Parallel heap algorithm implementations WIP

[Syntaf]

Implementation moving forward from #1888 , still WIP so this PR is for code review and inspect.

To-Do:

• Write is_heap, is_heap_until
• Benchmark algorithms to test performance
• Determine how chunk size should interact within these algorithms, as the chunk size is not guaranteed in level based parallelism
• Decide whether to create practitioners for these algorithms, or leave the implementation within the algorithm itself.

Currently:

• make_heap algorithm is implemented and all tests pass

[hkaiser]

@Syntaf: what's the status of this work?

[Syntaf]

@hkaiser All of the tests pass and the algorithms work, but I ran out of time to benchmark them and refine their implementation. A couple things to note

• I don't believe settings the chunk size via executor works, it currently splits it events among partitions and additionally divides it by 2. I chose to divide by some constant because an evenly partitioned set with the amount of cores would almost all be run sequentially in the heap algorithms.
• If the amount of items in a level is less than the chunk size, it is run sequentially
• I had to overload the parallel function in both is_heap and make_heap to account for throwing exceptions within futures, other than that their implementation is identical.

I created two functions inside of parallel/util/detail/chunk_size.hpp , get_bottomup_heap_bulk_iteration_shape and get_topdown_heap_bulk_iteration_shape. Both of these functions return a shape vector as the other chunk_size functions do, and runs any sequential work (if the level is less than the chunk_size). The difference is that they do not partition the level, they only return what levels can be parallelized. So inside parallel I loop through the shape and chunk/execute the items, this is because each element in shape must synchronize before moving on to the next element.

[sithhell]

What's the status here? Can we close the PR and you open it again once everything is done?

[hkaiser]

@sithhell I'm working on this ...

[hkaiser]

@taeguk Before I close this PR without merging, does this contain anything you might be of value for your work?

[taeguk]

@hkaiser I don't refer the implementation in this PR.

[hkaiser]

Closing this unmerged as similar work is being done independently.