JuliaSIMD / JuliaSIMD/LoopVectorization.jl

manually provide reduction isomorphisms so that expensive operations can be factored out of the loop

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Descrizione

I do not know the proper name for this concept; feel free to change the title.

Based on discussion here: https://discourse.julialang.org/t/how-to-do-simd-code-with-wide-register-accumulators-simd-vs-loopvectorization-jl-vs-simd-jl/63322

Consider
```julia
accumulator = 0
for i in 1:length(array)
accumulator ⊻= array[i]
end
result = count_ones(accumulator)
```

Here `count_ones(a⊻b) = count_ones(a)+count_ones(b)` modulo 2 which permits to vectorize as

```julia
accumulator = zero(lane)
for i in 1:lanesize:length(array)
accumulator ⊻= array[i+lane]
end
result = sum(count_ones(a) for a in accumulator)
```

However, all one can do automagically with `@turbo` is

```julia
accumulator = 0
@turbo for i in 1:length(array)
accumulator += count_ones(array[i])
end
result = accumulator
```
This is **slower** because `count_ones` is called each time instead of being called only once at the end.

**This feature request is asking for a way to teach `@turbo` that it is permitted to use an isomorphism of the type `operatorA(f.(array)...) == f(operatorB(array...))`.**

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