> On old x86 systems, the x87 registers were 80-bits and the bottom bits were undefined. You could theoretically have a 1-bit difference on some results

I spent a long time once debugging an issue arising from this. Code was basically:

  double x = y;
  [...]
  if (x>y) fail;

Nothing in between the assignment and the check changed the value of x or y, yet the check triggered the fail condition. Turned out to be that one of the value stayed in the 80 bit x87 register and one was written to RAM as a 64 bit value, then loaded back into an x87 register for the check, resulting in the inequality. Running in a debugger wrote both values out of the registers before the check, making the problem unreproducible.