#include <iostream>
#include <iomanip>
#include <random>
#include <cstdint>
#include <cmath>
/*****************************************************************************************/
typedef std::uint_fast32_t random_num_type;

/*****************************************************************************************/
// Wrapper for random number generator (RNG)
/*****************************************************************************************/
std::random_device seed_generator;
std::mersenne_twister_engine <random_num_type,
                              32, 624, 397, 31,
                              0x9908b0df, 11,
                              0xffffffff, 7,
                              0x9d2c5680, 15,
                              0xefc60000, 18, 1812433253> gen(seed_generator());

random_num_type generate_number()
{
    return gen();
}

/*****************************************************************************************/
// GCD Calculator (Euclid's Devision Lemma/Algorithm)
/*****************************************************************************************/
random_num_type gcd(random_num_type a, random_num_type b)
{
    return b == 0 ? a : gcd(b, a % b);
}

/*****************************************************************************************/
// GCD Calculator (Euclid's Devision Lemma/Algorithm)
/*****************************************************************************************/
int main()
{
    std::cout << std::setprecision(8);

    int count_coprime = 0, trials;
    std::cout << "Enter the number of number pairs/number of trials to use: ";
    std::cin >> trials;

    int trials_per_percent = trials / 100;

    for (int i = trials; i > 0; i--)
    {
        random_num_type a = generate_number();
        random_num_type b = generate_number();
        if (gcd(a, b) == 1) count_coprime++;

        if (i%trials_per_percent == 0) std::cout << ".";
    }

    double pi = std::sqrt(static_cast<double>(6*trials)/count_coprime);

    std::cout << std::endl << "Out of " << trials << " pairs, " <<count_coprime<< "were co-prime pairs." << std::endl;
    std::cout << "Approximate value of pi is: " << pi;
    std::cin >> trials;
    return 0;
}