[circuits] [cli] create production-friendly tree depth combinations

[weijiekoh]

The larger the state and message tree depths, the more gas that a user (or relayer) has to pay to sign up or publish a message. The larger the vote option tree, state tree, and message tree depths, the longer it will take for the coordinator to generate proofs.

We can assume that the coordinator has more computational power than the average user, so it's okay to set the vote option tree to the maximum feasible size on consumer hardware (5 ^ 5 = 3125 leaves).

The message tree size should be large enough such that each user can cast 1 vote per vote option, plus an additional key-change message on top of that.

Let the depth of the state tree be s, the depth of the message tree be m, the depth of the vote option tree be v, and the number of voice credits as c.

Each user should be able to publish at least c + 1 messages, or 5 ** v + 1 messages, whichever is smaller. This is to let them either spend all their voice credits (1 credit per vote) or vote for up to all available vote options. Let this value be n.

The depth of the message tree should therefore be ceil(log2(2 ** s * n)).

E.g. Assuming that each user has 99 voice credits, the vote option tree depth is 4, and the state tree depth is 4:

n = 2 ** 4 + 1 = 17
ceil(log2(2 ** 4 * 17)) = 9

Predefined tree depths

State tree depth	Message tree depth	Vote option tree depth	Deployment gas	Signup gas	Publish message gas
10	17	5	9136375	551133	1055361
4	4	2	7274945	333357	583713

Ultimately, whoever builds upon MACI has to decide exactly which tree depths works for their use case, and they have to be responsible for its specific trusted setup.

That said, if we use a Quadtree (see #101), we can support larger trees.

CC: we should just use Large because the gas savings are not that large