C.16.MR:5.3 - Interpret a wrapping event counter

A modeled counter increments once for each event and retains a value from 0 to 15, returning to 0 after 15. Readings immediately before and after an interval are r0 and r1. The sought quantity is the number N of intervening events. Assume no reset, no missed increment and readings taken at the stated interval boundaries.

The counter operation gives

r1 = (r0+N) mod 16
N = d + 16*k

Here d is the least nonnegative remainder of r1-r0 modulo 16, and k is a nonnegative integer. With r0=14 and r1=3, d=5: the compatible counts are 5,21,37 and so on.

If the interval is known to contain fewer than 16 events, N=5. Without that bound, subtracting the displayed numbers or returning the modular difference loses possible complete wraps. A wider counter, a recorded wrap count or shorter observation intervals can supply the missing information for a later measurement.

To infer elapsed time, another relation is needed: the counter must count timing ticks with an applicable tick-duration account. A counter of arbitrary work events alone measures no duration. This identifies a missing relation rather than inventing one from the numerical display.