Hi Keith, please note that actually the cause of the issue was early identified in (8) and the solution of using round also explained in (9). So at that point, I think it is obvious that I knew about floating point arithmetic and the way to fix it. discussing further about the goodness or the evilness of floating point arithmethic (by the way if not invented at least used in the first computer Z3 by Konrad Zuse in 1940!, pretty old stuff) is simply floating-pointless ;)