Why is numeric_limits<int>::max() > numeric_limits<int>::infinity()?

Question

I was reading Setting an int to Infinity in C++. I understand that when one needs true infinity, one is supposed to use numeric_limits<float>::infinity(); I guess the rationale behind it is that usually integral types have no values designated for representing special states like NaN, Inf, etc. like IEEE 754 floats do (again C++ doesn't mandate neither - int & float used are left to the implementation); but still it's misleading that max > infinity for a given type. I'm trying to understand the rationale behind this call in the standard. If having infinity doesn't make sense for a type, then shouldn't it be disallowed instead of having a flag to be checked for its validity?

Answer 1

The function numeric_limits<T>::infinity() makes sense for those T for which numeric_limits<T>::has_infinity returns true.

In case of T=int, it returns false. So that comparison doesn't make sense, because numeric_limits<int>::infinity() does not return any meaningful value to compare with.

Answer 2

If you read e.g. this reference you will see a table showing infinity to be zero for integer types. That's because integer types in C++ can't, by definition, be infinite.

Answer 3

Suppose, conversely, the standard did reserve some value to represent inifity, and that numeric_limits<int>::infinity() > numeric_limits<int>::max(). That means that there would be some value of int which is greater than max(), that is, some representable value of int is greater than the greatest representable value of int.

Clearly, whichever way the Standard specifies, some natural understanding is violated. Either inifinity() <= max(), or there exists x such that int(x) > max(). The Standard must choose which rule of nature to violate.

I believe they chose wisely.

Answer 4

numeric_limits<int>::infinity() returns the representation of positive infinity, if available.

In case of integers, positive infinity does not exists:

cout << "int has infinity: " << numeric_limits<int>::has_infinity << endl;

prints

int has infinity: false