The Use of Sub-Routines in Programmes (1951) [pdf]
laputan.org
laputan.org
https://www.youtube.com/watch?v=B2EDE8Srdcw
So even the discoveries from 1840 still hold: without the parallel carry circuitry, an adder is simply too slow. Babbage was proud of his implementation, but not many were able to understand then what was that about.
I wouldn't be surprised that Augusta Ada King, Countess of Lovelace, also already thought about the subroutines in 19th century, when considering the programs for the Babbage's machine.