Implement ec_gpu:GpuField for Fp/Fq

[vmx]

This commit introduces a new feature called "gpu", which enables an
ec_gpu:GpuField implementation of Fp and Fq. This enables the
field arithmetics to be run on a GPU.

The code to convert from a u64 to a u32 vector was taken from
https://github.com/filecoin-project/blstrs/blob/07a84f9727d2fb7387efb2df0f17ddc5d35571d3/src/lib.rs#L102-L108

[daira]

utACK

[str4d]

@vmx can you confirm this will close #22? At the time I opened that issue, it looked to me like we'd need to implement GpuEngine in this crate; has the API changed?

[vmx]

@str4d it won't close all things from #22. It will enable finite field arithmetic, but nothing else yet. Though we surely want halo2 to run on the GPU, so I'd consider this PR as a first step towards that goal.

[str4d]

#22 is documented as covering only this change:

• The curve implementation needs to support producing the GPU kernel for finite field arithmetic.

My question above was, is that what this PR achieves? And what (if any) purpose does the GpuEngine trait (which existed in October last year) serve? (EDIT: I see it still exists.)

[vmx]

My question above was, is that what this PR achieves?

It will enable finite field arithmetic to be run on GPUs. This can, e.g. be used by Neptune to run Poseidon hashing with the paste curves (lurk-lab/neptune#135).

[DrPeterVanNostrand]

Hi @str4d

This PR allows the field arithmetic kernel source code to be generated for the Pasta scalar fields using ec_gpu_gen::field::<F>() (for example, as we do in neptune here).

The curve implementation needs to support producing the GPU kernel for finite field arithmetic.

I believe that this PR does that (cc. @vmx). What this PR does not achieve is the ability to generate FFT and MSM kernels for the Pasta curves.

Implementing GpuEngine for the Pallas and Vesta curves would allow for the generation of each curve's FFT and MSM kernel's source code (I believe by calling ec_gpu_gen::gen_source() link). For example, we implement GpuEngine for Bls12 (here) and generate FFT and MSM kernel source code for the G1 and G2 curves in bellperson here.

[str4d]

utACK