Re: floating point comparison

[jac@ibms48.scri.fsu.edu (Jim Carr)]

Andrew says
 
 <<        Strongly disagree. There ARE roundoff errors even in the IEEE 754
  arithemtic model. Moreover, the standard clearly specifies rounding models.>>
 
dewar@merv.cs.nyu.edu (Robert Dewar) writes:
>
>There are no *errors*, the discrepancies between IEEE arithmetic and
>real arithmetic are not errors, they are simply differences that come from
>two different arithmetic models.

 It could be useful to adopt the terminology of experimental science 
 here, and use "uncertainty" to denote the variance between the 
 results of real arithmetic and floating point arithmetic done 
 'correctly' in a particular model.  The two have much in common, 
 since one propagates those uncertainties in a similar way, and 
 since the confusion associated with calling them "errors" is 
 equally strong.  And both are poorly known.  ;-) 

>When we have integer arithmetic and we divide 10 by 3 to get 3, we do
>not say this is an error. The result is different from the mathematical
>value of 10.0/3.0, but there is no error here, just a different arithmetic 
>model.

 And you _should_ know that 10/3 = 3 could mean 3 +/- 0.5, or it 
 could mean (10 +/- 0.5)/(3 +/- 0.5) depending on the circumstances. 

 Or it could be an _error_ if you are using 10/3 as an exponent when 
 you meant to use 10./3. = 3.33333....

>I know perfectly well that the phrase "rounding error" is well established,
>but my point is that calling it an error leads people into the niave trap
>of thinking of floating-point arithmetic as being real arithmetic.

 So is the phrase "experimental error" in physics and other fields, 
 and it causes similar difficulties.  It is not an error to read a 
 ruler with the maximum possible accuracy.  Similarly, it is not an 
 error to store a floating point approximation with the maximum 
 possible bits, correctly rounded per the floating point model. 

 It _is_ an error to treat those numbers as if they were real numbers. 

-- 
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