def num_spike_powers(FWHM):
    """
    num_spike_powers(FWHM):
        Return the (approx.) number of powers from a triangular spike
        pulse profile which are greater than one half the power
        perfect sinusoidal pulse profile.  Both the spike and the
        sine are assumed to have an area under one full pulse of 1 unit.
        Note:  A gaussian profile gives almost identical numbers of
        high powers as a spike profile of the same width.  This
        expression was determined using a least-squares fit.
        (Errors get large as FWHM -> 0).
            'FWHM' is the full width at half-max of the spike.
                (0.0 < FWHM <= 0.5)
    """
    return -3.95499721563e-05 / FWHM**2 + 0.562069634689 / FWHM - \
           0.683604041138