[Numpy-discussion] problem with float64's str()

[Bruce Southey]

Hi,
Note that at least under Python 2.5.1:
 >>> a=0.0012
 >>> a
0.0011999999999999999
 >>> str(a)
'0.0012'
 >>> repr(a)
'0.0011999999999999999'

 From Python docs, repr(): 'Return a string containing a printable 
representation of an object' and str(): 'Return a nice string 
representation of the object'. In this case the object is a Python 
float  that approximates the base 10 number  of 0.0012.  This is not 
equivalent to convert the base 10 number 0.0012 to a string because 
computer numbers are base 2. Thus, repr() converts a Python object into 
a string but nothing about the numerical precision whereas str() tries 
to do something about maing a 'nice string'.

The only consistent way to get 0.0012 (or any number that can not be 
represented exactly) is to use a Python object that stores 0.0012 
exactly. For example, the Decimal module was introduced in Python 2.4:
http://www.python.org/doc/2.5/lib/module-decimal.html

 >>> str(Decimal('0.0012'))
'0.0012'
 >>> float(Decimal('0.0012'))
0.0011999999999999999

Also, see PEP 3141 'A Type Hierarchy for Numbers' 
(http://www.python.org/dev/peps/pep-3141/).

Regards
Bruce


Dag Sverre Seljebotn wrote:
> Bruce Southey wrote:
>   
>> Hi,
>> This topic has come up many times and the only problem is the lack of 
>> understanding how computers store numbers and computer numerical precision.
>>
>> The NumPy output is consistent with Python on my x86_64 linux system 
>> with Python 2.5.1:
>>  >>> a=0.0012
>>  >>> a
>> 0.0011999999999999999
>>   
>>     
> Wasn't this discussion about the repr vs. str functions?
>
>  >>> repr(0.0012)
> '0.0011999999999999999'
>  >>> str(0.0012)
> '0.0012'
>
>
>
> Dag Sverre
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