/* 
   Compute integral from 0  to 1  4/(1+x*x). 
   This should be equal to PI. 
   
   Sequential program, no parallelism.
   
   Lauras-MacBook-Pro:OpenMP ltoma$ gcc-6  -fopenmp pi.c 
   Lauras-MacBook-Pro:OpenMP ltoma$ ./a.out 
   Start. Done. PI=3.142, time = 0.0
   Lauras-MacBook-Pro:OpenMP ltoma$ 
   
*/ 


#include <stdio.h> 
#include <stdlib.h> 
#include <omp.h>



int main(int argc, char** argv) {

  long num_steps = 1000000; 
  double step, x, pi, sum =0; 
  int i; 
  double t1, t2; 
  
  step = 1/(double)num_steps; 

  t1 = omp_get_wtime(); 

  printf("Start. ");
  for (i=0; i<num_steps; i++) {

    //value in the middle of the rectangle
    x = (i+.5)*step; 
    //add the area of the rectangle to the sum 
    sum = sum + 4/(1+x*x); 
  }
  pi = step * sum; 
  printf("PI=%.3f ", pi);

  t2 = omp_get_wtime();   
  printf("Done. time = %.1f\n",  t2-t1);
  
  return 0; 
}