From: Lloyd Zusman <ljz@...>
Date: 2004-10-30T16:46:48+09:00
Subject: Re: Rounding error ... [remainder of huge subject line truncated]

Steven Jenkins <steven.jenkins@ieee.org> writes:

> trans. (T. Onoma) wrote:
>> On Saturday 30 October 2004 12:00 am, Hal Fulton wrote:
>> |
>> | [ ... ]
>> |
>> | Given a choice between improved floating point and a mission to Mars,
>> | I'd take the latter.
>> Ha ha! When the spacecraft crashes and burns b/c of an overlooked
>> rounding error, I'll accept your apology ;)
>
> I work in a place that actually sends missions to Mars, and I can assure
> you that floating-point arithmetic is a well-understood phenomenon here.
>
>> [ ... ]
>
> There is nothing you or anyone else can do to make a finite number of
> bits behave like the real number line. Whatever you do to fix things
> up for the utterly unimportant class of rationals whose binary
> expansion repeats in less than 64 bits will come at the expense of
> some other characteristics that genuine experts have agreed is more
> important. Unless you're a world-class numerical analyst, your odds of
> improving on 754 are smaller than roundoff error. Give it a rest.

In addition to being completely in agreement with Mr. Jenkins, I want to
add that in my Introduction to Computer Programming course in 1969, we
were taught about fixed-point and floating-point arithmetic.  We were
required to master these and other numerical concepts before we were
taught any computer language, and we were expected to know the strengths
and weaknesses of the various numerical techniques that are available in
computers.

In other words, the understanding of fixed-point and floating-point
numbers is so basic and fundamental to programming that I believe that
these topics should be mastered before anyone learns to write even one
line of code.

Sadly, it seems that many texts and professors nowadays do not teach
these important concepts, at least not in introductory courses.

I believe that a fuller understanding of the strengths and limitations
of various numerical methods, including floating-point arithmetic, would
have greatly lowered the probability that the "Ha ha! ..."  statement
above would ever have been written.  This also applies to a number of
other assertions that have been made in this thread.


-- 
 Lloyd Zusman
 ljz@asfast.com
 God bless you.