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Implement two-adic fields in MSL (Metal) #123

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@xqft

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@xqft

We need operations over finite fields defined in the Metal Shading Language for implementing FFT (#116) and possibly other future algorithms in the GPU. So it's required to make implementations that mimic the ones we already have in Rust.

Some requirements:

  • Basic operations like sum, sub, mul, div.
  • Watch out for integer overflow, special care is needed to implement the mul operation for example.
  • Ideally we could build a field with a custom module (represented as an uint64_t or whichever type is needed)
  • MSL only supports up to 64-bit integers, so it would be needed to also implement classes for bigger ints (specifically see which fields with big integers there are implemented on Rust right now)
  • The work directory will be math/src/fft/metal/

Relevant resources:

  • MSL Specification (MSL is based on C++)
  • The Metal documentation and also see our metal_playground repo for examples on how to use the metal crate in Rust, useful for testing.
  • risc0 and ministark have some examples of prime fields implemented in C or MSL.
  • Us
  • General information about finite fields and modular arithmetic can be easily found on the web.

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