class Precision {

    /**
     * Offset to order signed double numbers lexicographically.
     */
    private static final long SGN_MASK = 0x8000000000000000L;
    /**
     * Positive zero bits.
     */
    private static final long POSITIVE_ZERO_DOUBLE_BITS = Double.doubleToRawLongBits(+0.0);
    /**
     * Negative zero bits.
     */
    private static final long NEGATIVE_ZERO_DOUBLE_BITS = Double.doubleToRawLongBits(-0.0);

    /**
     * Returns {@code true} if there is no double value strictly between the
     * arguments or the difference between them is within the range of allowed
     * error (inclusive).
     *
     * @param x   First value.
     * @param y   Second value.
     * @param eps Amount of allowed absolute error.
     * @return {@code true} if the values are two adjacent floating point
     * numbers or they are within range of each other.
     */
    public static boolean isEquals(double x, double y, double eps) {
        return isEquals(x, y, 1) || Math.abs(y - x) <= eps;
    }

    /**
     * Returns {@code true} if both arguments are equal or within the range of allowed
     * error (inclusive).
     * <p>
     * Two float numbers are considered equal if there are {@code (maxUlps - 1)}
     * (or fewer) floating point numbers between them, i.e. two adjacent
     * floating point numbers are considered equal.
     * <p>
     * Adapted from <a
     * href="http://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/">
     * Bruce Dawson</a>
     *
     * @param x       first value
     * @param y       second value
     * @param maxUlps {@code (maxUlps - 1)} is the number of floating point
     *                values between {@code x} and {@code y}.
     * @return {@code true} if there are fewer than {@code maxUlps} floating
     * point values between {@code x} and {@code y}.
     */
    public static boolean isEquals(final double x, final double y, final int maxUlps) {<FILL_FUNCTION_BODY>}
}


        final long xInt = Double.doubleToRawLongBits(x);
        final long yInt = Double.doubleToRawLongBits(y);

        final boolean isEqual;
        if (((xInt ^ yInt) & SGN_MASK) == 0L) {
            // number have same sign, there is no risk of overflow
            isEqual = Math.abs(xInt - yInt) <= maxUlps;
        } else {
            // number have opposite signs, take care of overflow
            final long deltaPlus;
            final long deltaMinus;
            if (xInt < yInt) {
                deltaPlus = yInt - POSITIVE_ZERO_DOUBLE_BITS;
                deltaMinus = xInt - NEGATIVE_ZERO_DOUBLE_BITS;
            } else {
                deltaPlus = xInt - POSITIVE_ZERO_DOUBLE_BITS;
                deltaMinus = yInt - NEGATIVE_ZERO_DOUBLE_BITS;
            }

            if (deltaPlus > maxUlps) {
                isEqual = false;
            } else {
                isEqual = deltaMinus <= (maxUlps - deltaPlus);
            }
        }

        return isEqual && !Double.isNaN(x) && !Double.isNaN(y);

    
<no_super_class>