Re: Precision of floating point multiply

From: G.F. Thomas (gfthomas_at_sympatico.ca)
Date: 10/01/03 

Date: Wed, 1 Oct 2003 13:29:26 -0400

"Brooks Moses" <bmoses-usenet@cits1.stanford.edu> wrote in message
news:3F7747E8.A97E8C67@cits1.stanford.edu...
[...]
> Ken Plotkin wrote:
> > On Sun, 28 Sep 2003 11:37:49 -0700, Brooks Moses
> > <bmoses-usenet@cits1.stanford.edu> wrote:
> > >This is not the meaning of "significant digits" that I'm familiar
with,
> > >and which has been used in all of my engineering classes....
> > >"Significant digits" means the number of digits of meaningful
> > >information (i.e., information that corresponds to reality) that
the
> > >result contains.
> > [snip]
> >
> > Counting the decimal digits isn't necessarily a measure of
precision.
> > Consider 1.001 vs .999. One is four digits, while one is three.
>
> Indeed; thus the common habit of not counting a leading 1 as a
> significant digit, so they're both at three significant digits. Of
> course, this only shifts the problem off to 2.001 vs. 1.999, so it's
not
> much of a solution!
>
> > Throw in issues of significant figures vs number of decimal
places,
> > addition/subtraction vs multiplication vs division, multiple steps
in
> > a complex algorithm, etc., and Gordon's point about error analysis
> > becomes very valuable.
>
> Oh, indeed. I was mainly complaining about the (in my opinion
> incorrect) use of "significant digits" in his explanation, and
> particularly the misuse of counting four of them in 0.0242. I agree
> that the point itself was quite valuable, and I probably should have
> said so more explicitly.
>
> - Brooks

Look into the important role of 'guard digits' in fp arithmetic. 

-- 
Ciao,
Gerry T.
______
"Competent engineers rightly distrust all numerical computations and
seek corroboration from alternative numerical methods, from scale
models, from prototypes, from experience... ."  W.V. Kahan.

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