1 files changed, 71 insertions, 0 deletions

diff --git a/templates/zmodn-4.cpp b/templates/zmodn-4.cpp
new file mode 100644
index 0000000..d3530c2
--- /dev/null
+++ b/templates/zmodn-4.cpp
@@ -0,0 +1,71 @@
+#include "bigint.h"
+
+#include <iostream>
+#include <optional>
+#include <tuple>
+#include <type_traits>
+
+template<typename T>
+concept Integer = requires(T a, T b, int i) {
+        {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>;
+};
+
+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:
+        decltype(N) value;
+
+        Zmod(decltype(N) z) : value{(z%N + N) % N} {}
+
+        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; }
+
+        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;
+        }
+};
+
+int main() {
+        constexpr BigInt N("1000000000000000000000000000000");
+        Zmod<N> x(BigInt("123456781234567812345678"));
+        Zmod<N> y(BigInt("987654321987654321"));
+
+        std::cout << x.value << " * "
+                  << y.value << " (mod " << N << ") = "
+                  << (x * y).value << std::endl;
+
+        // The following line gives an error when trying to specialize Zmod<M>
+        // constexpr double M = 3.14;
+        // Zmod<M> z(4);
+
+        return 0;
+}