Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!ncar!asuvax!mcdphx!udc!chant!aglew
From: aglew@urbana.mcd.mot.com (Andy-Krazy-Glew)
Newsgroups: comp.arch
Subject: IEEE FP denorms and Deming's Arithmetics With Variable Precision
Message-ID: 
Date: 29 Sep 89 17:50:55 GMT
Sender: aglew@urbana.mcd.mot.com
Organization: Work: Motorola MCD, Urbana Design Center; School: University of Illinois at Urbana-Champaign
Lines: 43

(Is this a good place for computer arithmetic questions?)

I just read a paper by Deming in the 8th Computer Arithmetic
Symposium, which basically deflates some of the proposed alternate
arithmetics, such as level index (where a floating point number
consists of three fields: pointer, exponent, and mantissa, and the
pointer indicates how many bits are "borrowed" from the mantissa to
expand the exponent and prevent overflow or underflow) or what I call
the meta-exponential form, where a number is expressed as
exp(exp(...(exp(m)))), and you store the number of exponentiations
necessary to bring the value m within the desired range.
    Level index basically has a much larger range than normal FP,
so overflow more rarely, while the meta-exponential form can be
shown to be closed under +-*/ for a given number of bits in the
representation.
    IE. both of these representations trade range for reduced
relative precision at the extrema of the range.

Deming shows how this tradeoff moves the complexity of coding
reliable numerical software from avoiding overflow, to handling
roundoff.  
    IE. reduced precision makes rounding error analysis more
complicated.

QUESTION:
    Don't the same arguments apply to IEEE Floating Point with
denormalized numbers?  Ie. don't denormalized numbers complicate
roundoff error analysis in the same way reduced precision complicates
the other arithmetics?

Deming suggests a sticky register which tracks the least relative
precision ever used in the calculation of intermediate results, which
will give you worst-case rounding error.
    Would such a register be worthwhile tracking the most extremely
denormalized IEEE FP number encountered?
    Does anyone do this sort of thing?

--
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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