text: # Licensed under a 3-clause BSD style license - see PYFITS.rst
  
  import copy
  import operator
  import re
  import sys
  import warnings
  import weakref
  import numbers
  
  from functools import reduce
  from collections import OrderedDict
  from contextlib import suppress
  
  import numpy as np
  from numpy import char as chararray
  
  from . import _numpy_hacks as nh
  from .card import Card, CARD_LENGTH
  from .util import (pairwise, _is_int, _convert_array, encode_ascii, cmp,
                     NotifierMixin)
  from .verify import VerifyError, VerifyWarning
  
  from ...utils import lazyproperty, isiterable, indent
  
  __all__ = ['Column', 'ColDefs', 'Delayed']
  
  
  # mapping from TFORM data type to numpy data type (code)
  # L: Logical (Boolean)
  # B: Unsigned Byte
  # I: 16-bit Integer
  # J: 32-bit Integer
  # K: 64-bit Integer
  # E: Single-precision Floating Point
  # D: Double-precision Floating Point
  # C: Single-precision Complex
  # M: Double-precision Complex
  # A: Character
  FITS2NUMPY = {'L': 'i1', 'B': 'u1', 'I': 'i2', 'J': 'i4', 'K': 'i8', 'E': 'f4',
                'D': 'f8', 'C': 'c8', 'M': 'c16', 'A': 'a'}
  
  # the inverse dictionary of the above
  NUMPY2FITS = {val: key for key, val in FITS2NUMPY.items()}
  # Normally booleans are represented as ints in Astropy, but if passed in a numpy
  # boolean array, that should be supported
  NUMPY2FITS['b1'] = 'L'
  # Add unsigned types, which will be stored as signed ints with a TZERO card.
  NUMPY2FITS['u2'] = 'I'
  NUMPY2FITS['u4'] = 'J'
  NUMPY2FITS['u8'] = 'K'
  # Add half precision floating point numbers which will be up-converted to
  # single precision.
  NUMPY2FITS['f2'] = 'E'
  
  # This is the order in which values are converted to FITS types
  # Note that only double precision floating point/complex are supported
  FORMATORDER = ['L', 'B', 'I', 'J', 'K', 'D', 'M', 'A']
  
  # Convert single precision floating point/complex to double precision.
  FITSUPCONVERTERS = {'E': 'D', 'C': 'M'}
  
  # mapping from ASCII table TFORM data type to numpy data type
  # A: Character
  # I: Integer (32-bit)
  # J: Integer (64-bit; non-standard)
  # F: Float (64-bit; fixed decimal notation)
  # E: Float (64-bit; exponential notation)
  # D: Float (64-bit; exponential notation, always 64-bit by convention)
  ASCII2NUMPY = {'A': 'a', 'I': 'i4', 'J': 'i8', 'F': 'f8', 'E': 'f8', 'D': 'f8'}
  
  # Maps FITS ASCII column format codes to the appropriate Python string
  # formatting codes for that type.
  ASCII2STR = {'A': '', 'I': 'd', 'J': 'd', 'F': 'f', 'E': 'E', 'D': 'E'}
  
  # For each ASCII table format code, provides a default width (and decimal
  # precision) for when one isn't given explicitly in the column format
  ASCII_DEFAULT_WIDTHS = {'A': (1, 0), 'I': (10, 0), 'J': (15, 0),
                          'E': (15, 7), 'F': (16, 7), 'D': (25, 17)}
  
  
  # tuple of column/field definition common names and keyword names, make
  # sure to preserve the one-to-one correspondence when updating the list(s).
  # Use lists, instead of dictionaries so the names can be displayed in a
  # preferred order.
  KEYWORD_NAMES = ('TTYPE', 'TFORM', 'TUNIT', 'TNULL', 'TSCAL', 'TZERO',
                   'TDISP', 'TBCOL', 'TDIM', 'TCTYP', 'TCUNI', 'TCRPX',
                   'TCRVL', 'TCDLT', 'TRPOS')
  KEYWORD_ATTRIBUTES = ('name', 'format', 'unit', 'null', 'bscale', 'bzero',
                        'disp', 'start', 'dim', 'coord_type', 'coord_unit',
                        'coord_ref_point', 'coord_ref_value', 'coord_inc',
                        'time_ref_pos')
  """This is a list of the attributes that can be set on `Column` objects."""
  
  
  KEYWORD_TO_ATTRIBUTE = OrderedDict(zip(KEYWORD_NAMES, KEYWORD_ATTRIBUTES))
  
  ATTRIBUTE_TO_KEYWORD = OrderedDict(zip(KEYWORD_ATTRIBUTES, KEYWORD_NAMES))
  
  
  # TODO: Define a list of default comments to associate with each table keyword
  
  # TFORMn regular expression
  TFORMAT_RE = re.compile(r'(?P<repeat>^[0-9]*)(?P<format>[LXBIJKAEDCMPQ])'
                          r'(?P<option>[!-~]*)', re.I)
  
  # TFORMn for ASCII tables; two different versions depending on whether
  # the format is floating-point or not; allows empty values for width
  # in which case defaults are used
  TFORMAT_ASCII_RE = re.compile(r'(?:(?P<format>[AIJ])(?P<width>[0-9]+)?)|'
                                r'(?:(?P<formatf>[FED])'
                                r'(?:(?P<widthf>[0-9]+)\.'
                                r'(?P<precision>[0-9]+))?)')
  
  TTYPE_RE = re.compile(r'[0-9a-zA-Z_]+')
  """
  Regular expression for valid table column names.  See FITS Standard v3.0 section
  7.2.2.
  """
  
  # table definition keyword regular expression
  TDEF_RE = re.compile(r'(?P<label>^T[A-Z]*)(?P<num>[1-9][0-9 ]*$)')
  
  # table dimension keyword regular expression (fairly flexible with whitespace)
  TDIM_RE = re.compile(r'\(\s*(?P<dims>(?:\d+,\s*)+\s*\d+)\s*\)\s*')
  
  # value for ASCII table cell with value = TNULL
  # this can be reset by user.
  ASCIITNULL = 0
  
  # The default placeholder to use for NULL values in ASCII tables when
  # converting from binary to ASCII tables
  DEFAULT_ASCII_TNULL = '---'
  
  
  class Delayed:
      """Delayed file-reading data."""
  
      def __init__(self, hdu=None, field=None):
          self.hdu = weakref.proxy(hdu)
          self.field = field
  
      def __getitem__(self, key):
          # This forces the data for the HDU to be read, which will replace
          # the corresponding Delayed objects in the Tables Columns to be
          # transformed into ndarrays.  It will also return the value of the
          # requested data element.
          return self.hdu.data[key][self.field]
  
  
  class _BaseColumnFormat(str):
      """
      Base class for binary table column formats (just called _ColumnFormat)
      and ASCII table column formats (_AsciiColumnFormat).
      """
  
      def __eq__(self, other):
          if not other:
              return False
  
          if isinstance(other, str):
              if not isinstance(other, self.__class__):
                  try:
                      other = self.__class__(other)
                  except ValueError:
                      return False
          else:
              return False
  
          return self.canonical == other.canonical
  
      def __hash__(self):
          return hash(self.canonical)
  
      @lazyproperty
      def dtype(self):
          """
          The Numpy dtype object created from the format's associated recformat.
          """
  
          return np.dtype(self.recformat)
  
      @classmethod
      def from_column_format(cls, format):
          """Creates a column format object from another column format object
          regardless of their type.
  
          That is, this can convert a _ColumnFormat to an _AsciiColumnFormat
          or vice versa at least in cases where a direct translation is possible.
          """
  
          return cls.from_recformat(format.recformat)
  
  
  class _ColumnFormat(_BaseColumnFormat):
      """
      Represents a FITS binary table column format.
  
      This is an enhancement over using a normal string for the format, since the
      repeat count, format code, and option are available as separate attributes,
      and smart comparison is used.  For example 1J == J.
      """
  
      def __new__(cls, format):
          self = super().__new__(cls, format)
          self.repeat, self.format, self.option = _parse_tformat(format)
          self.format = self.format.upper()
          if self.format in ('P', 'Q'):
              # TODO: There should be a generic factory that returns either
              # _FormatP or _FormatQ as appropriate for a given TFORMn
              if self.format == 'P':
                  recformat = _FormatP.from_tform(format)
              else:
                  recformat = _FormatQ.from_tform(format)
              # Format of variable length arrays
              self.p_format = recformat.format
          else:
              self.p_format = None
          return self
  
      @classmethod
      def from_recformat(cls, recformat):
          """Creates a column format from a Numpy record dtype format."""
  
          return cls(_convert_format(recformat, reverse=True))
  
      @lazyproperty
      def recformat(self):
          """Returns the equivalent Numpy record format string."""
  
          return _convert_format(self)
  
      @lazyproperty
      def canonical(self):
          """
          Returns a 'canonical' string representation of this format.
  
          This is in the proper form of rTa where T is the single character data
          type code, a is the optional part, and r is the repeat.  If repeat == 1
          (the default) it is left out of this representation.
          """
  
          if self.repeat == 1:
              repeat = ''
          else:
              repeat = str(self.repeat)
  
          return '{}{}{}'.format(repeat, self.format, self.option)
  
  
  class _AsciiColumnFormat(_BaseColumnFormat):
      """Similar to _ColumnFormat but specifically for columns in ASCII tables.
  
      The formats of ASCII table columns and binary table columns are inherently
      incompatible in FITS.  They don't support the same ranges and types of
      values, and even reuse format codes in subtly different ways.  For example
      the format code 'Iw' in ASCII columns refers to any integer whose string
      representation is at most w characters wide, so 'I' can represent
      effectively any integer that will fit in a FITS columns.  Whereas for
      binary tables 'I' very explicitly refers to a 16-bit signed integer.
  
      Conversions between the two column formats can be performed using the
      ``to/from_binary`` methods on this class, or the ``to/from_ascii``
      methods on the `_ColumnFormat` class.  But again, not all conversions are
      possible and may result in a `ValueError`.
      """
  
      def __new__(cls, format, strict=False):
          self = super().__new__(cls, format)
          self.format, self.width, self.precision = \
              _parse_ascii_tformat(format, strict)
  
          # This is to support handling logical (boolean) data from binary tables
          # in an ASCII table
          self._pseudo_logical = False
          return self
  
      @classmethod
      def from_column_format(cls, format):
          inst = cls.from_recformat(format.recformat)
          # Hack
          if format.format == 'L':
              inst._pseudo_logical = True
          return inst
  
      @classmethod
      def from_recformat(cls, recformat):
          """Creates a column format from a Numpy record dtype format."""
  
          return cls(_convert_ascii_format(recformat, reverse=True))
  
      @lazyproperty
      def recformat(self):
          """Returns the equivalent Numpy record format string."""
  
          return _convert_ascii_format(self)
  
      @lazyproperty
      def canonical(self):
          """
          Returns a 'canonical' string representation of this format.
  
          This is in the proper form of Tw.d where T is the single character data
          type code, w is the width in characters for this field, and d is the
          number of digits after the decimal place (for format codes 'E', 'F',
          and 'D' only).
          """
  
          if self.format in ('E', 'F', 'D'):
              return '{}{}.{}'.format(self.format, self.width, self.precision)
  
          return '{}{}'.format(self.format, self.width)
  
  
  class _FormatX(str):
      """For X format in binary tables."""
  
      def __new__(cls, repeat=1):
          nbytes = ((repeat - 1) // 8) + 1
          # use an array, even if it is only ONE u1 (i.e. use tuple always)
          obj = super().__new__(cls, repr((nbytes,)) + 'u1')
          obj.repeat = repeat
          return obj
  
      def __getnewargs__(self):
          return (self.repeat,)
  
      @property
      def tform(self):
          return '{}X'.format(self.repeat)
  
  
  # TODO: Table column formats need to be verified upon first reading the file;
  # as it is, an invalid P format will raise a VerifyError from some deep,
  # unexpected place
  class _FormatP(str):
      """For P format in variable length table."""
  
      # As far as I can tell from my reading of the FITS standard, a type code is
      # *required* for P and Q formats; there is no default
      _format_re_template = (r'(?P<repeat>\d+)?{}(?P<dtype>[LXBIJKAEDCM])'
                             r'(?:\((?P<max>\d*)\))?')
      _format_code = 'P'
      _format_re = re.compile(_format_re_template.format(_format_code))
      _descriptor_format = '2i4'
  
      def __new__(cls, dtype, repeat=None, max=None):
          obj = super().__new__(cls, cls._descriptor_format)
          obj.format = NUMPY2FITS[dtype]
          obj.dtype = dtype
          obj.repeat = repeat
          obj.max = max
          return obj
  
      def __getnewargs__(self):
          return (self.dtype, self.repeat, self.max)
  
      @classmethod
      def from_tform(cls, format):
          m = cls._format_re.match(format)
          if not m or m.group('dtype') not in FITS2NUMPY:
              raise VerifyError('Invalid column format: {}'.format(format))
          repeat = m.group('repeat')
          array_dtype = m.group('dtype')
          max = m.group('max')
          if not max:
              max = None
          return cls(FITS2NUMPY[array_dtype], repeat=repeat, max=max)
  
      @property
      def tform(self):
          repeat = '' if self.repeat is None else self.repeat
          max = '' if self.max is None else self.max
          return '{}{}{}({})'.format(repeat, self._format_code, self.format, max)
  
  
  class _FormatQ(_FormatP):
      """Carries type description of the Q format for variable length arrays.
  
      The Q format is like the P format but uses 64-bit integers in the array
      descriptors, allowing for heaps stored beyond 2GB into a file.
      """
  
      _format_code = 'Q'
      _format_re = re.compile(_FormatP._format_re_template.format(_format_code))
      _descriptor_format = '2i8'
  
  
  class ColumnAttribute:
      """
      Descriptor for attributes of `Column` that are associated with keywords
      in the FITS header and describe properties of the column as specified in
      the FITS standard.
  
      Each `ColumnAttribute` may have a ``validator`` method defined on it.
      This validates values set on this attribute to ensure that they meet the
      FITS standard.  Invalid values will raise a warning and will not be used in
      formatting the column.  The validator should take two arguments--the
      `Column` it is being assigned to, and the new value for the attribute, and
      it must raise an `AssertionError` if the value is invalid.
  
      The `ColumnAttribute` itself is a decorator that can be used to define the
      ``validator`` for each column attribute.  For example::
  
          @ColumnAttribute('TTYPE')
          def name(col, name):
              if not isinstance(name, str):
                  raise AssertionError
  
      The actual object returned by this decorator is the `ColumnAttribute`
      instance though, not the ``name`` function.  As such ``name`` is not a
      method of the class it is defined in.
  
      The setter for `ColumnAttribute` also updates the header of any table
      HDU this column is attached to in order to reflect the change.  The
      ``validator`` should ensure that the value is valid for inclusion in a FITS
      header.
      """
  
      def __init__(self, keyword):
          self._keyword = keyword
          self._validator = None
  
          # The name of the attribute associated with this keyword is currently
          # determined from the KEYWORD_NAMES/ATTRIBUTES lists.  This could be
          # make more flexible in the future, for example, to support custom
          # column attributes.
          self._attr = '_' + KEYWORD_TO_ATTRIBUTE[self._keyword]
  
      def __get__(self, obj, objtype=None):
          if obj is None:
              return self
          else:
              return getattr(obj, self._attr)
  
      def __set__(self, obj, value):
          if self._validator is not None:
              self._validator(obj, value)
  
          old_value = getattr(obj, self._attr, None)
          setattr(obj, self._attr, value)
          obj._notify('column_attribute_changed', obj, self._attr[1:], old_value,
                      value)
  
      def __call__(self, func):
          """
          Set the validator for this column attribute.
  
          Returns ``self`` so that this can be used as a decorator, as described
          in the docs for this class.
          """
  
          self._validator = func
  
          return self
  
      def __repr__(self):
          return "{0}('{1}')".format(self.__class__.__name__, self._keyword)
  
  
  class Column(NotifierMixin):
      """
      Class which contains the definition of one column, e.g.  ``ttype``,
      ``tform``, etc. and the array containing values for the column.
      """
  
      def __init__(self, name=None, format=None, unit=None, null=None,
                   bscale=None, bzero=None, disp=None, start=None, dim=None,
                   array=None, ascii=None, coord_type=None, coord_unit=None,
                   coord_ref_point=None, coord_ref_value=None, coord_inc=None,
                   time_ref_pos=None):
          """
          Construct a `Column` by specifying attributes.  All attributes
          except ``format`` can be optional; see :ref:`column_creation` and
          :ref:`creating_ascii_table` for more information regarding
          ``TFORM`` keyword.
  
          Parameters
          ----------
          name : str, optional
              column name, corresponding to ``TTYPE`` keyword
  
          format : str
              column format, corresponding to ``TFORM`` keyword
  
          unit : str, optional
              column unit, corresponding to ``TUNIT`` keyword
  
          null : str, optional
              null value, corresponding to ``TNULL`` keyword
  
          bscale : int-like, optional
              bscale value, corresponding to ``TSCAL`` keyword
  
          bzero : int-like, optional
              bzero value, corresponding to ``TZERO`` keyword
  
          disp : str, optional
              display format, corresponding to ``TDISP`` keyword
  
          start : int, optional
              column starting position (ASCII table only), corresponding
              to ``TBCOL`` keyword
  
          dim : str, optional
              column dimension corresponding to ``TDIM`` keyword
  
          array : iterable, optional
              a `list`, `numpy.ndarray` (or other iterable that can be used to
              initialize an ndarray) providing initial data for this column.
              The array will be automatically converted, if possible, to the data
              format of the column.  In the case were non-trivial ``bscale``
              and/or ``bzero`` arguments are given, the values in the array must
              be the *physical* values--that is, the values of column as if the
              scaling has already been applied (the array stored on the column
              object will then be converted back to its storage values).
  
          ascii : bool, optional
              set `True` if this describes a column for an ASCII table; this
              may be required to disambiguate the column format
  
          coord_type : str, optional
              coordinate/axis type corresponding to ``TCTYP`` keyword
  
          coord_unit : str, optional
              coordinate/axis unit corresponding to ``TCUNI`` keyword
  
          coord_ref_point : int-like, optional
              pixel coordinate of the reference point corresponding to ``TCRPX``
              keyword
  
          coord_ref_value : int-like, optional
              coordinate value at reference point corresponding to ``TCRVL``
              keyword
  
          coord_inc : int-like, optional
              coordinate increment at reference point corresponding to ``TCDLT``
              keyword
  
          time_ref_pos : str, optional
              reference position for a time coordinate column corresponding to
              ``TRPOS`` keyword
          """
  
          if format is None:
              raise ValueError('Must specify format to construct Column.')
  
          # any of the input argument (except array) can be a Card or just
          # a number/string
          kwargs = {'ascii': ascii}
          for attr in KEYWORD_ATTRIBUTES:
              value = locals()[attr]  # get the argument's value
  
              if isinstance(value, Card):
                  value = value.value
  
              kwargs[attr] = value
  
          valid_kwargs, invalid_kwargs = self._verify_keywords(**kwargs)
  
          if invalid_kwargs:
              msg = ['The following keyword arguments to Column were invalid:']
  
              for val in invalid_kwargs.values():
                  msg.append(indent(val[1]))
  
              raise VerifyError('\n'.join(msg))
  
          for attr in KEYWORD_ATTRIBUTES:
              setattr(self, attr, valid_kwargs.get(attr))
  
          # TODO: Try to eliminate the following two special cases
          # for recformat and dim:
          # This is not actually stored as an attribute on columns for some
          # reason
          recformat = valid_kwargs['recformat']
  
          # The 'dim' keyword's original value is stored in self.dim, while
          # *only* the tuple form is stored in self._dims.
          self._dims = self.dim
          self.dim = dim
  
          # Awful hack to use for now to keep track of whether the column holds
          # pseudo-unsigned int data
          self._pseudo_unsigned_ints = False
  
          # if the column data is not ndarray, make it to be one, i.e.
          # input arrays can be just list or tuple, not required to be ndarray
          # does not include Object array because there is no guarantee
          # the elements in the object array are consistent.
          if not isinstance(array,
                            (np.ndarray, chararray.chararray, Delayed)):
              try:  # try to convert to a ndarray first
                  if array is not None:
                      array = np.array(array)
              except Exception:
                  try:  # then try to convert it to a strings array
                      itemsize = int(recformat[1:])
                      array = chararray.array(array, itemsize=itemsize)
                  except ValueError:
                      # then try variable length array
                      # Note: This includes _FormatQ by inheritance
                      if isinstance(recformat, _FormatP):
                          array = _VLF(array, dtype=recformat.dtype)
                      else:
                          raise ValueError('Data is inconsistent with the '
                                           'format `{}`.'.format(format))
  
          array = self._convert_to_valid_data_type(array)
  
          # We have required (through documentation) that arrays passed in to
          # this constructor are already in their physical values, so we make
          # note of that here
          if isinstance(array, np.ndarray):
              self._physical_values = True
          else:
              self._physical_values = False
  
          self._parent_fits_rec = None
          self.array = array
  
      def __repr__(self):
          text = ''
          for attr in KEYWORD_ATTRIBUTES:
              value = getattr(self, attr)
              if value is not None:
                  text += attr + ' = ' + repr(value) + '; '
          return text[:-2]
  
      def __eq__(self, other):
          """
          Two columns are equal if their name and format are the same.  Other
          attributes aren't taken into account at this time.
          """
  
          # According to the FITS standard column names must be case-insensitive
          a = (self.name.lower(), self.format)
          b = (other.name.lower(), other.format)
          return a == b
  
      def __hash__(self):
          """
          Like __eq__, the hash of a column should be based on the unique column
          name and format, and be case-insensitive with respect to the column
          name.
          """
  
          return hash((self.name.lower(), self.format))
  
      @property
      def array(self):
          """
          The Numpy `~numpy.ndarray` associated with this `Column`.
  
          If the column was instantiated with an array passed to the ``array``
          argument, this will return that array.  However, if the column is
          later added to a table, such as via `BinTableHDU.from_columns` as
          is typically the case, this attribute will be updated to reference
          the associated field in the table, which may no longer be the same
          array.
          """
  
          # Ideally the .array attribute never would have existed in the first
          # place, or would have been internal-only.  This is a legacy of the
          # older design from Astropy that needs to have continued support, for
          # now.
  
          # One of the main problems with this design was that it created a
          # reference cycle.  When the .array attribute was updated after
          # creating a FITS_rec from the column (as explained in the docstring) a
          # reference cycle was created.  This is because the code in BinTableHDU
          # (and a few other places) does essentially the following:
          #
          # data._coldefs = columns  # The ColDefs object holding this Column
          # for col in columns:
          #     col.array = data.field(col.name)
          #
          # This way each columns .array attribute now points to the field in the
          # table data.  It's actually a pretty confusing interface (since it
          # replaces the array originally pointed to by .array), but it's the way
          # things have been for a long, long time.
          #
          # However, this results, in *many* cases, in a reference cycle.
          # Because the array returned by data.field(col.name), while sometimes
          # an array that owns its own data, is usually like a slice of the
          # original data.  It has the original FITS_rec as the array .base.
          # This results in the following reference cycle (for the n-th column):
          #
          #    data -> data._coldefs -> data._coldefs[n] ->
          #     data._coldefs[n].array -> data._coldefs[n].array.base -> data
          #
          # Because ndarray objects do not handled by Python's garbage collector
          # the reference cycle cannot be broken.  Therefore the FITS_rec's
          # refcount never goes to zero, its __del__ is never called, and its
          # memory is never freed.  This didn't occur in *all* cases, but it did
          # occur in many cases.
          #
          # To get around this, Column.array is no longer a simple attribute
          # like it was previously.  Now each Column has a ._parent_fits_rec
          # attribute which is a weakref to a FITS_rec object.  Code that
          # previously assigned each col.array to field in a FITS_rec (as in
          # the example a few paragraphs above) is still used, however now
          # array.setter checks if a reference cycle will be created.  And if
          # so, instead of saving directly to the Column's __dict__, it creates
          # the ._prent_fits_rec weakref, and all lookups of the column's .array
          # go through that instead.
          #
          # This alone does not fully solve the problem.  Because
          # _parent_fits_rec is a weakref, if the user ever holds a reference to
          # the Column, but deletes all references to the underlying FITS_rec,
          # the .array attribute would suddenly start returning None instead of
          # the array data.  This problem is resolved on FITS_rec's end.  See the
          # note in the FITS_rec._coldefs property for the rest of the story.
  
          # If the Columns's array is not a reference to an existing FITS_rec,
          # then it is just stored in self.__dict__; otherwise check the
          # _parent_fits_rec reference if it 's still available.
          if 'array' in self.__dict__:
              return self.__dict__['array']
          elif self._parent_fits_rec is not None:
              parent = self._parent_fits_rec()
              if parent is not None:
                  return parent[self.name]
          else:
              return None
  
      @array.setter
      def array(self, array):
          # The following looks over the bases of the given array to check if it
          # has a ._coldefs attribute (i.e. is a FITS_rec) and that that _coldefs
          # contains this Column itself, and would create a reference cycle if we
          # stored the array directly in self.__dict__.
          # In this case it instead sets up the _parent_fits_rec weakref to the
          # underlying FITS_rec, so that array.getter can return arrays through
          # self._parent_fits_rec().field(self.name), rather than storing a
          # hard reference to the field like it used to.
          base = array
          while True:
              if (hasattr(base, '_coldefs') and
                      isinstance(base._coldefs, ColDefs)):
                  for col in base._coldefs:
                      if col is self and self._parent_fits_rec is None:
                          self._parent_fits_rec = weakref.ref(base)
  
                          # Just in case the user already set .array to their own
                          # array.
                          if 'array' in self.__dict__:
                              del self.__dict__['array']
                          return
  
              if getattr(base, 'base', None) is not None:
                  base = base.base
              else:
                  break
  
          self.__dict__['array'] = array
  
      @array.deleter
      def array(self):
          try:
              del self.__dict__['array']
          except KeyError:
              pass
  
          self._parent_fits_rec = None
  
      @ColumnAttribute('TTYPE')
      def name(col, name):
          if name is None:
              # Allow None to indicate deleting the name, or to just indicate an
              # unspecified name (when creating a new Column).
              return
  
          # Check that the name meets the recommended standard--other column
          # names are *allowed*, but will be discouraged
          if isinstance(name, str) and not TTYPE_RE.match(name):
              warnings.warn(
                  'It is strongly recommended that column names contain only '
                  'upper and lower-case ASCII letters, digits, or underscores '
                  'for maximum compatibility with other software '
                  '(got {0!r}).'.format(name), VerifyWarning)
  
          # This ensures that the new name can fit into a single FITS card
          # without any special extension like CONTINUE cards or the like.
          if (not isinstance(name, str)
                  or len(str(Card('TTYPE', name))) != CARD_LENGTH):
              raise AssertionError(
                  'Column name must be a string able to fit in a single '
                  'FITS card--typically this means a maximum of 68 '
                  'characters, though it may be fewer if the string '
                  'contains special characters like quotes.')
  
      @ColumnAttribute('TCTYP')
      def coord_type(col, coord_type):
          if coord_type is None:
              return
  
          if (not isinstance(coord_type, str)
                  or len(coord_type) > 8):
              raise AssertionError(
                  'Coordinate/axis type must be a string of atmost 8 '
                  'characters.')
  
      @ColumnAttribute('TCUNI')
      def coord_unit(col, coord_unit):
          if (coord_unit is not None
                  and not isinstance(coord_unit, str)):
              raise AssertionError(
                  'Coordinate/axis unit must be a string.')
  
      @ColumnAttribute('TCRPX')
      def coord_ref_point(col, coord_ref_point):
          if (coord_ref_point is not None
                  and not isinstance(coord_ref_point, numbers.Real)):
              raise AssertionError(
                  'Pixel coordinate of the reference point must be '
                  'real floating type.')
  
      @ColumnAttribute('TCRVL')
      def coord_ref_value(col, coord_ref_value):
          if (coord_ref_value is not None
                  and not isinstance(coord_ref_value, numbers.Real)):
              raise AssertionError(
                  'Coordinate value at reference point must be real '
                  'floating type.')
  
      @ColumnAttribute('TCDLT')
      def coord_inc(col, coord_inc):
          if (coord_inc is not None
                  and not isinstance(coord_inc, numbers.Real)):
              raise AssertionError(
                  'Coordinate increment must be real floating type.')
  
      @ColumnAttribute('TRPOS')
      def time_ref_pos(col, time_ref_pos):
          if (time_ref_pos is not None
                  and not isinstance(time_ref_pos, str)):
              raise AssertionError(
                  'Time reference position must be a string.')
  
      format = ColumnAttribute('TFORM')
      unit = ColumnAttribute('TUNIT')
      null = ColumnAttribute('TNULL')
      bscale = ColumnAttribute('TSCAL')
      bzero = ColumnAttribute('TZERO')
      disp = ColumnAttribute('TDISP')
      start = ColumnAttribute('TBCOL')
      dim = ColumnAttribute('TDIM')
  
      @lazyproperty
      def ascii(self):
          """Whether this `Column` represents a column in an ASCII table."""
  
          return isinstance(self.format, _AsciiColumnFormat)
  
      @lazyproperty
      def dtype(self):
          return self.format.dtype
  
      def copy(self):
          """
          Return a copy of this `Column`.
          """
          tmp = Column(format='I')  # just use a throw-away format
          tmp.__dict__ = self.__dict__.copy()
          return tmp
  
      @staticmethod
      def _convert_format(format, cls):
          """The format argument to this class's initializer may come in many
          forms.  This uses the given column format class ``cls`` to convert
          to a format of that type.
  
          TODO: There should be an abc base class for column format classes
          """
  
          # Short circuit in case we're already a _BaseColumnFormat--there is at
          # least one case in which this can happen
          if isinstance(format, _BaseColumnFormat):
              return format, format.recformat
  
          if format in NUMPY2FITS:
              with suppress(VerifyError):
                  # legit recarray format?
                  recformat = format
                  format = cls.from_recformat(format)
  
          try:
              # legit FITS format?
              format = cls(format)
              recformat = format.recformat
          except VerifyError:
              raise VerifyError('Illegal format `{}`.'.format(format))
  
          return format, recformat
  
      @classmethod
      def _verify_keywords(cls, name=None, format=None, unit=None, null=None,
                           bscale=None, bzero=None, disp=None, start=None,
                           dim=None, ascii=None, coord_type=None, coord_unit=None,
                           coord_ref_point=None, coord_ref_value=None,
                           coord_inc=None, time_ref_pos=None):
          """
          Given the keyword arguments used to initialize a Column, specifically
          those that typically read from a FITS header (so excluding array),
          verify that each keyword has a valid value.
  
          Returns a 2-tuple of dicts.  The first maps valid keywords to their
          values.  The second maps invalid keywords to a 2-tuple of their value,
          and a message explaining why they were found invalid.
          """
  
          valid = {}
          invalid = {}
  
          format, recformat = cls._determine_formats(format, start, dim, ascii)
          valid.update(format=format, recformat=recformat)
  
          # Currently we don't have any validation for name, unit, bscale, or
          # bzero so include those by default
          # TODO: Add validation for these keywords, obviously
          for k, v in [('name', name), ('unit', unit), ('bscale', bscale),
                       ('bzero', bzero)]:
              if v is not None and v != '':
                  valid[k] = v
  
          # Validate null option
          # Note: Enough code exists that thinks empty strings are sensible
          # inputs for these options that we need to treat '' as None
          if null is not None and null != '':
              msg = None
              if isinstance(format, _AsciiColumnFormat):
                  null = str(null)
                  if len(null) > format.width:
                      msg = (
                          "ASCII table null option (TNULLn) is longer than "
                          "the column's character width and will be truncated "
                          "(got {!r}).".format(null))
              else:
                  tnull_formats = ('B', 'I', 'J', 'K')
  
                  if not _is_int(null):
                      # Make this an exception instead of a warning, since any
                      # non-int value is meaningless
                      msg = (
                          'Column null option (TNULLn) must be an integer for '
                          'binary table columns (got {!r}).  The invalid value '
                          'will be ignored for the purpose of formatting '
                          'the data in this column.'.format(null))
  
                  elif not (format.format in tnull_formats or
                            (format.format in ('P', 'Q') and
                             format.p_format in tnull_formats)):
                      # TODO: We should also check that TNULLn's integer value
                      # is in the range allowed by the column's format
                      msg = (
                          'Column null option (TNULLn) is invalid for binary '
                          'table columns of type {!r} (got {!r}).  The invalid '
                          'value will be ignored for the purpose of formatting '
                          'the data in this column.'.format(format, null))
  
              if msg is None:
                  valid['null'] = null
              else:
                  invalid['null'] = (null, msg)
  
          # Validate the disp option
          # TODO: Add full parsing and validation of TDISPn keywords
          if disp is not None and disp != '':
              msg = None
              if not isinstance(disp, str):
                  msg = (
                      'Column disp option (TDISPn) must be a string (got {!r}).'
                      'The invalid value will be ignored for the purpose of '
                      'formatting the data in this column.'.format(disp))
  
              elif (isinstance(format, _AsciiColumnFormat) and
                      disp[0].upper() == 'L'):
                  # disp is at least one character long and has the 'L' format
                  # which is not recognized for ASCII tables
                  msg = (
                      "Column disp option (TDISPn) may not use the 'L' format "
                      "with ASCII table columns.  The invalid value will be "
                      "ignored for the purpose of formatting the data in this "
                      "column.")
  
              if msg is None:
                  valid['disp'] = disp
              else:
                  invalid['disp'] = (disp, msg)
  
          # Validate the start option
          if start is not None and start != '':
              msg = None
              if not isinstance(format, _AsciiColumnFormat):
                  # The 'start' option only applies to ASCII columns
                  msg = (
                      'Column start option (TBCOLn) is not allowed for binary '
                      'table columns (got {!r}).  The invalid keyword will be '
                      'ignored for the purpose of formatting the data in this '
                      'column.'.format(start))
              else:
                  try:
                      start = int(start)
                  except (TypeError, ValueError):
                      pass
  
                  if not _is_int(start) or start < 1:
                      msg = (
                          'Column start option (TBCOLn) must be a positive integer '
                          '(got {!r}).  The invalid value will be ignored for the '
                          'purpose of formatting the data in this column.'.format(start))
  
              if msg is None:
                  valid['start'] = start
              else:
                  invalid['start'] = (start, msg)
  
          # Process TDIMn options
          # ASCII table columns can't have a TDIMn keyword associated with it;
          # for now we just issue a warning and ignore it.
          # TODO: This should be checked by the FITS verification code
          if dim is not None and dim != '':
              msg = None
              dims_tuple = tuple()
              # NOTE: If valid, the dim keyword's value in the the valid dict is
              # a tuple, not the original string; if invalid just the original
              # string is returned
              if isinstance(format, _AsciiColumnFormat):
                  msg = (
                      'Column dim option (TDIMn) is not allowed for ASCII table '
                      'columns (got {!r}).  The invalid keyword will be ignored '
                      'for the purpose of formatting this column.'.format(dim))
  
              elif isinstance(dim, str):
                  dims_tuple = _parse_tdim(dim)
              elif isinstance(dim, tuple):
                  dims_tuple = dim
              else:
                  msg = (
                      "`dim` argument must be a string containing a valid value "
                      "for the TDIMn header keyword associated with this column, "
                      "or a tuple containing the C-order dimensions for the "
                      "column.  The invalid value will be ignored for the purpose "
                      "of formatting this column.")
  
              if dims_tuple:
                  if reduce(operator.mul, dims_tuple) > format.repeat:
                      msg = (
                          "The repeat count of the column format {!r} for column {!r} "
                          "is fewer than the number of elements per the TDIM "
                          "argument {!r}.  The invalid TDIMn value will be ignored "
                          "for the purpose of formatting this column.".format(
                              name, format, dim))
  
              if msg is None:
                  valid['dim'] = dims_tuple
              else:
                  invalid['dim'] = (dim, msg)
  
          if coord_type is not None and coord_type != '':
              msg = None
              if not isinstance(coord_type, str):
                  msg = (
                      "Coordinate/axis type option (TCTYPn) must be a string "
                      "(got {!r}). The invalid keyword will be ignored for the "
                      "purpose of formatting this column.".format(coord_type))
              elif len(coord_type) > 8:
                  msg = (
                      "Coordinate/axis type option (TCTYPn) must be a string "
                      "of atmost 8 characters (got {!r}). The invalid keyword "
                      "will be ignored for the purpose of formatting this "
                      "column.".format(coord_type))
  
              if msg is None:
                  valid['coord_type'] = coord_type
              else:
                  invalid['coord_type'] = (coord_type, msg)
  
          if coord_unit is not None and coord_unit != '':
              msg = None
              if not isinstance(coord_unit, str):
                  msg = (
                      "Coordinate/axis unit option (TCUNIn) must be a string "
                      "(got {!r}). The invalid keyword will be ignored for the "
                      "purpose of formatting this column.".format(coord_unit))
  
              if msg is None:
                  valid['coord_unit'] = coord_unit
              else:
                  invalid['coord_unit'] = (coord_unit, msg)
  
          for k, v in [('coord_ref_point', coord_ref_point),
                       ('coord_ref_value', coord_ref_value),
                       ('coord_inc', coord_inc)]:
              if v is not None and v != '':
                  msg = None
                  if not isinstance(v, numbers.Real):
                      msg = (
                          "Column {} option ({}n) must be a real floating type (got {!r}). "
                          "The invalid value will be ignored for the purpose of formatting "
                          "the data in this column.".format(k, ATTRIBUTE_TO_KEYWORD[k], v))
  
                  if msg is None:
                      valid[k] = v
                  else:
                      invalid[k] = (v, msg)
  
          if time_ref_pos is not None and time_ref_pos != '':
              msg=None
              if not isinstance(time_ref_pos, str):
                  msg = (
                      "Time coordinate reference position option (TRPOSn) must be "
                      "a string (got {!r}). The invalid keyword will be ignored for "
                      "the purpose of formatting this column.".format(time_ref_pos))
  
              if msg is None:
                  valid['time_ref_pos'] = time_ref_pos
              else:
                  invalid['time_ref_pos'] = (time_ref_pos, msg)
  
          return valid, invalid
  
      @classmethod
      def _determine_formats(cls, format, start, dim, ascii):
          """
          Given a format string and whether or not the Column is for an
          ASCII table (ascii=None means unspecified, but lean toward binary table
          where ambiguous) create an appropriate _BaseColumnFormat instance for
          the column's format, and determine the appropriate recarray format.
  
          The values of the start and dim keyword arguments are also useful, as
          the former is only valid for ASCII tables and the latter only for
          BINARY tables.
          """
  
          # If the given format string is unambiguously a Numpy dtype or one of
          # the Numpy record format type specifiers supported by Astropy then that
          # should take priority--otherwise assume it is a FITS format
          if isinstance(format, np.dtype):
              format, _, _ = _dtype_to_recformat(format)
  
          # check format
          if ascii is None and not isinstance(format, _BaseColumnFormat):
              # We're just give a string which could be either a Numpy format
              # code, or a format for a binary column array *or* a format for an
              # ASCII column array--there may be many ambiguities here.  Try our
              # best to guess what the user intended.
              format, recformat = cls._guess_format(format, start, dim)
          elif not ascii and not isinstance(format, _BaseColumnFormat):
              format, recformat = cls._convert_format(format, _ColumnFormat)
          elif ascii and not isinstance(format, _AsciiColumnFormat):
              format, recformat = cls._convert_format(format,
                                                      _AsciiColumnFormat)
          else:
              # The format is already acceptable and unambiguous
              recformat = format.recformat
  
          return format, recformat
  
      @classmethod
      def _guess_format(cls, format, start, dim):
          if start and dim:
              # This is impossible; this can't be a valid FITS column
              raise ValueError(
                  'Columns cannot have both a start (TCOLn) and dim '
                  '(TDIMn) option, since the former is only applies to '
                  'ASCII tables, and the latter is only valid for binary '
                  'tables.')
          elif start:
              # Only ASCII table columns can have a 'start' option
              guess_format = _AsciiColumnFormat
          elif dim:
              # Only binary tables can have a dim option
              guess_format = _ColumnFormat
          else:
              # If the format is *technically* a valid binary column format
              # (i.e. it has a valid format code followed by arbitrary
              # "optional" codes), but it is also strictly a valid ASCII
              # table format, then assume an ASCII table column was being
              # requested (the more likely case, after all).
              with suppress(VerifyError):
                  format = _AsciiColumnFormat(format, strict=True)
  
              # A safe guess which reflects the existing behavior of previous
              # Astropy versions
              guess_format = _ColumnFormat
  
          try:
              format, recformat = cls._convert_format(format, guess_format)
          except VerifyError:
              # For whatever reason our guess was wrong (for example if we got
              # just 'F' that's not a valid binary format, but it an ASCII format
              # code albeit with the width/precision omitted
              guess_format = (_AsciiColumnFormat
                              if guess_format is _ColumnFormat
                              else _ColumnFormat)
              # If this fails too we're out of options--it is truly an invalid
              # format, or at least not supported
              format, recformat = cls._convert_format(format, guess_format)
  
          return format, recformat
  
      def _convert_to_valid_data_type(self, array):
          # Convert the format to a type we understand
          if isinstance(array, Delayed):
              return array
          elif array is None:
              return array
          else:
              format = self.format
              dims = self._dims
  
              if dims:
                  shape = dims[:-1] if 'A' in format else dims
                  shape = (len(array),) + shape
                  array = array.reshape(shape)
  
              if 'P' in format or 'Q' in format:
                  return array
              elif 'A' in format:
                  if array.dtype.char in 'SU':
                      if dims:
                          # The 'last' dimension (first in the order given
                          # in the TDIMn keyword itself) is the number of
                          # characters in each string
                          fsize = dims[-1]
                      else:
                          fsize = np.dtype(format.recformat).itemsize
                      return chararray.array(array, itemsize=fsize, copy=False)
                  else:
                      return _convert_array(array, np.dtype(format.recformat))
              elif 'L' in format:
                  # boolean needs to be scaled back to storage values ('T', 'F')
                  if array.dtype == np.dtype('bool'):
                      return np.where(array == np.False_, ord('F'), ord('T'))
                  else:
                      return np.where(array == 0, ord('F'), ord('T'))
              elif 'X' in format:
                  return _convert_array(array, np.dtype('uint8'))
              else:
                  # Preserve byte order of the original array for now; see #77
                  numpy_format = array.dtype.byteorder + format.recformat
  
                  # Handle arrays passed in as unsigned ints as pseudo-unsigned
                  # int arrays; blatantly tacked in here for now--we need columns
                  # to have explicit knowledge of whether they treated as
                  # pseudo-unsigned
                  bzeros = {2: np.uint16(2**15), 4: np.uint32(2**31),
                            8: np.uint64(2**63)}
                  if (array.dtype.kind == 'u' and
                          array.dtype.itemsize in bzeros and
                          self.bscale in (1, None, '') and
                          self.bzero == bzeros[array.dtype.itemsize]):
                      # Basically the array is uint, has scale == 1.0, and the
                      # bzero is the appropriate value for a pseudo-unsigned
                      # integer of the input dtype, then go ahead and assume that
                      # uint is assumed
                      numpy_format = numpy_format.replace('i', 'u')
                      self._pseudo_unsigned_ints = True
  
                  # The .base here means we're dropping the shape information,
                  # which is only used to format recarray fields, and is not
                  # useful for converting input arrays to the correct data type
                  dtype = np.dtype(numpy_format).base
  
                  return _convert_array(array, dtype)
  
  
  class ColDefs(NotifierMixin):
      """
      Column definitions class.
  
      It has attributes corresponding to the `Column` attributes
      (e.g. `ColDefs` has the attribute ``names`` while `Column`
      has ``name``). Each attribute in `ColDefs` is a list of
      corresponding attribute values from all `Column` objects.
      """
  
      _padding_byte = '\x00'
      _col_format_cls = _ColumnFormat
  
      def __new__(cls, input, ascii=False):
          klass = cls
  
          if (hasattr(input, '_columns_type') and
                  issubclass(input._columns_type, ColDefs)):
              klass = input._columns_type
          elif (hasattr(input, '_col_format_cls') and
                  issubclass(input._col_format_cls, _AsciiColumnFormat)):
              klass = _AsciiColDefs
  
          if ascii:  # force ASCII if this has been explicitly requested
              klass = _AsciiColDefs
  
          return object.__new__(klass)
  
      def __getnewargs__(self):
          return (self._arrays,)
  
      def __init__(self, input, ascii=False):
          """
          Parameters
          ----------
  
          input : sequence of `Column`, `ColDefs`, other
              An existing table HDU, an existing `ColDefs`, or any multi-field
              Numpy array or `numpy.recarray`.
  
          ascii : bool
              Use True to ensure that ASCII table columns are used.
  
          """
          from .hdu.table import _TableBaseHDU
          from .fitsrec import FITS_rec
  
          if isinstance(input, ColDefs):
              self._init_from_coldefs(input)
          elif (isinstance(input, FITS_rec) and hasattr(input, '_coldefs') and
                  input._coldefs):
              # If given a FITS_rec object we can directly copy its columns, but
              # only if its columns have already been defined, otherwise this
              # will loop back in on itself and blow up
              self._init_from_coldefs(input._coldefs)
          elif isinstance(input, np.ndarray) and input.dtype.fields is not None:
              # Construct columns from the fields of a record array
              self._init_from_array(input)
          elif isiterable(input):
              # if the input is a list of Columns
              self._init_from_sequence(input)
          elif isinstance(input, _TableBaseHDU):
              # Construct columns from fields in an HDU header
              self._init_from_table(input)
          else:
              raise TypeError('Input to ColDefs must be a table HDU, a list '
                              'of Columns, or a record/field array.')
  
          # Listen for changes on all columns
          for col in self.columns:
              col._add_listener(self)
  
      def _init_from_coldefs(self, coldefs):
          """Initialize from an existing ColDefs object (just copy the
          columns and convert their formats if necessary).
          """
  
          self.columns = [self._copy_column(col) for col in coldefs]
  
      def _init_from_sequence(self, columns):
          for idx, col in enumerate(columns):
              if not isinstance(col, Column):
                  raise TypeError('Element {} in the ColDefs input is not a '
                                  'Column.'.format(idx))
  
          self._init_from_coldefs(columns)
  
      def _init_from_array(self, array):
          self.columns = []
          for idx in range(len(array.dtype)):
              cname = array.dtype.names[idx]
              ftype = array.dtype.fields[cname][0]
              format = self._col_format_cls.from_recformat(ftype)
  
              # Determine the appropriate dimensions for items in the column
              # (typically just 1D)
              dim = array.dtype[idx].shape[::-1]
              if dim and (len(dim) > 1 or 'A' in format):
                  if 'A' in format:
                      # n x m string arrays must include the max string
                      # length in their dimensions (e.g. l x n x m)
                      dim = (array.dtype[idx].base.itemsize,) + dim
                  dim = repr(dim).replace(' ', '')
              else:
                  dim = None
  
              # Check for unsigned ints.
              bzero = None
              if 'I' in format and ftype == np.dtype('uint16'):
                  bzero = np.uint16(2**15)
              elif 'J' in format and ftype == np.dtype('uint32'):
                  bzero = np.uint32(2**31)
              elif 'K' in format and ftype == np.dtype('uint64'):
                  bzero = np.uint64(2**63)
  
              c = Column(name=cname, format=format,
                         array=array.view(np.ndarray)[cname], bzero=bzero,
                         dim=dim)
              self.columns.append(c)
  
      def _init_from_table(self, table):
          hdr = table._header
          nfields = hdr['TFIELDS']
  
          # go through header keywords to pick out column definition keywords
          # definition dictionaries for each field
          col_keywords = [{} for i in range(nfields)]
          for keyword, value in hdr.items():
              key = TDEF_RE.match(keyword)
              try:
                  keyword = key.group('label')
              except Exception:
                  continue  # skip if there is no match
              if keyword in KEYWORD_NAMES:
                  col = int(key.group('num'))
                  if 0 < col <= nfields:
                      attr = KEYWORD_TO_ATTRIBUTE[keyword]
                      if attr == 'format':
                          # Go ahead and convert the format value to the
                          # appropriate ColumnFormat container now
                          value = self._col_format_cls(value)
                      col_keywords[col - 1][attr] = value
  
          # Verify the column keywords and display any warnings if necessary;
          # we only want to pass on the valid keywords
          for idx, kwargs in enumerate(col_keywords):
              valid_kwargs, invalid_kwargs = Column._verify_keywords(**kwargs)
              for val in invalid_kwargs.values():
                  warnings.warn(
                      'Invalid keyword for column {}: {}'.format(idx + 1, val[1]),
                      VerifyWarning)
              # Special cases for recformat and dim
              # TODO: Try to eliminate the need for these special cases
              del valid_kwargs['recformat']
              if 'dim' in valid_kwargs:
                  valid_kwargs['dim'] = kwargs['dim']
              col_keywords[idx] = valid_kwargs
  
          # data reading will be delayed
          for col in range(nfields):
              col_keywords[col]['array'] = Delayed(table, col)
  
          # now build the columns
          self.columns = [Column(**attrs) for attrs in col_keywords]
  
          # Add the table HDU is a listener to changes to the columns
          # (either changes to individual columns, or changes to the set of
          # columns (add/remove/etc.))
          self._add_listener(table)
  
      def __copy__(self):
          return self.__class__(self)
  
      def __deepcopy__(self, memo):
          return self.__class__([copy.deepcopy(c, memo) for c in self.columns])
  
      def _copy_column(self, column):
          """Utility function used currently only by _init_from_coldefs
          to help convert columns from binary format to ASCII format or vice
          versa if necessary (otherwise performs a straight copy).
          """
  
          if isinstance(column.format, self._col_format_cls):
              # This column has a FITS format compatible with this column
              # definitions class (that is ascii or binary)
              return column.copy()
  
          new_column = column.copy()
  
          # Try to use the Numpy recformat as the equivalency between the
          # two formats; if that conversion can't be made then these
          # columns can't be transferred
          # TODO: Catch exceptions here and raise an explicit error about
          # column format conversion
          new_column.format = self._col_format_cls.from_column_format(
                  column.format)
  
          # Handle a few special cases of column format options that are not
          # compatible between ASCII an binary tables
          # TODO: This is sort of hacked in right now; we really need
          # separate classes for ASCII and Binary table Columns, and they
          # should handle formatting issues like these
          if not isinstance(new_column.format, _AsciiColumnFormat):
              # the column is a binary table column...
              new_column.start = None
              if new_column.null is not None:
                  # We can't just "guess" a value to represent null
                  # values in the new column, so just disable this for
                  # now; users may modify it later
                  new_column.null = None
          else:
              # the column is an ASCII table column...
              if new_column.null is not None:
                  new_column.null = DEFAULT_ASCII_TNULL
              if (new_column.disp is not None and
                      new_column.disp.upper().startswith('L')):
                  # ASCII columns may not use the logical data display format;
                  # for now just drop the TDISPn option for this column as we
                  # don't have a systematic conversion of boolean data to ASCII
                  # tables yet
                  new_column.disp = None
  
          return new_column
  
      def __getattr__(self, name):
          """
          Automatically returns the values for the given keyword attribute for
          all `Column`s in this list.
  
          Implements for example self.units, self.formats, etc.
          """
          cname = name[:-1]
          if cname in KEYWORD_ATTRIBUTES and name[-1] == 's':
              attr = []
              for col in self.columns:
                  val = getattr(col, cname)
                  attr.append(val if val is not None else '')
              return attr
          raise AttributeError(name)
  
      @lazyproperty
      def dtype(self):
          # Note: This previously returned a dtype that just used the raw field
          # widths based on the format's repeat count, and did not incorporate
          # field *shapes* as provided by TDIMn keywords.
          # Now this incorporates TDIMn from the start, which makes *this* method
          # a little more complicated, but simplifies code elsewhere (for example
          # fields will have the correct shapes even in the raw recarray).
          fields = []
          offsets = [0]
  
          for name, format_, dim in zip(self.names, self.formats, self._dims):
              dt = format_.dtype
  
              if len(offsets) < len(self.formats):
                  # Note: the size of the *original* format_ may be greater than
                  # one would expect from the number of elements determined by
                  # dim.  The FITS format allows this--the rest of the field is
                  # filled with undefined values.
                  offsets.append(offsets[-1] + dt.itemsize)
  
              if dim:
                  if format_.format == 'A':
                      dt = np.dtype((dt.char + str(dim[-1]), dim[:-1]))
                  else:
                      dt = np.dtype((dt.base, dim))
  
              fields.append((name, dt))
  
          return nh.realign_dtype(np.dtype(fields), offsets)
  
      @lazyproperty
      def names(self):
          return [col.name for col in self.columns]
  
      @lazyproperty
      def formats(self):
          return [col.format for col in self.columns]
  
      @lazyproperty
      def _arrays(self):
          return [col.array for col in self.columns]
  
      @lazyproperty
      def _recformats(self):
          return [fmt.recformat for fmt in self.formats]
  
      @lazyproperty
      def _dims(self):
          """Returns the values of the TDIMn keywords parsed into tuples."""
  
          return [col._dims for col in self.columns]
  
      def __getitem__(self, key):
          if isinstance(key, str):
              key = _get_index(self.names, key)
  
          x = self.columns[key]
          if _is_int(key):
              return x
          else:
              return ColDefs(x)
  
      def __len__(self):
          return len(self.columns)
  
      def __repr__(self):
          rep = 'ColDefs('
          if hasattr(self, 'columns') and self.columns:
              # The hasattr check is mostly just useful in debugging sessions
              # where self.columns may not be defined yet
              rep += '\n    '
              rep += '\n    '.join([repr(c) for c in self.columns])
              rep += '\n'
          rep += ')'
          return rep
  
      def __add__(self, other, option='left'):
          if isinstance(other, Column):
              b = [other]
          elif isinstance(other, ColDefs):
              b = list(other.columns)
          else:
              raise TypeError('Wrong type of input.')
          if option == 'left':
              tmp = list(self.columns) + b
          else:
              tmp = b + list(self.columns)
          return ColDefs(tmp)
  
      def __radd__(self, other):
          return self.__add__(other, 'right')
  
      def __sub__(self, other):
          if not isinstance(other, (list, tuple)):
              other = [other]
          _other = [_get_index(self.names, key) for key in other]
          indx = list(range(len(self)))
          for x in _other:
              indx.remove(x)
          tmp = [self[i] for i in indx]
          return ColDefs(tmp)
  
      def _update_column_attribute_changed(self, column, attr, old_value,
                                           new_value):
          """
          Handle column attribute changed notifications from columns that are
          members of this `ColDefs`.
  
          `ColDefs` itself does not currently do anything with this, and just
          bubbles the notification up to any listening table HDUs that may need
          to update their headers, etc.  However, this also informs the table of
          the numerical index of the column that changed.
          """
  
          idx = 0
          for idx, col in enumerate(self.columns):
              if col is column:
                  break
  
          if attr == 'name':
              del self.names
          elif attr == 'format':
              del self.formats
  
          self._notify('column_attribute_changed', column, idx, attr, old_value,
                       new_value)
  
      def add_col(self, column):
          """
          Append one `Column` to the column definition.
          """
  
          if not isinstance(column, Column):
              raise AssertionError
  
          self._arrays.append(column.array)
          # Obliterate caches of certain things
          del self.dtype
          del self._recformats
          del self._dims
          del self.names
          del self.formats
  
          self.columns.append(column)
  
          # Listen for changes on the new column
          column._add_listener(self)
  
          # If this ColDefs is being tracked by a Table, inform the
          # table that its data is now invalid.
          self._notify('column_added', self, column)
          return self
  
      def del_col(self, col_name):
          """
          Delete (the definition of) one `Column`.
  
          col_name : str or int
              The column's name or index
          """
  
          indx = _get_index(self.names, col_name)
          col = self.columns[indx]
  
          del self._arrays[indx]
          # Obliterate caches of certain things
          del self.dtype
          del self._recformats
          del self._dims
          del self.names
          del self.formats
  
          del self.columns[indx]
  
          col._remove_listener(self)
  
          # If this ColDefs is being tracked by a table HDU, inform the HDU (or
          # any other listeners) that the column has been removed
          # Just send a reference to self, and the index of the column that was
          # removed
          self._notify('column_removed', self, indx)
          return self
  
      def change_attrib(self, col_name, attrib, new_value):
          """
          Change an attribute (in the ``KEYWORD_ATTRIBUTES`` list) of a `Column`.
  
          Parameters
          ----------
          col_name : str or int
              The column name or index to change
  
          attrib : str
              The attribute name
  
          new_value : object
              The new value for the attribute
          """
  
          setattr(self[col_name], attrib, new_value)
  
      def change_name(self, col_name, new_name):
          """
          Change a `Column`'s name.
  
          Parameters
          ----------
          col_name : str
              The current name of the column
  
          new_name : str
              The new name of the column
          """
  
          if new_name != col_name and new_name in self.names:
              raise ValueError('New name {} already exists.'.format(new_name))
          else:
              self.change_attrib(col_name, 'name', new_name)
  
      def change_unit(self, col_name, new_unit):
          """
          Change a `Column`'s unit.
  
          Parameters
          ----------
          col_name : str or int
              The column name or index
  
          new_unit : str
              The new unit for the column
          """
  
          self.change_attrib(col_name, 'unit', new_unit)
  
      def info(self, attrib='all', output=None):
          """
          Get attribute(s) information of the column definition.
  
          Parameters
          ----------
          attrib : str
              Can be one or more of the attributes listed in
              ``astropy.io.fits.column.KEYWORD_ATTRIBUTES``.  The default is
              ``"all"`` which will print out all attributes.  It forgives plurals
              and blanks.  If there are two or more attribute names, they must be
              separated by comma(s).
  
          output : file, optional
              File-like object to output to.  Outputs to stdout by default.
              If `False`, returns the attributes as a `dict` instead.
  
          Notes
          -----
          This function doesn't return anything by default; it just prints to
          stdout.
          """
  
          if output is None:
              output = sys.stdout
  
          if attrib.strip().lower() in ['all', '']:
              lst = KEYWORD_ATTRIBUTES
          else:
              lst = attrib.split(',')
              for idx in range(len(lst)):
                  lst[idx] = lst[idx].strip().lower()
                  if lst[idx][-1] == 's':
                      lst[idx] = list[idx][:-1]
  
          ret = {}
  
          for attr in lst:
              if output:
                  if attr not in KEYWORD_ATTRIBUTES:
                      output.write("'{}' is not an attribute of the column "
                                   "definitions.\n".format(attr))
                      continue
                  output.write("{}:\n".format(attr))
                  output.write('    {}\n'.format(getattr(self, attr + 's')))
              else:
                  ret[attr] = getattr(self, attr + 's')
  
          if not output:
              return ret
  
  
  class _AsciiColDefs(ColDefs):
      """ColDefs implementation for ASCII tables."""
  
      _padding_byte = ' '
      _col_format_cls = _AsciiColumnFormat
  
      def __init__(self, input, ascii=True):
          super().__init__(input)
  
          # if the format of an ASCII column has no width, add one
          if not isinstance(input, _AsciiColDefs):
              self._update_field_metrics()
          else:
              for idx, s in enumerate(input.starts):
                  self.columns[idx].start = s
  
              self._spans = input.spans
              self._width = input._width
  
      @lazyproperty
      def dtype(self):
          dtype = {}
  
          for j in range(len(self)):
              data_type = 'S' + str(self.spans[j])
              dtype[self.names[j]] = (data_type, self.starts[j] - 1)
  
          return np.dtype(dtype)
  
      @property
      def spans(self):
          """A list of the widths of each field in the table."""
  
          return self._spans
  
      @lazyproperty
      def _recformats(self):
          if len(self) == 1:
              widths = []
          else:
              widths = [y - x for x, y in pairwise(self.starts)]
  
          # Widths is the width of each field *including* any space between
          # fields; this is so that we can map the fields to string records in a
          # Numpy recarray
          widths.append(self._width - self.starts[-1] + 1)
          return ['a' + str(w) for w in widths]
  
      def add_col(self, column):
          super().add_col(column)
          self._update_field_metrics()
  
      def del_col(self, col_name):
          super().del_col(col_name)
          self._update_field_metrics()
  
      def _update_field_metrics(self):
          """
          Updates the list of the start columns, the list of the widths of each
          field, and the total width of each record in the table.
          """
  
          spans = [0] * len(self.columns)
          end_col = 0  # Refers to the ASCII text column, not the table col
          for idx, col in enumerate(self.columns):
              width = col.format.width
  
              # Update the start columns and column span widths taking into
              # account the case that the starting column of a field may not
              # be the column immediately after the previous field
              if not col.start:
                  col.start = end_col + 1
              end_col = col.start + width - 1
              spans[idx] = width
  
          self._spans = spans
          self._width = end_col
  
  
  # Utilities
  
  
  class _VLF(np.ndarray):
      """Variable length field object."""
  
      def __new__(cls, input, dtype='a'):
          """
          Parameters
          ----------
          input
              a sequence of variable-sized elements.
          """
  
          if dtype == 'a':
              try:
                  # this handles ['abc'] and [['a','b','c']]
                  # equally, beautiful!
                  input = [chararray.array(x, itemsize=1) for x in input]
              except Exception:
                  raise ValueError(
                      'Inconsistent input data array: {0}'.format(input))
  
          a = np.array(input, dtype=object)
          self = np.ndarray.__new__(cls, shape=(len(input),), buffer=a,
                                    dtype=object)
          self.max = 0
          self.element_dtype = dtype
          return self
  
      def __array_finalize__(self, obj):
          if obj is None:
              return
          self.max = obj.max
          self.element_dtype = obj.element_dtype
  
      def __setitem__(self, key, value):
          """
          To make sure the new item has consistent data type to avoid
          misalignment.
          """
  
          if isinstance(value, np.ndarray) and value.dtype == self.dtype:
              pass
          elif isinstance(value, chararray.chararray) and value.itemsize == 1:
              pass
          elif self.element_dtype == 'a':
              value = chararray.array(value, itemsize=1)
          else:
              value = np.array(value, dtype=self.element_dtype)
          np.ndarray.__setitem__(self, key, value)
          self.max = max(self.max, len(value))
  
  
  def _get_index(names, key):
      """
      Get the index of the ``key`` in the ``names`` list.
  
      The ``key`` can be an integer or string.  If integer, it is the index
      in the list.  If string,
  
          a. Field (column) names are case sensitive: you can have two
             different columns called 'abc' and 'ABC' respectively.
  
          b. When you *refer* to a field (presumably with the field
             method), it will try to match the exact name first, so in
             the example in (a), field('abc') will get the first field,
             and field('ABC') will get the second field.
  
          If there is no exact name matched, it will try to match the
          name with case insensitivity.  So, in the last example,
          field('Abc') will cause an exception since there is no unique
          mapping.  If there is a field named "XYZ" and no other field
          name is a case variant of "XYZ", then field('xyz'),
          field('Xyz'), etc. will get this field.
      """
  
      if _is_int(key):
          indx = int(key)
      elif isinstance(key, str):
          # try to find exact match first
          try:
              indx = names.index(key.rstrip())
          except ValueError:
              # try to match case-insentively,
              _key = key.lower().rstrip()
              names = [n.lower().rstrip() for n in names]
              count = names.count(_key)  # occurrence of _key in names
              if count == 1:
                  indx = names.index(_key)
              elif count == 0:
                  raise KeyError("Key '{}' does not exist.".format(key))
              else:              # multiple match
                  raise KeyError("Ambiguous key name '{}'.".format(key))
      else:
          raise KeyError("Illegal key '{!r}'.".format(key))
  
      return indx
  
  
  def _unwrapx(input, output, repeat):
      """
      Unwrap the X format column into a Boolean array.
  
      Parameters
      ----------
      input
          input ``Uint8`` array of shape (`s`, `nbytes`)
  
      output
          output Boolean array of shape (`s`, `repeat`)
  
      repeat
          number of bits
      """
  
      pow2 = np.array([128, 64, 32, 16, 8, 4, 2, 1], dtype='uint8')
      nbytes = ((repeat - 1) // 8) + 1
      for i in range(nbytes):
          _min = i * 8
          _max = min((i + 1) * 8, repeat)
          for j in range(_min, _max):
              output[..., j] = np.bitwise_and(input[..., i], pow2[j - i * 8])
  
  
  def _wrapx(input, output, repeat):
      """
      Wrap the X format column Boolean array into an ``UInt8`` array.
  
      Parameters
      ----------
      input
          input Boolean array of shape (`s`, `repeat`)
  
      output
          output ``Uint8`` array of shape (`s`, `nbytes`)
  
      repeat
          number of bits
      """
  
      output[...] = 0  # reset the output
      nbytes = ((repeat - 1) // 8) + 1
      unused = nbytes * 8 - repeat
      for i in range(nbytes):
          _min = i * 8
          _max = min((i + 1) * 8, repeat)
          for j in range(_min, _max):
              if j != _min:
                  np.left_shift(output[..., i], 1, output[..., i])
              np.add(output[..., i], input[..., j], output[..., i])
  
      # shift the unused bits
      np.left_shift(output[..., i], unused, output[..., i])
  
  
  def _makep(array, descr_output, format, nrows=None):
      """
      Construct the P (or Q) format column array, both the data descriptors and
      the data.  It returns the output "data" array of data type `dtype`.
  
      The descriptor location will have a zero offset for all columns
      after this call.  The final offset will be calculated when the file
      is written.
  
      Parameters
      ----------
      array
          input object array
  
      descr_output
          output "descriptor" array of data type int32 (for P format arrays) or
          int64 (for Q format arrays)--must be nrows long in its first dimension
  
      format
          the _FormatP object representing the format of the variable array
  
      nrows : int, optional
          number of rows to create in the column; defaults to the number of rows
          in the input array
      """
  
      # TODO: A great deal of this is redundant with FITS_rec._convert_p; see if
      # we can merge the two somehow.
  
      _offset = 0
  
      if not nrows:
          nrows = len(array)
  
      data_output = _VLF([None] * nrows, dtype=format.dtype)
  
      if format.dtype == 'a':
          _nbytes = 1
      else:
          _nbytes = np.array([], dtype=format.dtype).itemsize
  
      for idx in range(nrows):
          if idx < len(array):
              rowval = array[idx]
          else:
              if format.dtype == 'a':
                  rowval = ' ' * data_output.max
              else:
                  rowval = [0] * data_output.max
          if format.dtype == 'a':
              data_output[idx] = chararray.array(encode_ascii(rowval),
                                                 itemsize=1)
          else:
              data_output[idx] = np.array(rowval, dtype=format.dtype)
  
          descr_output[idx, 0] = len(data_output[idx])
          descr_output[idx, 1] = _offset
          _offset += len(data_output[idx]) * _nbytes
  
      return data_output
  
  
  def _parse_tformat(tform):
      """Parse ``TFORMn`` keyword for a binary table into a
      ``(repeat, format, option)`` tuple.
      """
  
      try:
          (repeat, format, option) = TFORMAT_RE.match(tform.strip()).groups()
      except Exception:
          # TODO: Maybe catch this error use a default type (bytes, maybe?) for
          # unrecognized column types.  As long as we can determine the correct
          # byte width somehow..
          raise VerifyError('Format {!r} is not recognized.'.format(tform))
  
      if repeat == '':
          repeat = 1
      else:
          repeat = int(repeat)
  
      return (repeat, format.upper(), option)
  
  
  def _parse_ascii_tformat(tform, strict=False):
      """
      Parse the ``TFORMn`` keywords for ASCII tables into a ``(format, width,
      precision)`` tuple (the latter is always zero unless format is one of 'E',
      'F', or 'D').
      """
  
      match = TFORMAT_ASCII_RE.match(tform.strip())
      if not match:
          raise VerifyError('Format {!r} is not recognized.'.format(tform))
  
      # Be flexible on case
      format = match.group('format')
      if format is None:
          # Floating point format
          format = match.group('formatf').upper()
          width = match.group('widthf')
          precision = match.group('precision')
          if width is None or precision is None:
              if strict:
                  raise VerifyError('Format {!r} is not unambiguously an ASCII '
                                    'table format.')
              else:
                  width = 0 if width is None else width
                  precision = 1 if precision is None else precision
      else:
          format = format.upper()
          width = match.group('width')
          if width is None:
              if strict:
                  raise VerifyError('Format {!r} is not unambiguously an ASCII '
                                    'table format.')
              else:
                  # Just use a default width of 0 if unspecified
                  width = 0
          precision = 0
  
      def convert_int(val):
          msg = ('Format {!r} is not valid--field width and decimal precision '
                 'must be integers.')
          try:
              val = int(val)
          except (ValueError, TypeError):
              raise VerifyError(msg.format(tform))
  
          return val
  
      if width and precision:
          # This should only be the case for floating-point formats
          width, precision = convert_int(width), convert_int(precision)
      elif width:
          # Just for integer/string formats; ignore precision
          width = convert_int(width)
      else:
          # For any format, if width was unspecified use the set defaults
          width, precision = ASCII_DEFAULT_WIDTHS[format]
  
      if width <= 0:
          raise VerifyError("Format {!r} not valid--field width must be a "
                            "positive integeter.".format(tform))
  
      if precision >= width:
          raise VerifyError("Format {!r} not valid--the number of decimal digits "
                            "must be less than the format's total "
                            "width {}.".format(tform, width))
  
      return format, width, precision
  
  
  def _parse_tdim(tdim):
      """Parse the ``TDIM`` value into a tuple (may return an empty tuple if
      the value ``TDIM`` value is empty or invalid).
      """
  
      m = tdim and TDIM_RE.match(tdim)
      if m:
          dims = m.group('dims')
          return tuple(int(d.strip()) for d in dims.split(','))[::-1]
  
      # Ignore any dim values that don't specify a multidimensional column
      return tuple()
  
  
  def _scalar_to_format(value):
      """
      Given a scalar value or string, returns the minimum FITS column format
      that can represent that value.  'minimum' is defined by the order given in
      FORMATORDER.
      """
  
      # First, if value is a string, try to convert to the appropriate scalar
      # value
      for type_ in (int, float, complex):
          try:
              value = type_(value)
              break
          except ValueError:
              continue
  
      numpy_dtype_str = np.min_scalar_type(value).str
      numpy_dtype_str = numpy_dtype_str[1:]  # Strip endianness
  
      try:
          fits_format = NUMPY2FITS[numpy_dtype_str]
          return FITSUPCONVERTERS.get(fits_format, fits_format)
      except KeyError:
          return "A" + str(len(value))
  
  
  def _cmp_recformats(f1, f2):
      """
      Compares two numpy recformats using the ordering given by FORMATORDER.
      """
  
      if f1[0] == 'a' and f2[0] == 'a':
          return cmp(int(f1[1:]), int(f2[1:]))
      else:
          f1, f2 = NUMPY2FITS[f1], NUMPY2FITS[f2]
          return cmp(FORMATORDER.index(f1), FORMATORDER.index(f2))
  
  
  def _convert_fits2record(format):
      """
      Convert FITS format spec to record format spec.
      """
  
      repeat, dtype, option = _parse_tformat(format)
  
      if dtype in FITS2NUMPY:
          if dtype == 'A':
              output_format = FITS2NUMPY[dtype] + str(repeat)
              # to accommodate both the ASCII table and binary table column
              # format spec, i.e. A7 in ASCII table is the same as 7A in
              # binary table, so both will produce 'a7'.
              # Technically the FITS standard does not allow this but it's a very
              # common mistake
              if format.lstrip()[0] == 'A' and option != '':
                  # make sure option is integer
                  output_format = FITS2NUMPY[dtype] + str(int(option))
          else:
              repeat_str = ''
              if repeat != 1:
                  repeat_str = str(repeat)
              output_format = repeat_str + FITS2NUMPY[dtype]
  
      elif dtype == 'X':
          output_format = _FormatX(repeat)
      elif dtype == 'P':
          output_format = _FormatP.from_tform(format)
      elif dtype == 'Q':
          output_format = _FormatQ.from_tform(format)
      elif dtype == 'F':
          output_format = 'f8'
      else:
          raise ValueError('Illegal format `{}`.'.format(format))
  
      return output_format
  
  
  def _convert_record2fits(format):
      """
      Convert record format spec to FITS format spec.
      """
  
      recformat, kind, dtype = _dtype_to_recformat(format)
      shape = dtype.shape
      itemsize = dtype.base.itemsize
      if dtype.char == 'U':
          # Unicode dtype--itemsize is 4 times actual ASCII character length,
          # which what matters for FITS column formats
          # Use dtype.base--dtype may be a multi-dimensional dtype
          itemsize = itemsize // 4
  
      option = str(itemsize)
  
      ndims = len(shape)
      repeat = 1
      if ndims > 0:
          nel = np.array(shape, dtype='i8').prod()
          if nel > 1:
              repeat = nel
  
      if kind == 'a':
          # This is a kludge that will place string arrays into a
          # single field, so at least we won't lose data.  Need to
          # use a TDIM keyword to fix this, declaring as (slength,
          # dim1, dim2, ...)  as mwrfits does
  
          ntot = int(repeat) * int(option)
  
          output_format = str(ntot) + 'A'
      elif recformat in NUMPY2FITS:  # record format
          if repeat != 1:
              repeat = str(repeat)
          else:
              repeat = ''
          output_format = repeat + NUMPY2FITS[recformat]
      else:
          raise ValueError('Illegal format `{}`.'.format(format))
  
      return output_format
  
  
  def _dtype_to_recformat(dtype):
      """
      Utility function for converting a dtype object or string that instantiates
      a dtype (e.g. 'float32') into one of the two character Numpy format codes
      that have been traditionally used by Astropy.
  
      In particular, use of 'a' to refer to character data is long since
      deprecated in Numpy, but Astropy remains heavily invested in its use
      (something to try to get away from sooner rather than later).
      """
  
      if not isinstance(dtype, np.dtype):
          dtype = np.dtype(dtype)
  
      kind = dtype.base.kind
  
      if kind in ('U', 'S'):
          recformat = kind = 'a'
      else:
          itemsize = dtype.base.itemsize
          recformat = kind + str(itemsize)
  
      return recformat, kind, dtype
  
  
  def _convert_format(format, reverse=False):
      """
      Convert FITS format spec to record format spec.  Do the opposite if
      reverse=True.
      """
  
      if reverse:
          return _convert_record2fits(format)
      else:
          return _convert_fits2record(format)
  
  
  def _convert_ascii_format(format, reverse=False):
      """Convert ASCII table format spec to record format spec."""
  
      if reverse:
          recformat, kind, dtype = _dtype_to_recformat(format)
          itemsize = dtype.itemsize
  
          if kind == 'a':
              return 'A' + str(itemsize)
          elif NUMPY2FITS.get(recformat) == 'L':
              # Special case for logical/boolean types--for ASCII tables we
              # represent these as single character columns containing 'T' or 'F'
              # (a la the storage format for Logical columns in binary tables)
              return 'A1'
          elif kind == 'i':
              # Use for the width the maximum required to represent integers
              # of that byte size plus 1 for signs, but use a minimum of the
              # default width (to keep with existing behavior)
              width = 1 + len(str(2 ** (itemsize * 8)))
              width = max(width, ASCII_DEFAULT_WIDTHS['I'][0])
              return 'I' + str(width)
          elif kind == 'f':
              # This is tricky, but go ahead and use D if float-64, and E
              # if float-32 with their default widths
              if itemsize >= 8:
                  format = 'D'
              else:
                  format = 'E'
              width = '.'.join(str(w) for w in ASCII_DEFAULT_WIDTHS[format])
              return format + width
          # TODO: There may be reasonable ways to represent other Numpy types so
          # let's see what other possibilities there are besides just 'a', 'i',
          # and 'f'.  If it doesn't have a reasonable ASCII representation then
          # raise an exception
      else:
          format, width, precision = _parse_ascii_tformat(format)
  
          # This gives a sensible "default" dtype for a given ASCII
          # format code
          recformat = ASCII2NUMPY[format]
  
          # The following logic is taken from CFITSIO:
          # For integers, if the width <= 4 we can safely use 16-bit ints for all
          # values [for the non-standard J format code just always force 64-bit]
          if format == 'I' and width <= 4:
              recformat = 'i2'
          elif format == 'A':
              recformat += str(width)
  
          return recformat
  