Path: utzoo!attcan!uunet!cs.utexas.edu!rutgers!mcnc!ecsgate!ecsvax!urjlew
From: urjlew@uncecs.edu (Rostyk Lewyckyj)
Newsgroups: comp.lang.fortran
Subject: Re: Explain this output to me
Summary: appearances can be deceiving.
Message-ID: <1990May27.193758.25099@uncecs.edu>
Date: 27 May 90 19:37:58 GMT
References: <1554@ns-mx.uiowa.edu> <90May23.184629edt.20043@me.utoronto.ca> <1543@charon.cwi.nl>
Organization: UNC Educational Computing Service
Lines: 30



In the original problem the program starts at -.5 and increments
by approximately .1 to approximately .5. The output of the steps
is displayed to 7 places.
Now in all current computers numbers are stored in binary and -.5
is representable exactly. So when -.5 is converted for printing,
it is nicely represented by   -.5000000.  .1 is not representable
exactly in binary. So the machine stores the nearest value to .1
that it can. When this representation of .1 (dx) is added to -.5 (x)
there is some error in the the resulting new x. But when the resulting
x .=. -.4 is converted for printing, it is still within .5e-9 of .4
and so to seven places prints out as -.40000000. What I am saying
is that the error is in there in the stored value of x, but it is
not evident in the displayed output. This same situation occurs
for the next several steps i.e. -.3 -.2 and -.1. But in the next
step the leading digit of the result becomes 0, and we have a massive
loss of significance. Internally the result x is normalized and when
the result is converted for display, we suddenly see all of the
accumulated error displayed  .2....... e -16 . When the next dx is
added the leading figure of the result is again not 0 and the error
is still less than .5 e-9 . So again the error disappears from view
off the right edge of the displayed result.
  
I hope that this description was illuminating and clarifying.
-----------------------------------------------
  Reply-To:  Rostyslaw Jarema Lewyckyj
             urjlew@ecsvax.UUCP ,  urjlew@unc.bitnet
       or    urjlew@uncvm1.acs.unc.edu    (ARPA,SURA,NSF etc. internet)
       tel.  (919)-962-6501