In x86 (intel notation) you can also:

add rax, rbx

rcr rax, 1

It explicitly uses the carry flag from the addition as the top bit of the right-rotated result.

Not super useful for anything other than averaging two uints but that's x86 for you.

What I missed in my first pass was

   * Forgetting exactly which register was the low index and which was the high index
   * Underflow if array size was zero from setting the last index to (size - 1)