Path: utzoo!attcan!uunet!munnari.oz.au!goanna!ok
From: ok@goanna.cs.rmit.oz.au (Richard A. O'Keefe)
Newsgroups: comp.lang.c
Subject: Re: floating point multiplication BUG in C (cc compiler)
Summary: not a bug in C, a misconception about floating point
Keywords: bug in C float multiplication
Message-ID: <4032@goanna.cs.rmit.oz.au>
Date: 22 Oct 90 01:19:42 GMT
References: <1348@banach.ACA.MCC.COM>
Organization: Comp Sci, RMIT, Melbourne, Australia
Lines: 36

In article <1348@banach.ACA.MCC.COM>, mishra@banach.ACA.MCC.COM (Aditya Mishra) writes:
> BUG !!!   BUG !!!   BUG !!!
> THIS PROGRAM DEMONSTRATES WHAT I BELIEVE IS A BUG IN FLOATING POINT
> MULTIPLICATION IN 'C' !! 

Please take the trouble to learn something about floating point arithmetic
before screaming to the world that the sky is falling.

> (1)   In the program, if float f = ... 0.64, 0.32, 0.16, 0.08, 0.04, 0.02, 
> 	0.01, 0.005, 0.0025, ..., etc (see the pattern?), the value 
> 	of i1 was one less than what it should be. 
[where i1 is calculated as
	float f = /* as above */;
	float factor = 10000.0;
	int i1 = factor * f;
]

The problem here is that a number like 0.64 *CANNOT* *POSSIBLY* be
represented exactly in (finite-precision) floating-point.  At all.
In *any* programming language.  Any compiler, any string->fp converter,
is going to have to round nearly every number there is (only numbers
which are an integer times a power of 2 are likely to be exact); some
of them will round up and some of them will round down.  If it rounds
down, i1 will be 1 less than you expected.  If it rounds up, because
floating pointer->integer conversion truncates towards zero, the error
will be zapped away by the conversion.

2nd year CS students here know about this...

One of the things I really like about C is that unlike Fortran and
Pascal, it doesn't lie to the user.  It doesn't make a false claim
to support "real" arithmetic.  It honestly and openly admits to
'float'.  Believe it:  what you get is floating-point, not real.

-- 
Fear most of all to be in error.	-- Kierkegaard, quoting Socrates.