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I opted to use had_12_paley to follow the original implementation. I added had_12 in the PR for the people who like to use had_12. It is configurable, but you need to recompile the package. Cheers!
Looks like the code generator just needs a one-line patch to replace had_12_paley by had_12, here: https://github.com/Dao-AILab/fast-hadamard-transform/blob/master/csrc/code_gen.py#L181
had_12 appears to match what QuaRot uses: https://github.com/spcl/QuaRot/blob/main/fake_quant/hadamard_utils.py#L152 (haven't exhaustively inspected it, but the first and second column match had_12 and not had_12_paley)
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