I just decided to migrate from Python+Fortran to Julia as Julia was faster in my test

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To get even further into the performance rabbit hole, it’s always fun to bring out LoopVectorization.jl. It doesn’t understand how to handle complex numbers yet, but fortunately we can just reinterpret a matrix of complex floats as a 3-D array of real floats and then operate on that. This example requires a new feature in VectorizationBase.jl, version 0.12.20 0.20.4, so make sure you use that version or newer if you try this.

using LoopVectorization: @tturbo

function eval_exp_tturbo(N)
    A = Matrix{Complex{Float64}}(undef, N, N)
    a = range(0, stop=2*pi, length=N)
    _A = reinterpret(reshape, Float64, A)
    @tturbo for i in 1:N, j in 1:N
        Aij_im, Aij_re = sincos(100*(a[i]^2 + a[j]^2))
        _A[1,i,j] = Aij_re
        _A[2,i,j] = Aij_im
    end
    A
end

print(string("running loop on ", Threads.nthreads(), " threads \n"))
for N in 1_000:1_000:10_000
    @show N
    A = @btime eval_exp($N)
    B = @btime eval_exp_tweaked_4($N)
    C = @btime eval_exp_tturbo($N)
    @assert A ≈ B ≈ C
    println()
end

running loop on 6 threads 
N = 1000
  7.497 ms (33 allocations: 15.26 MiB)
  2.720 ms (34 allocations: 15.27 MiB)
  999.171 μs (2 allocations: 15.26 MiB)

N = 2000
  36.936 ms (33 allocations: 61.04 MiB)
  13.246 ms (34 allocations: 61.05 MiB)
  6.112 ms (2 allocations: 61.04 MiB)

N = 3000
  74.096 ms (33 allocations: 137.33 MiB)
  29.550 ms (35 allocations: 137.35 MiB)
  13.667 ms (2 allocations: 137.33 MiB)

N = 4000
  131.016 ms (35 allocations: 244.14 MiB)
  52.159 ms (36 allocations: 244.17 MiB)
  24.066 ms (2 allocations: 244.14 MiB)

N = 5000
  215.135 ms (35 allocations: 381.47 MiB)
  80.854 ms (37 allocations: 381.51 MiB)
  37.622 ms (2 allocations: 381.47 MiB)

N = 6000
  319.400 ms (35 allocations: 549.32 MiB)
  122.928 ms (37 allocations: 549.37 MiB)
  62.631 ms (3 allocations: 549.32 MiB)

N = 7000
  491.836 ms (35 allocations: 747.68 MiB)
  164.792 ms (38 allocations: 747.74 MiB)
  79.859 ms (5 allocations: 747.68 MiB)

N = 8000
  883.225 ms (37 allocations: 976.57 MiB)
  227.527 ms (37 allocations: 976.63 MiB)
  114.281 ms (6 allocations: 976.56 MiB)

N = 9000
  827.222 ms (35 allocations: 1.21 GiB)
  283.081 ms (37 allocations: 1.21 GiB)
  162.987 ms (4 allocations: 1.21 GiB)

N = 10000
  1.095 s (37 allocations: 1.49 GiB)
  329.651 ms (38 allocations: 1.49 GiB)
  156.945 ms (4 allocations: 1.49 GiB)
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