🚀 go-pugleaf

In article AA05949@tetra.gsfc.nasa.gov, pence@tetra.gsfc.nasa.gov (William Pence) writes:
>As an aside, I'm sure you are aware that the VAX has 2 different R*8 data 
>representations.  The default D_floating representation which you are probably using
>reserves 8 bits for the exponent and 55 bits for the mantissa.  The G_floating
>representation on the otherhand is similar to the IEEE R*8  representation: both
>have 11 bits for the exponent and 52 bits for the mantissa.  The G_floating
>and IEEE values are still not identical though because the VAX interprets the
>exponent and mantissa numbers as normalized, ("hidden bit normalization") which
>effectively gives you another bit of precision compared to the IEEE value.
>If you were to use G_floating on the VAX, you probably would not notice the
>loss of precision in converting the data back and forth from FITS.

IEEE values are also normalized as long as they are greater than or equal
to 2 ** E_min, where E_min is the minimum exponent.  An IEEE-754 double
has a precision of 53 base-2 digits (identical to VAX G-floating) as long
as E >= E_min (E_min = -1022).  VAX G-floating and IEEE-754 doubles probably
differ in the bias of the exponent (this is the difference between normalized
IEEE singles and VAX F-floats).

Incidentally, if you think about it you will realize that the exponent can
not be normalized.

	Chris Flatters
	cflatter@nrao.edu

In article <9212171630.AA05949@tetra.gsfc.nasa.gov> William Pence writes:


   I think you mean 5B, not 8B  (?)

Yes, I meant 5B not 8B; sorry for the dyslexia

   My reaction to this is that it is not very useful to put information in a FITS file
   that only a particular machine will be able to interpret.  One of the main purposes of 
   FITS is to make the information in the file portable to any machine.  So I think
   you have 2 choices.

   1.  If this added precision in the VAX value is really significant, then you 
   need to find a portable way of including it in the FITS file.  One way might be
   to express the double precision value as 2 columns:  one containing the integer
   part, and the other containing the fractional part of the value.

   2.  If the added precision in the VAX value is not really significant (the VAX
   G_floating datatype has effectively 4 more bits of precision than an IEEE R*8 value)
   then one should not worry about it, and one should accept the fact that the
   FITS file cannot preserve every last bit of information on every type of machine.

The precision is significant, in that we must be able to repoduce the original
data byte for byte. Breaking the VAX R*8 up into an IEEE R*8 + remainder would
still introduce roundoff error.


   As an aside, I'm sure you are aware that the VAX has 2 different R*8 data 
   representations.  The default D_floating representation which you are probably using
   reserves 8 bits for the exponent and 55 bits for the mantissa.  The G_floating
   representation on the otherhand is similar to the IEEE R*8  representation: both
   have 11 bits for the exponent and 52 bits for the mantissa.  The G_floating
   and IEEE values are still not identical though because the VAX interprets the
   exponent and mantissa numbers as normalized, ("hidden bit normalization") which
   effectively gives you another bit of precision compared to the IEEE value.
   If you were to use G_floating on the VAX, you probably would not notice the
   loss of precision in converting the data back and forth from FITS.


I was aware of the D_floating and G_floating compiler options, but did not
know that much about them. Unfortunately, the data is produced using D_floating
and there is nothing we can do about it.

Thanks for your interest Bill. I'll think about what you had to say. 


                        Don Jennings

In article <JENNINGS.92Dec17144132@antwrp.antwrp.gsfc.nasa.gov>, 
jennings@antwrp.antwrp.gsfc.nasa.gov (Don Jennings) writes...
>In article <9212171630.AA05949@tetra.gsfc.nasa.gov> William Pence writes:
>   My reaction to this is that it is not very useful to put information in a FITS file
>   that only a particular machine will be able to interpret.  One of the main purposes of 
>   FITS is to make the information in the file portable to any machine.  So I think
>   you have 2 choices.
> 
>The precision is significant, in that we must be able to repoduce the original
>data byte for byte. Breaking the VAX R*8 up into an IEEE R*8 + remainder would
>still introduce roundoff error.

I just want to cast a vote that stuffing part of the VAX precision into
the IEEE format (with an auxiliary byte) seems like questionable  style
to me.  It would be much better to split the number up, as someone
suggested, into an exponent and mantissa, then store those as integers.
Extended precision formats you make up yourself from scratch, cleanly,
should be easier to deal with than ``IEEE-plus.''

Perhaps it would be better for user-friendliness to make the exponent

       fix(log10(stuff))    instead of   fix(log2(stuff) + offset)

with the corresponding change in the mantissa.


Robert S. Hill                  
bhill@stars.gsfc.nasa.gov