When such users are expected, there exists only one solution.

Do not mask the invalid operation exception, which was actually the original recommendation of the IEEE standard, which was that the default behavior should be to mask all exceptions, except the invalid operation exception.

When the invalid operation exception is not masked, NaNs are never generated and any NaN present in the input data will generate an exception, which will abort the program, unless the exception is handled.

This behavior avoids the bugs caused by careless programmers. Unfortunately, the original suggestion was not adopted by most programming language implementers, so nowadays the typical default setting is to have all exceptions masked. When the programmers also omit to handle the special values, bugs may remain unnoticed.

Special values need not be handled everywhere, because infinities and NaNs will propagate through many operations, so they will remain in the final results. But wherever a value is not persistent, but it is used in some decision and it is discarded after that, special values like NaNs must be handled correctly.