✨ Add rollover_t

[elbeno]

Problem:

• When dealing with a timer register that rolls over, it is useful to have a type that knows how to handle that.

Solution:

• Add rollover_t.
• rollover_t behaves like an unsigned integral type, with interesting comparison semantics.

[lukevalenty]

i'm worried about the fact that zero < half and half < zero both evaluate to true. is there a way we can avoid this? it feels very wrong.

[lukevalenty]

@elbeno: I think I remember what I did...it was with signed integers, but let's pretend that signed overflow is defined behavior for a moment:

bool operator<(auto a, auto b) {
    retutrn (a - b) < 0;
}

That implementation takes care of the wraparound case and there is no case in which a < b and b < a holds true. We should be able to implement the equivalent with unsigned integers.

[lukevalenty]

This is how it should work for uint32_t:

bool operator<(uint32_t a, uint32_t b) {
    retutrn (a - b) >> 31;
}

In 2s complement signed integers, a number is negative if the msb is set. This function does the equivalent check for uint32_t.

[elbeno]

You're right - and that's exactly equivalent to what I've written. > mid means the sign bit is set. Bear in mind the pesky integer promotion rules...

[lukevalenty]

You're right - and that's exactly equivalent to what I've written. > mid means the sign bit is set. Bear in mind the pesky integer promotion rules...

You're right! Ok....I need some more work to wrap my brain grapes around this one... 🧠🍇