# [Pharo-dev] float & fraction equality bug

Andres Valloud avalloud at smalltalk.comcastbiz.net
Thu Nov 9 14:07:29 EST 2017

```Because by definition, a floating point value is of the form

+/- 2^e * m

for some 0 <= m < M, and e in some range of values (some positive, some
negative).  There are other special cases that don't matter here, such
as NaN, INF, denormals, etc.

So now set up the equality you want.  Since it's positive we can skip
the sign.  Hence,

2^e * m = 1/10

Or, rather,

10 * 2^e * m = 1

The Fundamental Theorem of Arithmetic shows this is impossible.

Andres.

On 11/9/17 6:48 , Tudor Girba wrote:
> Hi,
>
> Thanks for the answer. The example I provided was for convenience.
>
> I still do not understand why it is wrong to expect 0.1 = (1/10) to be true.
>
> Doru
>
>
>> On Nov 9, 2017, at 3:36 PM, Nicolas Cellier <nicolas.cellier.aka.nice at gmail.com> wrote:
>>
>> Nope, not a bug.
>>
>> If you use Float, then you have to know that (x -y) isZero and (x = y) are two different things.
>> Example; Float infinity
>>
>> In your case you want to protect against (x-y) isZero, so just do that.
>>
>> 2017-11-09 15:15 GMT+01:00 Tudor Girba <tudor at tudorgirba.com>:
>> Hi,
>>
>> I just stumbled across this bug related to the equality between fraction and float:
>> https://pharo.fogbugz.com/f/cases/20488/x-y-iff-x-y-0-is-not-preserved-in-Pharo
>>
>> In essence, the problem can be seen that by doing this, you get a ZeroDivide:
>> x := 0.1.
>> y := (1/10).
>> x = y ifFalse: [ 1 / (x - y) ]
>>
>> The issue seems to come from the Float being turned to a Fraction, rather than the Fraction being turned into a Float:
>>
>> 	"If I am involved in comparison with a Float, convert rcvr to a
>> 	Fraction. This way, no bit is lost and comparison is exact."
>>
>> 	rcvr isFinite
>> 		ifFalse: [
>> 			selector == #= ifTrue: [^false].
>> 			selector == #~= ifTrue: [^true].
>> 			rcvr isNaN ifTrue: [^ false].
>> 			(selector = #< or: [selector = #'<='])
>> 				ifTrue: [^ rcvr positive not].
>> 			(selector = #> or: [selector = #'>='])
>> 				ifTrue: [^ rcvr positive].
>> 			^self error: 'unknow comparison selector'].
>>
>> 	^ rcvr asTrueFraction perform: selector with: self
>>
>> Even if the comment says that the comparison is exact, to me this is a bug because it seems to fail doing that. What do you think?
>>
>> Cheers,
>> Doru
>>
>>
>> --
>> www.tudorgirba.com
>> www.feenk.com
>>
>> "Problem solving should be focused on describing
>> the problem in a way that makes the solution obvious."
>>
>>
>>
>>
>>
>>
>
> --
> www.tudorgirba.com
> www.feenk.com
>
> "We are all great at making mistakes."
>
>
>
>
>
>
>
>
>
> .
>

```