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I added a binding to get the mat mul precision to the init_python_bindings.cpp
I exposed it as a brand new module, torch_xla.backends. This is an ackward name but the goal is to eventually migrate this to torch.backends.xla, to parallel torch.backends.{cuda, cpu, mps, etc}.
I got advice from on very exact numerics for default (1 pass). I made estimates on the 3 pass and 6 pass technique.
I was careful to ensure that there was a non-zero delta from the torch64 cpu calculation - it's easy to make a mistake and end up with your "reference" math also be rounded.
I have a detailed guide on this coming after this PR goes in.