#include <iostream>
#include <iomanip>
#include <cstdint>
#include <cmath>
#include <cfloat>
#include <random>

/*****************************************************************************************/
// Wrapper for random number generator (RNG)
/*****************************************************************************************/
typedef std::uint_fast32_t random_num_type;

std::random_device seed_generator;
std::mt19937 gen(seed_generator());

random_num_type generate_number()
{
    return gen();
}

/*****************************************************************************************/
// GCD Calculator (Euclid's Devision Algorithm)
/*****************************************************************************************/
random_num_type gcd(random_num_type a, random_num_type b)
{
    while (b != 0)
    {
        a %= b;
        if (a == 0) return b;
        b %= a;
    }
    return a;
}

/*****************************************************************************************/
// GCD Calculator (Euclid's Devision Lemma/Algorithm)
/*****************************************************************************************/
int main()
{
    int count_coprime = 0, trials;

    std::cout << "Enter the number of number pairs/number of trials to use: ";
    std::cin >> trials;
    while(trials < 0)
    {
        std::cout << "Huh, negative number of trials? Please try again." << std::endl;
        std::cout << "Enter the number of number pairs/number of trials to use: ";
        std::cin >> trials;
    }
    std::cout << std::endl;

    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 << ".";
    }
    std::cout << std::endl;

    double pi = std::sqrt(static_cast<double>(6*trials)/count_coprime);
    std::cout << std::endl << "Out of " << trials << " pairs, " <<count_coprime<< " pairs of random numbers were coprime." << std::endl;
    std::cout << std::setprecision(DBL_DIG)<< "Approximate value of pi is: " << pi;
    std::cin >> trials;
    return 0;
}