Under what circumstances is a file stream object’s ios::hardfail bit set? What member function reports the state of this bit?

ios::hardfail bit in C++ is an internal error control mechanism of the iostream library. It is set whenever a hard error occurs while performing stream buffer output operations, typically when the program tries to write on a failed stream. It's part of the stream's error state flags.

The ios::hardfail bit gets set in the event of a hard error. This might occur when a stream tries to write on a failed stream. For example, if there's an attempt to write to a file that has been closed or does not exist, the ios::hardfail bit of that file stream object would be set by the system.

To report the state of this bit, we use a member function called 'fail'. Therefore, the 'fail()' function can be used to determine whether the ios::hardfail bit (or any other error state flag) is set or not. This function returns 'true' if the bit is set (meaning a failure has occurred), and 'false' if the bit is not set. This bit is reset and the stream becomes usable again once the error is cleared by calling the 'clear()' function. E.g.: If "fstream file_obj" is a file stream object, then "file_obj.fail()" will return true if the ios::hardfail bit is set and false otherwise. This information is a part of the error analysis and handling in C++ input/output operations, which is vital in ensuring that your program behaves correctly and as expected, even in the presence of errors.