旋转正数和负数的基于零的范围

Question

Say I have a zero-based range like

[0, 1, 2, 3, 4]

these are essentially the indexes of an array with size = 5. Is it possible to use a signed integer variable to continuously loop up or down in that range?

By up or down, I mean that the variable is permitted to perform arbitrarily many increment or decrement operations :

++index;
--index;

So for example decrementing the index should map to following values:

index = 2;

while (/*...*/)
{
  --index;
  index_in_range(index, 5);
}

The function index_in_range(index, 5) would output:

[1, 0, 4, 3, 2, 1, 0, 4, 3, 2, 1, .... and so on]

The positive case is just a modulo operation over the range size, but for the negative I can't figure out how the mapping goes.

Answer 1

C made a really poor decision for % to round towards zero, rather than be a straightforward floor, so the math's clunkier than it has to be. Basically, though, you want (index % size + size) % size . That code starts by chopping off the negative or positive multiples to bring the index into the range (-size, size) , adds size to map it into (0,size*2) , and a final % to map it into [0,size) .

If size is not known at compile time, it's likely more performant to replace everything after the first modulus with a conditional: index %= size; if(index < 0) index += size; index %= size; if(index < 0) index += size; .

Answer 2

To increase

index = (index+1)%sz;

To decrease

index = (index-1+sz)%sz