Python sys.float_info.min value

[perfringo]

There is sys.float_info in Python:

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>>> 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=2.220446049250313e-16, radix=2, rounds=1) >>> sys.float_info.min 2.2250738585072014e-308

Python seems to recognise this value to be larger than zero:

1 2	>>> 0 < sys.float_info.min True

However, if I add this greater than zero value to integer it's not making value greater:

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>>> 1 < (1 + sys.float_info.min) False >>> 1 == (1 + sys.float_info.min) True

Any explanation why is that (some precision and/or normalised thingy)?

Technical stuff aside, this is somehow contra-intuitive (being larger than zero but not impacting value comparison).

[Gribouillis]

Suppose that instead of binary format, the computer stored the numbers in decimal format in exponential notation with 7 significant digits, this is how it would look

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>>> "{:e}".format(1.e-8) '1.000000e-08' >>> "{:e}".format(1) '1.000000e+00' >>> "{:e}".format(1+1.e-8) '1.000000e+00'

You would see a positive number for 1e-8 but you wouldn't see the difference between 1 and 1+1e-8 because the difference is beyond the last significant digit.

In real life, the same phenomenon occurs with binary numbers in memory in the IEEE 754 format, which is just a kind of exponential notation for binary numbers.

[perfringo]

Python recognises change in value up to 1.e-15 (or at least it does on my machine):

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>>> 1 + 1.e-15 == 1    # values are not even                                                            False >>> 1 + 1.e-16 == 1    # now values are even for Python                                                             True

[Gribouillis]

If you download my anyfloat module, you can visualize the internal binary representation of the floating numbers

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>>> from anyfloat import anyfloat >>> a = anyfloat.from_float(1 + 1e-15) >>> a.bin() '0 01111111111 0000000000000000000000000000000000000000000000000101' >>> a = anyfloat.from_float(1) >>> a.bin() '0 01111111111 0000000000000000000000000000000000000000000000000000' >>> a = anyfloat.from_float(1 + 1e-16) >>> a.bin() '0 01111111111 0000000000000000000000000000000000000000000000000000' >>> a = anyfloat.from_float(1 + 1e-13) >>> a.bin() '0 01111111111 0000000000000000000000000000000000000000000111000010' >>>