Re: floating point comparison

[dewar@merv.cs.nyu.edu (Robert Dewar)]

<<<<You're using the wrong definition of 'error'. Webster gives:

error

 4 a : the difference between an observed or calculated value and a true
value; specifically : variation in measurements, calculations, or
   observations of a quantity due to mistakes or to uncontrollable factors
---

This explains the use of the term 'error' in numerical analysis and
gives that round-off error can be defined as the difference between
the calculated value and the true mathematical value.>>



It is especially difficult for non-native speakers of a language to
accurately understand the connotation of words, as opposted to the
denotation. Dictionaries tend to concentrate only on the denotation,
especially if you just quote the definition -- you can sometimes get
a better feel for the connotation by looking through the references in
a comprehensive dictionary (really the only one for the English language
is the full edition of the OED).

The problem with the word error is that, while of course everyone knows
its denotation (certainly you don't have to go to a dictionary for that),
all native speakers of English also very much no its connotation, which
is bad, horrible, something-to-avoid, evil, unacceptable ... i.e. uniformly
negative (for a feeling of this connotation have a look at the use of the
word error by Mary Baker Eddy, who essentially uses it as a synonym for
what other religeons call sin -- now to be fair it is not as negative as
sin, and that was MBE's reason for arguing for using the word error instead,
but it most assuredly is something to avoid).

Of course the phrase "roundoff error" is denotationally appropriate, and
is not about to mislead people who understand FPT semantics and numerical
analysis.

But as this whole thread has made clear, there are a lot of people who
(a) want to use fpt, and (b) meet neither of these criteria.

FOr such people, the use of the word error is in practice damaging because
it suggests there is something wrong with floating-point, and it leads to
superstitious mumbo-jumbo like always use Float'Epsilon when comparing
any two floating-point quantities, to avoid the dreaded ERROR!

As I have repeatedly said, I do not seriously suggest the entire community
change its terminology, that is of course impossible, but I am suggesting
that by concentrating on the effect of this word, and suggesting that a
more neutral word like discrepancy would have been better (note that your
dictionary definition would apply almost unchanged to disccrepancy), we might
avoid some of this superstition!

Please understand that my point here is not technical. I perfectly well
understand how fpt works, and have written large numerical codes, properly
and carefully analyzed with respect to "error" propagation that are still
in wide use. My point is entirely about trying to get people to understand
that the use and implementation of floating-point is well defined in 
computer systems, and does not involve "error" in the informal connotative
sense.