Instrument field operations

[WizardOfMenlo]

Especially when prototyping a new protocol, having a accurate field operation counts is very important.
My proposal would be to add this behind a feature flag, adding a globally accessible stats counter that is then updated.
Ideally, by turning on the instrumentation flag, the user would be able to transparently instrument their code with no changes required.

[burdges]

You'd typically count curve operations plus FFTs.

You could've curve+field forks or wrapper types, which achieved this. If you only want curve operations, then you could check out https://github.com/paritytech/arkworks-extensions

If you opnly want curve operations, then you could integrate this approch with different benchmarking tools.

[WizardOfMenlo]

For my particular use-case, curve operations and FFTs are not too relevant. I really would just want to be able to count the number of field additions, multiplications and divisions.
I assume that, once that is done the common infrastructure could be extended to other functionalities.
Possibly we could decorate methods which should (optionally) be instrumented with some derive_macro which writes to a common (global, thread safe, possibly slow) counter. Then, on the counter itself we can implement some aggregation for better user functionality.

[burdges]

Above, we targeted the expensive operations above, without changing the fields, but..

It's likely easier to just count field operations, either cargo patch in your fork of ark-ff, or else simply fork the curve with one commit that sustitutes your ark-ff.