python - How are Inf and NaN implemented?

Question

As mathematical concepts, I am well aware of what inf and nan actually are. But what I am really interested in is how they are implemented in programming languages.

In python, I can use inf and nan in arithmetic and conditional expressions, like this:

>>> nan = float('nan')
>>> inf = float('inf')
>>> 1 + inf
inf
>>> inf + inf
inf
>>> inf - inf
nan

This would lead me to believe that python internally has a special reserved bit sequence for these two mathematical quantities, and no other number can assume these positions. Is my assumption correct? Can you please enlighten me in this regard?

If my assumption is correct, then this can be explained easily:

>>> inf == inf
True

However, this is not:

>>> nan == nan
False

Obviously, in mathematics, this is the right answer. But how does python know that it should spit out False in this instance?

Furthermore, how does python's implementation differ from that of java or c++?

Answer 1

Typically, the floating point arithmetic is implemented directly by hardware. There are indeed special bit patterns for infinity and NaN, which are recognized by the hardware floating-point unit.

IEEE 64-bit floating-point numbers, the kind used in CPython on typical systems, have 1 bit for the sign, 11 bits for the exponent, and 52 bits for the mantissa. See https://en.wikipedia.org/wiki/Double-precision_floating-point_format

If the exponent contains 0b11111111111 (all ones), then the number is either inf or nan, depending on what is stored in the mantissa. Python does not need to do anything special to handle these cases. You will get the same results whether you compare the numbers in Python, C, Java, or assembly language.