From 6cfb7b4d8e6b0838bfcde290e5fac18f46f18fb4 Mon Sep 17 00:00:00 2001
From: Sebastiano Tronto <sebastiano@tronto.net>
Date: Fri, 17 Jan 2025 16:53:40 +0100
Subject: Added first two zmodn versions

---
 templates/zmodn-1.cpp | 55 ++++++++++++++++++++++++++++++++++++++++++++++++++
 templates/zmodn-2.cpp | 56 +++++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 111 insertions(+)
 create mode 100644 templates/zmodn-1.cpp
 create mode 100644 templates/zmodn-2.cpp

(limited to 'templates')

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;
+}
-- 
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