evaluation - Get the current iteration count

I would like to be able to get the current iteration count, the one that if exceeds $IterationLimit makes the evaluation stop.

After not finding a magical variable that stores this value, or a magical built-in that retrieves it, I thought about TraceScan.

According to the documentation of $IterationLimit,

$IterationLimit gives an upper limit on the length of any list that can be generated by Trace

However, a quick test shows that this is not so simple. Let's define

ClearAll[f]
f[i_] := f[i - 1]
f[0] := "Yeah"

Now,

Block[{$IterationLimit = 20},
 Trace[f[18]] // Length//Print;
 Trace[f[18], TraceDepth -> 1] // Length//Print;
 f[18]
 ]

prints 56 and 38 respectively, while f[18]'s evaluation finishes successfully.

Looking at the output of the last trace, we see that the before and after argument evaluation are being traced. So,

Trace[f[3], TraceDepth -> 1]   
(* {f[3],f[3-1],f[2],f[2-1],f[1],f[1-1],f[0],Yeah} *)

Notice that the "two outputs per iteration" rule doesn't hold if we add a definition like f[3]=f[1], in which case

Trace[f[5], TraceDepth -> 1]
(* {f[5],f[5-1],f[4],f[4-1],f[3],f[1],f[1-1],f[0],Yeah} *)

If this happened, a hacky workround could exist along the lines of

SetAttributes[trackIterations, HoldFirst];
trackIterations[code_] := Block[{iterationCounter = 0},
  TraceScan[iterationCounter += 1/2, code, TraceDepth -> 1]
  ]

Question

How can I get that counter, or alternatively, how can I make Trace only trace once each iteration?

Comments

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