From 97c94018402c95f2ed1f59645f4b1cbdd255b978 Mon Sep 17 00:00:00 2001
From: Sebastiano Tronto <sebastiano@tronto.net>
Date: Tue, 21 Jan 2025 08:03:15 +0100
Subject: Final examples for templates

---
 templates/zmodn-3.cpp | 57 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 templates/zmodn-3.cpp

(limited to 'templates/zmodn-3.cpp')

diff --git a/templates/zmodn-3.cpp b/templates/zmodn-3.cpp
new file mode 100644
index 0000000..ca73783
--- /dev/null
+++ b/templates/zmodn-3.cpp
@@ -0,0 +1,57 @@
+#include "bigint.h"
+
+#include <iostream>
+#include <optional>
+#include <tuple>
+#include <type_traits>
+
+template<typename 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<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 gives a compile error on the first % operation
+	// constexpr double M = 3.14;
+	// Zmod<M> z(4);
+
+	return 0;
+}
-- 
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