On Wed, 29 May 2013 07:27:40 -0700, Ahmed Abdulshafy wrote:
> On Tuesday, May 28, 2013 3:48:17 PM UTC+2, Steven D'Aprano wrote:
>> On Mon, 27 May 2013 13:11:28 -0700, Ahmed Abdulshafy wrote:
>>
>>
>>
>> > That may be true for integers, but for floats, testing for equality
>> > is
>>
>> > not always precise
>>
>>
>>
>> Incorrect. Testing for equality is always precise, and exact. The
>> problem
>>
>> is not the *equality test*, but that you don't always have the number
>>
>> that you think you have. The problem lies elsewhere, not equality!
>>
>>
>> Steven
>
> Well, this is taken from my python shell>
>
>>>> 0.33455857352426283 == 0.33455857352426282
> True
This is an excellent example of misunderstanding what you are seeing.
Both 0.33455857352426283 and 0.33455857352426282 represent the same
float, so it is hardly a surprise that they compare equal -- they compare
equal because they are equal.
py> a, b = 0.33455857352426283, 0.33455857352426282
py> a.as_integer_ratio()
(6026871468229899, 18014398509481984)
py> b.as_integer_ratio()
(6026871468229899, 18014398509481984)
You've made a common error: neglecting to take into account the finite
precision of floats. Floats are not mathematical "real numbers", with
infinite precision. The error is more obvious if we exaggerate it:
py> 0.3 == 0.300000000000000000000000000000000000000000000000000001
True
Most people who have seen an ordinary four-function calculator will
realise that the issue here is *not* that the equality operator == is
wrongly stating that two unequal numbers are equal, but that just because
you enter 0.300...00001 doesn't mean that all those decimal places are
actually used.
> Anyway, man, those were not my words anyway, most programming books I've
> read state so. Here's an excerpt from the Python book, I'm currently
> reading>
>
> ">>> 0.0, 5.4, -2.5, 8.9e-4
> (0.0, 5.4000000000000004, -2.5, 0.00088999999999999995)
>
>
> The inexactness is not a problem specific to Python—all programming
> languages have this problem with floating-point numbers."
I'm not denying that floats are tricky to use correctly, or that testing
for exact equality is *sometimes* the wrong thing to do:
# Wrong, don't do this!
x = 0.1
while x != 17.3:
print(x)
x += 0.1
I'm just saying that a simple minded comparison with
sys.float_info.epsilon is *also* often wrong.
--
Steven
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