Estimate pi

piday.cpp

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

struct point {
    double x, y;

    inline double distance_squared() const
    {
        return x * x + y * y;
    }

    inline bool hits_circle(double radius_squared) const
    {
        return distance_squared() < radius_squared;
    }
};

point make_random_point(double radius)
{
    static std::random_device rd;
    static std::mt19937 rng{ rd() };

    std::uniform_real_distribution<> dist{ -radius, radius };
    return point{ dist(rng), dist(rng) };
}

double estimate_pi(unsigned int n, unsigned int m)
{
    double radius = std::pow(10, n);
    double radius_squared = radius * radius;
    unsigned int num_samples = std::pow(10, m);
    unsigned int num_hits = 0;

    for (unsigned int i = 0; i < num_samples; ++i) {
        auto sample = make_random_point(radius);
        if (sample.hits_circle(radius_squared))
            ++num_hits;
    }

    return static_cast<double>(num_hits) / num_samples * 4;
}

constexpr double distance_from_pi(double estimate)
{
    constexpr double pi = 3.14159265359;
    return std::abs(estimate - pi);
}

int main(int argc, char** argv)
{
    for (unsigned int n = 0; n <= 9; ++n) {
        for (unsigned int m = 0; m <= 7; ++m)
            std::cout << std::setw(12) << distance_from_pi(estimate_pi(n, m));

        std::cout << std::endl;
    }
}