Tim Peters <[email protected]> added the comment:
What did you expect? The precision of Python ints is limited only by the
amount of memory you have, but Python floats are IEEE-754 double precision
numbers, and have only 53 bits of precision.
2**53 + 1 simply can't be represented exactly as a float: it requires 54
significant bits. It must be rounded back to 53 significant bits. Because the
exact value of 2**53 + 1 is exactly half-way between the adjacent representable
floats 2**53 and 2**53+2, the IEEE "round to nearest/even" rule requires
rounding to the closest representable value whose 53rd (the least) significant
bit is 0, which is 2**53.
Note that the 53rd bit of 9007199254740994.0 (2**53 + 2) is odd (1):
>>> (9007199254740994.0).hex()
'0x1.0000000000001p+53'
^
That's why the nearest/even rule _must_ pick 2**53 instead.
You'll see the same behavior in every other language (C, C++, Java, ...)
supporting IEEE-754 double precision too.
Since this really has nothing to do with Python, and is working as intended,
I'll close this.
----------
nosy: +tim.peters
resolution: -> not a bug
stage: -> resolved
status: open -> closed
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Python tracker <[email protected]>
<https://bugs.python.org/issue33022>
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