Mod of negative number is melting my brain

Question

I'm trying to mod an integer to get an array position so that it will loop round. Doing i % arrayLength works fine for positive numbers but for negative numbers it all goes wrong.

 4 % 3 == 1
 3 % 3 == 0
 2 % 3 == 2
 1 % 3 == 1
 0 % 3 == 0
-1 % 3 == -1
-2 % 3 == -2
-3 % 3 == 0
-4 % 3 == -1

so i need an implementation of

int GetArrayIndex(int i, int arrayLength)

such that

GetArrayIndex( 4, 3) == 1
GetArrayIndex( 3, 3) == 0
GetArrayIndex( 2, 3) == 2
GetArrayIndex( 1, 3) == 1
GetArrayIndex( 0, 3) == 0
GetArrayIndex(-1, 3) == 2
GetArrayIndex(-2, 3) == 1
GetArrayIndex(-3, 3) == 0
GetArrayIndex(-4, 3) == 2

I've done this before but for some reason it's melting my brain today :(

Answer 1

For the more performance aware devs

uint wrap(int k, int n) ((uint)k)%n

A small performance comparison

Modulo: 00:00:07.2661827 ((n%x)+x)%x)
Cast:   00:00:03.2202334 ((uint)k)%n
If:     00:00:13.5378989 ((k %= n) < 0) ? k+n : k

As for performance cost of cast to uint have a look here

Answer 2

Adding some understanding.

By Euclidean definition the mod result must be always positive.

Ex:

 int n = 5;
 int x = -3;

 int mod(int n, int x)
 {
     return ((n%x)+x)%x;
 }

Output:

 -1

Answer 3

Just add your modulus (arrayLength) to the negative result of % and you'll be fine.