Understanding generated functions

General Usage
2

It mostly comes in handy when you have a very large (or infinite) number of parametric types for which you want to have really performant code. For instance, StaticArrays.StaticVector{N, T} is a vector of length N. To sum all the N elements, you could write

function sum(vec::StaticVector)
   res = 0
   for i in 1:length(vec)
      res += vec[i]
   end
   res
end

but looping actually has a (very small) cost. This code would be more efficient:

sum(vec::StaticVector{1}) = vec[1]
sum(vec::StaticVector{2}) = vec[1] + vec[2]
sum(vec::StaticVector{3}) = vec[1] + vec[2] + vec[3]
...

It’s painful to write that code manually. A macro would help, but since N is potentially infinite, you can’t cover all cases. You should use a generated function, so that Julia generates the above code automatically, but only for those types that are actually used in your program.

In my research, I use formal logic, with types like Add{Mul{Int, Variable}, Int}. Generated functions allow me to do a big part of unification (i.e. symbolic manipulations) at compile-time instead of runtime.

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