Newsgroups: comp.lang.fortran
Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!batcomputer!cornell!uw-beaver!milton!djo7613
From: djo7613@milton.u.washington.edu (Dick O'Connor)
Subject: What is zero, REALly??
Message-ID: <1991Jun11.143915.11722@milton.u.washington.edu>
Summary: Why does zero act like a small number?
Keywords: real numbers, old Fortran, zero comparison
Organization: University of Washington
Distribution: usa
Date: Tue, 11 Jun 1991 14:39:15 GMT

I'm trying to port an old Fortran program written to run on an IBM main-
frame to something a bit smaller.  Part of the "truth test" of the new code
(which is Pascal, but that's neither HNT) is that I have a printout of an
old run of input and output data that I have to be able to regenerate.
Fine except for one set of readings, which end up being a little bit off
in a way that's not DIRECTLY related to rounding.  I believe it's indirectly
related to rounding via The Law Of Small Numbers (a handy catch-all excuse
we use around here!), and I'd like some feedback from people with experience in
how Fortran handles very small numbers.

The routine in question takes the arithmetic mean of N positive real numbers
in the range, say 40.0 to 90.0, and uses subtraction to find the number that
is the furthest away from that mean.  It computes a "difference" from the mean
for each number and determines the greatest difference using the DABS
(double-precision absolute value) function.  The problem case is a
specific case where N equals 2, so both real numbers have the same difference.
The original code acts differently depending on which of the N numbers is
the furthest distant from the mean, and does it in the case N=2 with a
  IF ( DABS(A(1)) - DABS(A(2)) ) 800,900,900
where A is a double precision real array.  In almost every case, the middle
branch is taken, but there's one case in particular where the first branch
is taken, meaning there is a measurable difference between two numbers which
should be identical.

I believe it's a case of reaching the limits to which a binary machine can
express a decimal-based number, with the result that two "identical" numbers
are in fact only "very close", and their subtraction yields a number detectably
different from zero.  Anyone have any experience to corroborate or refute this?
Thanks!!

"Moby" Dick O'Connor                         djo7613@u.washington.edu 
Washington Department of Fisheries           *I brake for salmonids* 

-- 
"Moby" Dick O'Connor                         djo7613@u.washington.edu 
Washington Department of Fisheries           *I brake for salmonids*