Implement +(as...) etc. for Array

[ViralBShah]

There may be some gains to implementing +(as...) and other similar cases for arrays. This should be faster and also allocate fewer temporaries.

[JeffBezanson]

It would probably help a bit, but it seems to me A + B + C is actually less common than A + s*B. Also, currently we can only do this efficiently for specific numbers of arrays, e.g. +(A,B,C), +(A,B,C,D) etc.

[toivoh]

For the array types that it supports, + could call .+ after checking type compatibility. Or I could provide another entry point to the broadcast machinery that it could use. Even though this is not actually broadcasting, a lot of the optimizations are the same, especially for strided arrays. My plan is that the broadcast machinery should eventually be efficient for diverse kinds of arrays, and also in cases where you don't actually need broadcasting. But that will probably take some time yet.

Anyways, the broadcast machinery does include a limited form of staged functions so that this can be done once for any number of arguments. It shouldn't be so hard to hack together something similar (and simpler) for this case.

[ViralBShah]

The general case is the kinds of things that @lindahua does in Devectorize.jl. My guess is that every such little optimization over time will add up to significant gains overall.

[lindahua]

I agree with Jeff that x += a * y is probably more common in practice.

A fundamental way to boost these things is lazy evaluation, that is, actual codes are generated only when it sees the entire expression.

I think Devectorize.jl can be designed in a better way. I will revisit this when I get time in the summer.

[stevengj]

This should be closed by #17623, since x .+ y .+ z .+ ... will fuse into a single broadcast loop.

[stevengj]

Closed by #17623.