#include <iostream> //need this by default for cin
#include <math.h> //includes math functions
#include <cmath> //includes basic math 
#include <cfloat> //includes floating point numbers
#include <iomanip> //includes setprecision for decimal places
#include <cstdlib> //needed for rand and srand functions
#include <ctime> //needed for time function used to seed generator
#include <climits> 
 
using namespace std;
 
int main()
{
   cout << "The purpose of this program is to estimate pi using the monte "
      "carlo method and a random number generator" << endl << endl;
 
   unsigned seed = time(0);
   srand(seed);
 
   int trialcount = 0;
   int trials;
   float accuracy;
   const float pi = 3.14159265;
 
 
   cout << "The value of PI can be found as the ratio of areas of a circle of radius r located within a square of side 2r" << endl;
   cout << "This program runs a MonteCarlo Simulation that generates numbers located randomly within a square" << endl;
   cout << "The count of values within the square and the count of numbers within the circle approximate their areas" << endl;
   cout << "An input value of radius determines the size of the circle and square" << endl;
   cout << "The user specifies how many trials or test runs are desired" << endl << endl;
 
   cout << "The true value of PI to 8 decimal places is 3.14159265" << endl << endl;
 
   cout << endl;
   cout << "How many trials would you like? ";
   cin >> trials;
   cout << endl << endl;
 
   cout << "Square count gives the Total number of random samples (they are within the square)" << endl;
   cout << "Circle count gives the number of random samples that also fall within the circle" << endl << endl;
 
 
   while (trialcount != trials)
   {
      accuracy = 0.1;
      cout << "Trial " << trialcount + 1 << endl;
      cout << "Accuracy \t\t" << "Square Count \t\t" << "Circle Count \t\t" << "Pi" << endl << endl;
 
      for (int j = 0; j < 6; j++)
      {
         accuracy /= 10;
         float randpi = 0;
         int squarecount = 0;
         int circlecount = 0;
 
         int stopAt = (INT_MAX >> 8);
         for (int i = 0; (randpi >= pi + accuracy || randpi <= pi - accuracy) && i < stopAt; i++)
         {
            float x = ((float)(rand() % 32768) / 32767);
            float y = ((float)(rand() % 32768) / 32767);
 
            squarecount++;
 
            if ((x * x) + (y * y) <= 1.0 )
            {
               circlecount++;
            }
 
            randpi = float(4 * circlecount) / squarecount;
         }
 
         cout << setprecision(8) << fixed << accuracy << " \t\t" << squarecount << " \t\t" << circlecount << " \t\t" << randpi << endl << endl;
      }
 
      trialcount++;
   }
}
 
 

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