def mpfr_mod(rop, x, y, rnd):
    """
    Given two MPRF numbers x and y, compute
    x - floor(x / y) * y, rounded if necessary using the given
    rounding mode.  The result is placed in 'rop'.

    This is the 'remainder' operation, with sign convention
    compatible with Python's % operator (where x % y has
    the same sign as y).
    """
    # There are various cases:
    #
    # 0. If either argument is a NaN, the result is NaN.
    #
    # 1. If x is infinite or y is zero, the result is NaN.
    #
    # 2. If y is infinite, return 0 with the sign of y if x is zero, x if x has
    #    the same sign as y, and infinity with the sign of y if it has the
    #    opposite sign.
    #
    # 3. If none of the above cases apply then both x and y are finite,
    #    and y is nonzero.  If x and y have the same sign, simply
    #    return the result of fmod(x, y).
    #
    # 4. Now both x and y are finite, y is nonzero, and x and y have
    #    differing signs.  Compute r = fmod(x, y) with sufficient precision
    #    to get an exact result.  If r == 0, return 0 with the sign of y
    #    (which will be the opposite of the sign of x).  If r != 0,
    #    return r + y, rounded appropriately.

    if not mpfr.mpfr_number_p(x) or mpfr.mpfr_nan_p(y) or mpfr.mpfr_zero_p(y):
        return mpfr.mpfr_fmod(rop, x, y, rnd)
    elif mpfr.mpfr_inf_p(y):
        x_negative = mpfr.mpfr_signbit(x)
        y_negative = mpfr.mpfr_signbit(y)
        if mpfr.mpfr_zero_p(x):
            mpfr.mpfr_set_zero(rop, -y_negative)
            return 0
        elif x_negative == y_negative:
            return mpfr.mpfr_set(rop, x, rnd)
        else:
            mpfr.mpfr_set_inf(rop, -y_negative)
            return 0

    x_negative = mpfr.mpfr_signbit(x)
    y_negative = mpfr.mpfr_signbit(y)
    if x_negative == y_negative:
        return mpfr.mpfr_fmod(rop, x, y, rnd)
    else:
        p = max(mpfr.mpfr_get_prec(x), mpfr.mpfr_get_prec(y))
        z = mpfr.Mpfr_t()
        mpfr.mpfr_init2(z, p)
        # Doesn't matter what rounding mode we use here; the result
        # should be exact.
        ternary = mpfr.mpfr_fmod(z, x, y, rnd)
        assert ternary == 0
        if mpfr.mpfr_zero_p(z):
            mpfr.mpfr_set_zero(rop, -y_negative)
            return 0
        else:
            return mpfr.mpfr_add(rop, y, z, rnd)