python rounding problem.

[Florian Diesch]

"Thomas Bartkus" <thomasbartkus at comcast.net> wrote:

> "Grant Edwards" <grante at visi.com> wrote in message
> news:125v9g8q00o1d52 at corp.supernews.com...
>> On 2006-05-08, Thomas Bartkus <thomasbartkus at comcast.net> wrote:
>>
>> >> does python support true rations, which means that 1/3 is a
>> >> true one-third and not 0.333333333 rounded off at some
>> >> arbitrary precision?
>> >
>> > At risk of being boring  ;-)
>> >
>> > - Python supports both rational and irrational numbers as
>> >   floating point numbers the way any language on any digital
>> >   computer does - imprecisely.
>> >
>> > A "true" (1/3) can only be expressed as a fraction.
>>
>> At the risk of being both boring and overly pedantic, that's
>> not true.  In base 3, the value in question is precisely
>> representable in floating point: 0.1
>>
>> > As soon as you express it as a floating point - you are in a
>> > bit of trouble because that's impossible.
>>
>> It's not possible in base 2 or base 10.  It's perfectly
>> possible in base 9 (used by the Nenets of Northern Russia) base
>> 12 (popular on planets where everybody has twelve toes) or base
>> 60 (used by th Sumerians).  [I don't know if any of those
>> peoples used floating point in those bases -- I'm just pointing
>> out that your prejudice towards base 10 notation is showing.]
>>
>> > You can not express (1/3) as a floating point in Python any
>> > more than you can do it with pencil and paper.
>>
>> That's true assuming base 2 in Python and base 10 on paper. The
>> base used by Python is pretty much etched in stone (silicon, to
>> be precise).  There used to be articles about people working on
>> base-3 logic gates, but base-3 logic never made it out of the
>> lab. However, you can pick any base you want when using paper
>> and pencil.
>>
>> > You can be precise and write "1/3" or you can surrender to
>> > arithmetic convenience and settle for the imprecise by writing
>> > "0.333333333", chopping it off at some arbitrary precision.
>>
>> Or you can write  0.1
>>                      3
>>
>> :)
>
> Ahhh!
> But if I need to store the value 1/10 (decimal!), what kind of a precision
> pickle will I then find myself while working in base 3 ?  How much better
> for precision if we just learn our fractions and stick to storing integer
> numerators alongside integer denominators in big 128 bit double registers ?
>
> Even the Nenets might become more computationally precise by such means ;-)
> And how does a human culture come to decide on base 9 arithmetic anyway?

Just guessing: 
 * Use one thumb to point at one of the other 9 fingers
 * Every finger (except for the thumb) has 3 segments (and links), each
   of which can easily divided in three part (upper, middle, lower or left
   middle, right for the links) making 9 points for each finger.


> Even base 60 makes more sense if you like it when a lot of divisions come
> out nice and even.

You can count to 60 using two hands: Use the right thumb to point on
one of the 12 segments of the remaining 4 fingers and on the left hand
one finger for each dozen.


Of course this is wasting resources as you can count to 1023 with your
fingers. I never heard of a culture doing so, though.



   Florian
-- 
<http://www.florian-diesch.de/>