From 7f1b8a358515b45d717c3c4b5baf2fbc0f568170 Mon Sep 17 00:00:00 2001
From: Sebastiano Tronto <sebastiano@tronto.net>
Date: Wed, 26 Feb 2025 17:12:06 +0100
Subject: Initial commit

---
 code/cpp/zmodn.h | 79 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 79 insertions(+)
 create mode 100644 code/cpp/zmodn.h

(limited to 'code/cpp/zmodn.h')

diff --git a/code/cpp/zmodn.h b/code/cpp/zmodn.h
new file mode 100644
index 0000000..a24f293
--- /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
-- 
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