How about adding rational fraction to Python?

[Piet van Oostrum]

>>>>> "Gabriel Genellina" <gagsl-py2 at yahoo.com.ar> (GG) wrote:

>GG> En Tue, 04 Mar 2008 11:46:48 -0200, NickC <ncoghlan at gmail.com> escribió:
>>> A mildly interesting Py3k experiment:
>>> 
>>> Python 3.0a3+ (py3k:61229, Mar  4 2008, 21:38:15)
>>> [GCC 4.1.3 20070929 (prerelease) (Ubuntu 4.1.2-16ubuntu2)] on linux2
>>> Type "help", "copyright", "credits" or "license" for more information.
>>>>>> from fractions import Fraction
>>>>>> from decimal import Decimal
>>>>>> def check_accuracy(num_type, max_val=1000):
>>> ...     wrong = 0
>>> ...     for x in range(1, max_val):
>>> ...         for y in range(1, max_val):
>>> ...             wrong += (x / num_type(y)) * y != x
>>> ...     return wrong
>>> ...
>>>>>> check_accuracy(float)
>>> 101502
>>>>>> check_accuracy(Decimal)
>>> 310013
>>>>>> check_accuracy(Fraction)
>>> 0
>>> 
>>> 
>>> The conclusions I came to based on running that experiment are:
>>> - Decimal actually appears to suffer more rounding problems than float
>>> for rational arithmetic

>GG> Mmm, but I doubt that counting how many times the results are equal, is  
>GG> the right way to evaluate "accuracy".
>GG> A stopped clock shows the right time twice a day; a clock that loses one  
>GG> minute per day shows the right time once every two years. Clearly the  
>GG> stopped clock is much better!

But if the answer is incorrect (in the float calculation) the error is
limited. IEEE 754 prescribes that the error should be at most 1 LSB, IIRC.
And then the number of errors is the proper measure.
-- 
Piet van Oostrum <piet at cs.uu.nl>
URL: http://pietvanoostrum.com [PGP 8DAE142BE17999C4]
Private email: piet at vanoostrum.org