When running instant-carry adders at a reasonably fast pass I often got derped pistons. Therefore I started thinking what alternative methods could be used to get "fast" adders. Stacking normal full adders would be the easiest, but slow since the fastest would be 2 ticks, and therefore each carry propagation would add 2 ticks to the calculation time. Then you would come to the more complicated adders, like a Kogge-Stone adder, which use some sort of carry look-ahead. But then I thought of a more simple solution which would increase the speed, but still keep the design stackable. This solution depends on the fact that both the normal and the inverse carry-out can be calculated in 2 ticks, however if a full adder would also receive both a normal and the inverse carry-in, the propagation can be reduced to 1 tick, using the following logic:

However this does require more wiring, and therefore I was only able to make it 4 wide stackable. One full adder calculates the sum in 3 ticks, however the carry propagation due to a change in the carry-in would take 1 tick. Since the the first carry-out is calculated in 2 ticks and when the carry-in changes it takes in the worst case 2 ticks to calculate the new sum, therefore a N-bit adder using this design would in the worst case need N+3 ticks. So the worst case of an 8-bit adder would be 13 ticks.