Gaussian/Banker's Rounding

keith (Keith Gaughan) — Fri, 27 Jan 2006 20:47:37 GMT

Gaussian rounding (aka Banker's rounding) rounds numbers in such a way as there is no upwards bias when rounding x.5. This minimises cumulative error in summing, averaging, &c. rounded numbers.



/**

 * Gaussian rounding (aka Banker's rounding) is a method of statistically

 * unbiased rounding. It ensures against bias when rounding at x.5 by

 * rounding x.5 towards the nearest even number. Regular rounding has a

 * built-in upwards bias.

 */

function gaussianRound(x) {

    var absolute = Math.abs(x);

    var sign     = x == 0 ? 0 : (x < 0 ? -1 : 1);

    var floored  = Math.floor(absolute);

    if (absolute - floored != 0.5) {

        return Math.round(absolute) * sign;

    }

    if (floored % 2 == 1) {

        // Closest even is up.

        return Math.ceil(absolute) * sign;

    }

    // Closest even is down.

    return floored * sign;

}

Thanks to Dennis W Jay for pointing out a bug in the code.

DZone Snippets: maths code

Gaussian/Banker's Rounding