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From: Eric Sosman <esosman AT acm DOT org>
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Subject: Re: Cross Platform Incompatabilites? - code fragments
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Date: Fri, 20 Feb 2004 13:45:35 GMT
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Brian Inglis wrote:
> 
> In general, most programmers should not use 32 bit float for
> arithmetic, unless they do careful analysis and coding of algorithms
> to avoid the *SEVERE* loss of precision that can occur in just a
> single operation with unfortunate values.
> 
> A simple example of this would be when you do accumulation in float:
> you need to sort and add up the numbers from smallest to largest
> absolute value to avoid losing the effect of small values totally.

    Alternatively, look up Kahan's summation algorithm.

    It's distressingly simple to demonstrate the effect Brian
mentions.  This tiny program will do it:

	#include <stdio.h>
	int main(void) {
	    float sum, add;
	    for (add = 1.0;  add < 1e24f;  add *= 1024.0f) {
	        sum = 1.0 + add;
	        printf ("1.0 +- %g =? %g\n", add, sum - add);
	    }
	    return 0;
	}

Changing the per-step multiplier from 1024 to 1000 will demonstrate
yet another (perhaps even more distressing) problem with limited-
precision arithmetic.

    Switching from `float' to `double' or to `long double' (on
platforms where that makes a difference) doesn't really "solve"
the problem, but it postpones its onset until the numbers become
even more disparate in their magnitudes.

    Look for the paper "What Every Computer Scientist Should
Know About Floating-Point Arithmetic," which is widely available
on the Web.

-- 
Eric Sosman
esosman AT acm DOT org