SRS caching

[mitschabaude]

Cache SRS and Lagrange basis

closes #1119
bindings: o1-labs/o1js-bindings#192
proof-systems: o1-labs/proof-systems#1300

Details. This is a follow-up to #1187, which expands caching to include the SRS and Lagrange bases. Most of the lift is in the bindings PR, which refactors basis creation to happen in TS, and try to read from a user-defined cache first. The cache is put in a global variable at the start of compile() and unset at the end. This completely bypasses the Pickles caching logic, to avoid yet more refactors of the Pickles API.

In contrast to prover and verifier keys, SRS and Lagrange bases are very stable and won't need to be regenerated often. The SRS is a fixed list of curve points and exists once for both Pasta curves. So it will be generated once and not change after that. Lagrange bases have to be created once for every circuit size. The circuit size is a power of two and at most equal to the SRS size. In the typical case, a user will already have compiled a circuit of the same power of two, and will be able to read the Lagrange basis from cache.

In addition to enabling caching, the bindings PR uses a faster (multi-threaded) version of SRS creation. This brings a major speedup even on the first run, when the SRS isn't cached yet.

Results. Compiling the simple_zkapp.ts example becomes faster in various scenarios

• Before Cache prover keys #1187 and this PR:
  • Every time: 20.8s
• On this PR:
  • On the very first run (nothing cached): 13.7s / -34%
  • Bases cached, circuits changed: 12.7s / -39%
  • Everything cached: 2.93s / -86%

Note: Loading bases from cache is only 1s faster than regenerating them. The bottleneck is not reading the file, but conversion from the stored JSON format into the format needed by Rust. This should be easy to make faster and will be addressed in a future PR.

Cache directory now looks like this:

[mitschabaude]

Damn, it fails in the web version, I forgot to consider the weird worker-calling layer we have there 😞 Might need to refactor this a bit to work

EDIT: it was just updating the "wasm spec"