The minimal residue of 
is the value 
or 
,
whichever is smaller in absolute value, where 
. If 
(so that 
), then the minimal residue is taken as 
. The table below illustrates the common
(positive) and minimal residues for 0, 1, 2, and 3 (mod 4).
 | common residue  | minimal residue  |
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 |  |
| 3 | 3 |  |
The minimal residue is implemented in the Wolfram Language as Mod[a, m, -m/2].
