docs: def pixel_resolution_to_nside(resolution, round='nearest'):
      """Find closest HEALPix nside for a given angular resolution.
  
      This function is the inverse of `nside_to_pixel_resolution`,
      for the default rounding scheme of ``round='nearest'``.
  
      If you choose ``round='up'``, you'll get HEALPix pixels that
      have at least the requested resolution (usually a bit better
      due to rounding).
  
      Pixel resolution is defined as square root of pixel area.
  
      Parameters
      ----------
      resolution : `~astropy.units.Quantity`
          Angular resolution
      round : {'up', 'nearest', 'down'}
          Which way to round
  
      Returns
      -------
      nside : int
          The number of pixels on the side of one of the 12 'top-level' HEALPix tiles.
          Always a power of 2.
  
      Examples
      --------
      >>> from astropy import units as u
      >>> from astropy_healpix import pixel_resolution_to_nside
      >>> pixel_resolution_to_nside(13 * u.arcmin)
      256
      >>> pixel_resolution_to_nside(13 * u.arcmin, round='up')
      512
      """
      resolution = resolution.to(u.rad).value
      pixel_area = resolution * resolution
      npix = 4 * math.pi / pixel_area
      nside = np.sqrt(npix / 12)
  
      # Now we have to round to the closest ``nside``
      # Since ``nside`` must be a power of two,
      # we first compute the corresponding ``level = log2(nside)`
      # round the level and then go back to nside
      level = np.log2(nside)
  
      if round == 'up':
          level = np.ceil(level)
      elif round == 'nearest':
          level = np.round(level)
      elif round == 'down':
          level = np.floor(level)
      else:
          raise ValueError('Invalid value for round: {!r}'.format(round))
  
      # For very low requested resolution (i.e. large angle values), we
      # return ``level=0``, i.e. ``nside=1``, i.e. the lowest resolution
      # that exists with HEALPix
      level = np.clip(level.astype(int), 0, None)
  
      return level_to_nside(level)