NaN is just an encoding for "undefined operation".

As specified by the standard since its beginning, there are 2 methods for handling undefined operations:

1. Generate a dedicated exception.

2. Return the special value NaN.

The default is to return NaN because this means less work for the programmer, who does not have to write an exception handler, and also because on older CPUs it was expensive to add enough hardware to ensure that exceptions could be handled without slowing down all programs, regardless whether they generated exceptions or not. On modern CPUs with speculative execution this is not really a problem, because they must be able to discard any executed instruction anyway, while running at full speed. Therefore enabling additional reasons for discarding the previously executed instructions, e.g. because of exceptional conditions, just reuses the speculative execution mechanism.

Whoever does not want to handle NaNs must enable the exception for undefined operations and handle that. In that case no NaNs will ever be generated. Enabling this exception may be needed in any case when one sees unexpected NaNs, for debugging the program.