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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.