Add methods to get info about ConstraintSystem

[Pratyush]

It would be useful to add num_constraints, num_inputs and num_aux methods to the ConstraintSystem trait to get a quick sense of its cost. I think these methods are general enough to apply to all implementors of ConstraintSystem. If you'd like I can send in a pull request for this as well.

[ebfull]

I've created a test framework for simulating synthesis and getting statistics like this. The bellman API allows it to be implemented independently from this library:

https://github.com/zcash-hackworks/sapling-crypto/tree/master/src/circuit/test

The kinds of checks you're mentioning can be done using this, it even has constraint system hashing for integrity checking (useful for refactoring circuit code without intending to change its contents) and some printing of the constraint system and other stuff.

[Pratyush]

I've seen (and used!) your TestConstraintSystem, and it's great for finding information about the ConstraintSystem in an offline setting (like in tests). But my usecase for these functions would be print this information at runtime, for example during setup or proving, and the existing constraint system interface doesn't provide that information at runtime. But perhaps since we're going to implement GM17 anyway we can make our implementation provide that information. Thanks!

[ebfull]

Hm, I see what you mean. Maybe we can do this, but I have another idea.

I also wanted to attach something to the API which allowed you to pass in an abstract Profiler kind of object. The object would be given timings and other information for various operations, for benchmarking and optimization both of bellman and your own circuits. If you pass in () for the profiler, there's no runtime cost. If you pass in some kind of profiler tool, it'll have access to a lot of useful stats.

I suppose that could be hooked up to get info about the constraint system also!

[Pratyush]

That's a good idea, it sounds more general-purpose and informative! Let me know if I can help with implementing it.