Path: utzoo!attcan!uunet!nih-csl!lhc!adm!cmcl2!phri!roy
From: roy@phri.nyu.edu (Roy Smith)
Newsgroups: comp.sys.mac.programmer
Subject: Re: Why can't the Mac add?
Message-ID: <1990Sep27.222809.9210@phri.nyu.edu>
Date: 27 Sep 90 22:28:09 GMT
References: <45060@apple.Apple.COM> <4485@sage.cc.purdue.edu> <26fc2801.6f3@petunia.CalPoly.EDU>
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Organization: Public Health Research Institute, New York City
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rcfische@polyslo.CalPoly.EDU (Ray Fischer) writes:
> Although many floating point numbers ARE exact (0.125 for example), some
> cannot be, which is why testing for equality using floating point numbers
> is always dicey at best.

	It just occurred to me, that although you *should* be able to
represent 0.125 as an exact binary fraction (namely 0b001, where b
represents the binary point), there is no guarantee at all that if you
write the constant 0.125 in a program, the compiler will convert that into
the exact binary floating point constant 0.00100000...

	The process of converting the ascii string "0.125" into a binary
floating constant probably involves evaluating something like:

	1.0/10.0 + 2.0/100.0 + 5.0/1000.0

or maybe:

	(((5.0/10.0 + 2.0)/10.0 + 1.0)/10.0

both of which involve inexact intermediate results.  Somewhat to my
surprise, when I compiled and ran the following on a Sun-3/50 with both
-fsoft and -f68881, and on a 3/160 with -ffpa:

	main ()
	{
		double x, y;

		x = 0.125;
		y = (x * 1000.0) - 125.0;
		if (y == 0.0)
			printf ("Yowza!\n");
		else
			printf ("Cowabunga!\n");
	}

all three printed "Yowza!", but I'm sure you could find machines where that
wasn't true.
--
Roy Smith, Public Health Research Institute
455 First Avenue, New York, NY 10016
roy@alanine.phri.nyu.edu -OR- {att,cmcl2,rutgers,hombre}!phri!roy
"Arcane?  Did you say arcane?  It wouldn't be Unix if it wasn't arcane!"