cpython list __str__ method for floats

[Duncan Booth]

Bjoern Schliessmann <usenet-mail-0306.20.chr0n0ss at spamgourmet.com> 
wrote:

>> The idea that 13.3 is a 'rounded' value for the number,
>> and that 13.300000000000001 is not a 'rounded' value of
>> the number, is a common error of intuitive mathematics.
> 
> I'm intrigued how /you/'d explain this, please do explain.

I think he is correct here: 13.300000000000001 is not exactly 
representable in IEEE 754. It is a rounded approximation to the true 
value just as is 13.3.

An argument can be made that instead of rounding the internal value to 
17 digits which is sufficient to ensure that you can roundtrip float->
string->float for all values, you could just round it to the minimum 
number of digits which guarantee the float->string->float roundtrip for 
that particular value.

Consider this as we gradually lose the more significant digits we see 
that last digit wasn't exactly 1 at all:

>>> 13.3
13.300000000000001
>>> 13.3-13
0.30000000000000071
>>> (13.3-13)*10-3
7.1054273576010019e-015

but why shouldn't Python do this instead?:

>>> 13.3
13.3
>>> 13.3-13
0.3
>>> (13.3-13)*10-3
7.1054273576e-015

These values will still roundtrip to the exact same internal 
representations. BTW, I didn't have to work too hard to figure out what 
that last value should be, the first is cut/paste from CPython, the 
second is what IronPython gives you.

I believe the claim is that using the full 17 digits ensures the round-
tripping works even if you serialise and deserialise on different 
systems, so perhaps we all pay a cost in our interactive sessions for 
something which should really be buried deep in IPC code.