在C ++中比较无穷大和无穷大

Question

Suppose I have two variables which are both set to infinity

double l = std::numeric_limits<double>::infinity();
double r = std::numeric_limits<double>::infinity();

At another point in the code, I have a comparison of these two variables

if (l < r) {}

Is the result of this comparison properly defined in the library? (Within the logic of my program, I would expect the result to be false .)

Answer 1

(Within the logic of my program, I would expect the result to be false .)

According to this :

In comparison operations, positive infinity is larger than all values except itself and NaN

So you are indeed correct.

Note that this might not be valid if your compiler uses a different standard than IEEE 754, so make sure that std::numeric_limits<double>::is_iec559; returns true when in doubt.

Answer 2

C++ does not require an implementation to support infinity in its floating-point types. However, if an implementation does support infinity, we can expect that infinity < infinity is false. C++ implicitly assumes normal mathematics—it does not define mathematical addition, multiplication, division, cosine, logarithm, and so on, but just assumes mathematics is background information known to the reader.

Mathematicians do distinguish different types of infinities, but C++ makes no provision for this; it provides only one positive infinity and one negative infinity. So it is clear they are simple extensions of the real numbers.