/* This program demonstrates fun with roundoff error.  What I do is 
   use some general code to calculate the angle of point (x,x) for x = 1, 2, 3, ..., 9.

   You'll note that this angle should be the same.  When I calculate it in a reasonable
   way, the angle differs from point to point.

   I'm calculating it by calculating the hypotenuse of the triangle (0,0), (x,0), (x,x).
   I then divide x by this hypotenuse and call acos().  As you can see below, these
   values do not match for successive values of x.
 */

#include <cmath>
#include <iostream>
#include <cstdio>

int main()
{
  double x;
  double hyp;
  double angle;
  double lastangle;

  lastangle = 0;

  for (x = 1; x < 10; x++) {
    hyp = sqrt(x*x + x*x);
    angle = acos(x/hyp);
    if (x == 1) {
      printf("Point: (%lg,%lg).  Angle: %lf\n", x, x, angle);
    } else {
      printf("Point: (%lg,%lg).  Angle: %lf.  Equal to last angle? %s\n",
             x, x, angle, (angle == lastangle) ? "true" : "false");
    }
    lastangle = angle;
  }
  return 0;
}