How to index circular array in Julia?

Question

I'd like to access elements in an array in a circular manner. Normally a modulo suffices but in Julia arrays start at 1. At the moment I'm basically converting the indices to a 0-based index and back. But this doesn't work for negative indices.

A = 1:5
for i in -6:6
    println(i, " -> ", ((i - 1) % length(A)) + 1)
end

Output

-6 -> -1 # wrong
-5 ->  0 # wrong
-4 ->  1 # wrong
-3 -> -3 # wrong
-2 -> -2 # wrong
-1 -> -1 # wrong
 0 ->  0 # wrong
 1 ->  1
 2 ->  2
 3 ->  3
 4 ->  4
 5 ->  5
 6 ->  1

Answer 1

I usually use mod1 function for this. Here is an example:

julia> [-10:10 mod1.(-10:10, 5)]
21×2 Array{Int64,2}:
 -10  5
  -9  1
  -8  2
  -7  3
  -6  4
  -5  5
  -4  1
  -3  2
  -2  3
  -1  4
   0  5
   1  1
   2  2
   3  3
   4  4
   5  5
   6  1
   7  2
   8  3
   9  4
  10  5

Answer 2

The % operator is not the mod operator as you suspect, but the rem operator.

Replace your modulus operation with mod( i-1, length(A) ) and you will get your intended result.

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_{PS. I would have to add, the use-case for such circularity also matters. If you're trying to replicate python-like negative indices, where a negative index of -1 indexes the last element of the array, and continuing circularly in that fashion from that point on for negative numbers, would necessarily require a different treatment for 0 and two different branches, one for positive and one for negative numbers.}