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## Brief description This PR adds pre-computation to the MSM, for some theory see [this](https://youtu.be/KAWlySN7Hm8?si=XeR-htjbnK_ySbUo&t=1734) timecode of Niall Emmart's talk. In terms of public APIs, one method is added. It does the pre-computation on-device leaving resulting data on-device as well. No extra structures are added, only `precompute_factor` from `MSMConfig` is now activated. ## Performance While performance gains are for now often limited by our inflexibility in choice of `c` (for example, very large MSMs get basically no speedup from pre-compute because currently `c` cannot be larger than 16), there's still a number of MSM sizes which get noticeable improvement: | Pre-computation factor | bn254 size `2^20` MSM, ms. | bn254 size `2^12` MSM, size `2^10` batch, ms. | bls12-381 size `2^20` MSM, ms. | bls12-381 size `2^12` MSM, size `2^10` batch, ms. | | ------------- | ------------- | ------------- | ------------- | ------------- | | 1 | 14.1 | 82.8 | 25.5 | 136.7 | | 2 | 11.8 | 76.6 | 20.3 | 123.8 | | 4 | 10.9 | 73.8 | 18.1 | 117.8 | | 8 | 10.6 | 73.7 | 17.2 | 116.0 | Here for example pre-computation factor = 4 means that alongside each original base point, we pre-compute and pass into the MSM 3 of its "shifted" versions. Pre-computation factor = 1 means no pre-computation. GPU used for benchmarks is a 3090Ti. ## TODOs and open questions - Golang APIs are missing; - I mentioned that to utilise pre-compute to its full potential we need arbitrary choice of `c`. One issue with this is that pre-compute will become dependent on `c`. For now this is not the case as `c` can only be a power of 2 and powers of 2 can always share the same pre-computation. So apparently we need to make `c` a parameter of the precompute function to future-proof it from a breaking change. This is pretty unnatural and counterintuitive as `c` is typically chosen in runtime after pre-compute is done but I don't really see another way, pls let me know if you do. UPD: `c` is added into pre-compute function, for now it's unused and it's documented how it will change in the future. Resolves https://github.com/ingonyama-zk/icicle/issues/147 Co-authored with @ChickenLover --------- Co-authored-by: ChickenLover <romangg81@gmail.com> Co-authored-by: nonam3e <timur@ingonyama.com> Co-authored-by: nonam3e <71525212+nonam3e@users.noreply.github.com> Co-authored-by: LeonHibnik <leon@ingonyama.com>