Broadcasting in Julia (Illustrated)

That's the most basic feature of broadcasting, but not quite what Julia's broadcasting is all about. There's also the case of things like

    f(x,y) = cos(x)*sin(y)

    g(x,y) = tan(x)*inv(y)

    x, y = (rand(4), rand(4))
   
    z = rand(4)

    z .= f.(x,y') .+ g.(x',y)

to create create one loop that creates whole matrix of results and writes in-place into z. Is there a syntax for that in modern Fortran? I know that it has intrinsic functions which accepts vectors but its this fusion of multiple operations mixed with how it handles differently-sized objects that really defines the braodcasting operation.

The two major differences are that broadcasting in julia is

1. caller based. As a user, I can ask for a broadcasted version of any function (not only specific functions which implement broadcasting)

2. composable. The expression `sqrt.(exp.(x).+1)` in julia will generate a single loop over `x` compared to the numpy version which will make 3 passes over the memory.