Initial commit

1 files changed, 71 insertions, 0 deletions

diff --git a/zmodn.h b/zmodn.h
new file mode 100644
index 0000000..8981257
--- /dev/null
+++ b/zmodn.h
@@ -0,0 +1,71 @@
+#ifndef ZMODN_H
+#define ZMODN_H
+
+#include <cstdint>
+#include <iostream>
+#include <optional>
+#include <tuple>
+
+std::tuple<int64_t, int64_t, int64_t> extended_gcd(int64_t, int64_t);
+
+template<int64_t N> requires(N > 1)
+class Zmod {
+public:
+        Zmod(int64_t z) : int64{(z%N + N) % N} {}
+        int64_t toint64() const { return int64; }
+
+        Zmod operator+(const Zmod& z) const { return int64 + z.int64; }
+        Zmod operator-(const Zmod& z) const { return int64 - z.int64; }
+        Zmod operator*(const Zmod& z) const { return int64 * z.int64; }
+        Zmod operator+=(const Zmod& z) { return int64 += z.int64; }
+        Zmod operator-=(const Zmod& z) { return int64 -= z.int64; }
+        Zmod operator*=(const Zmod& z) { return int64 *= z.int64; }
+
+        bool operator==(const Zmod& z) const { return int64 == z.int64; }
+        bool operator!=(const Zmod& z) const { return int64 != z.int64; }
+
+        std::optional<Zmod> inverse() const {
+                auto [g, a, _] = extended_gcd(int64, N);
+                return g == 1 ? Zmod(a) : std::optional<Zmod>{};
+        }
+
+        std::optional<Zmod> operator/(const Zmod& d) const {
+                auto i = d.inverse();
+                return i ? (*this) * i.value() : i;
+        }
+
+        std::optional<Zmod> operator/=(const Zmod& d) {
+                auto q = *this / d;
+                return q ? (*this = q.value()) : q;
+        }
+
+        friend std::ostream& operator<<(std::ostream& os, const Zmod<N>& z) {
+                return os << "(" << z.int64 << " mod " << N << ")";
+        }
+private:
+        int64_t int64;
+};
+
+void swapdiv(int64_t& oldx, int64_t& x, int64_t q) {
+        int64_t tmp = x;
+        x = oldx - q*tmp;
+        oldx = tmp;
+}
+
+std::tuple<int64_t, int64_t, int64_t> extended_gcd(int64_t a, int64_t b) {
+        int64_t oldr = a;
+        int64_t r = b;
+        int64_t olds = 1;
+        int64_t s = 0;
+        int64_t oldt = 0;
+        int64_t t = 1;
+        while (r != 0) {
+                auto q = oldr / r;
+                swapdiv(oldr, r, q);
+                swapdiv(olds, s, q);
+                swapdiv(oldt, t, q);
+        }
+        return {oldr, olds, oldt};
+}
+
+#endif