Define metal::accumulate for zero input lists

[brunocodutra]

Speaking of accumulate I decided to have a look at it and realized it could be simplified if implemented in terms of metal::transform.

[brunocodutra]

@ecrypa would love your feedback on this.

[brunocodutra]

sigh.

[ecrypa]

I did see the troubles of old compilers. Anyway, I like the new code.

With Clang 9 and GCC 9 it is also faster than the old accumulate version of min_element.

[ecrypa]

In the final version we should check for superfluous includes, right?

[brunocodutra]

(Somehow I missed this comment the first time around).

Absolutely, thanks for catching this one!

[ecrypa]

Nice.

[ecrypa]

Does this exist for performance reasons? I wonder if we can also increase performance for a total number of two, three, and, say, four seqs. I understand that fold_left plays nicely with a single list, but maybe there is another shortcut if the number of seqs is known.

[brunocodutra]

Yes, by far the most common use case I expect to be accumulating a single list.

I wonder if we can also increase performance for a total number of two, three, and, say, four seqs.

We don't need to, that's the beauty of this version! Notice that it relies on transpose, which already specializes on 1, 2 and 3 lists. That's probably why accumulate got faster in your benchmark.

[brunocodutra]

With Clang 9 and GCC 9 it is also faster than the old accumulate version of min_element.

Wow nice, didn't expect that to be honest.

I did see the troubles of old compilers.

I hate MSVC with passion.

[brunocodutra]

While playing with this I realized metal::accumulate could be generalized to accept zero input lists and decided to change this PR to that instead.

[ecrypa]

Beautiful!

Besides, the discarded min_element index retrieval is even faster with this version (v21). See Clang 9 and GCC 9.

[brunocodutra]

Woah nice, thanks for checking!