[Mark Dickinson
] If you have a moment to share it, I'd be interested to know what value of `x` you used to achieve this, and what system you were on. This can't happen under IEEE 754 arithmetic.
I expect it might happen under one of the directed rounding modes (like "to +infinity").
PyPy (5.8):
x = 1e300 x.is_integer() True math.sqrt(x**2).is_integer() False x**2 inf
(It gives an OverflowError on my CPython installs.) I believe this is allowed, and Python is not required to raise OverflowError here: https://docs.python.org/3.6/library/exceptions.html#OverflowError says:
for historical reasons, OverflowError is sometimes raised for integers that are outside a required range. Because of the lack of standardization of floating point exception handling in C, most floating point operations are not checked
-- Devin