[Pitch] Balanced binary reduction (stdlib addition)

[Nevin]

@scanon

I would also be interested in implementations of exact accumulation and Kahan summation, which are both even more accurate than the tree reduction described here.

I wrote an implementation of Kahan summation here in a thread that you also participated in. Should I open a PR to add that to Numerics?

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Also, do you have feedback on the dynamic-dispatch / generic implementation ideas I sketched here a few posts later in the same thread?

More info

I’d really like to be able to call sum() in a generic context on a sequence whose elements are only constrained to AdditiveArithmetic, and have it use the proper algorithm for the actual element type dynamically.

This isn’t too difficult to achieve (I have a working prototype), but it does require a different design with a protocol requirement that each conforming element type implements with its preferred algorithm.

In order to make the constraint be AdditiveArithmetic, the requirement would have to be added to that protocol (with a default implementation), and the implementations for standard library types would have to be in the standard library itself rather than Numerics.