Am 18.11.2010 17:27, schrieb Daniel Fetchinson:
I do a recursive evaluation of an expression involving fractions and unsurprisingly the numerator and denominator grows pretty quickly. After 10-20 iterations the number of digits in the numerator and denominator (as integers) reaches 80-100. And I'm wondering until what point I can trust the result since I'm using fractions.Fraction for the whole procedure. Are Fraction's infinite precision? Or will I get some sort of an exception if python is not able to represent the numerator and/or denominator as integers?http://www.python.org/dev/peps/pep-3141/ was not very helpful in this regard nor was http://docs.python.org/library/fractions.html Any ideas? Cheers, Daniel
I'm not sure what you really want to know. Fractions are, by their math definition, of unlimited precision.For example, PI/2 is accurate (with endless precision as PI is a trancendent number),
but 3.1415926/2 (the decimal representation) is not. So is fraction.Fraction(1,3) of unlimited precision, thus giving this: from fractions import Fraction >>> one_tenth=Fraction(1,10) >>> a = one_tenth+one_tenth >>> a Fraction(1, 5) >>> a = one_tenth+one_tenth+one_tenth >>> a Fraction(3, 10) now compare to standard floats: >>> one_tenth=1.0/10 >>> a = one_tenth+one_tenth >>> a 0.2 >>> a = one_tenth+one_tenth+one_tenth >>> a 0.30000000000000004(this error is caused by the internal representation of floats as binary numbers, see No. 14 in Python tut).
I think you really want to know, how large numerator/denominator can be.As python has bignum support (type=long), the only limit is the one your virtual memory system
offers, which is almost always approx. the amount of ram.
If you need it really *precise*, cast your Fractions into type Decimal:
>>> from decimal import Decimal
>>> one_tenth=Fraction(1,10)
>>> three_tenth = one_tenth*3
>>> d = Decimal(three_tenth.numerator)/Decimal(three_tenth.denominator)
>>> d
Decimal('0.3')
The operator '/' (__div__) is properly over-written.
You can even tweak the precision getcontext().prec by setting it to a
higher value.
Cheers
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