The GInearest function returns the nearest Gaussian integer a to the given complex number c, that is, it finds a Gaussian integer a such that the distance between c and a is smallest.

In special cases when there are more than one possible values of a, the one with the smallest norm is chosen.

$\mathrm{with}\left(\mathrm{GaussInt}\right)\:$

$\mathrm{GInearest}\left(3+7\mathrm{I}\right)$

$3+7\mathrm{I}$

$\mathrm{GInearest}\left(\mathrm{sqrt}\left(-1-\mathrm{sqrt}\left(2\right)\right)\right)$

$2\mathrm{I}$