Shardy custom_partitioning.
The parsing of the sharding rule string very closely follows how einops parses
their rules in einops/parsing.py.
When a SdyShardingRule object is constructed, we check the syntax of the Einsum
like notation string and its consistency with the user provided factor_sizes,
and report errors accordingly. This is done during f.def_partition.
When SdyShardingRule.build is called, during JAX to MLIR lowering, we check
the consistency between the Einsum like notation string, the factor_sizes
and the MLIR operation, and report errors accordingly.
PiperOrigin-RevId: 703187962
2a4a0e8d6f