Re: demonic problem descriptions

From: Cameron MacKinnon (cmackin+nn_at_clearspot.net)
Date: 02/06/05 

Date: Sun, 06 Feb 2005 14:59:24 -0500

Christophe Rhodes wrote:
> If there is an exact number which, for some reason or other, is going
> to be used in a computer calculation as a floating point number,
> then the act of reading it in will introduce a source of error (to be
> accounted for along with all the other sources of error in the
> experiment). It's not the disaster that people in this thread seem
> to be thinking it is, as long as the error is quantified and verified
> to be small in comparison with other sources of error, which it
> often -- though of course not always -- is.

It's not even USUALLY a disaster in common practice (which is to say,
when no error analysis is done). The most insidious thing about floating
point is that it can be abused horribly and still give good results
99.99% of the time. And so, of course, most everyone abuses it horribly.
Occasionally there's a disaster. One can google for "floating
point"+disaster. Patriot missile malfunction kills 28, anyone?

> No "event" led to my education in these matters, unless you count my
> being born. Maybe I had the good fortune to be in an environment
> where knowledge was prized rather than dismissed or viewed simply as
> a means to a paycheque. (I'm not a computer scientist by training;
> while I was studying Physics, those who were learning Computer
> Science learnt about floating point representations and Numerical
> Analysis as part of their degree, and this hasn't changed.)

Your alma mater's CS department seems exceptional in that regard. When I
learned about FP it was done in software (on all the equipment available
to me) and implementing one's own fixed point representation to meet
given speed and accuracy targets wasn't unusual. This naturally led to
more awareness about the costs and benefits of floating point.

>> It seems to me that you're already admitting that your computer
>> doesn't interpret your 0.1111 in the same way as the people in your
>> field do. Do your programs take steps to interpret 0.1111
>> differently from the way Common Lisp normally would? Or do they
>> just do the wrong thing (according to your community's conventions)
>> and produce questionable output whose error is not quantified?
>
>
> If I'm reporting a scientific result, of course I take the care to
> compute an error estimate. Not to do such would not only be
> irresponsible, it would result in my work not being published, or if
> published it would either be ignored or be rebutted.

Well, you have a better understanding of the representation than the
vast majority of computer users. I hope that you're never burned by a
calculation you make whose error estimate (which you won't compute,
because the work isn't for publication, or is only a "back of the
envelope" calculation) ends up far higher than thought, spoiling your
answers undetected. I wish more coders (or their tools) were as
conscientious as you are.