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From: winalski@psw.DEC.COM (Paul S. Winalski)
Newsgroups: comp.os.vms
Subject: Re: Bafflement (or, when 33554432 + 1 = 33554432)
Message-ID: <8709192154.AA26147@decwrl.dec.com>
Date: Sat, 19-Sep-87 20:40:00 EDT
Article-I.D.: decwrl.8709192154.AA26147
Posted: Sat Sep 19 20:40:00 1987
Date-Received: Sun, 20-Sep-87 21:30:14 EDT
Sender: daemon@ucbvax.BERKELEY.EDU
Organization: The ARPA Internet
Lines: 22

You are being bitten by the precision limit for single-precision floating point
(the VAX F-float data type).  A FORTRAN variable declared simply REAL will
be REAL*4, which VAX FORTRAN implements as F-floating.  An F-floating number
can have a very wide exponent range, but the mantissa only has six or so
decimal digits of precision.  Thus, when you say:

	a = 33554432

the resulting value of A will be 3.35544E+7, more or less.  If you try adding
1.0 to this value, it winds up being a no-op because, when the two numbers
are scaled for the addition, the 1.0 just falls off the end of the available
precision.  If you keep trying to add larger and larger values, eventually you
hit one that is large enough to not scale off the low mantissa bit, and you
will actually increment the number.  In your case, this occurred at 4.

The solution is to use double precision (D-float or G-float), which gives you
15 decimal digits of precision.

Of course, the same problem occurs in Pascal because Pascal's single precision
also uses F-float.

--PSW