Index arithmetic - Fast converting index to 3D coordinates

Question

What is the fastes way in C++ to convert an index with such a formation to X, Y and Z coordinates and back ?

EDIT:

I want for example get for the index 15 the numbers X=0, Y=1, Z=2, for the index 17 the numbers X=2, Y=1, Z=2, and for the index 22 the numbers X=1, Y=2, Z=1.

I need this to emulate a multidimensional array.

Answer 1

To:

x = index % 3;
y = index / 3  % 3;
z = index / 9;

Back:

index = ((z) * 3 + y) * 3 + x;