julia metaprogramming and nloops variable evaluation - macros

Question

I am a noob at metaprogramming so maybe I am not understanding this. I thought the purpose of the #nloops macro in Base.Cartesian was to make it possible to code an arbitrary number of nested for loops, in circumstances where the dimension is unknown a priori. In the documentation for the module, the following example is given:
#nloops 3 i A begin
s += #nref 3 A i
end
which evaluates to
for i_3 = 1:size(A,3)
for i_2 = 1:size(A,2)
for i_1 = 1:size(A,1)
s += A[i_1,i_2,i_3]
end
end
end
Here, the number 3 is known a priori. For my purposes, however, and for the purposes that I thought nloops was created, the number of nested levels is not known ahead of time. So I would not be able to hard code the integer 3. Even in the documentation, it is stated:
The (basic) syntax of #nloops is as follows:
The first argument must be an integer (not a variable) specifying the number of loops.
...
If I assign an integer value - say the dimension of an array that is passed to a function - to some variable, the nloops macro no longer works:
b = 3
#nloops b i A begin
s += #nref b A i
end
This returns an error:
ERROR: LoadError: MethodError: no method matching _nloops(::Symbol, ::Symbol, ::Symbol, ::Expr)
Closest candidates are:
_nloops(::Int64, ::Symbol, ::Symbol, ::Expr...) at cartesian.jl:43
...
I don't know how to have nloops evaluate the b variable as an integer rather than a symbol. I have looked at the documentation and tried various iterations of eval and other functions and macros but it is either interpreted as a symbol or an Expr. What is the correct, julian way to write this?

Answer 1

See supplying the number of expressions:
julia> A = rand(4, 4, 3) # 3D array (Array{Int, 3})
A generated function is kinda like a macro, in that the resulting expression is not returned, but compiled and executed on invocation/call, it also sees the type (and their type parameters of course) of the arguments, ie:
inside the generated function, A is Array{T, N}, not the value of the array.
so T is Int and N is 3!
Here inside the quoted expression, N is interpolated into the expression, with the syntax $N, which evaluates to 3:
julia> #generated function mysum(A::Array{T,N}) where {T,N}
quote
s = zero(T)
#nloops $N i A begin
s += #nref $N A i
end
s
end
end
mysum (generic function with 1 method)
julia> mysum(A)
23.2791638775186
You could construct the expression and then evaluate it, ie.:
julia> s = 0; n = 3;
julia> _3loops = quote
#nloops $n i A begin
global s += #nref $n A i
end
end
quote
#nloops 3 i A begin
global s += #nref(3, A, i)
end
end
julia> eval(_3loops)
julia> s
23.2791638775186
I have scrubbed manually the LineNumberNodes from the AST for readability (there is also MacroTools.prettify, that does it for you).
Running this example in the REPL needs to declare s as global inside the loop in Julia 1.0.