python rounding problem.
Grant Edwards
grante at visi.com
Mon May 8 23:35:40 CEST 2006
On 2006-05-08, Thomas Bartkus <thomasbartkus at comcast.net> wrote:
>> 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?
Then we're right back where we started. No matter what base
you choose, any fixed length floating-point representation can
only represent 0% of all rational numbers.
So, clearly what we need are floating point objects with
configurable bases -- bases that automatically adjust to
maintain exact representation of calculation results. Which
probably exactly the same as just storing rational numbers as
numerator,denominator tuples as you suggest.
> 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?
I've no clue, whatsoever. I just stumbled across that factoid
when I used Wikipedia to look up which civilizations used
base-60. For some reason I can never remember whether it was
one of the mesoamerican ones or one of the mesopotamian ones.
> Even base 60 makes more sense if you like it when a lot of
> divisions come out nice and even.
Did they actually have 60 unique number symbols and use
place-weighting in a manner similar to the arabic/indian system
we use?
> Do the Nenets amputate the left pinky as a rite of adulthood
> ;-)
Nah, winters up there are so friggin' cold that nobody ever has
more than nine digits by the time they reach adulthood.
--
Grant Edwards grante Yow! Hello. Just walk
at along and try NOT to think
visi.com about your INTESTINES being
almost FORTY YARDS LONG!!
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