Strange math behaviour... could someone explain this ?

jbv jbv.silences at Club-Internet.fr
Sun Oct 9 09:16:26 EDT 2005


Mark,

Thanks for your explanations.
I fully understand the reasons why trunc((36-34.2)*100) returns 179.

Nevertheless, I still don't understand why the following :

  get ((36-34.2)*100)
  put it & cr & trunc(it)

returns :
  180
  179

at least javascript is less confusing, since ((36-34.2)*100) returns
179.99999999999971

JB


> Hi JB,
>
> The solution to the issue you have here is to always add a small
> 'epsilon' value to your numbers before truncating.
>
> What is manifesting itself here is the innate approximation methods used
> by floating-point arithmetic, combined with the fact the trunc function
> does not shield you from these (indeed, trunc is there so you can use it
> as a basis for your own rounding methods and shouldn't really be used
> raw).
>
> Any floating-point number should not be considered a single number at
> all, but a *range* of numbers (alternatively, you can view it as a
> single number +/- an error). So:
>   34.2 is actually: 34.2 - <epsilon> to 34.2 + <epsilon>
>   36 is actually: 36 - <epsilon> to 36 + <epsilon>
>
> Therefore, when you get to (36 - 34.2) * 100, what you actually have is
> the range:
>   180 - epsilon to 180 + epsilon
>
> The actual representative stored in the computer can be any number
> within this range, and it just turns out in the case in question, the
> representative is:
>   179.99999999999971578291
>
> All the trunc function does is chop off the fractional part, leaving
> 179.
>
> Therefore, in order to get the 'expected' answer, you need to ensure
> that you correct for maximum deviation *below* an integer that can occur
> before truncating. i.e. You need to add an epsilon value.
>
> As a general rule of thumb, if you require n decimal places of
> precision, you should use an epsilon value of 1e-(n+1).
>
> So, let's say that your calculations need no more precision than 7
> decimal places, then
>   epsilon = 0.00000001
>
> And your code becomes:
>   trunc((36 - 34.2) * 100 + 1e-8)
> Which does, indeed, return 180.
>
> I should point out that this is probably the only instance where you
> would get bitten by this precisely because the trunc function does
> nothing to correct for error in the floating-point approximation as it
> does not know the precision with which the number you passed to it was
> calculated.
>
> Warmest Regards,
>
> Mark.
>
> On Fri, 2005-10-07 at 13:16 +0200, jbv wrote:
> > Hi list,
> >
> > example 1 :
> >
> >   put 1.8 into myA
> >   put trunc(myA * 100) into myA
> >
> >   in that case, myA=180    which is OK
> > ------------------
> >
> > example 2 :
> >
> >   put 34.2 into myA
> >   put 36 into myT
> >
> >   if myA > 0 then
> >     if myA < myT then
> >       get myA
> >       put myT - myA into myA
> >       put it into myT
> >     else
> >       put 0 into myA
> >     end if
> >   end if
> >
> >   put trunc(myA * 100) into myA
> >
> >   in that case, myA=179    ?????????????????????
> >
> >
> > Best,
> > JB
> >
> > _______________________________________________
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>
> ------------------------------------------------------------------
>  Mark Waddingham ~ 36degrees at runrev.com ~ http://www.runrev.com
>        Runtime Revolution ~ User-Centric Development Tools
>
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