pi approximation using random points in a circle

random_pi.cpp

// approximate pi using random points in a square
// compile using: g++ pi.cpp -o pi
// and then run using: ./pi
#include <iostream>
#include <iomanip>
#include <random>
#include <cmath>
#include <chrono>

using namespace std;

int main() {
    const long int TOTAL = 1e6;
    cout.precision(15);

    random_device r;
    default_random_engine gen(r());
    uniform_real_distribution<long double> dist(0.0, 1.0);

    long double inside;
    inside = 1.0L;

    long double x, y;

    chrono::time_point<chrono::steady_clock> start, end;
    start = chrono::steady_clock::now();
    for(long int i = 0L; i < TOTAL; ++i) {
        // randomly select a point inside the square
        x = dist(gen);
        y = dist(gen);
        //check if it's inside the circle
        if(sqrt(x*x + y*y) <= 1.0L)
            ++inside;
    }
    end = chrono::steady_clock::now();
    chrono::duration<double> elapsed_seconds = end - start;
    double t = elapsed_seconds.count();

    // compare it with the area of the square
    // and multiply by 4 since we only considered
    // one fourth of the circle
    long double pi = 4.0L*(inside/TOTAL);

    cout << "calculated: " << pi << endl;
    cout << "actual: " << acos(-1.0L) << endl;
    cout << "difference: " << fabs(pi-acos(-1.0L)) << endl;
    cout << "it took " << t << " seconds" << endl;

    return 0;
}