Stable Sorting, ie, Minimally-Disruptive Sorting

Question

Suppose I have a list of things (numbers, to keep things simple here) and I have a function I want to use to sort them by, using SortBy. For example, the following sorts a list

Answer 1

This seems to work:

stableSortBy[list_, f_] := 
  SortBy[MapIndexed[List, list], {f@First[#], Last[#]}&][[All,1]]

But now I see rosettacode gives a much nicer way to do it:

stableSortBy[list_, f_] := list[[Ordering[f /@ list]]]

So Ordering is the key! It seems the Mathematica documentation makes no mention of this sometimes-important difference Sort and Ordering.