Re: floating point comparison

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

dewar@merv.cs.nyu.edu (Robert Dewar) writes:
>
><< So is the process of measurement with a device with less precision
> than necessary to make the measurement.  For example, in your case
> there is no uncertainty in the integer part of a 14 digit real in
> a double precision IEEE representation that has been properly
> rounded, but there is an uncertainty if it was stored as a float.>>
>
>I strongly agree with Christian here, uncertainty is an even WORSE
>term than round off error.

 I wrote the above, not Christian. 

 I prefer uncertainty because, in a university context, it is 
 familiar to students from their chemistry and physics labs and 
 the rules for propagating it are the same.  The tradition in 
 numerical analysis has always (?) been to identify two kinds 
 of "error" -- formula and round-off -- that compete in any 
 given kind of calculation.  Depends on the audience. 

>A common viewpoint of floating-point arithmetic held by many who don't
>know too much about it is that somehow floating-point arithmetic is
>inherently (slightly) unreliable and can't be trusted. The term
>uncertainty encourages this totally unuseful attitude.

 Are you saying that the floating point representation is not 
 an approximation to the real number being stored?  I don't 
 think so.  I think you are saying that the results of floating 
 point operations on numbers in that floating point representation 
 are deterministic.  I agree that they are.  The point is that 
 the difference between the real number being represented in the 
 machine and a particular floating point representation will be 
 propagated by the "exact" procedure and sometimes dramatically 
 increase the difference between the result of real arithmetic 
 on the original real number and the result of floating point 
 arithmetic on the original fl-pt representation. 

 The propagation of this uncertainty also follows deterministic 
 (albeit statistical) rules quite familiar from the sciences 
 in which measurement is commonly used.  I do not see how you 
 can claim that the difference between the result of real 
 arithmetic and floating point arithmetic for a range of input 
 values will not show a distribution of the type normally 
 associated with measurement uncertainty.  It does. 

 In the example cited, the uncertainty in one possible representation 
 (float) is greater than in another (double) with the result that 
 the desired integer conversion is not exact in some cases that 
 original author claimed they would be.  (The example also appeared 
 to ignore the minimum size of int mandated by C and present in 
 many common implementations, but that is irrelevant here.)  This 
 is obvious if one knows the relative uncertainty in those two 
 IEEE representations of real numbers. 

-- 
 James A. Carr   <jac@scri.fsu.edu>     | Commercial e-mail is _NOT_ 
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