Julia & Mojo Mandelbrot Benchmark

General Usage
16

This one runs 5x 8x faster then the original julia example posted here, and illustrates nicely how something like ComplexSIMD can be defined quite easily in Julia:

const xn = 960
const yn = 960
const xmin = -2.0
const xmax = 0.6
const ymin = -1.5
const ymax = 1.5
const MAX_ITERS = 200

struct ComplexSIMD{N,T}
    re::NTuple{N,T}
    im::NTuple{N,T}
end

Base.abs2(z::ComplexSIMD) = z.re .* z.re .+ z.im .* z.im
Base.:(*)(a::ComplexSIMD, b::ComplexSIMD) = ComplexSIMD(
    a.re .* b.re .- a.im .* b.im,
    a.re .* b.im .+ a.im .* b.re
)
Base.:(+)(a::ComplexSIMD, b::ComplexSIMD) = ComplexSIMD(a.re .+ b.re, a.im .+ b.im)

@inline function mandelbrot_kernel(c::ComplexSIMD{N,T}) where {N,T}
    z = c
    mask = ntuple(k -> true, N)
    iters = ntuple(k -> T(0), N)
    for i in 1:MAX_ITERS
        !any(mask) && return iters
        mask = abs2(z) .<= 4.0
        iters = iters .+ (mask .* 1)
        z = z * z + c
    end
    return iters
end

@inbounds function inner(result, x_range, y_range, y, ::Val{N}) where N
    ci = y_range[y]
    for x in 1:N:length(x_range)
        # Calculate whether the (x:x+7)-th real coordinates with
        # the y-th imaginary coordinate belong to the
        # mandelbrot set.
        c = ComplexSIMD(ntuple(k -> x_range[x+k-1], N), ntuple(k -> ci, N))
        iters = mandelbrot_kernel(c)
        foreach(enumerate(iters)) do (k, v)
            # Write the result to the output array
            result[y, x+k-1] = v
        end
    end
end

function mandelbrot(result, x_range, y_range, N)
    @sync for y in eachindex(y_range)
        # Threads.@spawn allows dynamic scheduling instead of static scheduling
        # of Threads.@threads macro.
        # See <https://github.com/JuliaLang/julia/issues/21017>.
        Threads.@spawn @inbounds begin
            inner(result, x_range, y_range, y, N)
        end
    end
    return result
end

using BenchmarkTools
result = zeros(yn, xn)
x_range = range(xmin, xmax, xn)
y_range = range(ymin, ymax, xn)
@btime mandelbrot(result, x_range, y_range, Val(4));

Edit:
Also allocated outside the function like Mojo, now its even a bit faster!

(Adapted from mandelbrot Julia #7 program (Benchmarks Game))

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