Added first two zmodn versions

2 files changed, 111 insertions, 0 deletions

diff --git a/templates/zmodn-1.cpp b/templates/zmodn-1.cpp
new file mode 100644
index 0000000..a8e26ca
--- /dev/null
+++ b/templates/zmodn-1.cpp
@@ -0,0 +1,55 @@
+#include <iostream>
+#include <optional>
+#include <tuple>
+
+std::tuple<int, int, int> extended_gcd(int a, int 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<int N>
+class Zmod {
+public:
+        int value;
+
+        Zmod(int z) : value{(z%N + N) % N} {}
+        int 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; }
+
+        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() {
+        Zmod<57> x(34);
+        Zmod<57> y(11);
+
+        std::cout << "34 * 11 = " << (x * y).value << " (mod 57)" << std::endl;
+
+        if (auto inv = y.inverse(); inv)
+                std::cout << "11 * " << inv.value().value << " = 1 (mod 57)" << std::endl;
+        else
+                std::cout << "11 is not invertible in Z/57Z" << std::endl;
+
+
+        // The following line gives a run-time exception
+        // Zmod<0> z(157);
+
+        return 0;
+}
diff --git a/templates/zmodn-2.cpp b/templates/zmodn-2.cpp
new file mode 100644
index 0000000..f96ef8c
--- /dev/null
+++ b/templates/zmodn-2.cpp
@@ -0,0 +1,56 @@
+#include <iostream>
+#include <optional>
+#include <tuple>
+
+std::tuple<int, int, int> extended_gcd(int a, int 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<int N>
+requires (N > 1)
+class Zmod {
+public:
+        int value;
+
+        Zmod(int z) : value{(z%N + N) % N} {}
+        int 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; }
+
+        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() {
+        Zmod<57> x(34);
+        Zmod<57> y(11);
+
+        std::cout << "34 * 11 = " << (x * y).value << " (mod 57)" << std::endl;
+
+        if (auto inv = y.inverse(); inv)
+                std::cout << "11 * " << inv.value().value << " = 1 (mod 57)" << std::endl;
+        else
+                std::cout << "11 is not invertible in Z/57Z" << std::endl;
+
+
+        // Contrary to zmodn-1.cpp, the following line does not compile at all
+        Zmod<0> z(157);
+
+        return 0;
+}