Faster evaluation

[saschatimme]

I think I found something to improve the evaluation performance!
I benchmarked exponent, e.g. x^3, and found that it was quite slow :O

julia> x = rand();
julia> @benchmark ^($x, $3)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     22.653 ns (0.00% GC)
  median time:      25.014 ns (0.00% GC)
  mean time:        27.691 ns (0.00% GC)
  maximum time:     260.665 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     995

But from this issue I found that there is a special LLVM instruction which is exposed under Base.FastMath.pow_fast

julia> @benchmark Base.FastMath.pow_fast($x, $3)
BenchmarkTools.Trial: 
  memory estimate:  0 bytes
  allocs estimate:  0
  --------------
  minimum time:     3.586 ns (0.00% GC)
  median time:      4.128 ns (0.00% GC)
  mean time:        4.423 ns (0.00% GC)
  maximum time:     194.732 ns (0.00% GC)
  --------------
  samples:          10000
  evals/sample:     1000

On the other hand Base.FastMath.pow_fast is quite slow for Complex128 (around 100ns) so I checked the normal ^ and found that it is actually faster than the Float64 case 🤔. I opened an issue in the julia repository, let's see how it goes from there.

[blegat]

Good catch ! Looks intriguing indeed, I am curious to see the result of the discussion on the julia repo.