🚀 go-pugleaf

A while back I posted concerning the following paper:

    "On Error Analysis in Arithmetic with Varying Relative Precision",
    James W. Demmel (Courant), Proc 8th Symp Comp Arith, 1987, pp. 148-152.

(I incorrectly named the author as Deming, instead of Demmel. My apologies
to both Messrs. Deming and Demmel)

I asked whether the arguments against varying relative precision for
level-index types of arithmetic do not also apply to denormalized numbers
in IEEE floating point.


I have received many answers, both by email and news, of the form "Of
course not - denorms preserve absolute precision on +/-".
    This is true enough.
    But isn't it also true that denorms lose relative precision?

Eg.
    If I compute (x-y)*z
    and x-y produces a denorm,
    then, instead of relative precision related to 1/2^M, 
where there are M bits in the mantissa,
    do you not have relative precision related to 1/2^D, 
where there are D valid bits in the denormalized difference.
    In fact, if you permit denorm-denorm, might you not be reducing
relative accuracy to 1/2 (since you can conceivably have only one significant
denormalized bit)?

    Note that I am not pushing the alternative, which would be to
make (x-y)*z => 0*z => 0, which may have much lower relative precision.
If anything, I was wondering whether the sticky precision register would
be useful.



--
Andy "Krazy" Glew,  Motorola MCD,    	    	    aglew@urbana.mcd.mot.com
1101 E. University, Urbana, IL 61801, USA.          {uunet!,}uiucuxc!udc!aglew
   
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