1 files changed, 78 insertions, 0 deletions
diff --git a/test/math/discreteNthRoot.cpp b/test/math/discreteNthRoot.cpp
new file mode 100644
index 0000000..d595e6d
--- /dev/null
+++ b/test/math/discreteNthRoot.cpp
@@ -0,0 +1,78 @@
+#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();
+	performance_test();
+}
+