Don Wells wrote:
While examining the differences document,
[at http://fits.gsfc.nasa.gov/fits_draft.html]
I encountered two sentences in
7.3.5 that seem to me to be inconsistent. The first is "The meaning of
a negative value for either of these integers [in the array descriptor]
is not defned by this standard." The second is "The storage referenced
by an array descriptor must lie entirely within the heap area; negative
offsets are not permitted." The first sentence leaves open the option of
a negative offset (and that is an obvious escape hatch, because the
integers are definitely *signed*), but the second sentence closes off
the option.

Back in 2005 when the IAU FITS Working Group approved the variable
length array convention as part of the FITS Standard, it was decided to
specifically define that the 2 integers in the "P" array descriptor are
"signed" 32-bit integers (and not "unsigned" integers) and to add the
statement that "The meaning of a negative value for either of these
integers is not defned by this standard."

Allowing negative array descriptor values is not necessarily a
contradiction to the later statement that "negative offsets [in the
heap] are not permitted", because it is possible to define a convention
that maps (via some mathematical function) a negative descriptor value
into a positive heap offset value. Note that the same thing was done
long ago with the BITPIX keyword; originally the BITPIX value had to be
positive, but later the definition was extended so that if the value is
negative then the actual number of bits per pixel is derived by
multiplying the BITPIX value by -1.

Arguably, the most useful function for mapping a negative array
descriptor value into a positive heap offset is this one:

heap_offset = 2**32 + descriptor_value
= 4294967296 + descriptor_value

(where the descriptor_value is a negative signed 32 bit integer in the
range -1 to -2147483648). This function effectively doubles the useful
size of the heap: positive descriptor values can refer to heap offsets
in the range 0 to 2147483647, and the negative descriptor values map
into heap offsets in the range 2147483648 to 4294967295.

Incidently, it is no coincidence that this mapping function produces
exactly the same positive heap offset value as would be given if one
were to interpret the 32-bit descriptor value as an unsigned 32-bit
integer.

This begs the question of what, if anything, should be done to clarify
the use or legality of negative array descriptor values in variable
length array columns in binary tables. Should the mapping function
described above be viewed as a blatant attempt to circumvent the
restriction on interpreting the array descriptors as "signed" integers
and thus should be expressly forbidden in the Standard, or, on the other
hand, is this a clever adaptation to work within the rules of FITS to
allow new functionality (by doubling the useful size of the heap area)?
My on feeling on this is that we should either leave the wording of
the Standard as it is (with the intentional ambiguity about the meaning
of negative array descriptor values), or, go back to the fundamental
issue and redefine the array descriptors to be unsigned integers, which
by definition would eliminate the need to explain the interpretation of
negative descriptor values.

Bill Pence
--
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Dr. William Pence
NASA/GSFC Code 662 HEASARC +1-301-286-4599 (voice)
Greenbelt MD 20771 +1-301-286-1684 (fax)