Wasm-friendly Field

[mitschabaude]

WIP, experiments towards #2634

define a "wasm-friendly" Field and test it with Poseidon

TODO: Poseidon results don't agree yet, need unit tests

Performance looks promising though: Close to 4x improvement, to reproduce run

./bench-wasm.sh --bench poseidon_bench

[sebastiencs]

Hi @mitschabaude, this is great work.
I've tried to integrate this implementation in openmina, but mul_assign does not give correct result:
openmina@3f8ed1f
When we multiply a number by 1, the result is zero

[mitschabaude]

Hi @mitschabaude, this is great work. I've tried to integrate this implementation in openmina, but mul_assign does not give correct result: openmina@3f8ed1f When we multiply a number by 1, the result is zero

@sebastiencs thanks for testing it, yeah these low-level algorithms are finicky, it will need some debugging to get right. I have an equivalent implementation here though that works perfectly, so I'm sure there's just some small fixable mistake.

I won't be able to finish this PR btw, no longer working at o1Labs -- sorry for leaving this here in an unsatisfying state :)

[volhovm]

@sebastiencs I'll look into this PR sometime soon, perhaps tomorrow, and will sync on what's the plan for continuing.