Re: floating point comparison

[nesterov@holo.ioffe.rssi.ru (Andrew V. Nesterov)]

In article <dewar.871221105@merv>, dewar@merv.cs.nyu.edu (Robert Dewar) wrote:
[snip]
>If we are talking about IEEE floating-point, the operations have no errors
>at all. There are no rounding errors or anything else in the arithemtic
>model defined in this standard.

        Strongly disagree. There ARE roundoff errors even in the IEEE 754
arithemtic model. Moreover, the standard clearly specifies rounding models.

>
>The results of the operations are exactly well defined to the last bit (*)
>and must be the same on all machines.
>
        Could be different due to unspecified length of the register
or extended precision numbers or rounding model chosen.

>
[snip]
>
>I really dislike the term "rounding error". Error is a loaded term which
>somehow indicates that something is wrong. When you take two IEEE numbers
>and do an addition, you get a precise answer, with no error. Perhaps a
>term like "real discrepancy" would be better, and would help avoid
>propagating the dangerous impression that floating-point arithmetic *is*
>real arithmetic that does not work right.

        When two representable (i.e. having no roundoff error) IEEE
numbers are added the result could be rounded, that is true result
cannot be stored as exact IEEE number. Similarly, results of other
operations (multiplications, square roots, etc) could be rounded.

Concidering the term itself, it sounds to me reasonably adequate. As
far as I could see, and since I am not native english I could be wrong, 
the term means "an error result from a roundoff", i.e. a floating point
number is approximate estimate to a precise number. Well, I better
refer to J.Wilkinson books, he used the term many times and thought
nothing is wrong with it.

[snip]

--
Andrew.