The nearest integer (round) function, which rounds to the nearest even integer. It was generated by the following Sage code:
(plot(round, -3.5, 3.5, exclude=[a - 0.5 for a in range(-3, 5)], ymax=3, zorder=3, axes_labels=['$x$', r'$\mathrm{nint}(x)$'], fontsize=14, thickness=1.5) +
point((-2.5, -2), rgbcolor='blue', pointsize=45, zorder=4) + point((-1.5, -2), rgbcolor='blue', pointsize=45, zorder=4) +
point((-0.5, 0), rgbcolor='blue', pointsize=45, zorder=4) + point((0.5, 0), rgbcolor='blue', pointsize=45, zorder=4) +
point((1.5, 2), rgbcolor='blue', pointsize=45, zorder=4) + point((2.5, 2), rgbcolor='blue', pointsize=45, zorder=4) +
point((-3.5, -3), pointsize=45, zorder=4) + point((-2.5, -3), pointsize=45, zorder=4) +
point((-1.5, -1), pointsize=45, zorder=4) + point((-0.5, -1), pointsize=45, zorder=4) +
point((0.5, 1), pointsize=45, zorder=4) + point((1.5, 1), pointsize=45, zorder=4) +
point((2.5, 3), pointsize=45, zorder=4) + point((3.5, 3), pointsize=45, zorder=4) +
point((-3.5, -3), rgbcolor='white', pointsize=20, zorder=5) +
point((-2.5, -3), rgbcolor='white', pointsize=20, zorder=5) +
point((-1.5, -1), rgbcolor='white', pointsize=20, zorder=5) +
point((-0.5, -1), rgbcolor='white', pointsize=20, zorder=5) +
point((0.5, 1), rgbcolor='white', pointsize=20, zorder=5) +
point((1.5, 1), rgbcolor='white', pointsize=20, zorder=5) +
point((2.5, 3), rgbcolor='white', pointsize=20, zorder=5) +
point((3.5, 3), rgbcolor='white', pointsize=20, zorder=5))