADD 3643 4580 M 13823 M (-12.99%)
869 43365 10949 M 210 13 dDBL + 231 dADD 4013 5464 M 16413 M 9566 M 462 36 dDBL + 128 dADD 3732 4680 M 14246 M (-13.20%)
898 44835 11291 M 210 13 dDBL + 238 dADD 4139 5632 M 16923 M 9849 M 462 36 dDBL + 130 dADD 3844 4804 M 14653 M (-13.41%)
928 46515 11553 M 210 13 dDBL + 245 dADD 4283 5818 M 17371 M 10089 M 462 38 dDBL + 132 dADD 3965 4947 M 15036 M (-13.44%)
959 47985 11989 M 210 13 dDBL + 251 dADD 4408 5979 M 17968 M 10470 M 462 39 dDBL + 133 dADD 4074 5067 M 15537 M (-13.53%)
990 49455 12383 M 210 13 dDBL + 258 dADD 4532 6145 M 18528 M 10807 M 462 39 dDBL + 135 dADD 4177 5182 M 15989 M (-13.70%)
1021 51135 12911 M 210 13 dDBL + 265 dADD 4680 6335 M 19246 M 11252 M 546 36 dDBL + 142 dADD 4298 5330 M 16582 M (-13.84%)
1053 52605 13357 M 210 13 dDBL + 271 dADD 4801 6492 M 19849 M 11698 M 546 37 dDBL + 143 dADD 4404 5447 M 17145 M (-13.62%)
1086 54285 13623 M 210 13 dDBL + 278 dADD 4941 6674 M 20297 M 11964 M 546 37 dDBL + 145 dADD 4527 5582 M 17546 M (-13.55%)
1118 55965 14250 M 210 13 dDBL + 286 dADD 5082 6863 M 21113 M 12591 M 546 38 dDBL + 146 dADD 4655 5721 M 18312 M (-13.27%)
1152 57645 14520 M 210 13 dDBL + 293 dADD 5236 7059 M 21579 M 12861 M 546 40 dDBL + 148 dADD 4788 5876 M 18737 M (-13.17%)