#include <iostream>
#include <iomanip>
#include <sstream>
#include <cassert>
#include <mpi.h>

using namespace std;

const double a = 0;
const double b = 1;
double f(double x) {
   return 4 / (1 + x*x);
}

// numerical integration according to the Simpson rule
// for f over the interval [a,b] using n subintervals
double simpson(double (*f)(double), double a, double b, int n) {
   assert(n > 0 && a <= b);
   double value = f(a)/2 + f(b)/2;
   double xleft;
   double x = a;
   for (int i = 1; i < n; ++i) {
      xleft = x; x = a + i * (b - a) / n;
      value += f(x) + 2 * f((xleft + x)/2);
   }
   value += 2 * f((x + b)/2);
   value *= (b - a) / n / 3;
   return value;
}

char* cmdname;
void usage() {
   cerr << "Usage: " << cmdname << " [# intervals] " << endl;
   MPI_Abort(MPI_COMM_WORLD, 1);
}

int main(int argc, char** argv) {
   MPI_Init(&argc, &argv);

   int nofprocesses; MPI_Comm_size(MPI_COMM_WORLD, &nofprocesses);
   int rank; MPI_Comm_rank(MPI_COMM_WORLD, &rank);

   // process command line arguments
   int n; // number of intervals
   if (rank == 0) {
      cmdname = argv[0];
      if (argc > 2) usage();
      if (argc == 1) {
         n = nofprocesses;
      } else {
         istringstream arg(argv[1]);
         if (!(arg >> n) || n <= 0) usage();
      }
   }
   // broadcast number of intervals
   MPI_Bcast(&n, 1, MPI_INT, 0, MPI_COMM_WORLD);

   double value = 0; // summed up value of our intervals;
   if (rank < n) {
      int nofintervals = n / nofprocesses;
      int remainder = n % nofprocesses;
      int first_interval = rank * nofintervals;
      if (rank < remainder) {
         ++nofintervals;
         if (rank > 0) first_interval += rank;
      } else {
         first_interval += remainder;
      }
      int next_interval = first_interval + nofintervals;

      double xleft = a + first_interval * (b - a) / n;
      double x = a + next_interval * (b - a) / n;
      value = simpson(f, xleft, x, nofintervals);
   }
   double sum;
   MPI_Reduce(&value, &sum, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);

   MPI_Finalize();

   if (rank == 0) {
      cout << setprecision(14) << sum << endl;
   }
}