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Tullio is a very flexible einsum macro. It understands many array operations written in index notation -- not just matrix multiplication and permutations, but also convolutions, stencils, scatter/gather, and broadcasting. Used by itself the macro writes ordinary nested loops much like Einsum.@einsum. One difference is that it can parse more expressions, and infer ranges for their indices. Another is that it will use multi-threading (via Threads.@spawn) and recursive tiling, on large enough arrays.