diff options
| author | mzuenni <michi.zuendorf@gmail.com> | 2022-06-27 17:19:28 +0200 |
|---|---|---|
| committer | mzuenni <michi.zuendorf@gmail.com> | 2022-06-27 17:19:28 +0200 |
| commit | 5ab8a5088b729a9953b8dff1b2a985dc8fb2098b (patch) | |
| tree | ed40d6936c0e9eee40ba62751cbf99ecddbaddc2 /math/squfof.cpp | |
| parent | adabbad9c51cf7cd3874bfde8eac1fbcf84fec10 (diff) | |
updated tcr
Diffstat (limited to 'math/squfof.cpp')
| -rw-r--r-- | math/squfof.cpp | 89 |
1 files changed, 89 insertions, 0 deletions
diff --git a/math/squfof.cpp b/math/squfof.cpp new file mode 100644 index 0000000..8a11a77 --- /dev/null +++ b/math/squfof.cpp @@ -0,0 +1,89 @@ +using lll = __int128;
+
+constexpr lll multipliers[] = {1, 3, 5, 7,
+ 11, 3*5, 3*7, 3*11,
+ 5*7, 5*11, 7*11,
+ 3*5*7, 3*5*11, 3*7*11,
+ 5*7*11, 3*5*7*11};
+
+lll root(lll x) {
+ lll r = sqrtl(x);
+ while(r*r < x) r++;
+ while(r*r > x) r--;
+ return r;
+}
+
+lll croot(lll x) {
+ lll r = cbrtl(x);
+ while(r*r*r < x) r++;
+ while(r*r*r > x) r--;
+ return r;
+}
+
+lll squfof(lll N) {
+ lll s = croot(N);
+ if (s*s*s == N) return s;
+ s = root(N);
+ if (s*s == N) return s;
+ for (lll k : multipliers) {
+ lll D = k * N;
+ lll Po, P, Pprev, q, b, r, i;
+ Po = Pprev = P = root(D);
+ lll Qprev = 1;
+ lll Q = D - Po*Po;
+ lll L = 2 * root(2 * s);
+ lll B = 3 * L;
+ for (i = 2; i < B; i++) {
+ b = (Po + P) / Q;
+ P = b*Q - P;
+ q = Q;
+ Q = Qprev + b * (Pprev - P);
+ r = root(Q);
+ if (!(i & 1) && r*r == Q) break;
+ Qprev = q;
+ Pprev = P;
+ }
+ if (i >= B) continue;
+ b = (Po - P) / r;
+ Pprev = P = b*r + P;
+ Qprev = r;
+ Q = (D-Pprev*Pprev)/Qprev;
+ i = 0;
+ do {
+ b = (Po + P) / Q;
+ Pprev = P;
+ P = b*Q - P;
+ q = Q;
+ Q = Qprev + b * (Pprev - P);
+ Qprev = q;
+ i++;
+ } while(P != Pprev);
+ r = gcd(N, Qprev);
+ if (r != 1 && r != N) return r;
+ }
+ exit(1);//try fallback to pollard rho
+}
+
+constexpr lll trialLim = 5000;
+
+void factor(lll n, map<lll, int>& facts) {
+ for (lll i = 2; i * i <= n && i <= trialLim; i++) {
+ while (n % i == 0) {
+ facts[i]++;
+ n /= i;
+ }}
+ if (n > 1 && n < trialLim * trialLim) {
+ facts[n]++;
+ } else {
+ vector<lll> todo = {n};
+ while (!todo.empty()) {
+ lll c = todo.back();
+ todo.pop_back();
+ if (c == 1) continue;
+ if (isPrime(c)) {
+ facts[c]++;
+ } else {
+ lll d = squfof(c);
+ todo.push_back(d);
+ todo.push_back(c / d);
+}}}}
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