// pi.c integral x=0 to 1 4.0/(1+x^2) dx
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#define Pi 3.1415926535897932384626433832795028841971

int main(int argc, char * argv[])
{
  long int n = 10;
  double h, x, pi, start;
  int i, k;

  printf("pi.c running \n");
  printf("pi = integral x=0 to 1 4.0/(1+x^2) dx \n");
  printf("pi += sum h*4.0/(1.0+x*x) x=0..1 \n");
  start = (double)time(NULL);

  for(k=0; k<14; k++)
  {
    pi = 0;
    h = 1.0/(double)(n-1);
    for(i=0; i<n; i++)
    {
      x = h*(double)i;
      pi += h*4.0/(1.0+x*x); 
    }
    printf("n=%d, h=%e, error=%e, at %f sec \n",
            n, h, pi-Pi, (double)time(NULL)-start);
    n *= 4;
  }
  printf("pi.c finished \n");
  return 0;
} // end pi.c