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#include "../util.h"
#define ll lll
#include <math/modPowIterativ.cpp>
#undef ll
#include <math/millerRabin.cpp>
#include <math/rho.cpp>
ll phi(ll pk, ll p, ll /*k*/) {return pk - pk / p;}
ll phi(ll n) { // O(sqrt(n))
ll res = 1;
for (ll p = 2; p * p <= n; p++) {
if (n % p == 0) {
ll pk = 1;
ll k = 0;
do {
n /= p;
pk *= p;
k++;
} while (n % p == 0);
res *= phi(pk, p, k);
}}
if (n > 1) res *= phi(n, n, 1);
return res;
}
#include <math/primitiveRoot.cpp>
#include <math/discreteLogarithm.cpp>
#include <math/discreteNthRoot.cpp>
//x^a=b mod m
ll naiveRoot(ll a, ll b, ll m) {
for (ll i = 0; i < m; i++) {
if (powMod(i, a, m) == b) return i;
}
return -1;
}
void stress_test() {
int queries = 0;
int found = 0;
for (int tries = 0; tries < 50'000; tries++) {
ll p = Random::prime<ll>(0, 1000);
ll a = Random::integer<ll>(1, p);
ll b = Random::integer<ll>(1, p);
ll got = root(a, b, p);
ll expected = naiveRoot(a, b, p);
if (got < -1 || got >= p) cerr << "error: out of range" << FAIL;
if (got >= 0 && powMod(got, a, p) != b) cerr << "error: wrong" << FAIL;
if ((got >= 0) != (expected >= 0)) cerr << "error" << FAIL;
queries++;
if (expected >= 0) found++;
}
cerr << "tested random queries: " << queries << " (" << found << ")" << endl;
}
constexpr int N = 50;
constexpr ll mod = 1'394'633'899;
void performance_test() {
timer t;
hash_t hash = 0;
for (int i = 0; i < N; i++) {
ll a = Random::integer<ll>(1, mod);
ll b = Random::integer<ll>(1, mod);
t.start();
hash += root(a, b, mod);
t.stop();
}
if (t.time > 500) cerr << "too slow: " << t.time << FAIL;
cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl;
}
int main() {
stress_test();
if (!sanitize) performance_test();
}
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