/*

COMPILATION: gcc  -fopenmp integral1d_OMP.c -lm
USAGE: ./a.out thread#  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 <omp.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 i;
   double sum = 0;
   double x;



   int thread_count = atoi(argv[1]); // number of threads participating computation is read from the command lile arguments
   int trials = atoi(argv[2]); // trials is total number of random points, it is read from the command line arguments


// multiple threads are started after this compiler directive, num_threads() function indicates number of threads to be started
// reduction(+:sum) function indicates end of the parallel region total_hits variables of each thread are gathered in master thread
// private(x) indicates variable x is private to each thread instead of being shared by threads
   #pragma omp parallel num_threads(thread_count) reduction(+:sum) private(x)
   {
      // It is desired every thread to generate different random numbers so
      // each thread are seeded with different number (thread id)
      srand(omp_get_thread_num());

      //this compiler directive divides the loop iterations between the spawned threads
      #pragma omp  for       
      for(i=0 ; i < trials ; i++ )
      {
         x = my_rand()  ;
         sum += ( f(x) / w(x) ) ;

      }
      
   }// all threads are joined after this block


   double integral = 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)));


   return 0;

}