WIP: leverage Base reduction functions

[simonbyrne]

This is something I have been meaning to do for a while. Basically the idea is to define a kbn addition operator, and define all the reductions in terms of that.

[ararslan]

Should these be restricted to T<:Real? Also do they necessarily have to be the same type? Using + as we do here should take care of any promotion that needs to happen.

[ararslan]

This is a lot of blank lines. Could you reduce it to just one, maybe two?

[simonbyrne]

No. I need those for caching

[ararslan]

This looks really cool! Is there any noticeable change in performance?

[simonbyrne]

AHHHHH!!!!!

This doesn't work on 0.7 because r_promote was removed (JuliaLang/julia#22825). The recommendation seems to be that you combine the promotion into the mapping function, but that will be pretty inefficient in this case, as it will end up calling plus_kbn(::TwicePrecisionN, ::TwicePrecisionN) instead of plus_kbn(::TwicePrecisionN, ::Float64).

[mgr327]

Would it be possible to re-activate/implement that pull request?

[JeffreySarnoff]

We do not care about support for Julia 0.7. If you can get this work as intended for Julia "1.6+", we are open to including it.

[asinghvi17]

I just looked at this code again and it seems to be fine in v1.11.

# this implementation
julia> @be sum_kbn($(rand(1000)))
Benchmark: 3348 samples with 16 evaluations
 min    1.677 μs
 median 1.734 μs
 mean   1.738 μs
 max    7.698 μs

# the implementation on master
julia> @be KahanSummation.sum_kbn($(rand(1000)))
Benchmark: 3336 samples with 16 evaluations
 min    1.682 μs
 median 1.698 μs
 mean   1.740 μs
 max    4.336 μs

# compared to current Base pairwise summation, slower of course
julia> @be sum($(rand(1000)))
Benchmark: 3198 samples with 290 evaluations
 min    98.131 ns
 median 98.707 ns
 mean   100.700 ns
 max    268.390 ns

I attached a timer output and it never calls the method for two TwicePrecisions. (Annotations mine)

julia> to
────────────────────────────────────────────────────────────────────
                           Time                    Allocations      
                  ───────────────────────   ────────────────────────
Tot / % measured:      2.13s /   0.8%           3.68MiB /   0.0%    

Section                           ncalls     time    %tot     avg     alloc    %tot      avg
───────────────────────────────────────────────────────────────────────────────
+(::Float64, ::TwicePrecisionN)     1.72M   17.9ms   99.9%  10.4ns     0.00B     - %    0.00B
+(::Float64, ::Float64)             1.72k   17.4μs    0.1%  10.1ns     0.00B     - %    0.00B
───────────────────────────────────────────────────────────────────────────────

But this seems mergeable as is.

cc @simonbyrne @JeffreySarnoff