Re: floating point comparison

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

dewar@merv.cs.nyu.edu (Robert Dewar) writes:
>
> There is no uncertaintly in the results of IEEE operations.

 The term "rounding error" and the alternative "rounding uncertainty" 
 both refer to the fact that the precise and deterministic result of 
 the conversion of a real number to a floating point value gives 
 a bit pattern that *also* results from the precise and deterministic 
 conversion of an uncountably infinite number of other real numbers. 

 It implies no prejudice concerning whether this is good or bad, 
 because it is inevitable.  That is what it has in common with 
 random (not systematic) measurement uncertainties, besides the 
 fact that students are familiar with the latter and propagation 
 of those uncertainties, that arise from the intrinsic limitations 
 in the precision of measurement apparatus -- which is why I have 
 found it to be a helpful alternative, a synonym as it were, when 
 introducing the concept to non-math-major (usually CS) students.  

 The difference is inevitable.  It does exist.  It has important 
 consequences when interpreting the result of a calculation that 
 is being used as a substitute for working with real numbers, a 
 major reason computers exist.  If you do not like the name, 
 propose another -- but do not pretend that it does not happen. 

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