Is “banker’s rounding” really more numerically stable?
Yes! It really is more numerically stable. For the case that you’re looking at, the numbers [0.0, 0.1, …, 0.9], note that under round-ties-to-away, only four of those numbers are rounding down (0.1 through 0.4), five are rounded up, and one (0.0) is unchanged by the rounding operation, and then of course that pattern repeats … Read more