A recent article by Faux and Godolphin explored issues of floating-point error in situations relevant to classical dynamics, numerical integration, cellular automata, statistical analysis, and digital timing.1 Examples were given that were suitable for discussion and student project work. One of the examples explored the properties of an algorithm, described in an IBM Knowledge Center document designed to convert a binary field representing the number of counts of a quartz oscillator to integers for digital display.2 In Ref. 1, it was demonstrated that the algorithm was vulnerable to rounding error resulting in an incorrect digital display. Investigation associated with this example forms the focus of this note.
The timing simulation results presented in Ref. 1 suggested that uncorrected rounding error in stopwatch timer displays could be impactful if used for precision timing, such as for race times or in experimental physics. Here, we present and analyse race...
