[Gambas-user] Best ways to format float values

[Gianluigi]

Great Tobias,

You are a good teacher and I am honored to have your attention.
OK I understand, never more extravagant mathematics.
Thank you very much for your explanations

Regards
Gianluigi

P.S. You will not believe it but some tests with Floor and Ceil I did :-(

2017-07-13 20:00 GMT+02:00 Tobias Boege <taboege at ...626...>:

> On Thu, 13 Jul 2017, Gianluigi wrote:
> > I would not be misunderstood.
> > I had understood that Alex wanted a forced increase "Round".
> >
> > To recap:
> >
> >   Dim n As Float = 26.6601666666666
> >   Dim b As Byte
> >
> >   Print Int(n * 100) / 100              ' Normal truncate, as already
> > mentioned by other
> >   Print Round(n, -2)                    ' Normal round, as already
> > mentioned by other
> >   If Len(CStr(Frac(n))) > 4 Then
> >     b = Val(Mid(CStr(Frac(n)), 5, 1))
> >     If b >= 5 Then
> >       Print Round(n, -2)
> >     Else
> >       Print Round(n + 0.01, -2)         ' Forced increase round, as
> > proposed by me
> >     Endif
> >   Endif
> >
>
> I would avoid arithmetic operations involving even more floats, such as you
> proposed. Consider this:
>
>   $ gbx3 -e 'Round(0.80999999950+0.1,-9)'
>   0.909999999
>   $ gbx3 -e 'Round(0.80999999951+0.1,-9)'
>   0.91
>
> I only changed the very last digit (of order 10^-11) from 0 to 1 which
> shouldn't influence the rouding to 9 decimals at all -- but it does!
>
> The problem here is, famously, that the decimal 0.1 has no finite binary
> representation, so *storing* the value that is represented in decimal by
> the string "0.1" in a binary float already gives you an unavoidable error.
> Whenever you use 0.1 in your program, this error propagates. Specifically,
> the error when storing 0.1 in a Single is about 1.49*10^-9, which is how
> I arrived at that example above.
>
> Of course, the same applies to the 0.01 you use above. You can think
> by yourself about a similar example where float addition with 0.01 makes
> the result of a later rounding unreliable.
>
> The other method
>
>   Floor(n*100)/100  ' round down to two decimals
>   Ceil(n*100)/100   ' round up to two decimals
>
> is reliable, since the *integer* 100 can be stored without error in a
> float and IEEE754 requires the outcome of float arithmetic to be the
> same as if the operation was performed exactly and then rounded to the
> limited precision of the float datatype [1].
>
> Regards,
> Tobi
>
> [1] http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html#865
>
> --
> "There's an old saying: Don't change anything... ever!" -- Mr. Monk
>
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