Open MLIR Meeting 10-26-2023: A Polynomial Dialect Proposal

This is a presentation of the proposal for a "poly" dialect for polynomial arithmetic. This is motivated by the use of such (high-degree) polynomials in a variety of post-quantum cryptography, including Fully Homomorphic Encryption (FHE). At a high level, poly will contain a type representing a polynomial, attributes specifying the domain of the polynomials (e.g., integer or real coefficients), and ops representing addition, multiplication, division/remainder, polynomial evaluation, etc. More details in the RFC thread: https://discourse.llvm.org/t/rfc-a-po... More info on Discourse: https://discourse.llvm.org/t/open-mli... Slides: https://mlir.llvm.org/OpenMeetings/20... More Tech talks on #MLIR: https://mlir.llvm.org/talks/