finding out the precision of floats

[Arnaud Delobelle]

On 27 Feb, 14:09, "Bart Ogryczak" <B.Ogryc... at gmail.com> wrote:
> On Feb 27, 1:36 pm, Facundo Batista <facu... at taniquetil.com.ar> wrote:
>
> > Arnaud Delobelle wrote:
> > > (and I don't want the standard Decimal class :)
>
> > Why?
>
> Why should you? It only gives you 28 significant digits, while 64-bit
> float (as in 32-bit version of Python) gives you 53 significant
> digits. Also note, that on x86 FPU uses 80-bit registers. An then
> Decimal executes over 1500 times slower.

Actually 28 significant digits is the default, it can be set to
anything you like.  Moreover 53 significant bits (as this is what 53
counts) is about 16 decimal digits.

> >>> from timeit import Timer
> >>> t1 = Timer('(1.0/3.0)*3.0 - 1.0')
> >>> t2 = Timer('(Decimal(1)/Decimal(3))*Decimal(3)-Decimal(1)',
>
> 'from decimal import Decimal')>>> t2.timeit()/t1.timeit()
>
> 1621.7838879255889

Yes. The internal representation of a Decimal is a tuple of one-digit
strings!
This is one of the reasons (by no means the main) why I decided to
write my own class.

> If that's not enough to forget about Decimal, take a look at this:
>
> >>> (Decimal(1)/Decimal(3))*Decimal(3) == Decimal(1)
> False
> >>> ((1.0/3.0)*3.0) == 1.0
>
> True

OTOH float is not the panacea:

>>> 0.1+0.1+0.1==0.3
False
>>> 3*0.1==0.3
False

Decimals will behave better in this case.

Cheers

--
Arnaud