pi_approx.cpp

#include <boost/range/algorithm/for_each.hpp>
#include <boost/range/algorithm/count_if.hpp>
#include <boost/range/irange.hpp>
#include <boost/range/adaptor/transformed.hpp>
#include <iostream>
#include <random>
#include <cmath>

using namespace boost;
using namespace adaptors;

constexpr auto pi=3.14159265359;

auto times(unsigned int n)
{
    return boost::irange(0u, n);
}

auto pi_approx(const double radius, const unsigned int point_count)
{
    static std::random_device rd;
    static std::mt19937 rng{rd()};
    std::uniform_real_distribution<double> dist(0, radius);
 
    auto inner_random_point_count=count_if(times(point_count), [&dist, &radius](auto)
        {
            const auto x=dist(rng);
            const auto y=dist(rng);
            return std::sqrt(x*x+y*y)<=radius;
        });
    
   return 4.0*inner_random_point_count/point_count;
}

int main()
{
    std::cout.setf(std::ios::fixed, std::ios::floatfield);
	std::cout.precision(5);

    for (auto radius: times(10) | transformed([](auto log10_radius){return std::pow(10, log10_radius);}))
    {
        for (auto diff: times(8) | transformed([&radius](auto log10_point_count){return std::fabs(pi-pi_approx(radius, std::pow(10, log10_point_count)));}))
        {
            std::cout<<diff<<" ";
        }
        std::cout<<std::endl;
    }
         
    return 0;
}