Menu
What are its smallest and biggest values in python?
293
The Python range() works only with integers. It doesn't support the float type, i.e., we cannot use floating-point/decimal value in any of its arguments.
Since the high-order bit of the mantissa is always 1, it is not stored in the number. This representation gives a range of approximately 3.4E-38 to 3.4E+38 for type float.
We found out the maximum value that a float variable can hold with the sys. float_info. max in the code above. The output shows that the upper limit of a float variable is 1.7976931348623157e+308.
Python float values are represented as 64-bit double-precision values. 1.8 X 10308 is an approximate maximum value for any floating-point number. If it exceeds or exceeds the max value, Python returns an error with string inf (infinity).
>>> import sys
>>> sys.float_info
sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308,
min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15,
mant_dig=53, epsilon=2.2204460492503131e-16, radix=2, rounds=1)
The smallest is sys.float_info.min (2.2250738585072014e-308) and the biggest is sys.float_info.max (1.7976931348623157e+308). See documentation for other properties.
sys.float_info.min is the normalized min. You can usually get the denormalized min as sys.float_info.min * sys.float_info.epsilon. Note that such numbers are represented with a loss of precision. As expected, the denormalized min is less than the normalized min.
146
See this post.
Relevant parts of the post:
In [2]: import kinds In [3]: kinds.default_float_kind.M kinds.default_float_kind.MAX kinds.default_float_kind.MIN kinds.default_float_kind.MAX_10_EXP kinds.default_float_kind.MIN_10_EXP kinds.default_float_kind.MAX_EXP kinds.default_float_kind.MIN_EXP In [3]: kinds.default_float_kind.MIN Out[3]: 2.2250738585072014e-308
33
As a kind of theoretical complement to the previous answers, I would like to mention that the "magic" value ±308 comes directly from the binary representation of floats. Double precision floats are of the form ±c*2**q with a "small" fractional value c (~1), and q an integer written with 11 binary digits (including 1 bit for its sign). The fact that 2**(2**10-1) has 308 (decimal) digits explains the appearance of 10**±308 in the extreme float values.
Calculation in Python:
>>> print len(repr(2**(2**10-1)).rstrip('L'))
308
Python uses double-precision floats, which can hold values from about 10 to the -308 to 10 to the 308 power.
http://en.wikipedia.org/wiki/Double_precision_floating-point_format
Try this experiment from the Python prompt:
>>> 1e308
1e+308
>>> 1e309
inf
10 to the 309 power is an overflow, but 10 to the 308 is not. QED.
Actually, you can probably get numbers smaller than 1e-308 via denormals, but there is a significant performance hit to this. I found that Python is able to handle 1e-324 but underflows on 1e-325 and returns 0.0 as the value.
7
Technically speaking, the smallest float is -inf and the max float inf:
>>> (float('-inf') # negative infinity
< -1.7976931348623157e+308 #* smallest float that is not negative infinity
< -4.9406564584124654e-324 #* biggest negative float that is not zero
< 0 # zero duh
< 4.9406564584124654e-324 #* smallest positive float that is not zero
< 1.7976931348623157e+308 #* biggest float that is not positive infinity
< float('inf')) # positive infinity
True
numbers with * are machine-dependent and implementation-dependent.
6
If you love us? You can donate to us via Paypal or buy me a coffee so we can maintain and grow! Thank you!
Donate Us With
