Path: utzoo!utgpu!news-server.csri.toronto.edu!bonnie.concordia.ca!uunet!mcsun!hp4nl!cwi.nl!dik From: dik@cwi.nl (Dik T. Winter) Newsgroups: comp.arch Subject: Re: IEEE arithmetic (Goldberg paper) Message-ID: <3696@charon.cwi.nl> Date: 14 Jun 91 00:04:38 GMT References: <9106120054.AA19903@ucbvax.Berkeley.EDU> Sender: news@cwi.nl Organization: CWI, Amsterdam Lines: 21 In article khb@chiba.Eng.Sun.COM (Keith Bierman fpgroup) writes: > In article <9106120054.AA19903@ucbvax.Berkeley.EDU> jbs@WATSON.IBM.COM writes: > 3. The real problem with interval arithmetic is not that it's > slow but that on real applications its error estimates are gener- > ally so pessimistic as to be useless. > At last, something we agree on! But I confess that I have not used it > extensively, so I am prepared to believe that it may have utility I am > not personally cognizant of. Interval techniques will have to be > deployed in large quantities before it can be counted out of the > running, IMHO. If we look at what the Karlsruhe people are doing there is no problem with the error estimates from interval arithmetic. To give an example: to solve a system of linear equations, first a standard method is used to approximate a solution. Next, using interval arithmetic (plus dot product with one rounding), in an iterative process the approximate solution is enclosed in a solution interval that is made as small as possible. I have seen from the process where the lower and upper bound of each solution component differed only in a single bit (and those bounds were guaranteed). -- dik t. winter, cwi, amsterdam, nederland dik@cwi.nl