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Just want to add that we really should thoroughly investigate the claim that storage needs to be aligned. On modern microprocessors, whether or not data is aligned may be largely irrelevant for performance reasons. Many SIMD instructions are identical for aligned/unaligned storage on modern hardware. There may be a slight issue with unaligned storage cross cache boundaries, however, but we should in any case try to measure any such effects.
On the other hand, dealing with alignment adds complexity. For an example of this complexity, just look at Eigen (C++ library): due to alignment considerations it is undefined behavior to store aligned types in standard library data structures (e.g. std::vector<Matrix4d>), or in structs (e.g. struct MyStruct { Matrix4d m; }).
See the discussion in #480 for details.
We need to see when and how we want pointers of matrices (including empty matrices) to be aligned.
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