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1 files changed, 79 insertions, 0 deletions

diff --git a/code/cpp/zmodn.h b/code/cpp/zmodn.h
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--- /dev/null
+++ b/code/cpp/zmodn.h
@@ -0,0 +1,79 @@
+#ifndef ZMODN_H
+#define ZMODN_H
+
+#include <cstdint>
+#include <iostream>
+#include <optional>
+#include <tuple>
+#include <type_traits>
+
+template<typename T>
+concept Integer = requires(T a, T b, int i, std::ostream& os) {
+        {T(i)};
+
+        {a + b} -> std::same_as<T>;
+        {a - b} -> std::same_as<T>;
+        {a * b} -> std::same_as<T>;
+        {a / b} -> std::same_as<T>;
+        {a % b} -> std::same_as<T>;
+
+        {a == b} -> std::same_as<bool>;
+        {a != b} -> std::same_as<bool>;
+
+        {os << a} -> std::same_as<std::ostream&>;
+};
+
+template<Integer T>
+std::tuple<T, T, T> extended_gcd(T a, T b) {
+        if (b == 0) return {a, 1, 0};
+        auto [g, x, y] = extended_gcd(b, a%b);
+        return {g, y, x - y*(a/b)};
+}
+
+template<Integer auto N>
+requires(N > 1)
+class Zmod {
+public:
+        Zmod(decltype(N) z) : value{(z%N + N) % N} {}
+        decltype(N) toint() const { return value; }
+
+        Zmod operator+(const Zmod& z) const { return value + z.value; }
+        Zmod operator-(const Zmod& z) const { return value - z.value; }
+        Zmod operator*(const Zmod& z) const { return value * z.value; }
+
+        Zmod operator+=(const Zmod& z) { return (*this) = value + z.value; }
+        Zmod operator-=(const Zmod& z) { return (*this) = value - z.value; }
+        Zmod operator*=(const Zmod& z) { return (*this) = value * z.value; }
+
+        Zmod operator^(decltype(N) z) const {
+                if (z == 0) return 1;
+                if (z % 2 == 0) return (((*this) * (*this)) ^ (z/2));
+                return (*this) * ((*this) ^ (z-1));
+        }
+
+        bool operator==(const Zmod& z) const { return value == z.value; }
+        bool operator!=(const Zmod& z) const { return value != z.value; }
+
+        std::optional<Zmod> inverse() const {
+                auto [g, a, _] = extended_gcd(value, 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.value << " mod " << N << ")";
+        }
+private:
+        decltype(N) value;
+};
+
+#endif