/*

COMPILATION: mpicc integral1d_mpi.c -lm
USAGE: mpirun -n processor# ./a.out trial#

This program computes integral of ( 1 / (1 + x*x) ) in x=[0,1] by using importance sampling Monte Carlo 


*/


#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <limits.h>
#include <mpi.h>

// f() is the function to be integrated
double f(double x)
{

   return (1.0 / (1.0 + x*x) ) ;

}

// random x values are generated according to probability distribution function w() 
double w(double x)
{


   return ((1.0/3.0) * (4 - 2 * x)) ;
}


// my_rand() function generates random numbers according to p.d.f w()
// this function uses inverse of the p.d.f w() 
double my_rand()
{


   double y = (double)rand() / (double)RAND_MAX ;

   return (2.0 - sqrt(4.0 - 3.0*y) ) ;
}


int main(int argc, char* argv[])
{
   int trials, trials_per_p; // trials is total number of random points and trials_per_p number of random points for each processor 
   int i;
   double partial_sum = 0; // each processor uses its variable partial_sum to sum function value
   double total_sum; // at the end of the computation all processors' partial_sum gathered in total_sum
   double x;
   int pnumber, myrank; // pnumber is the number of processor in the computation and myrank is the rank of the processor

   MPI_Init(&argc,&argv);  // Initialize the MPI execution environment
   MPI_Comm_rank(MPI_COMM_WORLD, &myrank); // Each processor learns its rank number
   MPI_Comm_size(MPI_COMM_WORLD, &pnumber); // Each processor learns how many processor participate to the calculation

   trials = atoi(argv[1]); // command line argument is readed for total random number

   trials_per_p = trials / pnumber ; // number of points for each processor is calculated


   srand(myrank); // It is desired every processor to generate different random numbers so
                  //      each processor seeded with different number (rank   oprocessor)


   for(i=0 ; i < trials_per_p ; i++ )
   {
      x = my_rand()  ;
    
      partial_sum += ( f(x) / w(x) ) ;

   }

   // Assume the processor which has rank=0 is master
   int master_p = 0;
   
   //total sum and total random number are gathered to the master processor   
   MPI_Reduce(&partial_sum,  &total_sum, 1,  MPI_DOUBLE,  MPI_SUM, master_p, MPI_COMM_WORLD);
   MPI_Reduce(&trials,  &trials_per_p, 1,  MPI_INT,  MPI_SUM, master_p, MPI_COMM_WORLD);

   //Master processor prints the result
   if(myrank == master_p)
   {
      double integral = total_sum / trials ;

      printf("computed value of the integral= %f \n", integral);
      printf("true value of the integral=     %f \n", atan(1.0));
      printf("error=                          %f  \n", fabs( integral - atan(1.0)));

   }


   MPI_Finalize(); //Terminates MPI execution environment


return 0;

}