finding out the precision of floats

[Arnaud Delobelle]

On 28 Feb, 11:38, "Bart Ogryczak" <B.Ogryc... at gmail.com> wrote:
> On Feb 27, 7:58 pm, "Arnaud Delobelle" <arno... at googlemail.com> wrote:
> > This is one of the reasons (by no means the main) why I decided to
> > write my own class.
>
> Why not GMP?

I need decimals.

> My point is, that neither is Decimal. It doesn't solve the problem,
> creating additional problem with efficiency.
>
> > >>> 0.1+0.1+0.1==0.3
> > False
> > >>> 3*0.1==0.3
>
> > False
>
> > Decimals will behave better in this case.
>
> Decimal will work fine as long as you deal only with decimal numbers
> and the most basic arithmetic. Any rational number with base that is
> not power of 10, or any irrational number won't have an exact
> representation.

My problem is precisely to represent rational numbers whose
denominator is a power of 10 (aka decimals) accurately.

> So as long as you're dealing with something like
> invoices, Decimal does just fine. When you start real calculations,
> not only scientific, but even financial ones[1], it doesn't do any
> better then binary float, and it's bloody slow.

I'm not doing 'real world' calcultations, I'm making an app to help
teach children maths.  I need numerical values that behave well as
decimals. I also need them to have an arbitrary number of significant
figures. Floats are great but they won't help me with either. Amongst
other things, I need 3.0*0.1==0.3 to be True.

Please do not make the assumption that I have chosen to use a decimal
type without some careful consideration.

--
Arnaud