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From: francis@arthur.uchicago.edu (Francis Stracke)
Newsgroups: comp.sys.mac.programmer
Subject: Re: Why can't the Mac add?
Message-ID: <1990Sep26.221434.16812@midway.uchicago.edu>
Date: 26 Sep 90 22:14:34 GMT
References: <45060@apple.Apple.COM> <4485@sage.cc.purdue.edu>
Sender: news@midway.uchicago.edu (News Administrator)
Organization: Mathematics Department, University of Chicago
Lines: 24

In article <4485@sage.cc.purdue.edu> ar4@sage.cc.purdue.edu (Piper Keairnes) writes:
>In <45060@apple.Apple.COM> das@Apple.COM (David Shayer) writes:
>
>>I was running this simple program.
>
>>main ()
>>{
>>	float	x; 
>>	
>>	for (x=0.0;x!=10.0;x+=0.2)
>>		printf ("x=%f \n",x);
>>}
>
>That isn't that simple of a program when dealing with floating point
>numbers. There is no such thing as an EXACT floating point number. Floating
>point numbers are close approximations to real numbers.

The problem is that, in binary, 0.2 is 0.001100110011... (repeating
0011 forever, in case you can't guess--in base 10 we'd call it a repeating
decimal.)  Think of what happens if you try to add 1/3 in base 10 with
small precision:
0.3333, 0.6666, 0.9999, 1.3332, 1.6665, 1.9998 
And so on.  If you ever want to do fractions on a computer, do them as
fractions, not as reals.  (SANE has the Fixed type, doesn't it?)