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].