#include <iostream>
#include <cmath>
 
template<class T>
// F(1) == F(2) == 1 なので X != 1 とする
T Fi(const T& X) {
	T Phi = (1 + std::sqrt(5)) / 2;
	T A01 = std::pow(-1, std::fmod(X + 1, 3));
	return (std::log(std::sqrt(5) * X + std::sqrt(5 * (X * X) - 4 * A01)) - std::log(2)) / std::log(Phi);
}
template<class T>
T F(const T& N) {
	T Phi = (1 + std::sqrt(5)) / 2;
 
	return (std::pow(Phi, N) - std::pow(-Phi, -N)) / std::sqrt(5);
}
 
int main() {
    // フィボナッチ数列 = {0, 1, 1, 2, 3, 5, 8, 13, 21, ...}
	double A = F<double>(8); // フィボナッチ数列の8番目
	double B = Fi<double>(21); // 21はフィボナッチ数列で何番目か(8番目)
 
	std::cout << A << std::endl;
	std::cout << B<< std::endl;
	// n != 2 のとき Fi(F(n)) == n になる
	std::cout << Fi<double>(F<double>(100)) << std::endl;
	return 0;
}

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