class RoundingMode

final class RoundingMode {
    
    /**
     * Private constructor. This class is not instantiable.
     *
     * @codeCoverageIgnore
     */
    private function __construct() {
    }
    
    /**
     * Asserts that the requested operation has an exact result, hence no
     * rounding is necessary.
     */
    public const UNNECESSARY = 0;
    
    /**
     * Rounds away from zero.
     *
     * Always increments the digit prior to a nonzero discarded fraction.
     * Note that this rounding mode never decreases the magnitude of the
     * calculated value.
     */
    public const UP = 1;
    
    /**
     * Rounds towards zero.
     *
     * Never increments the digit prior to a discarded fraction (i.e.,
     * truncates). Note that this rounding mode never increases the magnitude of
     * the calculated value.
     */
    public const DOWN = 2;
    
    /**
     * Rounds towards positive infinity.
     *
     * If the result is positive, behaves as for UP; if negative, behaves as for
     * DOWN. Note that this rounding mode never decreases the calculated value.
     */
    public const CEILING = 3;
    
    /**
     * Rounds towards negative infinity.
     *
     * If the result is positive, behave as for DOWN; if negative, behave as for
     * UP. Note that this rounding mode never increases the calculated value.
     */
    public const FLOOR = 4;
    
    /**
     * Rounds towards "nearest neighbor" unless both neighbors are equidistant,
     * in which case round up.
     *
     * Behaves as for UP if the discarded fraction is >= 0.5; otherwise, behaves
     * as for DOWN. Note that this is the rounding mode commonly taught at
     * school.
     */
    public const HALF_UP = 5;
    
    /**
     * Rounds towards "nearest neighbor" unless both neighbors are equidistant,
     * in which case round down.
     *
     * Behaves as for UP if the discarded fraction is > 0.5; otherwise, behaves
     * as for DOWN.
     */
    public const HALF_DOWN = 6;
    
    /**
     * Rounds towards "nearest neighbor" unless both neighbors are equidistant,
     * in which case round towards positive infinity.
     *
     * If the result is positive, behaves as for HALF_UP; if negative, behaves
     * as for HALF_DOWN.
     */
    public const HALF_CEILING = 7;
    
    /**
     * Rounds towards "nearest neighbor" unless both neighbors are equidistant,
     * in which case round towards negative infinity.
     *
     * If the result is positive, behaves as for HALF_DOWN; if negative, behaves
     * as for HALF_UP.
     */
    public const HALF_FLOOR = 8;
    
    /**
     * Rounds towards the "nearest neighbor" unless both neighbors are
     * equidistant, in which case rounds towards the even neighbor.
     *
     * Behaves as for HALF_UP if the digit to the left of the discarded fraction
     * is odd; behaves as for HALF_DOWN if it's even.
     *
     * Note that this is the rounding mode that statistically minimizes
     * cumulative error when applied repeatedly over a sequence of calculations.
     * It is sometimes known as "Banker's rounding", and is chiefly used in the
     * USA.
     */
    public const HALF_EVEN = 9;

}