Bubble sort

Six numbers sorted where they lie, with nowhere else to put them. The inner loop walks the array comparing each element with the one after it and swapping the pair when they are the wrong way round. The outer loop runs the inner one again, and again, until nothing is left out of order.

Step through the first pass with the memory panel open on 402000, and watch the 42. It starts at the front, loses its first comparison, and moves one place right. Then it loses the next one and moves again. By the end of the pass it has travelled the whole way to the end of the array in a single run, while everything else has shuffled one place left. That is the bubbling the name refers to, and the largest element is guaranteed to arrive after one pass however badly the array started.

[values + rbx*8] and [values + rbx*8 + 8] are an element and its neighbour, reached from one index register with two different constants added on. The addressing mode does the work a second register would do anywhere it could not.

That guarantee about the largest element is what dec rcx at the bottom of the outer loop is cashing in. After one pass the last element is certainly right, after two the last two are, so each pass can stop one element earlier than the one before it and the inner loop shortens as the outer one runs.

What the program does not do is notice when a pass swapped nothing. Change the data to dq 1, 2, 3, 4, 5, 6, already sorted, and it still makes all fifteen comparisons before deciding it is finished. One flag register, cleared at the top of each pass and set by the swap, tested at the bottom, turns this into a sort that costs one pass on data that is already in order.