[plt-scheme] ProfessorJ, ==, and double

Don Blaheta <dblaheta at knox.edu> writes:

>   For list-related administrative tasks:
>   http://list.cs.brown.edu/mailman/listinfo/plt-scheme
>
> Quoth Carl Eastlund:
>> The == operator doesn't operate on type double in ProfessorJ: Beginner
>> in DrScheme v209.  It works fine in ProfessorJ: Advanced, but we've
>> needed it in our earliest examples in the HtDCH class.  We can work
>> around it with new Double(x).equals(new Double(y)), but yuck.  Is
>> there any reason for this being left out of the Beginner level?
>
> Because floating point numbers shouldn't be tested for equality, due to
> numeric error.  Consider:
>
>   > double x = (1.0 / 6) * 10000;
>   > double y = 10000.0 / 6;
>   > x
>   1666.6666666666665
>   > y
>   1666.6666666666667

I understand the rationale here, but I disagree with the phrasing, and
perhaps the conclusion.  In floating point, equality comparison is
never a source of error.  In the example above, the division and
multiplication operations are the sources of error because the
mathematically correct results are not representable.

It seems a little odd to cite rounding errors as the rationale for
avoiding equality testing when 
   a) operations that cause rounding errors aren't discouraged
   b) equality testing is one of the few operations that don't round