def METHOD_NAME(self, fdsinx, fseries=None, atol=1e-8):
    """Tests ``apply_fd_time_shift`` with the given fdseries.
    If ``fdsinx`` is a FrequencySeries, this will test the shift code
    written in C. Otherwise, this will test the numpy version.
    Parameters
    ----------
    fdsinx : FrequencySeries
        The frequency series to shift and test.
    fseires : array, optional
        Array of the sample frequencies of ``fdsinx``. This is only needed
        for the numpy version.
    atol : float, optional
        The absolute tolerance for the comparison test. See
        ``numpy.isclose`` for details.
    """
    # shift by -pi/2: should be the same as the cosine
    tshift = 1./(4*self.freq)
    tdshift = self._shift_and_ifft(fdsinx, -tshift, fseries=fseries)
    # check
    comp = numpy.cos(self.time_series)
    if tdshift.precision == 'single':
        # cast to single
        comp = comp.astype(numpy.float32)
    self.assertTrue(numpy.isclose(tdshift, comp, atol=atol).all())
    # shift by +pi/2: should be the same as the -cosine
    tdshift = self._shift_and_ifft(fdsinx, tshift, fseries=fseries)
    self.assertTrue(numpy.isclose(tdshift, -1*comp, atol=atol).all())
    # shift by a non-integer fraction of the period; we'll do this by
    # shifting by a prime number times dt / 3
    # forward:
    tshift = 193 * self.time_series.delta_t / 3.
    tdshift = self._shift_and_ifft(fdsinx, tshift, fseries=fseries)
    comp = numpy.sin(self.time_series - 2*numpy.pi*self.freq*tshift)
    if tdshift.precision == 'single':
        # cast to single
        comp = comp.astype(numpy.float32)
    self.assertTrue(numpy.isclose(tdshift, comp, atol=atol).all())
    # backward:
    tdshift = self._shift_and_ifft(fdsinx, -tshift, fseries=fseries)
    comp = numpy.sin(self.time_series + 2*numpy.pi*self.freq*tshift)
    if tdshift.precision == 'single':
        # cast to single
        comp = comp.astype(numpy.float32)
    self.assertTrue(numpy.isclose(tdshift, comp, atol=atol).all())