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#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;
}
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