[racket] Decimal rounding problem

But why does 3.225 round differently than 4.225?

I see that this is different:

> (> 3.225 #e3.225)
#t

but I would have thought that the integer part wouldn't affect
anything here since floats have those parts separate? I thought?

Robby

On Thu, Nov 29, 2012 at 8:55 AM, Matthew Flatt <mflatt at cs.utah.edu> wrote:
> At Thu, 29 Nov 2012 14:44:38 +0000, Greg Graham wrote:
>> I am trying to report GPA calculation results to 2 decimal places, so I thought
>> real->decimal-string would do the trick. However, the following behavior
>> surprised me:
>>
>> > (real->decimal-string 3.225 2)
>> "3.23"
>> > (real->decimal-string 4.225 2)
>> "4.22"
>>
>> I would like the second answer to be "4.23", which is what a student would
>> expect to see if they did the calculations themselves. The documentation for
>> real->decimal-string says that it first converts the argument to an exact
>> number. I suspect the problem has something to do with this:
>>
>> > (inexact->exact 4.225)
>> 4 126663739519795/562949953421312
>> > (/ 126663739519795.0 562949953421312.0)
>> 0.22499999999999964
>>
>> Is there another rounding function that would just round the floating point
>> without going through the conversion to exact?
>
> There are a couple of issues here.
>
> First, the inexact number 4.225 is actually slightly smaller than the
> exact value 4.225:
>
>  > (< 4.225 #e4.225)
>  #t
>  > (pretty-print-exact-as-decimal #t)
>  > (inexact->exact 4.225)
>  4.2249999999999996447286321199499070644378662109375
>
> So, that's one reason to argue that "4.22" is the right answer.
>
>
> Even if you use the exact number 4.225, though, you get a "2" as the
> last digit:
>
>  > (real->decimal-string #e4.225 2)
>  "4.22"
>
> That's because rounding in Racket is to "even" --- a different
> convention than the one taught to most students, but one that it often
> preferred in computing (because it often reduces accumulated error, as I
> understand it).
>
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