28.13 Handling Infinity

As we noted earlier, the IEEE 754 model of computing is not to stop the program when exceptional conditions occur. It takes note of exceptional values or conditions by setting sticky exception flags, or by producing results with the special values Infinity and QNaN. In this section, we discuss Infinity; see Handling NaN for the other.

In GNU C, you can create a value of negative Infinity in software like this:

double x;

x = -1.0 / 0.0;

GNU C supplies the __builtin_inf, __builtin_inff, and __builtin_infl macros, and the GNU C Library provides the INFINITY macro, all of which are compile-time constants for positive infinity.

GNU C also provides a standard function to test for an Infinity: isinf (x) returns 1 if the argument is a signed infinity, and 0 if not.

Infinities can be compared, and all Infinities of the same sign are equal: there is no notion in IEEE 754 arithmetic of different kinds of Infinities, as there are in some areas of mathematics. Positive Infinity is larger than any finite value, and negative Infinity is smaller than any finite value.

Infinities propagate in addition, subtraction, multiplication, and square root, but in division, they disappear, because of the rule that finite / Infinity is 0.0. Thus, an overflow in an intermediate computation that produces an Infinity is likely to be noticed later in the final results. The programmer can then decide whether the overflow is expected, and acceptable, or whether the code possibly has a bug, or needs to be run in higher precision, or redesigned to avoid the production of the Infinity.