[fitsbits] Output array type when BZERO is an integer {External}

[Dubois-Felsmann, Gregory P.]

This is a bit of a logical/legal hole in the FITS standard, for a couple of reasons given below.  I agree with Paul that the best solution would be to issue a clarification.

I think it's an excellent moment for getting this right, when implementing a new client library from scratch instead of adiabatically as most of our others have been.

These questions also arise in the behavior of client applications -- for instance, IPAC Firefly, which I have some responsibility for -- so this isn't purely an issue for theoretical discussion.

1) Lack of clarity about the interpretation of missing headers and when the scaling should be applied at all

The FITS 4.00 standard specifies that BZERO and BSCALE both "shall" be floating point values, with defaults of "0.0" and "1.0", respectively -- and there's no discussion of the absence of BZERO and BSCALE being treated as a special case.  Thus, if you take this completely literally, it means that the inherently floating-point scaling operation is *always* performed (even when it's mathematically a no-op) and that the result should therefore *always* be a floating-point array.  That is obviously not the spirit of the standard!  It has to be possible to deliver an integer array as the output, which means we need a specification of how to trigger that.

Even then we are left to ask the question: if the absence of BZERO and BSCALE is supposed to trigger returning the array as its specified integer format, what is *explicit* specification of BZERO = 0.0 and BSCALE = 1.0 supposed to do?  The most legalistic reading of the standard is that the absence of a keyword and the explicit presence of the default value for that keyword are supposed to be treated the same way, but then we have define what it means for the explicitly specified value to be the same as the default.  The text says "1.0"; which of the following are equivalent: "1", "1.", "+1.0D0", "1.000000001" (equal to 1 in float32), "1.0000000000000000000000001", "0.99999999999999999999999999"?

If, as I do, you feel queasy about testing for floating-point equality in this situation, and you think "OK, the rule we should publish is:

'if either BZERO or BSCALE are present in the header, even if they are exactly 0.0 and 1.0 respectively, return the array in a floating-point format in which all possible values of the input are distinct in the output, if possible'"

(meaning that BITPIX 32 would yield a float64 output, and BITPIX 64 would have to be annotated as an exception, since we can't rely on a float128 being available), you have something that sounds defensible, but you still have another problem:

2) The unsigned-integer (and signed byte) special case

The standard also recommends the use of special values of BZERO to allow representation of unsigned 16/32/64-bit integers (and also signed 8-bit integers):

"... the BZERO keyword is also used when storing unsigned-integer values in the FITS array. In this special case the BSCALE keyword *shall* have the default value of 1.0, and the BZERO keyword *shall* have one of the integer values shown in Table 11."

Again, the spirit of this is obviously that if BSCALE is present with the value 1.0, and BITPIX is 32, say, and BZERO is 2147483648, the returned data should have type uint32, not some floating-point type.  What is a client library supposed to do if BZERO is 2147483648.0?  The same?  What if it's 2147483648.0000000000000000000000000001?  (In other words, is OK if the client library reads in the RHS of the BZERO header into an internal float64 first, before interpreting it, or is it supposed to handle the RHS of the BZERO header as a string and compare it only to exactly the value in Table 11?

Note that in this case the standard actually appears to say point blank that a BSCALE of 1.0 *shall* be supplied; it certainly doesn't say, e.g., "the BSCALE keyword shall be omitted".

NB: I have not tried to search the fitsbits archive -- I would not be at all surprised if this had come up before.

Gregory

________________________________________
From: fitsbits <fitsbits-bounces at listmgr.nrao.edu> on behalf of Barrett, Paul via fitsbits <fitsbits at listmgr.nrao.edu>
Sent: Saturday, March 9, 2024 11:20
To: fitsbits at listmgr.nrao.edu
Subject: [fitsbits] Output array type when BZERO is an integer {External}

I'm writing a FITS package for the Julia programming language. I have a question about the output type of the image when BZERO is an integer value. The documentation implies that the output image should be a floating point type because the BSCALE value is a float. Is this correct? If yes, then I recommend stating this explicitly in the FITS standard documentation. I also recommend suggesting the appropriate output type depending on the input type, e.g., UInt8 => Float32, Int16 => Float32, etc.

Thanks,
Paul