/******************************************************************************
 * Program that uses the Monte Carlo Method and the Central Limit Theorem
 * to compute π.
 * 
 * Copyright © 2017 Richard Lesh.  All rights reserved.
 *****************************************************************************/

#undef NDEBUG

#include <clocale>
#include <cmath>
#include <codecvt>
#include <ctime>
#include <fmt/format.h>
#include <fmt/xchar.h>
#include <iostream>
#include <string>

std::locale utf8loc(std::locale(), new std::codecvt_utf8<wchar_t>);
using namespace std;

static int const MAX_TRIALS = 20;
static int const SAMPLES_PER_TRIAL = 100000;
double calcpi(int samples) noexcept {
    int inside_count = 0;
    for (int i = 0; i < samples; ++i) {
        double const x = rand()/(RAND_MAX + 1.0);
        double const y = rand()/(RAND_MAX + 1.0);
        if (x * x + y * y <= 1.0) {
            ++inside_count;
        }
    }
    return (double(inside_count) / double(samples)) * 4;
}

int main(int argc, char **argv) {
    setlocale(LC_ALL, "en_US.UTF-8");
    wcout.imbue(utf8loc);
    wcin.imbue(utf8loc);

    srand(time(0));
    double sum = 0.0;
    for (int i = 0; i < MAX_TRIALS; ++i) {
        double const p = calcpi(SAMPLES_PER_TRIAL);
        wcout << fmt::format(L"PI{0:d}: {1:.15f}", i, p) << endl;
        sum += p;
    }
    double const PI = sum / MAX_TRIALS;
    wcout << fmt::format(L"PI: {0:.15f}", PI) << endl;
    wcout << fmt::format(L"abs(PI - π): {0:.10e}", abs(PI - M_PI)) << endl;
    return 0;
}