FredTingaud's proposal for Pi Day Challenge

pi_sampler.cpp

#include <range/v3/all.hpp>
#include <iostream>
#include <iterator>
#include <random>
#include <iomanip>

using namespace ranges::v3;

std::random_device random_device;
std::mt19937 engine{random_device()};

static const double REF_PI = 3.14159265359;

struct Point
{
  Point(int x1, int y1) : x(x1), y(y1) {}
  int x, y;
};

auto randomPoint(int max)
{
  std::uniform_int_distribution<int> dist(0, max);
  return Point(dist(engine), dist(engine));
}

bool inCircle(const Point& p, int radius)
{
  return p.x * p.x + p.y * p.y < radius * radius;
}

bool randomSample(int radius)
{
  return inCircle(randomPoint(radius), radius);
}

int power10(int n)
{
  return std::pow(10, n);
}

auto monteCarloEntries(int radius, int repeat)
{
  return view::repeat_n(radius, repeat);
}

double monteCarloSampling(int radius, int repeat)
{
  return 4. * distance(monteCarloEntries(radius, repeat) | view::filter(randomSample)) / repeat;
}

std::string formatResult(double result)
{
  std::ostringstream os;
  os << std::fixed << std::setfill(' ') << std::setw(15) << result;
  return os.str();
}

auto resultPrinter(int radius)
{
  return view::transform([=] (int repeat) {return std::abs(REF_PI - monteCarloSampling(radius, repeat));}) | view::transform(formatResult);
}

std::string printResultBySizeForRadius(int radius, int maxRepeats)
{
  return view::iota(1, maxRepeats + 1) | view::transform(power10) | resultPrinter(radius) | action::join;
}

auto printResultBySize(int maxRepeats)
{
  return view::transform([=] (int radius){return printResultBySizeForRadius(radius, maxRepeats); });
}

auto radiuses(int n)
{
  return view::iota(1, n + 1) | view::transform(power10);
}

void runSampling(int n, int m)
{
  copy(radiuses(n) | printResultBySize(m), ostream_iterator<>(std::cout, "\n"));
}

int main(int argc, char** argv)
{
  if (argc == 3)
    {
      int radius;
      int size;
      std::istringstream isRad(argv[1]);
      isRad >> radius;
      std::istringstream isSize(argv[2]);
      isSize >> size;
      runSampling(radius, size);
    }
  else
    std::cerr << "Usage: ./" << argv[0] << " radiusCount sizeCount" << std::endl;

  return 0;
}