Define BlockedTuple

[ogauthe]

This PR defines BlockedTuple, a Tuple of Tuple like structure with a BlockArrays.jl interface. Data is stored as one flat tuple, with divisions stored as a type parameter (as opposed to storing N tuples).

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 85.71%. Comparing base (74c6607) to head (f554927).
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+ Hits           0      288      +288     
+ Misses       284       48      -236     

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[mtfishman]

@ogauthe related to the discussions about type stability, can you add tests for type stability? You can use TestExtras.@constinferred for that, you can see its usage in TypeParameterAccessors.jl.

[mtfishman]

@ogauthe thanks for rewriting in terms of AbstractBlockTuple, can you reorganize the file so that code defined on AbstractBlockTuple goes above the definition of the BlockedTuple struct, and code specialized to BlockedTuple goes below the definition? I find that kind of organization makes it easier to distinguish generic code from type-specific code.

[mtfishman]

Looks great, thanks! This will be very useful, it will be nice to use this to simplify the implementation of BlockedPermutation. Also it would be nice to split this off into a separate BlockTuples.jl package since I imagine others will find it useful, after we test it out internally.

@lkdvos if you have time could you look into the remaining type instabilities? I imagine it shouldn't be too hard to fix those either by tweaking the code, adding @inline annotations or other compiler annotations, etc.