Fast lightweight method of detecting skipped values in a cyclic sequence

Question

I have a single value that, over time, increases from 1 to 6 and then returns to 1. So over several frames the sequence seen would be:

1, 2, 3, 4, 5, 6, 1, 2, 3, 4...

If a hardware device is defective one of those numbers may not read correctly and so the sequence may look like this:

1, 2, 6, 4, 5, 6, 1, 2, 6, 4...

What is a fast, short method of detecting this inconsistency?

Note:

• This is designed for a hard real-time environment
• My current method is to check that each new value every frame has a difference no greater than 1 from the last value, then there is a special case for the difference between 1 and 6 which is allowed to be 5
• I am wondering whether there is a simple algorithm or trick to solving this problem
• The sequence is also valid if it is in reverse, e.g.: 6, 5, 4, 3, 2, 1, 6, 5, 4, 3....

Answer 1

You can use the modulo operator:

(current_value - previous_value + 6) mod 6 == 1

The +6 is there to ensure a positive argument to mod. Different languages treat negative values differently, but if -5 mod 6 evaluates to 1 in yours, you can omit the +6.