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: Re: IEEE FP denorms and Deming's Arithmetics With Variable Precision Message-ID: Date: 3 Oct 89 16:34:39 GMT References: <16893@watdragon.waterloo.edu> Sender: aglew@urbana.mcd.mot.com Organization: Work: Motorola MCD, Urbana Design Center; School: University of Illinois at Urbana-Champaign Lines: 42 In-reply-to: ccplumb@rose.waterloo.edu's message of 2 Oct 89 22:41:46 GMT 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 My opinions are my own; I indicate my company only so that the reader may account for any possible bias I may have towards our products.