max / min / smallest float value on Python 2.5
Steve Holden
steve at holdenweb.com
Sun Feb 7 14:19:51 CET 2010
duncan smith wrote:
> Christian Heimes wrote:
>> duncan smith wrote:
>>> Hello,
>>> I'm trying to find a clean and reliable way of uncovering
>>> information about 'extremal' values for floats on versions of Python
>>> earlier than 2.6 (just 2.5 actually). I don't want to add a
>>> dependence on 3rd party modules just for this purpose. e.g. For the
>>> smallest positive float I'm using,
>>>
>>>
>>> import platform
>>> if platform.architecture()[0].startswith('64'):
>>> TINY = 2.2250738585072014e-308
>>> else:
>>> TINY = 1.1754943508222875e-38
>>>
>>>
>>> where I've extracted the values for TINY from numpy in IDLE,
>>>
>>>
>>> >>> float(numpy.finfo(numpy.float32).tiny)
>>> 1.1754943508222875e-38
>>> >>> float(numpy.finfo(numpy.float64).tiny)
>>> 2.2250738585072014e-308
>>
>> You are confusing a 32 / 64bit build with 32 / 64bit floats. Python's
>> float type is build upon C's double precision float type on both 32 and
>> 64 bit builds. The simple precision 32bit float type isn't used. The
>> DBL_MIN and DBL_MAX values are equal on all platforms that have full
>> IEEE 754 float point support. The radix may be different, though.
>>
>> Christian
>
> OK, this is the sort of confusion I suspected. I wasn't thinking
> straight. The precise issue is that I'm supplying a default value of
> 2.2250738585072014e-308 for a parameter (finishing temperature for a
> simulated annealing algorithm) in an application. I develop on
> Ubuntu64, but (I am told) it's too small a value when run on a Win32
> server. I assume it's being interpreted as zero and raising an
> exception. Thanks.
>
Whether this is relevant or not I can't say, but you must be careful to
note that the smallest representable floating-point value (i.e. the
smallest number distinguishable from zero) is not the same as the
smallest difference between two numbers of a given magnitude.
Consider a decimal floating-point system with a two-digit exponent and a
four-digit mantissa, and for convenience ignore negative mantissas. The
range of representable non-zero values runs from 1E-99 to 9999E99. But
adding 1E-99 to (say) 1 will just give you 1 because the system has
insufficient precision to represent the true result.
regards
Steve
--
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