python: composition of `int` and `float`

As part of some other calculations, I noticed that I sometimes apply float() and then int() function to an integer input. Is it safe to assume that:

int(float(x)) == x

if x is integer?

Why? (Or why not?) And is it documented anywhere?

If x needs more precision than provided by double-precision floating point numbers then the comparison will fail.

>>> int(float(10**23))
99999999999999991611392L

>>> x = 10**300
>>> int(float(x)) == x
False

Why? (Or why not?) And is it documented anywhere?

One of the definitive guides that every programmer should know well:

What Every Programmer Should Know About Floating-Point Arithmetic

All numbers of the form significant_digits * (2 ** exponent) have an exact representation as a floating point number, as long as you have enough bits to represent significant_digits and exponent. Most platforms use IEEE 754 double representation, and Python uses the platform's double. IEEE 754 doubles have 11 bits for exponent and 52 bits for significant digits. As long as your numbers fit these bounds they will come out as expected.

See Python's docs on floating point representation and Wikipedia's article on floating points.