/* 
   Compute integral from 0  to 1  4/(1+x*x). 
   This should be equal to PI. 
   

   First attempt at parallelization, which does not work for a couple of reasons: 

   1. each thread is computing the whole thing in parallel.

   2. there are a number of shared variable that cause race conditions
   and the result is wrong.

   
   [ltoma@lobster /Volumes/CS/ltoma/public_html/teaching/cs3225-GIS/fall16/Code/OpenMP]$gcc-6  -fopenmp pi1.c
[ltoma@lobster /Volumes/CS/ltoma/public_html/teaching/cs3225-GIS/fall16/Code/OpenMP]$./a.out 
Start(2)
Start(3)
Start(4)
Start(0)
Start(1)
Start(6)
Start(5)
Start(7)
Done(6): pi = 3.040
Done(3): pi = 3.035
Done(2): pi = 3.040
Done(4): pi = 3.040
Done(0): pi = 3.035
Done(7): pi = 3.035
Done(1): pi = 3.035
Done(5): pi = 3.035
Done. time = 1.0
Lauras-MacBook-Pro:OpenMP ltoma$ ./a.out 
Start(4)
Start(2)
Start(6)
Start(5)
Start(1)
Start(3)
Start(0)
Start(7)
Done(6): pi = 3.161
Done(4): pi = 3.161
Done(1): pi = 3.161
Done(5): pi = 3.161
Done(7): pi = 3.161
Done(2): pi = 3.161
Done(0): pi = 3.161
Done(3): pi = 3.161
Done. time = 1.1

*/ 


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



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

  long num_steps = 10000000; 
  double step, x, pi, sum =0; 
  int i; 
  double t1, t2; 
  
  step = 1/(double)num_steps; 
  
  t1 = omp_get_wtime(); 
  
#pragma omp parallel 
  { 
    int thread_id = omp_get_thread_num(); 
    printf("Start(%d)\n", thread_id); 
    
    for (i=0; i<num_steps; i++) {
      //value in the middle of the rectangle
      x = (i+.5)*step; 
      
      //add the area of the current rectangle to the sum
      sum = sum + 4/(1+x*x); 
    }
    pi = step * sum; 
    
    printf("Done(%d): pi = %.3f\n", thread_id, pi); 
  }
  
  t2 = omp_get_wtime();   
  printf("Done. time = %.1f\n",  t2-t1);
  
 
  return 0; 
}