When a float variable goes out of the float limits, what happens?

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Formally, the behavior is undefined. On a machine with IEEE
floating point, however, overflow after rounding will result
in Inf. The precision is limited, however, and the results
after rounding of FLT_MAX + 1 are FLT_MAX.

You can see the same effect with values well under FLT_MAX.
Try something like:

float f1 = 1e20;     // less than FLT_MAX
float f2 = f1 + 1.0;
if ( f1 == f2 ) ...

The if will evaluate to true, at least with IEEE arithmetic.
(There do exist, or at least have existed, machines where
float has enough precision for the if to evaluate to
false, but they aren’t very common today.)

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